NO Non-Confluence Proof

Non-Confluence Proof

by Hakusan

Input

The rewrite relation of the following TRS is considered.

a(x) g(h(b(x)))
a(x) g(c(x))
b(x) g(b(x))
g(a(x)) g(h(a(x)))

Proof

1 Non-Joinable Fork

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

t0 = a(y1)
ε g(c(y1))
= t1

t0 = a(y1)
ε g(h(b(y1)))
= t1

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

Tool configuration

Hakusan