Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z010)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 Switch to Innermost Termination

The TRS is overlay and locally confluent:

10

Hence, it suffices to show innermost termination in the following.

1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
a#(b(x1)) a#(x1) (3)
c#(b(x1)) c#(c(x1)) (4)
c#(b(x1)) c#(x1) (5)

1.1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.