NO

Problem 1: 


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


Problem 1: 

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

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


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

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

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


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

-> Unifications:
(R2 unifies with R1 at p: [1], l: h(b,b), lp: b, sig: {}, l': b, r: a, r': c)
(R2 unifies with R1 at p: [2], l: h(b,b), lp: b, sig: {}, l': b, r: a, r': c)

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

-> 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(c,b)
Nodes: [0,1,2]
Edges: [(0,1),(1,2)]
ID: 0 => ('h(c,b)', D0)
ID: 1 => ('h(c,c)', D1, R1, P[2], S{}), NR: 'c'
ID: 2 => ('c', D2, R3, P[], S{}), NR: 'c'
t: a
Nodes: [0]
Edges: []
ID: 0 => ('a', D0)
h(c,b) ->* no union *<- a
"Not joinable"

The problem is not confluent.