Certification Problem

Input (TPDB SRS_Standard/Mixed_SRS/turing_copy)

The rewrite relation of the following TRS is considered.

0(q0(0(x1))) → 0(0(q0(x1))) (1)
0(q0(h(x1))) → 0(0(q0(h(x1)))) (2)
0(q0(1(x1))) → 0(1(q0(x1))) (3)
1(q0(0(x1))) → 0(0(q1(x1))) (4)
1(q0(h(x1))) → 0(0(q1(h(x1)))) (5)
1(q0(1(x1))) → 0(1(q1(x1))) (6)
1(q1(0(x1))) → 1(0(q1(x1))) (7)
1(q1(h(x1))) → 1(0(q1(h(x1)))) (8)
1(q1(1(x1))) → 1(1(q1(x1))) (9)
0(q1(0(x1))) → 0(0(q2(x1))) (10)
0(q1(h(x1))) → 0(0(q2(h(x1)))) (11)
0(q1(1(x1))) → 0(1(q2(x1))) (12)
1(q2(0(x1))) → 1(0(q2(x1))) (13)
1(q2(h(x1))) → 1(0(q2(h(x1)))) (14)
1(q2(1(x1))) → 1(1(q2(x1))) (15)
0(q2(x1)) → q3(1(x1)) (16)
1(q3(x1)) → q3(1(x1)) (17)
0(q3(x1)) → q4(0(x1)) (18)
1(q4(x1)) → q4(1(x1)) (19)
0(q4(0(x1))) → 1(0(q5(x1))) (20)
0(q4(h(x1))) → 1(0(q5(h(x1)))) (21)
0(q4(1(x1))) → 1(1(q5(x1))) (22)
1(q5(0(x1))) → 0(0(q1(x1))) (23)
1(q5(h(x1))) → 0(0(q1(h(x1)))) (24)
1(q5(1(x1))) → 0(1(q1(x1))) (25)
h(q0(x1)) → h(0(q0(x1))) (26)
h(q1(x1)) → h(0(q1(x1))) (27)
h(q2(x1)) → h(0(q2(x1))) (28)
h(q3(x1)) → h(0(q3(x1))) (29)
h(q4(x1)) → h(0(q4(x1))) (30)
h(q5(x1)) → h(0(q5(x1))) (31)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by AProVE @ termCOMP 2023)

1 Looping derivation

There is a looping derivation.

0 q0 h →+ 0 0 q0 h ε

The derivation can be derived as follows.