Confluence Proof

by Toyama Example R1 in Okui's paper

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Toyama's parallel critical pair criterion

Confluence is proven since the TRS satisfies Toyama's criterion for parallel critical pairs. The joins can be performed within 4 step(s).

Tool configuration

Toyama Example R1 in Okui's paper