0.001/0.001	NO
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	
0.001/0.001	
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	Confluence Problem:
0.001/0.001	(VAR vNonEmpty:S x:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(*top*_0 1)
0.001/0.001	(f_0 1)
0.001/0.001	(f_1)
0.001/0.001	(g_0 1)
0.001/0.001	(b_0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(g_1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	*top*_0(f_0(f_1(f_0(g_0(x:S))))) -> *top*_0(f_0(x:S))
0.001/0.001	*top*_0(f_1(f_0(g_0(x:S)))) -> *top*_0(x:S)
0.001/0.001	*top*_0(f_1(f_0(g_1(x:S)))) -> *top*_0(x:S)
0.001/0.001	*top*_0(g_1(b_0)) -> *top*_0(f_0(g_1(b_0)))
0.001/0.001	f_0(f_0(f_1(f_0(g_0(x:S))))) -> f_1(f_0(x:S))
0.001/0.001	f_0(f_1(f_0(g_0(x:S)))) -> f_1(x:S)
0.001/0.001	f_0(f_1(f_0(g_1(x:S)))) -> f_0(x:S)
0.001/0.001	f_0(g_1(b_0)) -> f_1(f_0(g_1(b_0)))
0.001/0.001	f_1(f_0(g_0(x:S))) -> x:S
0.001/0.001	g_0(f_0(f_1(f_0(g_0(x:S))))) -> g_0(f_0(x:S))
0.001/0.001	g_0(f_1(f_0(g_0(x:S)))) -> g_0(x:S)
0.001/0.001	g_0(f_1(f_0(g_1(x:S)))) -> g_1(x:S)
0.001/0.001	g_0(g_1(b_0)) -> g_0(f_0(g_1(b_0)))
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	
0.001/0.001	CleanTRS Processor:
0.001/0.001	
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	Confluence Problem:
0.001/0.001	(VAR vNonEmpty:S x:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(*top*_0 1)
0.001/0.001	(f_0 1)
0.001/0.001	(f_1)
0.001/0.001	(g_0 1)
0.001/0.001	(b_0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(g_1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	*top*_0(f_0(f_1(f_0(g_0(x:S))))) -> *top*_0(f_0(x:S))
0.001/0.001	*top*_0(f_1(f_0(g_0(x:S)))) -> *top*_0(x:S)
0.001/0.001	*top*_0(f_1(f_0(g_1(x:S)))) -> *top*_0(x:S)
0.001/0.001	*top*_0(g_1(b_0)) -> *top*_0(f_0(g_1(b_0)))
0.001/0.001	f_0(f_0(f_1(f_0(g_0(x:S))))) -> f_1(f_0(x:S))
0.001/0.001	f_0(f_1(f_0(g_0(x:S)))) -> f_1(x:S)
0.001/0.001	f_0(f_1(f_0(g_1(x:S)))) -> f_0(x:S)
0.001/0.001	f_0(g_1(b_0)) -> f_1(f_0(g_1(b_0)))
0.001/0.001	f_1(f_0(g_0(x:S))) -> x:S
0.001/0.001	g_0(f_0(f_1(f_0(g_0(x:S))))) -> g_0(f_0(x:S))
0.001/0.001	g_0(f_1(f_0(g_0(x:S)))) -> g_0(x:S)
0.001/0.001	g_0(f_1(f_0(g_1(x:S)))) -> g_1(x:S)
0.001/0.001	g_0(g_1(b_0)) -> g_0(f_0(g_1(b_0)))
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	
0.001/0.001	Modular Confluence Combinations Decomposition Processor:
0.001/0.001	It is a CTRS -> No modular confluence
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	Left-Homogeneous u-Replacing Variables Processor:
0.001/0.001	R satisfies LHRV condition
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	Confluence Problem:
