NO

Problem 1: 


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


Problem 1: 

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

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


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

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

-> Rlps:
 (rule: f(b,x) -> b, id: 1, possubterms: f(b,x)->[], b->[1])
 (rule: f(x,a) -> a, 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,x' -> a}, l': f(b,x'), r: a, r': b)

-> Critical pairs info:
<b,a>   =>  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: 
Different Normal CP Terms Procedure:
<b,a>   =>  Not trivial, Overlay, Proper, NW0, N1, Normal and not trivial cp

The problem is not confluent.