Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-430)

The rewrite relation of the following TRS is considered.

a(x1) → b(b(c(x1))) (1)
a(b(x1)) → x1 (2)
c(c(b(x1))) → a(a(c(x1))) (3)

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(c(c(a(a(c(c(b(b(x1))))))))))))
→ b(b(b(b(c(c(b(b(c(a(c(c(b(b(x1))))))))))))))
→ b(b(b(b(a(a(c(b(c(a(c(c(b(b(x1))))))))))))))
→ b(b(b(b(a(b(b(c(c(b(c(a(c(c(b(b(x1))))))))))))))))
→ b(b(b(b(b(c(c(b(c(a(c(c(b(b(x1))))))))))))))
→ b(b(b(b(b(a(a(c(c(a(c(c(b(b(x1))))))))))))))
→ b(b(b(b(b(a(a(c(c(b(b(c(c(c(b(b(x1))))))))))))))))
→ b(b(b(b(b(a(a(a(a(c(b(c(c(c(b(b(x1))))))))))))))))
→ b(b(b(b(b(a(a(a(b(b(c(c(b(c(c(c(b(b(x1))))))))))))))))))
→ b(b(b(b(b(a(a(b(c(c(b(c(c(c(b(b(x1))))))))))))))))
→ b(b(b(b(b(a(c(c(b(c(c(c(b(b(x1))))))))))))))
→ b(b(b(b(b(a(a(a(c(c(c(c(b(b(x1))))))))))))))
→ b(b(b(b(b(a(b(b(c(a(c(c(c(c(b(b(x1))))))))))))))))
→ b(b(b(b(b(b(c(a(c(c(c(c(b(b(x1))))))))))))))
→ b(b(b(b(b(b(c(a(c(c(a(a(c(b(x1))))))))))))))
→ b(b(b(b(b(b(c(a(c(c(b(b(c(a(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(c(a(a(a(c(b(c(a(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(c(a(a(b(b(c(c(b(c(a(c(b(x1))))))))))))))))))
→ b(b(b(b(b(b(c(a(b(c(c(b(c(a(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(c(c(c(b(c(a(c(b(x1))))))))))))))
→ b(b(b(b(b(b(c(a(a(c(c(a(c(b(x1))))))))))))))
→ b(b(b(b(b(b(c(a(a(c(c(b(b(c(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(c(a(a(a(a(c(b(c(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(c(a(a(b(b(c(a(c(b(c(c(b(x1))))))))))))))))))
→ b(b(b(b(b(b(c(a(b(c(a(c(b(c(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(c(c(a(c(b(c(c(b(x1))))))))))))))
→ b(b(b(b(b(b(c(c(b(b(c(c(b(c(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(c(c(b(b(a(a(c(c(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(a(a(c(b(a(a(c(c(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(a(a(c(b(a(b(b(c(c(c(c(b(x1))))))))))))))))))
→ b(b(b(b(b(b(a(a(c(b(b(c(c(c(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(a(b(b(c(c(b(b(c(c(c(c(b(x1))))))))))))))))))
→ b(b(b(b(b(b(b(c(c(b(b(c(c(c(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(b(a(a(c(b(c(c(c(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(b(a(b(b(c(c(b(c(c(c(c(b(x1))))))))))))))))))
→ b(b(b(b(b(b(b(b(c(c(b(c(c(c(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(b(b(a(a(c(c(c(c(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(b(b(a(b(b(c(c(c(c(c(c(b(x1))))))))))))))))))
→ b(b(b(b(b(b(b(b(b(c(c(c(c(c(c(b(x1))))))))))))))))
→ b(b(b(b(b(b(b(b(b(c(c(c(c(a(a(c(x1))))))))))))))))
→ b(b(b(b(b(b(b(b(b(c(c(c(c(b(b(c(a(c(x1))))))))))))))))))
→ b(b(b(b(b(b(b(b(b(c(c(a(a(c(b(c(a(c(x1))))))))))))))))))
→ b(b(b(b(b(b(b(b(b(c(c(a(b(b(c(c(b(c(a(c(x1))))))))))))))))))))
→ b(b(b(b(b(b(b(b(b(c(c(b(c(c(b(c(a(c(x1))))))))))))))))))
→ b(b(b(b(b(b(b(b(b(c(c(b(a(a(c(c(a(c(x1))))))))))))))))))
→ b(b(b(b(b(b(b(b(b(a(a(c(a(a(c(c(a(c(x1))))))))))))))))))
→ b(b(b(b(b(b(b(b(b(a(b(b(c(c(a(a(c(c(a(c(x1))))))))))))))))))))
→ b(b(b(b(b(b(b(b(b(b(c(c(a(a(c(c(a(c(x1))))))))))))))))))
→ b(b(b(b(b(b(b(b(b(b(c(c(a(a(c(c(b(b(c(c(x1))))))))))))))))))))
= t48
where t48 = C[t0σ] and σ = {x1/c(c(x1))} and C = b(b(b(b(b(b(☐))))))