Certification Problem

Input (TPDB SRS_Standard/Trafo_06/hom03)

The rewrite relation of the following TRS is considered.

a(b(c(a(b(c(a(a(a(x1))))))))) a(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) (1)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
a#(b(c(a(b(c(a(a(a(x1))))))))) a#(b(c(x1))) (2)
a#(b(c(a(b(c(a(a(a(x1))))))))) a#(b(c(a(b(c(x1)))))) (3)
a#(b(c(a(b(c(a(a(a(x1))))))))) a#(b(c(a(b(c(a(b(c(x1))))))))) (4)
a#(b(c(a(b(c(a(a(a(x1))))))))) a#(a(b(c(a(b(c(a(b(c(x1)))))))))) (5)
a#(b(c(a(b(c(a(a(a(x1))))))))) a#(a(a(b(c(a(b(c(a(b(c(x1))))))))))) (6)
a#(b(c(a(b(c(a(a(a(x1))))))))) a#(a(a(a(b(c(a(b(c(a(b(c(x1)))))))))))) (7)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.