Certification Problem

Input (TPDB SRS_Standard/Waldmann_06_SRS/uni-3)

The rewrite relation of the following TRS is considered.

a(a(a(x1))) → b(b(c(a(a(x1))))) (1)
b(b(x1)) → c(a(b(x1))) (2)
c(x1) → 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(b(a(a(b(b(b(x1)))))))
→ a(b(a(a(c(a(b(b(x1))))))))
→ a(b(a(a(a(b(b(x1)))))))
→ a(b(b(b(c(a(a(b(b(x1)))))))))
→ a(b(b(b(a(a(b(b(x1))))))))
→ a(c(a(b(b(a(a(b(b(x1)))))))))
→ a(a(b(b(a(a(b(b(x1))))))))
→ a(a(c(a(b(a(a(b(b(x1)))))))))
→ a(a(a(b(a(a(b(b(x1))))))))
→ b(b(c(a(a(b(a(a(b(b(x1))))))))))
→ b(b(a(a(b(a(a(b(b(x1)))))))))
→ c(a(b(a(a(b(a(a(b(b(x1))))))))))
→ a(b(a(a(b(a(a(b(b(x1)))))))))
→ a(b(a(a(b(a(a(c(a(b(x1))))))))))
→ a(b(a(a(b(a(a(a(b(x1)))))))))
→ a(b(a(a(b(b(b(c(a(a(b(x1)))))))))))
= t15
where t15 = t0σ and σ = {x1/c(a(a(b(x1))))}