Certification Problem

Input (TPDB SRS_Standard/Wenzel_16/aabaaaaa-aaaaaaabaabaab.srs)

The rewrite relation of the following TRS is considered.

a(a(b(a(a(a(a(a(x1)))))))) a(a(a(a(a(a(a(b(a(a(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(a(a(a(a(a(x1)))))))) a#(b(x1)) (2)
a#(a(b(a(a(a(a(a(x1)))))))) a#(b(a(a(b(x1))))) (3)
a#(a(b(a(a(a(a(a(x1)))))))) a#(b(a(a(b(a(a(b(x1)))))))) (4)
a#(a(b(a(a(a(a(a(x1)))))))) a#(a(b(x1))) (5)
a#(a(b(a(a(a(a(a(x1)))))))) a#(a(b(a(a(b(x1)))))) (6)
a#(a(b(a(a(a(a(a(x1)))))))) a#(a(b(a(a(b(a(a(b(x1))))))))) (7)
a#(a(b(a(a(a(a(a(x1)))))))) a#(a(a(b(a(a(b(a(a(b(x1)))))))))) (8)
a#(a(b(a(a(a(a(a(x1)))))))) a#(a(a(a(b(a(a(b(a(a(b(x1))))))))))) (9)
a#(a(b(a(a(a(a(a(x1)))))))) a#(a(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) (10)
a#(a(b(a(a(a(a(a(x1)))))))) a#(a(a(a(a(a(b(a(a(b(a(a(b(x1))))))))))))) (11)
a#(a(b(a(a(a(a(a(x1)))))))) a#(a(a(a(a(a(a(b(a(a(b(a(a(b(x1)))))))))))))) (12)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.