Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-369)

The rewrite relation of the following TRS is considered.

a(x1) → b(x1) (1)
a(b(c(x1))) → c(c(b(a(a(x1))))) (2)
c(c(x1)) → 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(b(a(a(b(a(b(c(c(x1)))))))))))
→ b(b(b(b(a(a(b(c(c(b(a(a(c(x1)))))))))))))
→ b(b(b(b(a(a(b(c(c(b(a(b(c(x1)))))))))))))
→ b(b(b(b(a(c(c(b(a(a(c(b(a(b(c(x1)))))))))))))))
→ b(b(b(b(a(b(a(a(c(b(a(b(c(x1)))))))))))))
→ b(b(b(b(a(b(a(b(c(b(a(b(c(x1)))))))))))))
→ b(b(b(b(a(b(c(c(b(a(a(b(a(b(c(x1)))))))))))))))
→ b(b(b(b(c(c(b(a(a(c(b(a(a(b(a(b(c(x1)))))))))))))))))
→ b(b(b(b(b(a(a(c(b(a(a(b(a(b(c(x1)))))))))))))))
→ b(b(b(b(b(a(b(c(b(a(a(b(a(b(c(x1)))))))))))))))
→ b(b(b(b(b(c(c(b(a(a(b(a(a(b(a(b(c(x1)))))))))))))))))
→ b(b(b(b(b(b(a(a(b(a(a(b(a(b(c(x1)))))))))))))))
→ b(b(b(b(b(b(a(a(b(a(a(b(c(c(b(a(a(x1)))))))))))))))))
→ b(b(b(b(b(b(a(a(b(a(a(b(c(c(b(a(b(x1)))))))))))))))))
→ b(b(b(b(b(b(a(a(b(a(a(b(c(c(b(b(b(x1)))))))))))))))))
→ b(b(b(b(b(b(a(a(b(a(c(c(b(a(a(c(b(b(b(x1)))))))))))))))))))
→ b(b(b(b(b(b(a(a(b(a(b(a(a(c(b(b(b(x1)))))))))))))))))
→ b(b(b(b(b(b(a(a(b(a(b(a(b(c(b(b(b(x1)))))))))))))))))
→ b(b(b(b(b(b(a(a(b(a(b(c(c(b(a(a(b(b(b(x1)))))))))))))))))))
= t18
where t18 = C[t0σ] and σ = {x1/b(a(a(b(b(b(x1))))))} and C = b(b(☐))