Certification Problem

Input (TPDB SRS_Standard/Trafo_06/un06)

The rewrite relation of the following TRS is considered.

b(b(x1)) b(a(b(a(a(b(x1)))))) (1)
b(b(a(b(x1)))) b(a(b(b(x1)))) (2)
b(a(a(a(b(a(a(b(x1)))))))) b(a(a(a(b(b(x1)))))) (3)
b(b(a(a(b(x1))))) b(a(a(b(b(x1))))) (4)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
b#(b(x1)) b#(a(b(a(a(b(x1)))))) (5)
b#(b(x1)) b#(a(a(b(x1)))) (6)
b#(b(a(b(x1)))) b#(a(b(b(x1)))) (7)
b#(b(a(b(x1)))) b#(b(x1)) (8)
b#(a(a(a(b(a(a(b(x1)))))))) b#(a(a(a(b(b(x1)))))) (9)
b#(a(a(a(b(a(a(b(x1)))))))) b#(b(x1)) (10)
b#(b(a(a(b(x1))))) b#(a(a(b(b(x1))))) (11)
b#(b(a(a(b(x1))))) b#(b(x1)) (12)

1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.