YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

max(x,0) → x
max(0,y) → y
max(s(x),s(y)) → s(max(x,y))
max(x,y) → max(y,x)

Proof

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)
max(s(x),s(y)) → s(max(x,y))
max(0,y) → y
max(x,0) → x
max(x,y) → max(x,y)
max(s(x),s(y)) → s(max(y,x))

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 within 7 step(s).

Tool configuration

csi