NO

Problem 1: 


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Confluence Problem:
(VAR vNonEmpty y x)
(REPLACEMENT-MAP
(implies 1, 2)
(not 1)
(or 1, 2)
(fSNonEmpty)
(false)
(true)
)
(RULES
implies(false,y) -> true
implies(true,y) -> y
implies(x,y) -> or(not(x),y)
not(false) -> true
not(true) -> false
or(false,false) -> false
or(true,y) -> true
or(x,true) -> true
)
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Problem 1: 

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

Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty y x)
(REPLACEMENT-MAP
(implies 1, 2)
(not 1)
(or 1, 2)
(fSNonEmpty)
(false)
(true)
)
(RULES
implies(false,y) -> true
implies(true,y) -> y
implies(x,y) -> or(not(x),y)
not(false) -> true
not(true) -> false
or(false,false) -> false
or(true,y) -> true
or(x,true) -> true
)
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Huet Levy Procedure:
-> Rules:
 implies(false,y) -> true
 implies(true,y) -> y
 implies(x,y) -> or(not(x),y)
 not(false) -> true
 not(true) -> false
 or(false,false) -> false
 or(true,y) -> true
 or(x,true) -> true
-> Vars:
 y, y, y, x, y, x

-> Rlps:
 (rule: implies(false,y) -> true, id: 1, possubterms: implies(false,y)->[], false->[1])
 (rule: implies(true,y) -> y, id: 2, possubterms: implies(true,y)->[], true->[1])
 (rule: implies(x,y) -> or(not(x),y), id: 3, possubterms: implies(x,y)->[])
 (rule: not(false) -> true, id: 4, possubterms: not(false)->[], false->[1])
 (rule: not(true) -> false, id: 5, possubterms: not(true)->[], true->[1])
 (rule: or(false,false) -> false, id: 6, possubterms: or(false,false)->[], false->[1], false->[2])
 (rule: or(true,y) -> true, id: 7, possubterms: or(true,y)->[], true->[1])
 (rule: or(x,true) -> true, id: 8, possubterms: or(x,true)->[], true->[2])

-> Unifications:
(R3 unifies with R1 at p: [], l: implies(x,y), lp: implies(x,y), sig: {y -> y',x -> false}, l': implies(false,y'), r: or(not(x),y), r': true)
(R3 unifies with R2 at p: [], l: implies(x,y), lp: implies(x,y), sig: {y -> y',x -> true}, l': implies(true,y'), r: or(not(x),y), r': y')
(R8 unifies with R7 at p: [], l: or(x,true), lp: or(x,true), sig: {x -> true,y -> true}, l': or(true,y), r: true, r': true)

-> Critical pairs info:
<true,or(not(false),y')>   =>  Not trivial, Overlay, Proper, NW0, N1
<y',or(not(true),y')>   =>  Not trivial, Overlay, Proper, NW0, N2
<true,true>   =>  Trivial, Overlay, Proper, NW0, N3

-> 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: y'
Nodes: [0]
Edges: []
ID: 0 => ('y'', D0)
t: or(not(true),y')
Nodes: [0,1]
Edges: [(0,1)]
ID: 0 => ('or(not(true),y')', D0)
ID: 1 => ('or(false,y')', D1, R5, P[1], S{}), NR: 'false'
y' ->* no union *<- or(not(true),y')
"Not joinable"

The problem is not confluent.