Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-47)

The rewrite relation of the following TRS is considered.

a(x1) → x1 (1)
a(x1) → b(c(x1)) (2)
c(b(b(b(x1)))) → b(a(b(a(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(a(b(a(a(b(b(b(b(b(x1))))))))))))
→ b(b(b(a(b(a(b(c(b(b(b(b(b(x1)))))))))))))
→ b(b(b(a(b(b(c(b(c(b(b(b(b(b(x1))))))))))))))
→ b(b(b(b(c(b(b(c(b(c(b(b(b(b(b(x1)))))))))))))))
→ b(b(b(b(c(b(b(c(b(b(a(b(a(b(b(x1)))))))))))))))
→ b(b(b(b(c(b(b(c(b(b(a(b(b(b(x1))))))))))))))
→ b(b(b(b(c(b(b(c(b(b(b(c(b(b(b(x1)))))))))))))))
→ b(b(b(b(c(b(b(b(a(b(a(c(b(b(b(x1)))))))))))))))
→ b(b(b(b(b(a(b(a(a(b(a(c(b(b(b(x1)))))))))))))))
→ b(b(b(b(b(a(b(a(a(b(a(b(a(b(a(x1)))))))))))))))
→ b(b(b(b(b(a(b(a(a(b(a(b(b(a(x1))))))))))))))
→ b(b(b(b(b(a(b(a(a(b(a(b(b(b(c(x1)))))))))))))))
→ b(b(b(b(b(a(b(a(a(b(b(c(b(b(b(c(x1))))))))))))))))
→ b(b(b(b(b(a(b(a(a(b(b(b(a(b(a(c(x1))))))))))))))))
→ b(b(b(b(b(a(b(a(a(b(b(b(b(a(c(x1)))))))))))))))
→ b(b(b(b(b(a(b(a(a(b(b(b(b(b(c(c(x1))))))))))))))))
= t15
where t15 = C[t0σ] and σ = {x1/c(c(x1))} and C = b(b(☐))