0.001/0.001	(VAR vNonEmpty:S x:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(*top*_0 1)
0.001/0.001	(f_0 1)
0.001/0.001	(f_1)
0.001/0.001	(g_0 1)
0.001/0.001	(b_0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(g_1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	*top*_0(f_0(f_1(f_0(g_0(x:S))))) -> *top*_0(f_0(x:S))
0.001/0.001	*top*_0(f_1(f_0(g_0(x:S)))) -> *top*_0(x:S)
0.001/0.001	*top*_0(f_1(f_0(g_1(x:S)))) -> *top*_0(x:S)
0.001/0.001	*top*_0(g_1(b_0)) -> *top*_0(f_0(g_1(b_0)))
0.001/0.001	f_0(f_0(f_1(f_0(g_0(x:S))))) -> f_1(f_0(x:S))
0.001/0.001	f_0(f_1(f_0(g_0(x:S)))) -> f_1(x:S)
0.001/0.001	f_0(f_1(f_0(g_1(x:S)))) -> f_0(x:S)
0.001/0.001	f_0(g_1(b_0)) -> f_1(f_0(g_1(b_0)))
0.001/0.001	f_1(f_0(g_0(x:S))) -> x:S
0.001/0.001	g_0(f_0(f_1(f_0(g_0(x:S))))) -> g_0(f_0(x:S))
0.001/0.001	g_0(f_1(f_0(g_0(x:S)))) -> g_0(x:S)
0.001/0.001	g_0(f_1(f_0(g_1(x:S)))) -> g_1(x:S)
0.001/0.001	g_0(g_1(b_0)) -> g_0(f_0(g_1(b_0)))
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	Huet Levy Processor:
0.001/0.001	-> Rules:
0.001/0.001	 *top*_0(f_0(f_1(f_0(g_0(x:S))))) -> *top*_0(f_0(x:S))
0.001/0.001	 *top*_0(f_1(f_0(g_0(x:S)))) -> *top*_0(x:S)
0.001/0.001	 *top*_0(f_1(f_0(g_1(x:S)))) -> *top*_0(x:S)
0.001/0.001	 *top*_0(g_1(b_0)) -> *top*_0(f_0(g_1(b_0)))
0.001/0.001	 f_0(f_0(f_1(f_0(g_0(x:S))))) -> f_1(f_0(x:S))
0.001/0.001	 f_0(f_1(f_0(g_0(x:S)))) -> f_1(x:S)
0.001/0.001	 f_0(f_1(f_0(g_1(x:S)))) -> f_0(x:S)
0.001/0.001	 f_0(g_1(b_0)) -> f_1(f_0(g_1(b_0)))
0.001/0.001	 f_1(f_0(g_0(x:S))) -> x:S
0.001/0.001	 g_0(f_0(f_1(f_0(g_0(x:S))))) -> g_0(f_0(x:S))
0.001/0.001	 g_0(f_1(f_0(g_0(x:S)))) -> g_0(x:S)
0.001/0.001	 g_0(f_1(f_0(g_1(x:S)))) -> g_1(x:S)
0.001/0.001	 g_0(g_1(b_0)) -> g_0(f_0(g_1(b_0)))
0.001/0.001	-> Vars:
0.001/0.001	 x, x, x, x, x, x, x, x, x, x
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [x], UV-LFrozen: [x], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [x], UV-LFrozen: [x], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [x], UV-LFrozen: [x], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x], UV-RFrozen: [x])
0.001/0.001	 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x], UV-RFrozen: [x])
0.001/0.001	 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [x], UV-LFrozen: [x], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [x], UV-LFrozen: [x], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [x], UV-LFrozen: [x], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [x], UV-LFrozen: [x], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 12, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x], UV-RFrozen: [x])
