NO Non-Confluence Proof

Non-Confluence Proof

by Hakusan

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Non-Joinable Fork

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

t0 = b(b(b(x1)))
1 b(a(b(a(x1))))
= t1

t0 = b(b(b(x1)))
ε a(b(a(b(x1))))
= t1

The two resulting terms cannot be joined for the following reason:

Tool configuration

Hakusan