Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-353)

The rewrite relation of the following TRS is considered.

a(x1) → b(x1) (1)
a(b(x1)) → b(b(a(c(c(a(x1)))))) (2)
c(b(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(a(c(c(a(b(b(x1)))))))))
→ b(b(b(a(c(c(b(b(a(c(c(a(b(x1)))))))))))))
→ b(b(b(a(c(b(a(c(c(a(b(x1)))))))))))
→ b(b(b(a(a(c(c(a(b(x1)))))))))
→ b(b(b(a(a(c(c(b(b(a(c(c(a(x1)))))))))))))
→ b(b(b(a(a(c(b(a(c(c(a(x1)))))))))))
→ b(b(b(a(a(a(c(c(a(x1)))))))))
→ b(b(b(a(a(a(c(c(b(x1)))))))))
→ b(b(b(a(a(a(c(x1)))))))
→ b(b(b(a(a(b(c(x1)))))))
→ b(b(b(a(b(b(a(c(c(a(c(x1)))))))))))
→ b(b(b(a(b(b(a(c(c(b(c(x1)))))))))))
→ b(b(b(a(b(b(a(c(c(x1)))))))))
→ b(b(b(a(b(b(b(c(c(x1)))))))))
→ b(b(b(b(b(a(c(c(a(b(b(c(c(x1)))))))))))))
= t14
where t14 = C[t0σ] and σ = {x1/c(c(x1))} and C = b(b(☐))