YES

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x)
(REPLACEMENT-MAP
(f 1, 2)
(a)
(fSNonEmpty)
)
(RULES
f(a,f(x,a)) -> f(a,f(f(a,a),a))
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


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
(f 1, 2)
(a)
(fSNonEmpty)
)
(RULES
f(a,f(x,a)) -> f(a,f(f(a,a),a))
)
Linear:YES
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 f(a,f(x,a)) -> f(a,f(f(a,a),a))
-> Vars:
 x

-> Rlps:
 (rule: f(a,f(x,a)) -> f(a,f(f(a,a),a)), id: 1, possubterms: f(a,f(x,a))->[], a->[1], f(x,a)->[2], a->[2, 2])

-> Unifications:


-> Critical pairs info:


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


The problem is confluent.