Certification Problem

Input (TPDB SRS_Standard/Gebhardt_06/10)

The rewrite relation of the following TRS is considered.

0(0(0(0(x1)))) → 0(1(1(1(x1)))) (1)
1(0(0(1(x1)))) → 0(0(1(0(x1)))) (2)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = 0(1(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(0(0(0(1(0(1(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(1(1(0(1(0(1(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(0(0(0(0(1(0(1(0(1(0(1(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(1(1(1(0(0(1(0(1(0(1(0(1(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(1(1(0(0(0(0(1(0(0(1(0(1(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(1(1(0(0(0(0(0(0(1(0(0(1(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(1(1(0(0(0(0(0(0(0(0(1(0(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(1(1(0(0(0(1(1(1(0(0(1(0(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(0(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(1(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(x1)))))))))))))))))))))
→ 0(1(0(0(1(0(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(x1)))))))))))))))))))))
→ 0(0(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(x1)))))))))))))))))))))
→ 0(0(0(0(0(1(0(0(0(0(1(1(0(0(0(0(1(0(0(1(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(0(1(1(0(0(0(0(1(0(0(1(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(0(1(1(0(0(0(0(0(0(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(0(1(1(0(0(1(1(1(0(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(0(0(0(1(0(0(1(1(0(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(1(0(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(1(1(1(0(0(1(0(1(0(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(1(1(0(0(1(0(0(1(0(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(0(0(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(0(0(1(0(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(1(1(0(0(1(1(1(0(1(0(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(1(0(0(1(0(1(1(0(1(0(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(0(0(1(0(0(1(1(0(1(0(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(0(0(0(0(0(1(0(1(0(1(0(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(1(1(1(0(0(1(0(1(0(1(0(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(1(1(0(0(1(0(0(1(0(1(0(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(1(1(0(0(0(0(1(0(0(1(0(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(1(0(0(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(1(1(0(1(1(1(0(0(1(0(0(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(1(1(0(1(1(0(0(1(0(0(0(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(1(1(0(1(0(0(1(0(0(0(0(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(1(1(0(1(0(0(1(0(1(1(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(1(1(0(0(0(1(0(0(1(1(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(1(1(0(0(0(0(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(1(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(1(0(0(1(0(1(0(1(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(0(0(0(0(1(0(0(1(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(0(0(0(0(0(0(1(0(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(1(0(0(1(1(1(0(1(0(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(0(1(0(0(1(0(1(1(0(1(0(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(0(0(0(0(0(1(0(1(0(1(0(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(1(0(0(1(0(1(0(1(0(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(0(0(0(0(0(1(0(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(1(0(0(1(0(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(0(1(0(0(1(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(0(0(0(1(0(0(1(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(0(0(0(0(0(1(0(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(1(1(1(0(0(1(0(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(1(1(0(0(1(0(0(1(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(1(1(0(0(0(0(1(0(0(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(1(1(0(0(0(0(0(0(1(0(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(1(1(0(0(1(1(1(0(1(0(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(1(0(0(1(0(1(1(0(1(0(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(0(0(1(0(0(1(1(0(1(0(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(0(0(0(0(1(0(1(0(1(0(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(1(1(0(0(1(0(1(0(1(0(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(1(0(0(1(0(0(1(0(1(0(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(1(0(0(0(0(1(0(0(1(0(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(1(0(0(0(0(0(0(1(0(0(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(1(0(1(1(1(0(0(1(0(0(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(1(0(1(1(0(0(1(0(0(0(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(1(0(1(0(0(1(0(0(0(0(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(1(0(1(0(0(1(0(1(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(1(0(0(0(1(0(0(1(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(1(0(0(0(0(0(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(1(0(0(1(1(1(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(1(0(0(1(0(1(1(1(0(1(1(x1)))))))))))))))))))))
→ 0(1(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(1(0(1(1(x1)))))))))))))))))))))
= t80
where t80 = t0σ and σ = {x1/x1}