NO Non-Confluence Proof

Non-Confluence Proof

by Hakusan

Input

The rewrite relation of the following TRS is considered.

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

t₀ = f(h(h(b,a),h(f(c),c)))

→_1.1.2 f(h(h(b,h(a,f(b))),h(f(c),c)))

= t₁

t₀ = f(h(h(b,a),h(f(c),c)))

→_ε c

= 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.

Hakusan