NO

Problem 1: 


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


Problem 1: 

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

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

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


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

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

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

The problem is not confluent.