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))
+(x,0) → x
+(x,s(y)) → s(+(x,y))

Proof

1 Critical Pair Closing System

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

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

1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[+(x1, x2)] = 7 · x1 + 4 · x2 + 0
[0] = 0
[s(x1)] = 1 · x1 + 4
the rules
+(0,y) → y
+(x,0) → x
remain.

1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[+(x1, x2)] = 1 · x1 + 1 · x2 + 3
[0] = 4
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