Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-207)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = a(a(a(a(b(b(x1))))))
→ a(a(a(b(b(a(c(a(b(x1)))))))))
→ a(a(a(b(b(a(c(b(x1))))))))
→ a(a(a(b(b(c(b(x1)))))))
→ a(a(b(b(a(c(a(b(c(b(x1))))))))))
→ a(a(b(b(a(c(b(c(b(x1)))))))))
→ a(a(b(b(a(b(x1))))))
→ a(b(b(a(c(a(b(a(b(x1)))))))))
→ a(b(b(a(c(b(b(a(c(a(a(b(x1))))))))))))
→ a(b(b(a(c(b(b(c(a(a(b(x1)))))))))))
→ a(b(b(a(c(b(c(a(a(b(x1))))))))))
→ a(b(b(a(a(a(b(x1)))))))
→ b(b(a(c(a(b(a(a(a(b(x1))))))))))
→ b(a(c(a(b(a(a(a(b(x1)))))))))
→ a(c(a(b(a(a(a(b(x1))))))))
→ a(c(b(b(a(c(a(a(a(a(b(x1)))))))))))
→ a(c(b(b(c(a(a(a(a(b(x1))))))))))
→ a(c(b(c(a(a(a(a(b(x1)))))))))
→ a(a(a(a(a(b(x1))))))
→ a(a(a(a(b(b(a(c(a(x1)))))))))
= t19
where t19 = t0σ and σ = {x1/a(c(a(x1)))}