NO

Problem 1: 


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


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 1)
(b 1)
(c 1)
(fSNonEmpty)
)
(RULES
a(x) -> b(b(b(x)))
a(x) -> c(x)
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


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

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

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

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

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

-> Critical pairs info:
<b(b(b(x'))),c(x')>   =>  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(b(b(x'))),c(x')>   =>  Not trivial, Overlay, Proper, NW0, N1, Normal and not trivial cp

The problem is not confluent.