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 = 0(1(2(1(y1))))

→_ε 1(2(1(1(0(1(2(0(1(2(0(1(2(y1)))))))))))))

= t₁

t₀ = 0(1(2(1(y1))))

→_ε 1(2(1(1(0(1(2(0(1(2(y1))))))))))

= 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