Certification Problem

Input (COPS 686)

We consider the TRS containing the following rules:

The underlying signature is as follows:

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

Prove or disprove confluence.

No.

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

t₀	=	h(h(h(f(a),a),a),f(f(f(h(h(f(b),b),b)))))
	→	h(h(h(f(a),a),a),f(f(f(h(h(f(h(c,f(b))),b),b)))))
	→	h(h(h(f(a),a),a),f(f(f(h(h(f(h(h(f(h(c,f(f(c)))),f(b)),f(b))),b),b)))))
	→	h(h(h(f(a),a),a),f(f(f(h(h(f(h(h(f(h(h(f(h(c,f(f(c)))),f(b)),f(f(c)))),f(b)),f(b))),b),b)))))
	=	t₃

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.