Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-179)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by ttt2 @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t0 = a(b(b(c(b(x14362)))))
b(a(c(b(a(a(b(c(b(x14362)))))))))
b(a(c(b(a(b(a(c(b(a(a(c(b(x14362)))))))))))))
b(a(c(b(a(b(a(c(b(a(c(b(x14362))))))))))))
b(a(c(b(a(b(a(c(b(c(b(x14362)))))))))))
b(a(c(b(a(b(a(b(x14362))))))))
b(a(c(b(a(b(b(a(c(b(a(a(x14362))))))))))))
b(a(c(b(a(b(b(c(b(a(a(x14362)))))))))))
= t7
where t7 = C[t0σ] and σ = {x14362/a(a(x14362))} and C = b(a(c(b())))