Certification Problem

Input (COPS 955)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

{a/1, b/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.