Certification Problem

Input (COPS 689)

We consider the TRS containing the following rules:

The underlying signature is as follows:

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

Prove or disprove confluence.

No.

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

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