NO

Problem 1: 


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


Problem 1: 

Problem 1: 

Modular Confluence Combinations Decomposition Procedure:
TRS combination:
{a -> c
 h(b,a) -> a
 h(c,c) -> a}
{f(b) -> c}
Not disjoint
Constructor-sharing
Not composable
Left linear
Not layer-preserving
TRS1
Just (STRATEGY CONTEXTSENSITIVE
(a)
(h 1 2)
(b)
(c)
)
(RULES
a -> c
h(b,a) -> a
h(c,c) -> a
)

TRS2
Just (STRATEGY CONTEXTSENSITIVE
(f 1)
(b)
(c)
)
(RULES
f(b) -> c
)

Problem 1: 


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


Problem 1: 

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

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

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


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

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

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

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

The problem is not confluent.