Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-400)

The rewrite relation of the following TRS is considered.

a(x1) → b(x1) (1)
b(b(a(c(x1)))) → a(c(c(a(a(a(x1)))))) (2)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = b(b(b(b(a(c(c(a(c(c(b(b(b(b(b(b(x1))))))))))))))))
→ b(b(a(c(c(a(a(a(c(a(c(c(b(b(b(b(b(b(x1))))))))))))))))))
→ b(b(a(c(c(a(b(a(c(a(c(c(b(b(b(b(b(b(x1))))))))))))))))))
→ b(b(a(c(c(b(b(a(c(a(c(c(b(b(b(b(b(b(x1))))))))))))))))))
→ b(b(a(c(c(a(c(c(a(a(a(a(c(c(b(b(b(b(b(b(x1))))))))))))))))))))
→ b(b(a(c(c(a(c(c(a(a(b(a(c(c(b(b(b(b(b(b(x1))))))))))))))))))))
→ b(b(a(c(c(a(c(c(a(b(b(a(c(c(b(b(b(b(b(b(x1))))))))))))))))))))
→ b(b(a(c(c(a(c(c(b(b(b(a(c(c(b(b(b(b(b(b(x1))))))))))))))))))))
→ b(b(a(c(c(a(c(c(b(a(c(c(a(a(a(c(b(b(b(b(b(b(x1))))))))))))))))))))))
→ b(b(a(c(c(a(c(c(b(a(c(c(a(b(a(c(b(b(b(b(b(b(x1))))))))))))))))))))))
→ b(b(a(c(c(a(c(c(b(a(c(c(b(b(a(c(b(b(b(b(b(b(x1))))))))))))))))))))))
→ b(b(a(c(c(a(c(c(b(a(c(c(a(c(c(a(a(a(b(b(b(b(b(b(x1))))))))))))))))))))))))
→ b(b(a(c(c(a(c(c(b(a(c(c(a(c(c(a(a(b(b(b(b(b(b(b(x1))))))))))))))))))))))))
→ b(b(a(c(c(a(c(c(b(a(c(c(a(c(c(a(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))
→ b(b(a(c(c(a(c(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))
→ a(c(c(a(a(a(c(a(c(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))
→ a(c(c(a(b(a(c(a(c(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))
→ a(c(c(b(b(a(c(a(c(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))
→ b(c(c(b(b(a(c(a(c(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))
→ b(c(c(a(c(c(a(a(a(a(c(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))
→ b(c(c(a(c(c(a(a(b(a(c(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))
→ b(c(c(a(c(c(a(b(b(a(c(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))
→ b(c(c(a(c(c(b(b(b(a(c(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))
→ b(c(c(b(c(c(b(b(b(a(c(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))
→ b(c(c(b(c(c(b(a(c(c(a(a(a(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))))
→ b(c(c(b(c(c(b(a(c(c(a(b(a(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))))
→ b(c(c(b(c(c(b(a(c(c(b(b(a(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))))
→ b(c(c(b(c(c(b(b(c(c(b(b(a(c(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))))
→ b(c(c(b(c(c(b(b(c(c(a(c(c(a(a(a(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))))))
→ b(c(c(b(c(c(b(b(c(c(a(c(c(a(a(b(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))))))
→ b(c(c(b(c(c(b(b(c(c(a(c(c(a(b(b(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))))))
→ b(c(c(b(c(c(b(b(c(c(a(c(c(b(b(b(b(a(c(c(a(c(c(b(b(b(b(b(b(b(b(b(x1))))))))))))))))))))))))))))))))
= t31
where t31 = C[t0σ] and σ = {x1/b(b(b(x1)))} and C = b(c(c(b(c(c(b(b(c(c(a(c(c(☐)))))))))))))