Certification Problem

Input (TPDB SRS_Standard/Wenzel_16/aabbababa-abababaabbaab.srs)

The rewrite relation of the following TRS is considered.

a(a(b(b(a(b(a(b(a(x1))))))))) a(b(a(b(a(b(a(a(b(b(a(a(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#(a(b(b(a(b(a(b(a(x1))))))))) a#(b(x1)) (2)
a#(a(b(b(a(b(a(b(a(x1))))))))) a#(b(b(a(a(b(x1)))))) (3)
a#(a(b(b(a(b(a(b(a(x1))))))))) a#(b(a(b(a(b(a(a(b(b(a(a(b(x1))))))))))))) (4)
a#(a(b(b(a(b(a(b(a(x1))))))))) a#(b(a(b(a(a(b(b(a(a(b(x1))))))))))) (5)
a#(a(b(b(a(b(a(b(a(x1))))))))) a#(b(a(a(b(b(a(a(b(x1))))))))) (6)
a#(a(b(b(a(b(a(b(a(x1))))))))) a#(a(b(x1))) (7)
a#(a(b(b(a(b(a(b(a(x1))))))))) a#(a(b(b(a(a(b(x1))))))) (8)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.