NO

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty)
(REPLACEMENT-MAP
(a)
(f 1)
(b)
(fSNonEmpty)
(g 1)
)
(RULES
a -> b
f(g(a)) -> f(a)
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 

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

Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty)
(REPLACEMENT-MAP
(a)
(f 1)
(b)
(fSNonEmpty)
(g 1)
)
(RULES
a -> b
f(g(a)) -> f(a)
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 a -> b
 f(g(a)) -> f(a)
-> Vars:


-> Rlps:
 (rule: a -> b, id: 1, possubterms: a->[])
 (rule: f(g(a)) -> f(a), id: 2, possubterms: f(g(a))->[], g(a)->[1], a->[1, 1])

-> Unifications:
(R2 unifies with R1 at p: [1,1], l: f(g(a)), lp: a, sig: {}, l': a, r: f(a), r': b)

-> Critical pairs info:
<f(g(b)),f(a)>   =>  Not trivial, Not overlay, Proper, NW0, N1

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


Problem 1: 
No Convergence Brute Force Procedure:
-> Rewritings:
s: f(g(b))
Nodes: [0]
Edges: []
ID: 0 => ('f(g(b))', D0)
t: f(a)
Nodes: [0,1]
Edges: [(0,1)]
ID: 0 => ('f(a)', D0)
ID: 1 => ('f(b)', D1, R1, P[1], S{}), NR: 'b'
f(g(b)) ->* no union *<- f(a)
"Not joinable"

The problem is not confluent.