Certification Problem

Input (TPDB SRS_Standard/Wenzel_16/abbaaaa-aaaaabbaabbabb.srs)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
a#(b(b(a(a(a(a(x1))))))) a#(b(b(x1))) (2)
a#(b(b(a(a(a(a(x1))))))) a#(b(b(a(b(b(x1)))))) (3)
a#(b(b(a(a(a(a(x1))))))) a#(b(b(a(a(b(b(a(b(b(x1)))))))))) (4)
a#(b(b(a(a(a(a(x1))))))) a#(a(b(b(a(b(b(x1))))))) (5)
a#(b(b(a(a(a(a(x1))))))) a#(a(b(b(a(a(b(b(a(b(b(x1))))))))))) (6)
a#(b(b(a(a(a(a(x1))))))) a#(a(a(b(b(a(a(b(b(a(b(b(x1)))))))))))) (7)
a#(b(b(a(a(a(a(x1))))))) a#(a(a(a(b(b(a(a(b(b(a(b(b(x1))))))))))))) (8)
a#(b(b(a(a(a(a(x1))))))) a#(a(a(a(a(b(b(a(a(b(b(a(b(b(x1)))))))))))))) (9)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.