NO

Problem 1: 


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


Problem 1: 

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

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

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


-> Rlps:
 (rule: b -> h(b,a), id: 1, possubterms: b->[])
 (rule: b -> a, id: 2, possubterms: b->[])
 (rule: c -> a, id: 3, possubterms: c->[])
 (rule: f(c) -> c, id: 4, possubterms: f(c)->[], c->[1])
 (rule: h(a,a) -> c, id: 5, possubterms: h(a,a)->[], a->[1], a->[2])

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

-> Critical pairs info:
<f(a),c>   =>  Not trivial, Not overlay, Proper, NW0, N1
<h(b,a),a>   =>  Not trivial, 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: f(a)
Nodes: [0]
Edges: []
ID: 0 => ('f(a)', D0)
t: c
Nodes: [0,1]
Edges: [(0,1)]
ID: 0 => ('c', D0)
ID: 1 => ('a', D1, R3, P[], S{}), NR: 'a'
f(a) ->* no union *<- c
"Not joinable"

The problem is not confluent.