NO Non-Confluence Proof

Non-Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

a f(h(c,h(h(h(h(f(h(a,b)),a),h(h(h(f(f(a)),c),h(f(b),a)),a)),b),c)))
h(f(f(b)),h(c,h(f(f(h(h(b,h(c,c)),h(f(a),c)))),f(a)))) h(b,b)
f(c) c
f(f(h(f(h(c,h(a,f(a)))),f(c)))) b

Proof

1 Non-Joinable Fork

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

t0 = h(f(f(b)),h(c,h(f(f(h(h(b,h(c,c)),h(f(a),c)))),f(a))))
2.2.1.1.1.2.1.1 h(f(f(b)),h(c,h(f(f(h(h(b,h(c,c)),h(f(f(h(c,h(h(h(h(f(h(a,b)),a),h(h(h(f(f(a)),c),h(f(b),a)),a)),b),c)))),c)))),f(a))))
= t1

t0 = h(f(f(b)),h(c,h(f(f(h(h(b,h(c,c)),h(f(a),c)))),f(a))))
ε h(b,b)
= t1

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

Tool configuration

csi