0.002/0.002	NO
0.002/0.002	
0.002/0.002	Problem 1:
0.002/0.002	
0.002/0.002	
0.002/0.002	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.002/0.002	Confluence Problem:
0.002/0.002	(VAR vNonEmpty:S v_NonEmpty:S:S x:S:S)
0.002/0.002	(STRATEGY CONTEXTSENSITIVE
0.002/0.002	(*top*_0 1)
0.002/0.002	(f_0 1)
0.002/0.002	(f_1 1)
0.002/0.002	(a_1)
0.002/0.002	(c_0)
0.002/0.002	(fSNonEmpty)
0.002/0.002	)
0.002/0.002	(RULES
0.002/0.002	*top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1))))
0.002/0.002	*top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1)))
0.002/0.002	*top*_0(a_1) -> *top*_0(f_0(a_1))
0.002/0.002	f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1))))
0.002/0.002	f_1(f_0(f_0(f_0(x:S:S)))) -> c_0
0.002/0.002	f_1(f_1(f_0(f_0(x:S:S)))) -> c_0
0.002/0.002	f_1(f_1(f_1(f_0(x:S:S)))) -> c_0
0.002/0.002	f_1(f_1(f_1(f_1(x:S:S)))) -> c_0
0.002/0.002	)
0.002/0.002	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.002/0.002	
0.002/0.002	
0.002/0.002	Problem 1:
0.002/0.002	
0.002/0.002	CleanTRS Processor:
0.002/0.002	
0.002/0.002	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.002/0.002	Confluence Problem:
0.002/0.002	(VAR vNonEmpty:S v_NonEmpty:S:S x:S:S)
0.002/0.002	(STRATEGY CONTEXTSENSITIVE
0.002/0.002	(*top*_0 1)
0.002/0.002	(f_0 1)
0.002/0.002	(f_1 1)
0.002/0.002	(a_1)
0.002/0.002	(c_0)
0.002/0.002	(fSNonEmpty)
0.002/0.002	)
0.002/0.002	(RULES
0.002/0.002	*top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1))))
0.002/0.002	*top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1)))
0.002/0.002	*top*_0(a_1) -> *top*_0(f_0(a_1))
0.002/0.002	f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1))))
0.002/0.002	f_1(f_0(f_0(f_0(x:S:S)))) -> c_0
0.002/0.002	f_1(f_1(f_0(f_0(x:S:S)))) -> c_0
0.002/0.002	f_1(f_1(f_1(f_0(x:S:S)))) -> c_0
0.002/0.002	f_1(f_1(f_1(f_1(x:S:S)))) -> c_0
0.002/0.002	)
0.002/0.002	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.002/0.002	
0.002/0.002	
0.002/0.002	Problem 1:
0.002/0.002	
0.002/0.002	Modular Confluence Combinations Decomposition Processor:
0.002/0.002	
0.002/0.002	No usable combinations
0.002/0.002	
0.002/0.002	Problem 1:
0.002/0.002	Not CS-TRS Processor:
0.002/0.002	R is not a CS-TRS
0.002/0.002	
0.002/0.002	Problem 1:
0.002/0.002	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.002/0.002	Confluence Problem:
0.002/0.002	(VAR vNonEmpty:S v_NonEmpty:S:S x:S:S)
0.002/0.002	(STRATEGY CONTEXTSENSITIVE
0.002/0.002	(*top*_0 1)
0.002/0.002	(f_0 1)
0.002/0.002	(f_1 1)
0.002/0.002	(a_1)
0.002/0.002	(c_0)
0.002/0.002	(fSNonEmpty)
0.002/0.002	)
0.002/0.002	(RULES
0.002/0.002	*top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1))))
