NO

Problem 1: 


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


Problem 1: 

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

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

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


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

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

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

-> 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(f(h(b,b)))
Nodes: [0,1,2,3]
Edges: [(0,1),(0,2),(1,3),(2,3)]
ID: 0 => ('f(f(h(b,b)))', D0)
ID: 1 => ('f(f(h(c,b)))', D1, R2, P[1, 1, 1], S{}), NR: 'c'
ID: 2 => ('f(f(h(b,c)))', D1, R2, P[1, 1, 2], S{}), NR: 'c'
ID: 3 => ('f(f(h(c,c)))', D2, R2, P[1, 1, 2], S{}), NR: 'c'
t: a
Nodes: [0,1,2]
Edges: [(0,1),(1,2)]
ID: 0 => ('a', D0)
ID: 1 => ('b', D1, R1, P[], S{}), NR: 'b'
ID: 2 => ('c', D2, R2, P[], S{}), NR: 'c'
f(f(h(b,b))) ->* no union *<- a
"Not joinable"

The problem is not confluent.