NO

Problem 1: 


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


Problem 1: 

CleanTRS Procedure:
R was updated by simple cleaning of the TRS

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


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)
(b)
(fSNonEmpty)
)
(RULES
f(b,a) -> f(a,b)
f(x,a) -> b
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

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

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

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

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

The problem is not confluent.