Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z023)

The rewrite relation of the following TRS is considered.

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

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

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.