YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Redundant Rules Transformation

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

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

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

1.1 Critical Pair Closing System

Confluence is proven using the following terminating critical-pair-closing-system R:

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

1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[+(x1, x2)] = 6 · x1 + 1 · x2 + 2
[s(x1)] = 1 · x1 + 2
all rules could be removed.

1.1.1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.

Tool configuration

csi