0.005/0.005	NO
0.005/0.005	
0.005/0.005	Problem 1:
0.005/0.005	
0.005/0.005	
0.005/0.005	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.005/0.005	Confluence Problem:
0.005/0.005	(VAR vNonEmpty:S v_NonEmpty:S:S x:S:S)
0.005/0.005	(STRATEGY CONTEXTSENSITIVE
0.005/0.005	(*top*_0 1)
0.005/0.005	(f_0 1)
0.005/0.005	(f_1 1)
0.005/0.005	(g_1 1)
0.005/0.005	(s_0 1)
0.005/0.005	(a_0)
0.005/0.005	(b_0)
0.005/0.005	(fSNonEmpty)
0.005/0.005	)
0.005/0.005	(RULES
0.005/0.005	*top*_0(g_1(x:S:S)) -> *top*_0(f_0(g_1(x:S:S)))
0.005/0.005	f_0(g_1(x:S:S)) -> f_1(f_0(g_1(x:S:S)))
0.005/0.005	f_1(f_0(x:S:S)) -> b_0
0.005/0.005	f_1(f_1(x:S:S)) -> b_0
0.005/0.005	f_1(g_1(a_0)) -> f_0(s_0(g_1(b_0)))
0.005/0.005	g_1(x:S:S) -> f_1(g_1(x:S:S))
0.005/0.005	s_0(g_1(x:S:S)) -> s_0(f_0(g_1(x:S:S)))
0.005/0.005	)
0.005/0.005	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.005/0.005	
0.005/0.005	
0.005/0.005	Problem 1:
0.005/0.005	
0.005/0.005	CleanTRS Processor:
0.005/0.005	
0.005/0.005	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.005/0.005	Confluence Problem:
0.005/0.005	(VAR vNonEmpty:S v_NonEmpty:S:S x:S:S)
0.005/0.005	(STRATEGY CONTEXTSENSITIVE
0.005/0.005	(*top*_0 1)
0.005/0.005	(f_0 1)
0.005/0.005	(f_1 1)
0.005/0.005	(g_1 1)
0.005/0.005	(s_0 1)
0.005/0.005	(a_0)
0.005/0.005	(b_0)
0.005/0.005	(fSNonEmpty)
0.005/0.005	)
0.005/0.005	(RULES
0.005/0.005	*top*_0(g_1(x:S:S)) -> *top*_0(f_0(g_1(x:S:S)))
0.005/0.005	f_0(g_1(x:S:S)) -> f_1(f_0(g_1(x:S:S)))
0.005/0.005	f_1(f_0(x:S:S)) -> b_0
0.005/0.005	f_1(f_1(x:S:S)) -> b_0
0.005/0.005	f_1(g_1(a_0)) -> f_0(s_0(g_1(b_0)))
0.005/0.005	g_1(x:S:S) -> f_1(g_1(x:S:S))
0.005/0.005	s_0(g_1(x:S:S)) -> s_0(f_0(g_1(x:S:S)))
0.005/0.005	)
0.005/0.005	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.005/0.005	
0.005/0.005	
0.005/0.005	Problem 1:
0.005/0.005	
0.005/0.005	Modular Confluence Combinations Decomposition Processor:
0.005/0.005	
0.005/0.005	No usable combinations
0.005/0.005	
0.005/0.005	Problem 1:
0.005/0.005	Not CS-TRS Processor:
0.005/0.005	R is not a CS-TRS
0.005/0.005	
0.005/0.005	Problem 1:
0.005/0.005	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.005/0.005	Confluence Problem:
0.005/0.005	(VAR vNonEmpty:S v_NonEmpty:S:S x:S:S)
0.005/0.005	(STRATEGY CONTEXTSENSITIVE
0.005/0.005	(*top*_0 1)
0.005/0.005	(f_0 1)
0.005/0.005	(f_1 1)
0.005/0.005	(g_1 1)
