Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-340)

The rewrite relation of the following TRS is considered.

a(x1) → b(x1) (1)
a(a(b(c(x1)))) → c(c(a(a(a(a(x1)))))) (2)

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
a(x1) → b(x1) (1)
c(b(a(a(x1)))) → a(a(a(a(c(c(x1)))))) (3)

1.1 Loop

The following loop proves nontermination.

t0 = c(c(a(a(a(a(a(a(a(a(a(a(a(a(a(x1)))))))))))))))
→ c(c(b(a(a(a(a(a(a(a(a(a(a(a(a(x1)))))))))))))))
→ c(a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))
→ c(b(a(a(a(c(c(a(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))
→ a(a(a(a(c(c(a(c(c(a(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))
→ a(a(a(a(c(c(a(c(c(b(a(a(a(a(a(a(a(a(a(x1)))))))))))))))))))
→ a(a(a(a(c(c(a(c(a(a(a(a(c(c(a(a(a(a(a(a(a(x1)))))))))))))))))))))
→ a(a(a(a(c(c(a(c(b(a(a(a(c(c(a(a(a(a(a(a(a(x1)))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(c(c(a(c(c(a(a(a(a(a(a(a(x1)))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(c(c(a(c(c(b(a(a(a(a(a(a(x1)))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(c(c(a(c(a(a(a(a(c(c(a(a(a(a(x1)))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(c(c(a(c(b(a(a(a(c(c(a(a(a(a(x1)))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(c(c(a(a(a(a(a(c(c(a(c(c(a(a(a(a(x1)))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(c(c(b(a(a(a(a(c(c(a(c(c(a(a(a(a(x1)))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(c(a(a(a(a(c(c(a(a(c(c(a(c(c(a(a(a(a(x1)))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(c(b(a(a(a(c(c(a(a(c(c(a(c(c(a(a(a(a(x1)))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(a(a(a(a(x1)))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(b(a(a(a(x1)))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(c(c(a(a(c(c(a(c(a(a(a(a(c(c(a(x1)))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(c(c(a(a(c(c(a(c(b(a(a(a(c(c(a(x1)))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(c(c(a(a(c(c(a(a(a(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(c(c(a(a(c(c(b(a(a(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(c(c(a(a(c(a(a(a(a(c(c(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(c(c(a(a(c(b(a(a(a(c(c(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(c(c(a(a(a(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(c(c(b(a(a(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(c(a(a(a(a(c(c(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(c(b(a(a(a(c(c(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(a(a(a(a(a(c(c(a(c(c(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(c(b(a(a(a(a(c(c(a(c(c(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(a(a(a(a(c(c(a(a(c(c(a(c(c(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(c(b(a(a(a(c(c(a(a(c(c(a(c(c(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))))))))))))
→ a(a(a(a(c(c(a(a(a(a(a(a(a(a(a(a(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(a(x1)))))))))))))))))))))))))))))))))))))))))))))))
= t32
where t32 = C[t0σ] and σ = {x1/c(c(a(c(c(a(a(c(c(a(c(c(a(a(a(c(c(a(c(c(a(a(c(c(a(c(c(a(x1))))))))))))))))))))))))))))} and C = a(a(a(a(☐))))