YES

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x y)
(REPLACEMENT-MAP
(+ 1, 2)
(fSNonEmpty)
)
(RULES
+(x,y) -> +(y,x)
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 

Problem 1: 
Not CS-TRS Procedure:
R is not a CS-TRS

Problem 1: 
Linearity Procedure:
Linear?
YES

Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x y)
(REPLACEMENT-MAP
(+ 1, 2)
(fSNonEmpty)
)
(RULES
+(x,y) -> +(y,x)
)
Linear:YES
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 +(x,y) -> +(y,x)
-> Vars:
 x, y

-> Rlps:
 (rule: +(x,y) -> +(y,x), id: 1, possubterms: +(x,y)->[])

-> Unifications:


-> Critical pairs info:


-> Problem conclusions:
 Left linear, Right linear, Linear
 Weakly orthogonal, Almost orthogonal, Orthogonal
 Huet-Levy confluent, Not Newman confluent
 R is a TRS 


The problem is confluent.