Certification Problem

Input (TPDB TRS_Standard/Strategy_removed_AG01/#4.37)

The rewrite relation of the following TRS is considered.

f(c(s(x),y)) f(c(x,s(y))) (1)
g(c(x,s(y))) g(c(s(x),y)) (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.
f#(c(s(x),y)) f#(c(x,s(y))) (3)
g#(c(x,s(y))) g#(c(s(x),y)) (4)

1.1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.