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 = h(h(h(b,b),f(f(a))),f(f(f(a))))

→_1.1.1 h(h(h(h(h(f(a),c),f(a)),b),f(f(a))),f(f(f(a))))

= t₁

t₀ = h(h(h(b,b),f(f(a))),f(f(f(a))))

→_ε a

= 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