Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-211)

The rewrite relation of the following TRS is considered.

a(x1) → x1 (1)
a(b(x1)) → b(b(a(c(a(x1))))) (2)
c(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 = a(a(a(b(b(c(x1))))))
→ a(a(b(b(a(c(a(b(c(x1)))))))))
→ a(a(b(b(c(a(b(c(x1))))))))
→ a(a(b(b(c(b(b(a(c(a(c(x1)))))))))))
→ a(a(b(b(c(b(b(a(c(c(x1))))))))))
→ a(a(b(b(c(b(b(c(c(x1)))))))))
→ a(b(b(a(c(a(b(c(b(b(c(c(x1))))))))))))
→ a(b(b(c(a(b(c(b(b(c(c(x1)))))))))))
→ a(b(b(c(b(b(a(c(a(c(b(b(c(c(x1))))))))))))))
→ a(b(b(c(b(b(a(c(c(b(b(c(c(x1)))))))))))))
→ a(b(b(c(b(b(a(a(b(c(c(x1)))))))))))
→ a(b(b(c(b(b(a(b(b(a(c(a(c(c(x1))))))))))))))
→ a(b(b(c(b(b(a(b(b(a(c(c(c(x1)))))))))))))
→ a(b(b(c(b(b(a(b(b(c(c(c(x1))))))))))))
→ a(b(b(c(b(b(b(b(a(c(a(b(c(c(c(x1)))))))))))))))
→ a(b(b(c(b(b(b(b(c(a(b(c(c(c(x1))))))))))))))
→ a(b(b(c(b(b(b(b(c(b(b(a(c(a(c(c(c(x1)))))))))))))))))
→ a(b(b(c(b(b(b(b(c(b(b(a(c(c(c(c(x1))))))))))))))))
→ a(b(b(c(b(b(b(b(c(b(b(c(c(c(c(x1)))))))))))))))
→ b(b(a(c(a(b(c(b(b(b(b(c(b(b(c(c(c(c(x1))))))))))))))))))
→ b(b(c(a(b(c(b(b(b(b(c(b(b(c(c(c(c(x1)))))))))))))))))
→ b(b(c(b(b(a(c(a(c(b(b(b(b(c(b(b(c(c(c(c(x1))))))))))))))))))))
→ b(b(c(b(b(a(c(c(b(b(b(b(c(b(b(c(c(c(c(x1)))))))))))))))))))
→ b(b(c(b(b(a(a(b(b(b(c(b(b(c(c(c(c(x1)))))))))))))))))
→ b(b(c(b(b(a(b(b(a(c(a(b(b(c(b(b(c(c(c(c(x1))))))))))))))))))))
→ b(b(c(b(b(a(b(b(c(a(b(b(c(b(b(c(c(c(c(x1)))))))))))))))))))
→ b(b(c(b(b(b(b(a(c(a(b(c(a(b(b(c(b(b(c(c(c(c(x1))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(a(b(c(a(b(b(c(b(b(c(c(c(c(x1)))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(a(c(a(c(a(b(b(c(b(b(c(c(c(c(x1))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(a(c(c(a(b(b(c(b(b(c(c(c(c(x1)))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(c(c(a(b(b(c(b(b(c(c(c(c(x1))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(c(c(b(b(a(c(a(b(c(b(b(c(c(c(c(x1)))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(a(b(a(c(a(b(c(b(b(c(c(c(c(x1)))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(a(b(c(a(b(c(b(b(c(c(c(c(x1))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(a(b(c(b(b(a(c(a(c(b(b(c(c(c(c(x1)))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(a(b(c(b(b(a(c(c(b(b(c(c(c(c(x1))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(a(b(c(b(b(a(a(b(c(c(c(c(x1))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(c(a(c(b(b(a(a(b(c(c(c(c(x1)))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(c(c(b(b(a(a(b(c(c(c(c(x1))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(a(b(a(a(b(c(c(c(c(x1))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(a(b(a(b(b(a(c(a(c(c(c(c(x1)))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(a(b(a(b(b(a(c(c(c(c(c(x1))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(a(b(a(b(b(c(c(c(c(c(x1)))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(a(b(b(b(a(c(a(b(c(c(c(c(c(x1))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(a(b(b(b(c(a(b(c(c(c(c(c(x1)))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(a(b(b(b(c(b(b(a(c(a(c(c(c(c(c(x1))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(a(b(b(b(c(b(b(a(c(c(c(c(c(c(x1)))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(a(b(b(b(c(b(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(b(b(a(c(a(b(b(c(b(b(c(c(c(c(c(c(x1)))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(b(b(c(a(b(b(c(b(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(b(b(c(b(b(a(c(a(b(c(b(b(c(c(c(c(c(c(x1)))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(b(b(c(b(b(c(a(b(c(b(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(b(b(c(b(b(c(b(b(a(c(a(c(b(b(c(c(c(c(c(c(x1)))))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(b(b(c(b(b(c(b(b(a(c(c(b(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(b(b(c(b(b(c(b(b(a(a(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(b(b(c(b(b(c(b(b(a(b(c(c(c(c(c(c(x1)))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(a(b(b(c(b(b(c(b(b(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(b(b(a(c(a(b(c(b(b(c(b(b(b(c(c(c(c(c(c(x1)))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(b(b(c(a(b(c(b(b(c(b(b(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(b(b(c(b(b(a(c(a(c(b(b(c(b(b(b(c(c(c(c(c(c(x1)))))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(b(b(c(b(b(a(c(c(b(b(c(b(b(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(b(b(c(b(b(a(a(b(c(b(b(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(b(b(c(b(b(a(b(b(a(c(a(c(b(b(b(c(c(c(c(c(c(x1)))))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(b(b(c(b(b(a(b(b(a(c(c(b(b(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(b(b(c(b(b(a(b(b(a(a(b(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(b(b(c(b(b(b(b(a(c(a(b(a(a(b(b(c(c(c(c(c(c(x1)))))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(b(b(c(b(b(b(b(c(a(b(a(a(b(b(c(c(c(c(c(c(x1))))))))))))))))))))))))))))))))
→ b(b(c(b(b(b(b(c(b(b(b(b(b(b(c(b(b(b(b(c(b(b(a(c(a(a(a(b(b(c(c(c(c(c(c(x1)))))))))))))))))))))))))))))))))))
= t67
where t67 = C[t0σ] and σ = {x1/c(c(c(c(c(x1)))))} and C = b(b(c(b(b(b(b(c(b(b(b(b(b(b(c(b(b(b(b(c(b(b(a(c(☐))))))))))))))))))))))))