Certification Problem

Input (TPDB SRS_Standard/Trafo_06/un10)

The rewrite relation of the following TRS is considered.

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

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.