NO

Problem 1: 


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


Problem 1: 

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

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


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

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

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


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

-> Unifications:
(R3 unifies with R1 at p: [1,1], l: f(h(b,a)), lp: b, sig: {}, l': b, r: a, r': c)

-> Critical pairs info:
<f(h(c,a)),a>   =>  Not trivial, Not 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: 
No Convergence Brute Force Procedure:
-> Rewritings:
s: f(h(c,a))
Nodes: [0]
Edges: []
ID: 0 => ('f(h(c,a))', D0)
t: a
Nodes: [0]
Edges: []
ID: 0 => ('a', D0)
f(h(c,a)) ->* no union *<- a
"Not joinable"

The problem is not confluent.