YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 Critical Pair Closing System

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

+(x,p(y)) → p(+(x,y))
s(p(x)) → x
-(x,p(y)) → s(-(x,y))
p(s(x)) → x
+(x,s(y)) → s(+(x,y))
-(x,s(y)) → p(-(x,y))

1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[-(x1, x2)] = 1 · x1 + 6 · x2 + 0
[s(x1)] = 1 · x1 + 1
[+(x1, x2)] = 4 · x1 + 2 · x2 + 0
[p(x1)] = 1 · x1 + 4
all rules could be removed.

1.1.1 R is empty

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

Tool configuration

csi