YES

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x y)
(REPLACEMENT-MAP
(+ 1, 2)
(0)
(fSNonEmpty)
(s 1)
)
(RULES
+(0,x) -> x
+(s(x),y) -> s(+(x,y))
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


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)
(0)
(fSNonEmpty)
(s 1)
)
(RULES
+(0,x) -> x
+(s(x),y) -> s(+(x,y))
)
Linear:YES
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 +(0,x) -> x
 +(s(x),y) -> s(+(x,y))
-> Vars:
 x, x, y

-> Rlps:
 (rule: +(0,x) -> x, id: 1, possubterms: +(0,x)->[], 0->[1])
 (rule: +(s(x),y) -> s(+(x,y)), id: 2, possubterms: +(s(x),y)->[], s(x)->[1])

-> 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.