NO

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x)
(REPLACEMENT-MAP
(a)
(f 1, 2, 3)
(b)
(c)
(fSNonEmpty)
)
(RULES
a -> c
f(a,b,x) -> f(x,x,x)
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 

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

Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x)
(REPLACEMENT-MAP
(a)
(f 1, 2, 3)
(b)
(c)
(fSNonEmpty)
)
(RULES
a -> c
f(a,b,x) -> f(x,x,x)
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

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

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

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

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

-> Problem conclusions:
 Left linear, Not right linear, Not 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(c,b,x)
Nodes: [0]
Edges: []
ID: 0 => ('f(c,b,x)', D0)
t: f(x,x,x)
Nodes: [0]
Edges: []
ID: 0 => ('f(x,x,x)', D0)
f(c,b,x) ->* no union *<- f(x,x,x)
"Not joinable"

The problem is not confluent.