Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 25

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 2.

Print how many distinct binary strings of length exactly 6 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=6)


Transition rows fully define the next-state function.

the automaton is complete and deterministic over {{0, 1}}: each row lists exactly two successor states

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

the defining fixpoint admits exactly one value

Answer: 4

the unique verified answer

import json
import sys

data = json.load(sys.stdin)
transitions = data["transitions"]
start = data["start"]
accepting = data["accepting"]
length = data["length"]

size = len(accepting)
counts = [0] * size
counts[start] = 1
steps = 0
while steps < length:
    nxt = [0] * size
    for state in range(size):
        amount = counts[state]
        if amount != 0:
            for nxt_state in transitions[state]:
                nxt[nxt_state] += amount
    counts = nxt
    steps += 1
total = 0
for state in range(size):
    if accepting[state]:
        total += counts[state]
print(total)

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 6 states numbered 0 to 5. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 0.

Print how many distinct binary strings of length exactly 3 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=6, L=3)

Explanation: Canonical verified instance: Z3 proved satisfiability and blocked 1 model(s) to establish uniqueness.


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 4

the unique verified answer

import json
import sys

data = json.load(sys.stdin)
first = data["first"]
second = data["second"]

rows = len(first["accepting"])
cols = len(second["accepting"])
seen = [[0] * cols for _ in range(rows)]
start_left = first["start"]
start_right = second["start"]
seen[start_left][start_right] = 1
stack = [[start_left, start_right]]
total = 0
while stack:
    left, right = stack.pop()
    total += 1
    for symbol in range(2):
        nxt_left = first["transitions"][left][symbol]
        nxt_right = second["transitions"][right][symbol]
        if not seen[nxt_left][nxt_right]:
            seen[nxt_left][nxt_right] = 1
            stack.append([nxt_left, nxt_right])
print(total)

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(1, 2) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (4x4 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 2

the unique verified answer

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(3, 0) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (5x6 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 24

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 6 states numbered 0 to 5. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 2.

Print how many distinct binary strings of length exactly 6 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=6, L=6)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 5

the unique verified answer

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(3, 3) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (5x7 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 10

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 1.

Print how many distinct binary strings of length exactly 4 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=4)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 4

the unique verified answer

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(3, 1) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (4x5 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 3

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 4.

Print how many distinct binary strings of length exactly 3 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=3)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 16

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 4 states numbered 0 to 3. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 0.

Print how many distinct binary strings of length exactly 5 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=4, L=5)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 3

the unique verified answer

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(2, 1) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (4x5 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 33

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 4.

Print how many distinct binary strings of length exactly 6 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=6)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 5

the unique verified answer

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(4, 2) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (5x7 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 205

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 4.

Print how many distinct binary strings of length exactly 8 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=8)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 399

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 6 states numbered 0 to 5. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 1.

Print how many distinct binary strings of length exactly 9 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=6, L=9)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 24

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 4.

Print how many distinct binary strings of length exactly 5 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=5)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 203

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 6 states numbered 0 to 5. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 0.

Print how many distinct binary strings of length exactly 8 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=6, L=8)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 53

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 2.

Print how many distinct binary strings of length exactly 6 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=6)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 104

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 1.

Print how many distinct binary strings of length exactly 7 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=7)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 5

the unique verified answer

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(1, 0) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (6x6 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 6

the unique verified answer

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(0, 4) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (6x6 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 160

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 1.

Print how many distinct binary strings of length exactly 8 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=8)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 3

the unique verified answer

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(4, 3) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (5x7 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 6

the unique verified answer

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(2, 5) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (6x6 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 17

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 1.

Print how many distinct binary strings of length exactly 6 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=6)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 385

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 0.

Print how many distinct binary strings of length exactly 9 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=9)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 13

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 1.

Print how many distinct binary strings of length exactly 5 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=5)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 5

the unique verified answer

DFA Product Reachability (5x6 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 273

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 4.

Print how many distinct binary strings of length exactly 9 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=9)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 64

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 5 states numbered 0 to 4. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 2.

Print how many distinct binary strings of length exactly 7 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=5, L=7)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 30

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 6 states numbered 0 to 5. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 5.

Print how many distinct binary strings of length exactly 5 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=6, L=5)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 2

the unique verified answer

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(2, 3) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (5x6 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 5

the unique verified answer

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(3, 3) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (6x7 states)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 64

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 6 states numbered 0 to 5. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 4.

Print how many distinct binary strings of length exactly 7 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=6, L=7)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 74

the unique verified answer

You are given a deterministic finite automaton over the binary alphabet
{0, 1} with 6 states numbered 0 to 5. The row transitions[s]
contains exactly two entries: the successor state after reading a 0 and the
successor state after reading a 1, respectively. The automaton starts in
state 1.

Print how many distinct binary strings of length exactly 7 move the
automaton from its start state to an accepting state. The count is unique;
it has been formally proven for this instance with the Z3 SMT solver.

DFA String Acceptance Count (states=6, L=7)


Transition rows fully define the next-state function.

The declarative semantics of the task over the concrete machine; Z3 reports this system satisfiable.

Proven by Z3 model exclusion: blocking the witness model makes the system unsatisfiable.

Answer: 4

the unique verified answer

You are given two deterministic finite automata over the binary alphabet
{0, 1} that recognize the same language (equivalence holds by construction).
Consider their synchronous product: execution starts from the state pair
(3, 0) and every input symbol advances both machines
simultaneously.

Print how many distinct state pairs are reachable in this product. The count
is unique; it has been formally proven for this instance with the Z3 SMT
solver.

DFA Product Reachability (5x5 states)