NO

Problem 1: 


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

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


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

-> Unifications:
(R2 unifies with R1 at p: [], l: b, lp: b, sig: {}, l': b, r: f(c), r': h(b,a))
(R3 unifies with R1 at p: [1], l: h(b,h(a,f(h(a,f(f(f(b))))))), lp: b, sig: {}, l': b, r: h(a,f(a)), r': h(b,a))
(R3 unifies with R2 at p: [1], l: h(b,h(a,f(h(a,f(f(f(b))))))), lp: b, sig: {}, l': b, r: h(a,f(a)), r': f(c))
(R3 unifies with R1 at p: [2,2,1,2,1,1,1], l: h(b,h(a,f(h(a,f(f(f(b))))))), lp: b, sig: {}, l': b, r: h(a,f(a)), r': h(b,a))
(R3 unifies with R2 at p: [2,2,1,2,1,1,1], l: h(b,h(a,f(h(a,f(f(f(b))))))), lp: b, sig: {}, l': b, r: h(a,f(a)), r': f(c))
(R4 unifies with R1 at p: [1,1], l: h(f(b),c), lp: b, sig: {}, l': b, r: f(c), r': h(b,a))
(R4 unifies with R2 at p: [1,1], l: h(f(b),c), lp: b, sig: {}, l': b, r: f(c), r': f(c))

-> Critical pairs info:
<h(f(f(c)),c),f(c)>   =>  Not trivial, Not overlay, Proper, NW0, N1
<h(f(c),h(a,f(h(a,f(f(f(b))))))),h(a,f(a))>   =>  Not trivial, Not overlay, Proper, NW0, N2
<h(b,h(a,f(h(a,f(f(f(f(c)))))))),h(a,f(a))>   =>  Not trivial, Not overlay, Proper, NW0, N3
<h(h(b,a),h(a,f(h(a,f(f(f(b))))))),h(a,f(a))>   =>  Not trivial, Not overlay, Proper, NW0, N4
<h(b,h(a,f(h(a,f(f(f(h(b,a)))))))),h(a,f(a))>   =>  Not trivial, Not overlay, Proper, NW0, N5
<h(b,a),f(c)>   =>  Not trivial, Overlay, Proper, NW0, N6
<h(f(h(b,a)),c),f(c)>   =>  Not trivial, Not overlay, Proper, NW0, N7

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

The problem is not confluent.