Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z004)

The rewrite relation of the following TRS is considered.

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

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.
a#(b(a(a(x1)))) a#(b(a(x1))) (3)
a#(c(b(x1))) a#(a(b(c(b(a(x1)))))) (4)
a#(c(b(x1))) a#(b(c(b(a(x1))))) (5)
a#(c(b(x1))) a#(x1) (6)

1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.