NO

Problem 1: 


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


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)
(a')
(b)
(c)
(fSNonEmpty)
)
(RULES
a -> a'
f(a) -> b
f(b) -> c
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

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


-> Rlps:
 (rule: a -> a', id: 1, possubterms: a->[])
 (rule: f(a) -> b, id: 2, possubterms: f(a)->[], a->[1])
 (rule: f(b) -> c, id: 3, possubterms: f(b)->[], b->[1])

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

-> Critical pairs info:
<f(a'),b>   =>  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(a')
Nodes: [0]
Edges: []
ID: 0 => ('f(a')', D0)
t: b
Nodes: [0]
Edges: []
ID: 0 => ('b', D0)
f(a') ->* no union *<- b
"Not joinable"

The problem is not confluent.