YES

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x y z)
(REPLACEMENT-MAP
(Ap 1, 2)
(I)
(K)
(S)
(fSNonEmpty)
)
(RULES
Ap(Ap(Ap(S,x),y),z) -> Ap(Ap(x,z),Ap(y,z))
Ap(Ap(K,x),y) -> x
Ap(I,x) -> x
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 

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

Problem 1: 
Linearity Procedure:
Linear?
NO

Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x y z)
(REPLACEMENT-MAP
(Ap 1, 2)
(I)
(K)
(S)
(fSNonEmpty)
)
(RULES
Ap(Ap(Ap(S,x),y),z) -> Ap(Ap(x,z),Ap(y,z))
Ap(Ap(K,x),y) -> x
Ap(I,x) -> x
)
Linear:NO
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 Ap(Ap(Ap(S,x),y),z) -> Ap(Ap(x,z),Ap(y,z))
 Ap(Ap(K,x),y) -> x
 Ap(I,x) -> x
-> Vars:
 x, y, z, x, y, x

-> Rlps:
 (rule: Ap(Ap(Ap(S,x),y),z) -> Ap(Ap(x,z),Ap(y,z)), id: 1, possubterms: Ap(Ap(Ap(S,x),y),z)->[], Ap(Ap(S,x),y)->[1], Ap(S,x)->[1, 1], S->[1, 1, 1])
 (rule: Ap(Ap(K,x),y) -> x, id: 2, possubterms: Ap(Ap(K,x),y)->[], Ap(K,x)->[1], K->[1, 1])
 (rule: Ap(I,x) -> x, id: 3, possubterms: Ap(I,x)->[], I->[1])

-> Unifications:


-> Critical pairs info:


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


The problem is confluent.