NO Non-Confluence Proof

Non-Confluence Proof

by ACP

Input

The rewrite relation of the following TRS is considered.

f(g(x,a,b)) x
p(a) c
g(f(h(c,d)),x,y) h(p(x),q(x))
q(b) d

Proof

1 Non-Joinable Fork

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

t0 = f(f(g(g(f(h(c,d)),a,b),a,b)))
1 f(g(f(h(c,d)),a,b))
1 f(h(p(a),q(a)))
1.1 f(h(c,q(a)))
= t3

t0 = f(f(g(g(f(h(c,d)),a,b),a,b)))
1 f(g(f(h(c,d)),a,b))
ε f(h(c,d))
= t2

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

Tool configuration

ACP