Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-368)

The rewrite relation of the following TRS is considered.

a(x1) → b(x1) (1)
a(b(c(x1))) → c(c(a(a(x1)))) (2)
c(c(x1)) → b(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(a(b(a(b(a(b(c(c(x1))))))))))
→ b(b(a(b(a(b(c(c(a(a(c(x1)))))))))))
→ b(b(a(b(a(b(c(c(a(b(c(x1)))))))))))
→ b(b(a(b(c(c(a(a(c(a(b(c(x1))))))))))))
→ b(b(a(b(c(c(a(b(c(a(b(c(x1))))))))))))
→ b(b(a(b(c(c(c(c(a(a(a(b(c(x1)))))))))))))
→ b(b(a(b(c(b(c(a(a(a(b(c(x1))))))))))))
→ b(b(a(b(c(b(c(a(b(a(b(c(x1))))))))))))
→ b(b(c(c(a(a(b(c(a(b(a(b(c(x1)))))))))))))
→ b(b(b(a(a(b(c(a(b(a(b(c(x1))))))))))))
→ b(b(b(a(c(c(a(a(a(b(a(b(c(x1)))))))))))))
→ b(b(b(a(b(a(a(a(b(a(b(c(x1))))))))))))
→ b(b(b(a(b(a(b(a(b(a(b(c(x1))))))))))))
→ b(b(b(a(b(a(b(a(b(c(c(a(a(x1)))))))))))))
= t13
where t13 = C[t0σ] and σ = {x1/a(a(x1))} and C = b(☐)