YES

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x y)
(REPLACEMENT-MAP
(or 1, 2)
(fSNonEmpty)
(true)
)
(RULES
or(true,true) -> true
or(x,y) -> or(y,x)
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 

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

Problem 1: 
Linearity Procedure:
Linear?
YES

Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x y)
(REPLACEMENT-MAP
(or 1, 2)
(fSNonEmpty)
(true)
)
(RULES
or(true,true) -> true
or(x,y) -> or(y,x)
)
Linear:YES
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 or(true,true) -> true
 or(x,y) -> or(y,x)
-> Vars:
 x, y

-> Rlps:
 (rule: or(true,true) -> true, id: 1, possubterms: or(true,true)->[], true->[1], true->[2])
 (rule: or(x,y) -> or(y,x), id: 2, possubterms: or(x,y)->[])

-> Unifications:
(R2 unifies with R1 at p: [], l: or(x,y), lp: or(x,y), sig: {x -> true,y -> true}, l': or(true,true), r: or(y,x), r': true)

-> Critical pairs info:
<true,or(true,true)>   =>  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 1.1: 
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Confluence Problem:
(VAR x y)
(REPLACEMENT-MAP
(or 1, 2)
(fSNonEmpty)
(true)
)
(RULES
or(true,true) -> true
or(x,y) -> or(y,x)
)
Critical Pairs:
<true,or(true,true)>   =>  Not trivial, Overlay, Proper, NW0, N1
Linear:YES
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Strong Confluence Procedure:
-> Rewritings:
s: true
Nodes: [0]
Edges: []
ID: 0 => ('true', D0)
t: or(true,true)
Nodes: [0,1]
Edges: [(0,0),(0,1)]
ID: 0 => ('or(true,true)', D0)
ID: 1 => ('true', D1, R1, P[], S{}), NR: 'true'
SNodesPath1: true
TNodesPath1: or(true,true) -> true
SNodesPath2: true
TNodesPath2: or(true,true) -> true
true ->= true *<- or(true,true)
or(true,true) ->= true *<- true
"Strongly closed critical pair"

The problem is confluent.