NO

Problem 1: 


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


Problem 1: 

CleanTRS Procedure:
R was updated by simple cleaning of the TRS

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


Problem 1: 

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

TRS2
Just (VAR x)
(STRATEGY CONTEXTSENSITIVE
(c)
(d)
(f 1 2)
(A)
(a)
(e)
)
(RULES
d -> c
d -> e
f(c,x) -> A
f(x,A) -> A
f(x,a) -> A
f(x,e) -> A
)

Problem 1: 


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


Problem 1: 

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

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

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


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

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

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

The problem is not confluent.