NO

Problem 1: 


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

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


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

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

-> Critical pairs info:
<h(h(b,c),f(f(h(h(c,c),c)))),c>   =>  Not trivial, Not overlay, Proper, NW0, N1
<f(c),b>   =>  Not trivial, Not overlay, Proper, NW0, N2
<h(h(c,b),f(f(h(h(c,c),c)))),c>   =>  Not trivial, Not 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(h(b,c),f(f(h(h(c,c),c))))
Nodes: [0,1]
Edges: [(0,1)]
ID: 0 => ('h(h(b,c),f(f(h(h(c,c),c))))', D0)
ID: 1 => ('h(h(c,c),f(f(h(h(c,c),c))))', D1, R1, P[1, 1], S{}), NR: 'c'
t: c
Nodes: [0]
Edges: []
ID: 0 => ('c', D0)
h(h(b,c),f(f(h(h(c,c),c)))) ->* no union *<- c
"Not joinable"

The problem is not confluent.