NO

Problem 1: 


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


Problem 1: 

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

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

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


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

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

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

The problem is not confluent.