YES

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x y)
(REPLACEMENT-MAP
(f 1, 2)
(0)
(1)
(fSNonEmpty)
)
(RULES
f(0,0) -> f(0,1)
f(1,0) -> f(0,0)
f(x,y) -> f(y,x)
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 

Problem 1: 

Commutativity Transform Procedure:

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x y)
(REPLACEMENT-MAP
(f 1, 2)
(0)
(1)
(fSNonEmpty)
)
(RULES
f(0,0) -> f(0,1)
f(0,1) -> f(0,0)
f(1,0) -> f(0,0)
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x y)
(REPLACEMENT-MAP
(f 1, 2)
(0)
(1)
(fSNonEmpty)
)
(RULES
f(0,0) -> f(0,1)
f(0,1) -> f(0,0)
f(1,0) -> f(0,0)
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


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
(f 1, 2)
(0)
(1)
(fSNonEmpty)
)
(RULES
f(0,0) -> f(0,1)
f(0,1) -> f(0,0)
f(1,0) -> f(0,0)
)
Linear:YES
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 f(0,0) -> f(0,1)
 f(0,1) -> f(0,0)
 f(1,0) -> f(0,0)
-> Vars:


-> Rlps:
 (rule: f(0,0) -> f(0,1), id: 1, possubterms: f(0,0)->[], 0->[1], 0->[2])
 (rule: f(0,1) -> f(0,0), id: 2, possubterms: f(0,1)->[], 0->[1], 1->[2])
 (rule: f(1,0) -> f(0,0), id: 3, possubterms: f(1,0)->[], 1->[1], 0->[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.