0.00/0.02	NO
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	
0.00/0.02	
0.00/0.02	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.00/0.02	Confluence Problem:
0.00/0.02	(VAR vNonEmpty x)
0.00/0.02	(REPLACEMENT-MAP
0.00/0.02	(a 1)
0.00/0.02	(b 1)
0.00/0.02	(fSNonEmpty)
0.00/0.02	)
0.00/0.02	(RULES
0.00/0.02	a(a(x)) -> b(b(b(x)))
0.00/0.02	b(b(b(b(x)))) -> a(a(a(x)))
0.00/0.02	)
0.00/0.02	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.00/0.02	
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	Not CS-TRS Procedure:
0.00/0.02	R is not a CS-TRS
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.00/0.02	Confluence Problem:
0.00/0.02	(VAR vNonEmpty x)
0.00/0.02	(REPLACEMENT-MAP
0.00/0.02	(a 1)
0.00/0.02	(b 1)
0.00/0.02	(fSNonEmpty)
0.00/0.02	)
0.00/0.02	(RULES
0.00/0.02	a(a(x)) -> b(b(b(x)))
0.00/0.02	b(b(b(b(x)))) -> a(a(a(x)))
0.00/0.02	)
0.00/0.02	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.00/0.02	
0.00/0.02	Huet Levy Procedure:
0.00/0.02	-> Rules:
0.00/0.02	 a(a(x)) -> b(b(b(x)))
0.00/0.02	 b(b(b(b(x)))) -> a(a(a(x)))
0.00/0.02	-> Vars:
0.00/0.02	 x, x
0.00/0.02	
0.00/0.02	-> Rlps:
0.00/0.02	 (rule: a(a(x)) -> b(b(b(x))), id: 1, possubterms: a(a(x))->[], a(x)->[1])
0.00/0.02	 (rule: b(b(b(b(x)))) -> a(a(a(x))), id: 2, possubterms: b(b(b(b(x))))->[], b(b(b(x)))->[1], b(b(x))->[1, 1], b(x)->[1, 1, 1])
0.00/0.02	
0.00/0.02	-> Unifications:
0.00/0.02	(R1 unifies with R1 at p: [1], l: a(a(x)), lp: a(x), sig: {x -> a(x')}, l': a(a(x')), r: b(b(b(x))), r': b(b(b(x'))))
0.00/0.02	(R2 unifies with R2 at p: [1], l: b(b(b(b(x)))), lp: b(b(b(x))), sig: {x -> b(x')}, l': b(b(b(b(x')))), r: a(a(a(x))), r': a(a(a(x'))))
0.00/0.02	(R2 unifies with R2 at p: [1,1], l: b(b(b(b(x)))), lp: b(b(x)), sig: {x -> b(b(x'))}, l': b(b(b(b(x')))), r: a(a(a(x))), r': a(a(a(x'))))
0.00/0.02	(R2 unifies with R2 at p: [1,1,1], l: b(b(b(b(x)))), lp: b(x), sig: {x -> b(b(b(x')))}, l': b(b(b(b(x')))), r: a(a(a(x))), r': a(a(a(x'))))
0.00/0.02	
0.00/0.02	-> Critical pairs info:
0.00/0.02	<b(b(a(a(a(x'))))),a(a(a(b(b(x')))))>   =>  Not trivial, Not overlay, Proper, NW0, N1
0.00/0.02	<b(b(b(a(a(a(x')))))),a(a(a(b(b(b(x'))))))>   =>  Not trivial, Not overlay, Proper, NW0, N2
0.00/0.02	<b(a(a(a(x')))),a(a(a(b(x'))))>   =>  Not trivial, Not overlay, Proper, NW0, N3
0.00/0.02	<a(b(b(b(x')))),b(b(b(a(x'))))>   =>  Not trivial, Not overlay, Proper, NW0, N4
0.00/0.02	
0.00/0.02	-> Problem conclusions:
0.00/0.02	 Left linear, Right linear, Linear
0.00/0.02	 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
0.00/0.02	 Not Huet-Levy confluent, Not Newman confluent
0.00/0.02	 R is a TRS 
0.00/0.02	
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	No Convergence Brute Force Procedure:
0.00/0.02	-> Rewritings:
0.00/0.02	s: a(b(b(b(x'))))
0.00/0.02	Nodes: [0]
0.00/0.02	Edges: []
0.00/0.02	ID: 0 => ('a(b(b(b(x'))))', D0)
0.00/0.02	t: b(b(b(a(x'))))
0.00/0.02	Nodes: [0]
0.00/0.02	Edges: []
0.00/0.02	ID: 0 => ('b(b(b(a(x'))))', D0)
0.00/0.02	a(b(b(b(x')))) ->* no union *<- b(b(b(a(x'))))
0.00/0.02	"Not joinable"
0.00/0.02	
0.00/0.02	The problem is not confluent.
0.00/0.02	EOF