NO

Problem 1: 


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


Problem 1: 

Problem 1: 

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

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

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(REPLACEMENT-MAP
(b)
(a)
(c)
)
(RULES
b -> a
b -> c
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 

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

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

Huet Levy Procedure:
-> Rules:
 b -> a
 b -> c
-> Vars:


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

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

-> Critical pairs info:
<a,c>   =>  Not trivial, 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: 
Different Normal CP Terms Procedure:
<a,c>   =>  Not trivial, Overlay, Proper, NW0, N1, Normal and not trivial cp

The problem is not confluent.