Certification Problem

Input (COPS 690)

We consider the TRS containing the following rules:

h(f(f(c)),b) f(h(h(h(c,h(f(h(c,f(b))),a)),b),c)) (1)
c c (2)
f(f(h(h(f(a),a),c))) f(h(f(c),b)) (3)
h(f(h(f(b),h(h(f(h(c,f(c))),b),a))),h(a,c)) c (4)

The underlying signature is as follows:

{h/2, f/1, c/0, b/0, a/0}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2021)

1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 2 step(s).