YES

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x y)
(REPLACEMENT-MAP
(f 1, 2)
(g 1, 2)
(a)
(b)
(fSNonEmpty)
(h 1)
)
(RULES
f(x,a) -> f(x,g(x,b))
g(a,y) -> y
g(h(x),y) -> g(x,h(y))
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


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)
(REPLACEMENT-MAP
(f 1, 2)
(g 1, 2)
(a)
(b)
(fSNonEmpty)
(h 1)
)
(RULES
f(x,a) -> f(x,g(x,b))
g(a,y) -> y
g(h(x),y) -> g(x,h(y))
)
Linear:NO
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 f(x,a) -> f(x,g(x,b))
 g(a,y) -> y
 g(h(x),y) -> g(x,h(y))
-> Vars:
 x, y, x, y

-> Rlps:
 (rule: f(x,a) -> f(x,g(x,b)), id: 1, possubterms: f(x,a)->[], a->[2])
 (rule: g(a,y) -> y, id: 2, possubterms: g(a,y)->[], a->[1])
 (rule: g(h(x),y) -> g(x,h(y)), id: 3, possubterms: g(h(x),y)->[], h(x)->[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.