NO

Problem 1: 


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


Problem 1: 

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

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

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

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

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

-> Critical pairs info:
<a(b(b(b(b(a(x')))))),b(b(b(a(b(a(x'))))))>   =>  Not trivial, Not overlay, Proper, NW0, N1
<b(b(b(b(b(b(a(x'))))))),a(a(a(b(b(a(x'))))))>   =>  Not trivial, Not overlay, Proper, NW0, N2

-> 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
(a 1)
(b 1)
(fSNonEmpty)
)
(RULES
a(b(a(x))) -> b(b(b(a(x))))
b(b(b(a(x)))) -> a(a(a(b(x))))
)
Critical Pairs:
<b(b(b(b(b(b(a(x'))))))),a(a(a(b(b(a(x'))))))>   =>  Not trivial, Not overlay, Proper, NW0, N2
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

No Convergence InfChecker Procedure:
Infeasible convergence?
YES

Problem 1: 

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

Problem 1: 

Obtaining a model using AGES:

 -> Theory (Usable Rules):
a(b(a(x))) -> b(b(b(a(x))))
b(b(b(a(x)))) -> a(a(a(b(x))))

 -> AGES Output:




The problem is infeasible.


The problem is not confluent.