NO

Problem 1: 


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


Problem 1: 

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

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

Huet Levy Ordered by Num of Vars and Symbs Procedure:
-> Rules:
 f(f(x,a),a) -> f(f(a,f(f(f(a,x),a),a)),a)
-> Vars:
 x

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

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

-> Critical pairs info:
<f(f(f(a,f(f(f(a,x'),a),a)),a),a),f(f(a,f(f(f(a,f(x',a)),a),a)),a)>   =>  Not trivial, Not 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: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR x x')
(REPLACEMENT-MAP
(f 1, 2)
(a)
(fSNonEmpty)
)
(RULES
f(f(x,a),a) -> f(f(a,f(f(f(a,x),a),a)),a)
)
Critical Pairs:
<f(f(f(a,f(f(f(a,x'),a),a)),a),a),f(f(a,f(f(f(a,f(x',a)),a),a)),a)>   =>  Not trivial, Not overlay, Proper, NW0, N1
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

No Convergence InfChecker Procedure:
Infeasible convergence?
YES

Problem 1: 

Infeasibility Problem:
[(VAR vNonEmpty x x1 vNonEmpty z0)
(STRATEGY CONTEXTSENSITIVE
(f 1 2)
(a)
(c_x1)
(fSNonEmpty)
)
(RULES
f(f(x,a),a) -> f(f(a,f(f(f(a,x),a),a)),a)
)]
Infeasibility Conditions:
f(f(f(a,f(f(f(a,c_x1),a),a)),a),a) ->* z0, f(f(a,f(f(f(a,f(c_x1,a)),a),a)),a) ->* z0

Problem 1: 

Obtaining a model using AGES:

 -> Theory (Usable Rules):
f(f(x,a),a) -> f(f(a,f(f(f(a,x),a),a)),a)

 -> AGES Output:




The problem is infeasible.


The problem is not confluent.