NO Non-Confluence Proof

Non-Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Non-Joinable Fork

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

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

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

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

Tool configuration

csi