Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-2-num-11)

The rewrite relation of the following TRS is considered.

a(a(a(a(b(x1))))) → b(b(a(a(a(a(a(x1))))))) (1)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
b(a(a(a(a(x1))))) → a(a(a(a(a(b(b(x1))))))) (2)

1.1 Loop

The following loop proves nontermination.

t0 = b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))
→ a(a(a(a(a(b(b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(b(a(a(a(a(a(b(b(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(b(b(a(b(b(a(a(a(a(a(a(a(a(x1)))))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(b(b(a(b(a(a(a(a(a(b(b(a(a(a(a(x1)))))))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(b(b(a(a(a(a(a(a(b(b(a(b(b(a(a(a(a(x1)))))))))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(b(a(a(a(a(a(b(b(a(a(b(b(a(b(b(a(a(a(a(x1)))))))))))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(b(a(b(b(a(a(b(b(a(b(b(a(a(a(a(x1)))))))))))))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(b(a(b(b(a(a(b(b(a(b(a(a(a(a(a(b(b(x1)))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(b(a(b(b(a(a(b(b(a(a(a(a(a(a(b(b(a(b(b(x1)))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(b(a(b(b(a(a(b(a(a(a(a(a(b(b(a(a(b(b(a(b(b(x1)))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(b(a(b(b(a(a(a(a(a(a(a(b(b(a(b(b(a(a(b(b(a(b(b(x1)))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(b(a(b(a(a(a(a(a(b(b(a(a(a(b(b(a(b(b(a(a(b(b(a(b(b(x1)))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(b(a(a(a(a(a(a(b(b(a(b(b(a(a(a(b(b(a(b(b(a(a(b(b(a(b(b(x1)))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(a(a(a(a(a(b(b(a(a(b(b(a(b(b(a(a(a(b(b(a(b(b(a(a(b(b(a(b(b(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(b(a(b(b(a(a(b(b(a(b(b(a(a(a(b(b(a(b(b(a(a(b(b(a(...display limit reached...)))))))))))))))))))))))))))))))))))))))))))))))))))
= t16
where t16 = C[t0σ] and σ = {x1/b(b(a(b(b(a(a(b(b(a(b(b(a(a(a(b(b(a(b(b(a(a(b(b(a(b(b(x1)))))))))))))))))))))))))))} and C = a(a(a(a(a(☐)))))