Certification Problem

Input (COPS 66)

We consider the TRS containing the following rules:

f(g(x,a,b)) → x (1)
g(f(h(c,d)),x,y) → h(k1(x),k2(y)) (2)
k1(a) → c (3)
k2(b) → d (4)
f(h(k1(a),k2(b))) → f(h(c,d)) (5)
f(h(c,k2(b))) → f(h(c,d)) (6)
f(h(k1(a),d)) → f(h(c,d)) (7)

The underlying signature is as follows:

{f/1, g/3, a/0, b/0, h/2, c/0, d/0, k1/1, k2/1}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2020)

1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 4 step(s).