Certification Problem

Input (COPS 672)

We consider the TRS containing the following rules:

The underlying signature is as follows:

{a/0, h/2, b/0, f/1}

Prove or disprove confluence.

No.

The system is not confluent due to the following forking derivations.

The two resulting terms cannot be joined for the following reason:

When applying the cap-function on both terms (where variables may be treated like constants) then the resulting terms do not unify.