YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

+(x,0) x
+(x,s(y)) s(+(y,x))
+(x,y) +(y,x)

Proof

1 Redundant Rules Transformation

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

+(x,y) +(y,x)
+(x,s(y)) s(+(y,x))
+(x,0) x
+(0,x) x
+(s(y),x) s(+(y,x))
+(s(x32),x) s(+(x32,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