0.001/0.001	 (UV-RuleId: 13, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	-> FVars:
0.001/0.001	 x2, x3, x4, x5, x6, x7, x8, x9, x10, x11
0.001/0.001	-> PVars:
0.001/0.001	 x: [x2, x3, x4, x5, x6, x7, x8, x9, x10, x11]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: *top*_0(f_0(f_1(f_0(g_0(x2:S))))) -> *top*_0(f_0(x2:S)), id: 1, possubterms: *top*_0(f_0(f_1(f_0(g_0(x2:S)))))->[], f_0(f_1(f_0(g_0(x2:S))))->[1], f_1(f_0(g_0(x2:S)))->[1, 1])
0.001/0.001	 (rule: *top*_0(f_1(f_0(g_0(x3:S)))) -> *top*_0(x3:S), id: 2, possubterms: *top*_0(f_1(f_0(g_0(x3:S))))->[], f_1(f_0(g_0(x3:S)))->[1])
0.001/0.001	 (rule: *top*_0(f_1(f_0(g_1(x4:S)))) -> *top*_0(x4:S), id: 3, possubterms: *top*_0(f_1(f_0(g_1(x4:S))))->[], f_1(f_0(g_1(x4:S)))->[1])
0.001/0.001	 (rule: *top*_0(g_1(b_0)) -> *top*_0(f_0(g_1(b_0))), id: 4, possubterms: *top*_0(g_1(b_0))->[], g_1(b_0)->[1])
0.001/0.001	 (rule: f_0(f_0(f_1(f_0(g_0(x5:S))))) -> f_1(f_0(x5:S)), id: 5, possubterms: f_0(f_0(f_1(f_0(g_0(x5:S)))))->[], f_0(f_1(f_0(g_0(x5:S))))->[1], f_1(f_0(g_0(x5:S)))->[1, 1])
0.001/0.001	 (rule: f_0(f_1(f_0(g_0(x6:S)))) -> f_1(x6:S), id: 6, possubterms: f_0(f_1(f_0(g_0(x6:S))))->[], f_1(f_0(g_0(x6:S)))->[1])
0.001/0.001	 (rule: f_0(f_1(f_0(g_1(x7:S)))) -> f_0(x7:S), id: 7, possubterms: f_0(f_1(f_0(g_1(x7:S))))->[], f_1(f_0(g_1(x7:S)))->[1])
0.001/0.001	 (rule: f_0(g_1(b_0)) -> f_1(f_0(g_1(b_0))), id: 8, possubterms: f_0(g_1(b_0))->[], g_1(b_0)->[1])
0.001/0.001	 (rule: f_1(f_0(g_0(x8:S))) -> x8:S, id: 9, possubterms: f_1(f_0(g_0(x8:S)))->[])
0.001/0.001	 (rule: g_0(f_0(f_1(f_0(g_0(x9:S))))) -> g_0(f_0(x9:S)), id: 10, possubterms: g_0(f_0(f_1(f_0(g_0(x9:S)))))->[], f_0(f_1(f_0(g_0(x9:S))))->[1], f_1(f_0(g_0(x9:S)))->[1, 1])
0.001/0.001	 (rule: g_0(f_1(f_0(g_0(x10:S)))) -> g_0(x10:S), id: 11, possubterms: g_0(f_1(f_0(g_0(x10:S))))->[], f_1(f_0(g_0(x10:S)))->[1])
0.001/0.001	 (rule: g_0(f_1(f_0(g_1(x11:S)))) -> g_1(x11:S), id: 12, possubterms: g_0(f_1(f_0(g_1(x11:S))))->[], f_1(f_0(g_1(x11:S)))->[1])
0.001/0.001	 (rule: g_0(g_1(b_0)) -> g_0(f_0(g_1(b_0))), id: 13, possubterms: g_0(g_1(b_0))->[], g_1(b_0)->[1])
0.001/0.001	
0.001/0.001	-> Unifications:
0.001/0.001	(R1 unifies with R6 at p: [1], l: *top*_0(f_0(f_1(f_0(g_0(x2:S))))), lp: f_0(f_1(f_0(g_0(x2:S)))), sig: {x2:S -> x:S}, l': f_0(f_1(f_0(g_0(x:S)))), r: *top*_0(f_0(x2:S)), r': f_1(x:S))
0.001/0.001	(R1 unifies with R9 at p: [1,1], l: *top*_0(f_0(f_1(f_0(g_0(x2:S))))), lp: f_1(f_0(g_0(x2:S))), sig: {x2:S -> x:S}, l': f_1(f_0(g_0(x:S))), r: *top*_0(f_0(x2:S)), r': x:S)
0.001/0.001	(R2 unifies with R9 at p: [1], l: *top*_0(f_1(f_0(g_0(x3:S)))), lp: f_1(f_0(g_0(x3:S))), sig: {x3:S -> x:S}, l': f_1(f_0(g_0(x:S))), r: *top*_0(x3:S), r': x:S)
