Certification Problem

Input (COPS 958)

We consider the TRS containing the following rules:

b(b(b(x)))	→	a(a(a(x)))	(1)
a(a(a(x)))	→	b(a(b(x)))	(2)

The underlying signature is as follows:

{b/1, a/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.