Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-247)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by matchbox @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = c(c(c(b(b(c(x1))))))
c(c(b(a(b(b(c(x1)))))))
c(c(b(b(c(a(a(b(c(x1)))))))))
c(c(b(b(c(a(b(c(a(a(c(x1)))))))))))
c(c(b(b(c(a(b(c(a(c(x1))))))))))
c(c(b(b(c(a(b(c(c(x1)))))))))
c(c(b(b(c(a(b(c(b(a(x1))))))))))
c(c(b(b(c(a(b(c(b(x1)))))))))
c(c(b(b(c(b(c(a(a(c(b(x1)))))))))))
c(c(b(b(c(b(c(a(c(b(x1))))))))))
c(c(b(b(c(b(c(c(b(x1)))))))))
c(c(b(b(c(b(c(b(a(b(x1))))))))))
c(c(b(b(c(b(c(b(b(x1)))))))))
c(b(a(b(b(c(b(c(b(b(x1))))))))))
c(b(b(c(a(a(b(c(b(c(b(b(x1))))))))))))
c(b(b(c(a(b(c(a(a(c(b(c(b(b(x1))))))))))))))
c(b(b(c(a(b(c(a(c(b(c(b(b(x1)))))))))))))
c(b(b(c(a(b(c(c(b(c(b(b(x1))))))))))))
c(b(b(c(b(c(a(a(c(c(b(c(b(b(x1))))))))))))))
c(b(b(c(b(c(a(c(c(b(c(b(b(x1)))))))))))))
c(b(b(c(b(c(c(c(b(c(b(b(x1))))))))))))
c(b(b(c(b(c(c(b(a(b(c(b(b(x1)))))))))))))
c(b(b(c(b(c(c(b(b(c(a(a(c(b(b(x1)))))))))))))))
c(b(b(c(b(c(c(b(b(c(a(c(b(b(x1))))))))))))))
c(b(b(c(b(c(c(b(b(c(c(b(b(x1)))))))))))))
c(b(b(c(b(c(c(b(b(c(b(a(b(b(x1))))))))))))))
c(b(b(c(b(c(c(b(b(c(b(b(c(a(a(b(x1))))))))))))))))
c(b(b(c(b(c(c(b(b(c(b(b(c(a(b(x1)))))))))))))))
c(b(b(c(b(c(c(b(b(c(b(b(c(b(x1))))))))))))))
c(b(b(c(b(c(b(a(b(b(c(b(b(c(b(x1)))))))))))))))
c(b(b(c(b(c(b(b(c(a(a(b(c(b(b(c(b(x1)))))))))))))))))
c(b(b(c(b(c(b(b(c(a(b(c(a(a(c(b(b(c(b(x1)))))))))))))))))))
c(b(b(c(b(c(b(b(c(a(b(c(a(c(b(b(c(b(x1))))))))))))))))))
c(b(b(c(b(c(b(b(c(a(b(c(c(b(b(c(b(x1)))))))))))))))))
c(b(b(c(b(c(b(b(c(b(c(a(a(c(c(b(b(c(b(x1)))))))))))))))))))
c(b(b(c(b(c(b(b(c(b(c(a(c(c(b(b(c(b(x1))))))))))))))))))
c(b(b(c(b(c(b(b(c(b(c(c(c(b(b(c(b(x1)))))))))))))))))
= t36
where t36 = C[t0σ] and σ = {x1/b(x1)} and C = c(b(b(c(b(c(b(b(c(b())))))))))