0.001/0.001	(R5 unifies with R6 at p: [1], l: f_0(f_0(f_1(f_0(g_0(x5:S))))), lp: f_0(f_1(f_0(g_0(x5:S)))), sig: {x5:S -> x:S}, l': f_0(f_1(f_0(g_0(x:S)))), r: f_1(f_0(x5:S)), r': f_1(x:S))
0.001/0.001	(R5 unifies with R9 at p: [1,1], l: f_0(f_0(f_1(f_0(g_0(x5:S))))), lp: f_1(f_0(g_0(x5:S))), sig: {x5:S -> x:S}, l': f_1(f_0(g_0(x:S))), r: f_1(f_0(x5:S)), r': x:S)
0.001/0.001	(R6 unifies with R9 at p: [1], l: f_0(f_1(f_0(g_0(x6:S)))), lp: f_1(f_0(g_0(x6:S))), sig: {x6:S -> x:S}, l': f_1(f_0(g_0(x:S))), r: f_1(x6:S), r': x:S)
0.001/0.001	(R10 unifies with R6 at p: [1], l: g_0(f_0(f_1(f_0(g_0(x9:S))))), lp: f_0(f_1(f_0(g_0(x9:S)))), sig: {x9:S -> x:S}, l': f_0(f_1(f_0(g_0(x:S)))), r: g_0(f_0(x9:S)), r': f_1(x:S))
0.001/0.001	(R10 unifies with R9 at p: [1,1], l: g_0(f_0(f_1(f_0(g_0(x9:S))))), lp: f_1(f_0(g_0(x9:S))), sig: {x9:S -> x:S}, l': f_1(f_0(g_0(x:S))), r: g_0(f_0(x9:S)), r': x:S)
0.001/0.001	(R11 unifies with R9 at p: [1], l: g_0(f_1(f_0(g_0(x10:S)))), lp: f_1(f_0(g_0(x10:S))), sig: {x10:S -> x:S}, l': f_1(f_0(g_0(x:S))), r: g_0(x10:S), r': x:S)
0.001/0.001	
0.001/0.001	-> Critical pairs info:
0.001/0.001	<f_0(f_1(x:S)),f_1(f_0(x:S))>   =>  Not trivial, Not overlay, NW0, N1
0.001/0.001	<g_0(x:S),g_0(x:S)>   =>  Trivial, Not overlay, NW0, N2
0.001/0.001	<f_0(x:S),f_1(x:S)>   =>  Not trivial, Not overlay, NW0, N3
0.001/0.001	<g_0(f_0(x:S)),g_0(f_0(x:S))>   =>  Trivial, Not overlay, NW0, N4
0.001/0.001	<*top*_0(f_1(x:S)),*top*_0(f_0(x:S))>   =>  Not trivial, Not overlay, NW0, N5
0.001/0.001	<g_0(f_1(x:S)),g_0(f_0(x:S))>   =>  Not trivial, Not overlay, NW0, N6
0.001/0.001	<*top*_0(x:S),*top*_0(x:S)>   =>  Trivial, Not overlay, NW0, N7
0.001/0.001	<*top*_0(f_0(x:S)),*top*_0(f_0(x:S))>   =>  Trivial, Not overlay, NW0, N8
0.001/0.001	<f_0(f_0(x:S)),f_1(f_0(x:S))>   =>  Not trivial, Not overlay, NW0, N9
0.001/0.001	
0.001/0.001	-> Problem conclusions:
0.001/0.001	 Left linear, Right linear, Linear
0.001/0.001	 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
0.001/0.001	 Not Huet-Levy confluent, Not Newman confluent
0.001/0.001	 R is a CS-TRS, Left-homogeneous u-replacing variables
0.001/0.001	
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	Different Normal CP Terms Processor:
0.001/0.001	<f_0(f_1(x:S)),f_1(f_0(x:S))>   =>  Not trivial, Not overlay, NW0, N1, Normal and not trivial cp
0.001/0.001	
0.001/0.001	The problem is not joinable.
0.001/0.001	0.00user 0.00system 0:00.01elapsed 75%CPU (0avgtext+0avgdata 10344maxresident)k
0.001/0.001	0inputs+0outputs (0major+875minor)pagefaults 0swaps