Certification Problem

Input (COPS 983)

We consider the TRS containing the following rules:

a(b(a(a(a(a(a(a(a(a(a(x)))))))))))

→

a(a(a(a(a(a(a(a(a(a(a(b(a(b(x))))))))))))))

(1)

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.

t₀	=	a(b(a(a(a(a(a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(x61)))))))))))))))))))))
	→	a(b(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(a(b(x61))))))))))))))))))))))))
	→	a(a(a(a(a(a(a(a(a(a(a(b(a(b(a(a(a(a(a(a(a(a(a(a(b(a(b(x61)))))))))))))))))))))))))))
	→	a(a(a(a(a(a(a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(a(a(b(a(b(a(b(a(b(x61))))))))))))))))))))))))))))))
	→	a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(a(b(a(a(b(a(b(a(b(a(b(x61)))))))))))))))))))))))))))))))))
	=	t₄

t₀	=	a(b(a(a(a(a(a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(x61)))))))))))))))))))))
	→	a(a(a(a(a(a(a(a(a(a(a(b(a(b(b(a(a(a(a(a(a(a(a(a(x61))))))))))))))))))))))))
	=	t₁

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.