Certification Problem

Input (COPS 697)

We consider the TRS containing the following rules:

h(h(c,a),b) b (1)
a h(a,b) (2)
a a (3)

The underlying signature is as follows:

{h/2, c/0, a/0, b/0}

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2020)

1 Non-Joinable Fork

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

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

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

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