0.002/0.002	*top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1)))
0.002/0.002	*top*_0(a_1) -> *top*_0(f_0(a_1))
0.002/0.002	f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1))))
0.002/0.002	f_1(f_0(f_0(f_0(x:S:S)))) -> c_0
0.002/0.002	f_1(f_1(f_0(f_0(x:S:S)))) -> c_0
0.002/0.002	f_1(f_1(f_1(f_0(x:S:S)))) -> c_0
0.002/0.002	f_1(f_1(f_1(f_1(x:S:S)))) -> c_0
0.002/0.002	)
0.002/0.002	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.002/0.002	
0.002/0.002	Huet Levy Processor:
0.002/0.002	-> Rules:
0.002/0.002	 *top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1))))
0.002/0.002	 *top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1)))
0.002/0.002	 *top*_0(a_1) -> *top*_0(f_0(a_1))
0.002/0.002	 f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1))))
0.002/0.002	 f_1(f_0(f_0(f_0(x:S:S)))) -> c_0
0.002/0.002	 f_1(f_1(f_0(f_0(x:S:S)))) -> c_0
0.002/0.002	 f_1(f_1(f_1(f_0(x:S:S)))) -> c_0
0.002/0.002	 f_1(f_1(f_1(f_1(x:S:S)))) -> c_0
0.002/0.002	-> Vars:
0.002/0.002	 x:S, x:S, x:S, x:S
0.002/0.002	-> FVars:
0.002/0.002	 x3, x4, x5, x6
0.002/0.002	-> PVars:
0.002/0.002	 x:S: [x3, x4, x5, x6]
0.002/0.002	
0.002/0.002	-> Rlps:
0.002/0.002	 (rule: *top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1)))), id: 1, possubterms: *top*_0(f_0(f_0(a_1)))->[], f_0(f_0(a_1))->[1], f_0(a_1)->[1, 1], a_1->[1, 1, 1])
0.002/0.002	 (rule: *top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1))), id: 2, possubterms: *top*_0(f_0(a_1))->[], f_0(a_1)->[1], a_1->[1, 1])
0.002/0.002	 (rule: *top*_0(a_1) -> *top*_0(f_0(a_1)), id: 3, possubterms: *top*_0(a_1)->[], a_1->[1])
0.002/0.002	 (rule: f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1)))), id: 4, possubterms: f_0(f_0(f_0(a_1)))->[], f_0(f_0(a_1))->[1], f_0(a_1)->[1, 1], a_1->[1, 1, 1])
0.002/0.002	 (rule: f_1(f_0(f_0(f_0(x3:S)))) -> c_0, id: 5, possubterms: f_1(f_0(f_0(f_0(x3:S))))->[], f_0(f_0(f_0(x3:S)))->[1], f_0(f_0(x3:S))->[1, 1], f_0(x3:S)->[1, 1, 1])
0.002/0.002	 (rule: f_1(f_1(f_0(f_0(x4:S)))) -> c_0, id: 6, possubterms: f_1(f_1(f_0(f_0(x4:S))))->[], f_1(f_0(f_0(x4:S)))->[1], f_0(f_0(x4:S))->[1, 1], f_0(x4:S)->[1, 1, 1])
0.002/0.002	 (rule: f_1(f_1(f_1(f_0(x5:S)))) -> c_0, id: 7, possubterms: f_1(f_1(f_1(f_0(x5:S))))->[], f_1(f_1(f_0(x5:S)))->[1], f_1(f_0(x5:S))->[1, 1], f_0(x5:S)->[1, 1, 1])
0.002/0.002	 (rule: f_1(f_1(f_1(f_1(x6:S)))) -> c_0, id: 8, possubterms: f_1(f_1(f_1(f_1(x6:S))))->[], f_1(f_1(f_1(x6:S)))->[1], f_1(f_1(x6:S))->[1, 1], f_1(x6:S)->[1, 1, 1])
0.002/0.002	
0.002/0.002	-> Unifications:
