Certification Problem

Input (TPDB TRS_Standard/Various_04/25)

The rewrite relation of the following TRS is considered.

g(a) → g(b) (1)
b → f(a,a) (2)
f(a,a) → g(d) (3)

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.
g#(a) → g#(b) (4)
g#(a) → b# (5)
b# → f#(a,a) (6)
f#(a,a) → g#(d) (7)

1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.