NO

Problem 1: 


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


Problem 1: 

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

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

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


-> Rlps:
 (rule: a -> f(b), id: 1, possubterms: a->[])
 (rule: b -> f(b), id: 2, possubterms: b->[])
 (rule: b -> f(c), id: 3, possubterms: b->[])
 (rule: h(b,f(c)) -> c, id: 4, possubterms: h(b,f(c))->[], b->[1], f(c)->[2], c->[2, 1])
 (rule: h(c,c) -> c, id: 5, possubterms: h(c,c)->[], c->[1], c->[2])

-> Unifications:
(R3 unifies with R2 at p: [], l: b, lp: b, sig: {}, l': b, r: f(c), r': f(b))
(R4 unifies with R2 at p: [1], l: h(b,f(c)), lp: b, sig: {}, l': b, r: c, r': f(b))
(R4 unifies with R3 at p: [1], l: h(b,f(c)), lp: b, sig: {}, l': b, r: c, r': f(c))

-> Critical pairs info:
<h(f(c),f(c)),c>   =>  Not trivial, Not overlay, Proper, NW0, N1
<h(f(b),f(c)),c>   =>  Not trivial, Not overlay, Proper, NW0, N2
<f(b),f(c)>   =>  Not trivial, Overlay, Proper, NW0, N3

-> 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: h(f(c),f(c))
Nodes: [0]
Edges: []
ID: 0 => ('h(f(c),f(c))', D0)
t: c
Nodes: [0]
Edges: []
ID: 0 => ('c', D0)
h(f(c),f(c)) ->* no union *<- c
"Not joinable"

The problem is not confluent.