0.002/0.002	(R5 unifies with R4 at p: [1], l: f_1(f_0(f_0(f_0(x3:S)))), lp: f_0(f_0(f_0(x3:S))), sig: {x3:S -> a_1}, l': f_0(f_0(f_0(a_1))), r: c_0, r': f_1(f_0(f_0(f_0(a_1)))))
0.002/0.002	(R5 unifies with R4 at p: [1,1], l: f_1(f_0(f_0(f_0(x3:S)))), lp: f_0(f_0(x3:S)), sig: {x3:S -> f_0(a_1)}, l': f_0(f_0(f_0(a_1))), r: c_0, r': f_1(f_0(f_0(f_0(a_1)))))
0.002/0.002	(R5 unifies with R4 at p: [1,1,1], l: f_1(f_0(f_0(f_0(x3:S)))), lp: f_0(x3:S), sig: {x3:S -> f_0(f_0(a_1))}, l': f_0(f_0(f_0(a_1))), r: c_0, r': f_1(f_0(f_0(f_0(a_1)))))
0.002/0.002	(R6 unifies with R5 at p: [1], l: f_1(f_1(f_0(f_0(x4:S)))), lp: f_1(f_0(f_0(x4:S))), sig: {x4:S -> f_0(x:S:S)}, l': f_1(f_0(f_0(f_0(x:S:S)))), r: c_0, r': c_0)
0.002/0.002	(R6 unifies with R4 at p: [1,1], l: f_1(f_1(f_0(f_0(x4:S)))), lp: f_0(f_0(x4:S)), sig: {x4:S -> f_0(a_1)}, l': f_0(f_0(f_0(a_1))), r: c_0, r': f_1(f_0(f_0(f_0(a_1)))))
0.002/0.002	(R6 unifies with R4 at p: [1,1,1], l: f_1(f_1(f_0(f_0(x4:S)))), lp: f_0(x4:S), sig: {x4:S -> f_0(f_0(a_1))}, l': f_0(f_0(f_0(a_1))), r: c_0, r': f_1(f_0(f_0(f_0(a_1)))))
0.002/0.002	(R7 unifies with R6 at p: [1], l: f_1(f_1(f_1(f_0(x5:S)))), lp: f_1(f_1(f_0(x5:S))), sig: {x5:S -> f_0(x:S:S)}, l': f_1(f_1(f_0(f_0(x:S:S)))), r: c_0, r': c_0)
0.002/0.002	(R7 unifies with R5 at p: [1,1], l: f_1(f_1(f_1(f_0(x5:S)))), lp: f_1(f_0(x5:S)), sig: {x5:S -> f_0(f_0(x:S:S))}, l': f_1(f_0(f_0(f_0(x:S:S)))), r: c_0, r': c_0)
0.002/0.002	(R7 unifies with R4 at p: [1,1,1], l: f_1(f_1(f_1(f_0(x5:S)))), lp: f_0(x5:S), sig: {x5:S -> f_0(f_0(a_1))}, l': f_0(f_0(f_0(a_1))), r: c_0, r': f_1(f_0(f_0(f_0(a_1)))))
0.002/0.002	(R8 unifies with R7 at p: [1], l: f_1(f_1(f_1(f_1(x6:S)))), lp: f_1(f_1(f_1(x6:S))), sig: {x6:S -> f_0(x:S:S)}, l': f_1(f_1(f_1(f_0(x:S:S)))), r: c_0, r': c_0)
0.002/0.002	(R8 unifies with R8 at p: [1], l: f_1(f_1(f_1(f_1(x6:S)))), lp: f_1(f_1(f_1(x6:S))), sig: {x6:S -> f_1(x:S:S)}, l': f_1(f_1(f_1(f_1(x:S:S)))), r: c_0, r': c_0)
0.002/0.002	(R8 unifies with R6 at p: [1,1], l: f_1(f_1(f_1(f_1(x6:S)))), lp: f_1(f_1(x6:S)), sig: {x6:S -> f_0(f_0(x:S:S))}, l': f_1(f_1(f_0(f_0(x:S:S)))), r: c_0, r': c_0)
0.002/0.002	(R8 unifies with R7 at p: [1,1], l: f_1(f_1(f_1(f_1(x6:S)))), lp: f_1(f_1(x6:S)), sig: {x6:S -> f_1(f_0(x:S:S))}, l': f_1(f_1(f_1(f_0(x:S:S)))), r: c_0, r': c_0)
0.002/0.002	(R8 unifies with R8 at p: [1,1], l: f_1(f_1(f_1(f_1(x6:S)))), lp: f_1(f_1(x6:S)), sig: {x6:S -> f_1(f_1(x:S:S))}, l': f_1(f_1(f_1(f_1(x:S:S)))), r: c_0, r': c_0)
0.002/0.002	(R8 unifies with R5 at p: [1,1,1], l: f_1(f_1(f_1(f_1(x6:S)))), lp: f_1(x6:S), sig: {x6:S -> f_0(f_0(f_0(x:S:S)))}, l': f_1(f_0(f_0(f_0(x:S:S)))), r: c_0, r': c_0)
