Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-497)

The rewrite relation of the following TRS is considered.

a(a(x1)) → b(a(b(c(c(x1))))) (1)
c(a(x1)) → x1 (2)
c(b(x1)) → 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(a(b(b(a(b(a(a(b(a(c(a(a(a(b(x1)))))))))))))))
→ b(a(b(b(a(b(a(a(b(a(c(b(a(b(c(c(a(b(x1))))))))))))))))))
→ b(a(b(b(a(b(a(a(b(a(a(a(b(c(c(a(b(x1)))))))))))))))))
→ b(a(b(b(a(b(a(a(b(a(b(a(b(c(c(b(c(c(a(b(x1))))))))))))))))))))
→ b(a(b(b(a(b(a(a(b(a(b(a(b(c(a(c(c(a(b(x1)))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(c(c(b(a(b(a(b(c(a(c(c(a(b(x1))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(c(a(a(b(a(b(c(a(c(c(a(b(x1)))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(c(b(a(b(c(c(b(a(b(c(a(c(c(a(b(x1))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(c(b(a(b(c(a(a(b(c(a(c(c(a(b(x1)))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(a(a(b(c(a(a(b(c(a(c(c(a(b(x1))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(a(a(b(c(b(a(b(c(c(b(c(a(c(c(a(b(x1)))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(a(a(b(c(b(a(b(c(a(c(a(c(c(a(b(x1))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(a(a(b(a(a(b(c(a(c(a(c(c(a(b(x1)))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(b(a(b(c(c(b(a(a(b(c(a(c(a(c(c(a(b(x1))))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(b(a(b(c(a(a(a(b(c(a(c(a(c(c(a(b(x1)))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(b(a(b(c(b(a(b(c(c(a(b(c(a(c(a(c(c(a(b(x1))))))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(b(a(b(c(b(a(b(c(b(c(a(c(a(c(c(a(b(x1))))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(b(a(b(c(b(a(b(a(c(a(c(a(c(c(a(b(x1)))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(b(a(b(a(a(b(a(c(a(c(a(c(c(a(b(x1))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(b(a(b(a(a(b(a(c(a(c(a(c(b(x1))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(b(a(b(a(a(b(a(c(a(c(a(a(x1)))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(b(a(b(a(a(b(a(c(a(c(b(a(b(c(c(x1))))))))))))))))))))))))
→ b(a(b(b(a(b(b(a(b(b(a(b(a(a(b(a(c(a(a(a(b(c(c(x1)))))))))))))))))))))))
= t22
where t22 = C[t0σ] and σ = {x1/c(c(x1))} and C = b(a(b(b(a(b(☐))))))