NO Non-Confluence Proof

Non-Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

f(g(f(x))) x
f(g(x)) g(f(x))

Proof

1 Non-Joinable Fork

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

t0 = f(g(f(f(g(f(x5))))))
ε f(g(f(x5)))
ε g(f(f(x5)))
= t2

t0 = f(g(f(f(g(f(x5))))))
ε f(g(f(x5)))
ε x5
= t2

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

Tool configuration

csi