0.002/0.002	(R8 unifies with R6 at p: [1,1,1], l: f_1(f_1(f_1(f_1(x6:S)))), lp: f_1(x6:S), sig: {x6:S -> f_1(f_0(f_0(x:S:S)))}, l': f_1(f_1(f_0(f_0(x:S:S)))), r: c_0, r': c_0)
0.002/0.002	(R8 unifies with R7 at p: [1,1,1], l: f_1(f_1(f_1(f_1(x6:S)))), lp: f_1(x6:S), sig: {x6:S -> f_1(f_1(f_0(x:S:S)))}, l': f_1(f_1(f_1(f_0(x:S:S)))), r: c_0, r': c_0)
0.002/0.002	(R8 unifies with R8 at p: [1,1,1], l: f_1(f_1(f_1(f_1(x6:S)))), lp: f_1(x6:S), sig: {x6:S -> f_1(f_1(f_1(x:S:S)))}, l': f_1(f_1(f_1(f_1(x:S:S)))), r: c_0, r': c_0)
0.002/0.002	
0.002/0.002	-> Critical pairs info:
0.002/0.002	<f_1(f_1(c_0)),c_0>   =>  Not trivial, Not overlay, NW0, N1
0.002/0.002	<f_1(f_0(f_1(f_0(f_0(f_0(a_1)))))),c_0>   =>  Not trivial, Not overlay, NW0, N2
0.002/0.002	<f_1(f_1(f_1(f_0(f_0(f_0(a_1)))))),c_0>   =>  Not trivial, Not overlay, NW0, N3
0.002/0.002	<f_1(f_1(c_0)),c_0>   =>  Not trivial, Not overlay, NW0, N4
0.002/0.002	<f_1(f_1(f_0(f_0(f_0(a_1))))),c_0>   =>  Not trivial, Not overlay, NW0, N5
0.002/0.002	<f_1(c_0),c_0>   =>  Not trivial, Not overlay, NW0, N6
0.002/0.002	<f_1(f_1(f_0(f_1(f_0(f_0(f_0(a_1))))))),c_0>   =>  Not trivial, Not overlay, NW0, N7
0.002/0.002	<f_1(c_0),c_0>   =>  Not trivial, Not overlay, NW0, N8
0.002/0.002	<f_1(f_1(f_1(c_0))),c_0>   =>  Not trivial, Not overlay, NW0, N9
0.002/0.002	<f_1(f_1(f_1(c_0))),c_0>   =>  Not trivial, Not overlay, NW0, N10
0.002/0.002	<f_1(c_0),c_0>   =>  Not trivial, Not overlay, NW0, N11
0.002/0.002	<f_1(f_1(c_0)),c_0>   =>  Not trivial, Not overlay, NW0, N12
0.002/0.002	<f_1(c_0),c_0>   =>  Not trivial, Not overlay, NW0, N13
0.002/0.002	<f_1(f_1(f_1(f_1(f_0(f_0(f_0(a_1))))))),c_0>   =>  Not trivial, Not overlay, NW0, N14
0.002/0.002	<f_1(f_1(f_1(c_0))),c_0>   =>  Not trivial, Not overlay, NW0, N15
0.002/0.002	<f_1(f_1(c_0)),c_0>   =>  Not trivial, Not overlay, NW0, N16
0.002/0.002	<f_1(f_1(f_1(c_0))),c_0>   =>  Not trivial, Not overlay, NW0, N17
0.002/0.002	<f_1(f_0(f_0(f_1(f_0(f_0(f_0(a_1))))))),c_0>   =>  Not trivial, Not overlay, NW0, N18
0.002/0.002	
0.002/0.002	-> Problem conclusions:
0.002/0.002	 Left linear, Right linear, Linear
0.002/0.002	 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
0.002/0.002	 Not Huet-Levy confluent, Not Newman confluent
0.002/0.002	 R is a TRS
0.002/0.002	
0.002/0.002	
0.002/0.002	Problem 1:
0.002/0.002	Different Normal CP Terms Processor:
0.002/0.002	<f_1(f_1(c_0)),c_0>   =>  Not trivial, Not overlay, NW0, N1, Normal and not trivial cp
0.002/0.002	
0.002/0.002	The problem is not joinable.
0.002/0.002	0.01user 0.00system 0:00.02elapsed 72%CPU (0avgtext+0avgdata 10604maxresident)k
0.002/0.002	8inputs+0outputs (0major+974minor)pagefaults 0swaps