Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-20)

The rewrite relation of the following TRS is considered.

a(x1) → x1 (1)
a(x1) → b(x1) (2)
b(a(c(x1))) → c(c(a(b(a(x1))))) (3)
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 = b(b(a(c(c(c(b(b(x1))))))))
→ b(c(c(a(b(a(c(c(b(b(x1))))))))))
→ b(c(a(b(a(c(c(b(b(x1)))))))))
→ b(a(b(a(c(c(b(b(x1))))))))
→ b(a(c(c(a(b(a(c(b(b(x1))))))))))
→ b(a(c(c(b(a(c(b(b(x1)))))))))
→ b(a(c(c(c(c(a(b(a(b(b(x1)))))))))))
→ b(a(c(c(c(c(a(b(b(b(x1))))))))))
→ b(a(c(c(c(c(b(b(b(x1)))))))))
→ c(c(a(b(a(c(c(c(b(b(b(x1)))))))))))
→ c(a(b(a(c(c(c(b(b(b(x1))))))))))
→ a(b(a(c(c(c(b(b(b(x1)))))))))
→ b(b(a(c(c(c(b(b(b(x1)))))))))
= t12
where t12 = t0σ and σ = {x1/b(x1)}