Certification Problem

Input (COPS 135)

We consider the TRS containing the following rules:

max(x,0) x (1)
max(0,y) y (2)
max(s(x),s(y)) s(max(y,x)) (3)
max(x,y) max(y,x) (4)

The underlying signature is as follows:

{max/2, 0/0, s/1}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by csi @ CoCo 2021)

1 Redundant Rules Transformation

To prove that the TRS is (non-)confluent, we show (non-)confluence of the following modified system:

max(x,y) max(y,x) (4)
max(s(x),s(y)) s(max(y,x)) (3)
max(0,y) y (2)
max(x,0) x (1)
max(x,y) max(x,y) (5)
max(s(x),s(y)) s(max(x,y)) (6)

All redundant rules that were added or removed can be simulated in 2 steps .

1.1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 7 step(s).