Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-328)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = c(a(a(a(a(c(b(c(c(b(c(x1)))))))))))
→ c(a(a(a(b(b(c(c(b(c(c(b(c(x1)))))))))))))
→ c(a(b(b(c(a(b(b(c(c(b(c(c(b(c(x1)))))))))))))))
→ c(a(b(b(a(c(a(b(c(c(b(c(c(b(c(x1)))))))))))))))
→ c(a(b(b(a(a(c(a(c(c(b(c(c(b(c(x1)))))))))))))))
→ c(a(b(b(a(a(c(b(c(c(b(c(c(b(c(x1)))))))))))))))
→ c(a(b(b(b(a(c(b(c(c(b(c(c(b(c(x1)))))))))))))))
→ a(c(a(b(b(a(c(b(c(c(b(c(c(b(c(x1)))))))))))))))
→ a(a(c(a(b(a(c(b(c(c(b(c(c(b(c(x1)))))))))))))))
→ a(a(a(c(a(a(c(b(c(c(b(c(c(b(c(x1)))))))))))))))
→ a(a(a(c(a(b(b(c(c(b(c(c(b(c(c(b(c(x1)))))))))))))))))
→ a(a(a(a(c(a(b(c(c(b(c(c(b(c(c(b(c(x1)))))))))))))))))
→ a(a(a(a(a(c(a(c(c(b(c(c(b(c(c(b(c(x1)))))))))))))))))
→ a(a(a(a(a(c(b(c(c(b(c(c(b(c(c(b(c(x1)))))))))))))))))
→ b(b(c(a(a(a(a(c(b(c(c(b(c(c(b(c(c(b(c(x1)))))))))))))))))))
= t14
where t14 = C[t0σ] and σ = {x1/c(b(c(c(b(c(x1))))))} and C = b(b(☐))