Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-21)

The rewrite relation of the following TRS is considered.

a(x1) → x1 (1)
a(x1) → b(x1) (2)
b(b(c(x1))) → a(c(c(c(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 = b(b(b(c(c(c(x1))))))
→ b(a(c(c(c(a(a(c(c(x1)))))))))
→ b(a(c(c(c(a(b(c(c(x1)))))))))
→ b(a(c(c(c(b(b(c(c(x1)))))))))
→ b(b(c(c(c(b(b(c(c(x1)))))))))
→ b(b(c(c(c(a(c(c(c(a(a(c(x1))))))))))))
→ b(b(c(c(c(c(c(c(a(a(c(x1)))))))))))
→ b(b(c(c(c(c(c(c(a(b(c(x1)))))))))))
→ b(b(c(c(c(c(c(c(b(b(c(x1)))))))))))
→ b(b(c(c(c(c(c(c(a(c(c(c(a(a(x1))))))))))))))
→ b(b(c(c(c(c(c(c(a(c(c(c(a(x1)))))))))))))
→ b(b(c(c(c(c(c(c(a(c(c(c(x1))))))))))))
→ b(b(c(c(c(c(c(c(b(c(c(c(x1))))))))))))
→ a(c(c(c(a(a(c(c(c(c(c(b(c(c(c(x1)))))))))))))))
→ c(c(c(a(a(c(c(c(c(c(b(c(c(c(x1))))))))))))))
→ c(c(c(a(b(c(c(c(c(c(b(c(c(c(x1))))))))))))))
→ c(c(c(b(b(c(c(c(c(c(b(c(c(c(x1))))))))))))))
→ c(c(c(a(c(c(c(a(a(c(c(c(c(b(c(c(c(x1)))))))))))))))))
→ c(c(c(c(c(c(a(a(c(c(c(c(b(c(c(c(x1))))))))))))))))
→ c(c(c(c(c(c(a(b(c(c(c(c(b(c(c(c(x1))))))))))))))))
→ c(c(c(c(c(c(b(b(c(c(c(c(b(c(c(c(x1))))))))))))))))
→ c(c(c(c(c(c(a(c(c(c(a(a(c(c(c(b(c(c(c(x1)))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(a(a(c(c(c(b(c(c(c(x1))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(a(b(c(c(c(b(c(c(c(x1))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(b(b(c(c(c(b(c(c(c(x1))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(a(c(c(c(a(a(c(c(b(c(c(c(x1)))))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(a(a(c(c(b(c(c(c(x1))))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(a(b(c(c(b(c(c(c(x1))))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(b(b(c(c(b(c(c(c(x1))))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(a(c(c(c(a(a(c(b(c(c(c(x1)))))))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(a(a(c(b(c(c(c(x1))))))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(a(b(c(b(c(c(c(x1))))))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(b(b(c(b(c(c(c(x1))))))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(a(c(c(c(a(a(b(c(c(c(x1)))))))))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(a(a(b(c(c(c(x1))))))))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(a(b(b(c(c(c(x1))))))))))))))))))))))))
→ c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(b(b(b(c(c(c(x1))))))))))))))))))))))))
= t36
where t36 = C[t0σ] and σ = {x1/x1} and C = c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(☐))))))))))))))))))