YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

+(x,0) x
+(s(x),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)
+(s(x),y) s(+(y,x))
+(x,0) x
s(+(0,x33)) s(x33)
+(0,x) x
+(y,s(x)) s(+(y,x))
s(+(0,x)) s(x)
+(y,s(x31)) s(+(y,x31))

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