Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-249)

The rewrite relation of the following TRS is considered.

a(x1) → x1 (1)
a(b(x1)) → b(c(a(a(a(x1))))) (2)
a(c(c(x1))) → 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 = a(a(a(b(c(c(x1))))))
→ a(a(b(c(a(a(a(c(c(x1)))))))))
→ a(a(b(c(a(a(b(x1)))))))
→ a(a(b(c(a(b(c(a(a(a(x1))))))))))
→ a(a(b(c(a(b(c(a(a(x1)))))))))
→ a(a(b(c(a(b(c(a(x1))))))))
→ a(a(b(c(a(b(c(x1)))))))
→ a(a(b(c(b(c(a(a(a(c(x1))))))))))
→ a(a(b(c(b(c(a(a(c(x1)))))))))
→ a(a(b(c(b(c(a(c(x1))))))))
→ a(a(b(c(b(c(c(x1)))))))
→ a(b(c(a(a(a(c(b(c(c(x1))))))))))
→ a(b(c(a(a(c(b(c(c(x1)))))))))
→ a(b(c(a(c(b(c(c(x1))))))))
→ a(b(c(c(b(c(c(x1)))))))
→ b(c(a(a(a(c(c(b(c(c(x1))))))))))
→ b(c(a(a(b(b(c(c(x1))))))))
→ b(c(a(b(b(c(c(x1)))))))
→ b(c(b(c(a(a(a(b(c(c(x1))))))))))
= t18
where t18 = C[t0σ] and σ = {x1/x1} and C = b(c(b(c(☐))))