YES

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x)
(REPLACEMENT-MAP
(p 1)
(s 1)
(fSNonEmpty)
)
(RULES
p(s(x)) -> x
s(p(x)) -> 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)
(REPLACEMENT-MAP
(p 1)
(s 1)
(fSNonEmpty)
)
(RULES
p(s(x)) -> x
s(p(x)) -> x
)
Linear:YES
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 p(s(x)) -> x
 s(p(x)) -> x
-> Vars:
 x, x

-> Rlps:
 (rule: p(s(x)) -> x, id: 1, possubterms: p(s(x))->[], s(x)->[1])
 (rule: s(p(x)) -> x, id: 2, possubterms: s(p(x))->[], p(x)->[1])

-> Unifications:
(R1 unifies with R2 at p: [1], l: p(s(x)), lp: s(x), sig: {x -> p(x')}, l': s(p(x')), r: x, r': x')
(R2 unifies with R1 at p: [1], l: s(p(x)), lp: p(x), sig: {x -> s(x')}, l': p(s(x')), r: x, r': x')

-> Critical pairs info:
<p(x'),p(x')>   =>  Trivial, Not overlay, Proper, NW0, N1
<s(x'),s(x')>   =>  Trivial, Not overlay, Proper, NW0, N2

-> Problem conclusions:
 Left linear, Right linear, Linear
 Weakly orthogonal, Not almost orthogonal, Not orthogonal
 Huet-Levy confluent, Not Newman confluent
 R is a TRS 


The problem is confluent.