Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-83)

The rewrite relation of the following TRS is considered.

a(x1) → x1 (1)
a(a(x1)) → b(a(b(c(x1)))) (2)
c(x1) → x1 (3)
c(b(x1)) → a(c(x1)) (4)

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = c(a(a(a(a(b(x1))))))
→ c(a(a(b(a(b(c(b(x1))))))))
→ c(a(a(b(a(b(a(c(x1))))))))
→ c(a(a(b(a(b(a(x1)))))))
→ c(b(a(b(c(b(a(b(a(x1)))))))))
→ c(b(b(c(b(a(b(a(x1))))))))
→ c(b(b(a(c(a(b(a(x1))))))))
→ c(b(b(a(a(b(a(x1)))))))
→ c(b(b(b(a(b(c(b(a(x1)))))))))
→ c(b(b(b(b(c(b(a(x1))))))))
→ c(b(b(b(b(a(c(a(x1))))))))
→ c(b(b(b(b(a(a(x1)))))))
→ c(b(b(b(b(b(a(b(c(x1)))))))))
→ c(b(b(b(b(b(a(b(x1))))))))
→ a(c(b(b(b(b(a(b(x1))))))))
→ a(a(c(b(b(b(a(b(x1))))))))
→ a(a(a(c(b(b(a(b(x1))))))))
→ a(a(a(a(c(b(a(b(x1))))))))
→ a(a(a(a(a(c(a(b(x1))))))))
→ a(a(a(a(a(a(b(x1)))))))
→ b(a(b(c(a(a(a(a(b(x1)))))))))
= t20
where t20 = C[t0σ] and σ = {x1/x1} and C = b(a(b(☐)))