Certification Problem

Input (TPDB SRS_Standard/Bouchare_06/07)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by NaTT @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
b#(a(b(x1))) a#(a(x1)) (4)
a#(a(a(x1))) b#(x1) (5)
b#(a(x1)) b#(b(x1)) (6)
a#(a(a(x1))) b#(b(x1)) (7)
b#(a(b(x1))) a#(x1) (8)
b#(a(b(x1))) b#(a(a(x1))) (9)
b#(a(x1)) b#(x1) (10)
a#(a(a(x1))) a#(b(b(x1))) (11)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.