Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-488)

The rewrite relation of the following TRS is considered.

a(a(x1)) → b(x1) (1)
a(b(x1)) → c(a(x1)) (2)
c(c(x1)) → b(a(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(c(c(c(a(c(a(b(a(x1)))))))))
→ b(c(c(c(a(c(c(a(a(x1)))))))))
→ b(c(c(c(a(b(a(b(a(a(x1))))))))))
→ b(c(c(c(c(a(a(b(a(a(x1))))))))))
→ b(c(c(c(c(b(b(a(a(x1)))))))))
→ b(c(c(b(a(b(b(b(a(a(x1))))))))))
→ b(c(c(b(c(a(b(b(a(a(x1))))))))))
→ b(c(c(b(c(c(a(b(a(a(x1))))))))))
→ b(c(c(b(c(c(c(a(a(a(x1))))))))))
→ b(b(a(b(b(c(c(c(a(a(a(x1)))))))))))
→ b(b(c(a(b(c(c(c(a(a(a(x1)))))))))))
→ b(b(c(c(a(c(c(c(a(a(a(x1)))))))))))
→ b(b(c(c(a(b(a(b(c(a(a(a(x1))))))))))))
→ b(b(c(c(a(b(c(a(c(a(a(a(x1))))))))))))
→ b(b(c(c(c(a(c(a(c(a(a(a(x1))))))))))))
→ b(b(c(c(c(a(c(a(c(a(b(x1)))))))))))
→ b(b(c(c(c(a(c(a(c(c(a(x1)))))))))))
→ b(b(c(c(c(a(c(a(b(a(b(a(x1))))))))))))
= t17
where t17 = C[t0σ] and σ = {x1/b(a(x1))} and C = b(☐)