Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-120)

The rewrite relation of the following TRS is considered.

a(x1) → x1 (1)
a(a(b(x1))) → c(a(x1)) (2)
a(c(x1)) → c(b(a(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 = a(a(c(b(c(c(b(x1)))))))
→ a(c(b(a(a(b(c(c(b(x1)))))))))
→ a(c(b(c(a(c(c(b(x1))))))))
→ a(c(b(c(c(b(a(a(c(b(x1))))))))))
→ a(c(b(c(c(b(a(c(b(a(a(b(x1))))))))))))
→ a(c(b(c(c(b(a(c(b(a(b(x1)))))))))))
→ a(c(b(c(c(b(a(c(b(b(x1))))))))))
→ a(c(b(c(c(b(c(b(a(a(b(b(x1))))))))))))
→ a(c(b(c(c(b(c(b(c(a(b(x1)))))))))))
→ a(c(b(c(c(b(c(b(c(b(x1))))))))))
→ c(b(a(a(b(c(c(b(c(b(c(b(x1))))))))))))
→ c(b(c(a(c(c(b(c(b(c(b(x1)))))))))))
→ c(b(c(c(b(a(a(c(b(c(b(c(b(x1)))))))))))))
→ c(b(c(c(b(a(c(b(a(a(b(c(b(c(b(x1)))))))))))))))
→ c(b(c(c(b(a(c(b(c(a(c(b(c(b(x1))))))))))))))
→ c(b(c(c(b(a(c(b(c(c(b(a(a(b(c(b(x1))))))))))))))))
→ c(b(c(c(b(a(c(b(c(c(b(c(a(c(b(x1)))))))))))))))
→ c(b(c(c(b(a(c(b(c(c(b(c(c(b(x1))))))))))))))
→ c(b(c(c(b(c(b(a(a(b(c(c(b(c(c(b(x1))))))))))))))))
→ c(b(c(c(b(c(b(c(a(c(c(b(c(c(b(x1)))))))))))))))
→ c(b(c(c(b(c(b(c(c(b(a(a(c(b(c(c(b(x1)))))))))))))))))
= t20
where t20 = C[t0σ] and σ = {x1/x1} and C = c(b(c(c(b(c(b(c(c(b(☐))))))))))