0.005/0.005	(s_0 1)
0.005/0.005	(a_0)
0.005/0.005	(b_0)
0.005/0.005	(fSNonEmpty)
0.005/0.005	)
0.005/0.005	(RULES
0.005/0.005	*top*_0(g_1(x:S:S)) -> *top*_0(f_0(g_1(x:S:S)))
0.005/0.005	f_0(g_1(x:S:S)) -> f_1(f_0(g_1(x:S:S)))
0.005/0.005	f_1(f_0(x:S:S)) -> b_0
0.005/0.005	f_1(f_1(x:S:S)) -> b_0
0.005/0.005	f_1(g_1(a_0)) -> f_0(s_0(g_1(b_0)))
0.005/0.005	g_1(x:S:S) -> f_1(g_1(x:S:S))
0.005/0.005	s_0(g_1(x:S:S)) -> s_0(f_0(g_1(x:S:S)))
0.005/0.005	)
0.005/0.005	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.005/0.005	
0.005/0.005	Huet Levy Processor:
0.005/0.005	-> Rules:
0.005/0.005	 *top*_0(g_1(x:S:S)) -> *top*_0(f_0(g_1(x:S:S)))
0.005/0.005	 f_0(g_1(x:S:S)) -> f_1(f_0(g_1(x:S:S)))
0.005/0.005	 f_1(f_0(x:S:S)) -> b_0
0.005/0.005	 f_1(f_1(x:S:S)) -> b_0
0.005/0.005	 f_1(g_1(a_0)) -> f_0(s_0(g_1(b_0)))
0.005/0.005	 g_1(x:S:S) -> f_1(g_1(x:S:S))
0.005/0.005	 s_0(g_1(x:S:S)) -> s_0(f_0(g_1(x:S:S)))
0.005/0.005	-> Vars:
0.005/0.005	 x:S, x:S, x:S, x:S, x:S, x:S
0.005/0.005	-> FVars:
0.005/0.005	 x3, x4, x5, x6, x7, x8
0.005/0.005	-> PVars:
0.005/0.005	 x:S: [x3, x4, x5, x6, x7, x8]
0.005/0.005	
0.005/0.005	-> Rlps:
0.005/0.005	 (rule: *top*_0(g_1(x3:S)) -> *top*_0(f_0(g_1(x3:S))), id: 1, possubterms: *top*_0(g_1(x3:S))->[], g_1(x3:S)->[1])
0.005/0.005	 (rule: f_0(g_1(x4:S)) -> f_1(f_0(g_1(x4:S))), id: 2, possubterms: f_0(g_1(x4:S))->[], g_1(x4:S)->[1])
0.005/0.005	 (rule: f_1(f_0(x5:S)) -> b_0, id: 3, possubterms: f_1(f_0(x5:S))->[], f_0(x5:S)->[1])
0.005/0.005	 (rule: f_1(f_1(x6:S)) -> b_0, id: 4, possubterms: f_1(f_1(x6:S))->[], f_1(x6:S)->[1])
0.005/0.005	 (rule: f_1(g_1(a_0)) -> f_0(s_0(g_1(b_0))), id: 5, possubterms: f_1(g_1(a_0))->[], g_1(a_0)->[1], a_0->[1, 1])
0.005/0.005	 (rule: g_1(x7:S) -> f_1(g_1(x7:S)), id: 6, possubterms: g_1(x7:S)->[])
0.005/0.005	 (rule: s_0(g_1(x8:S)) -> s_0(f_0(g_1(x8:S))), id: 7, possubterms: s_0(g_1(x8:S))->[], g_1(x8:S)->[1])
0.005/0.005	
0.005/0.005	-> Unifications:
0.005/0.005	(R1 unifies with R6 at p: [1], l: *top*_0(g_1(x3:S)), lp: g_1(x3:S), sig: {x3:S -> x:S:S}, l': g_1(x:S:S), r: *top*_0(f_0(g_1(x3:S))), r': f_1(g_1(x:S:S)))
0.005/0.005	(R2 unifies with R6 at p: [1], l: f_0(g_1(x4:S)), lp: g_1(x4:S), sig: {x4:S -> x:S:S}, l': g_1(x:S:S), r: f_1(f_0(g_1(x4:S))), r': f_1(g_1(x:S:S)))
0.005/0.005	(R3 unifies with R2 at p: [1], l: f_1(f_0(x5:S)), lp: f_0(x5:S), sig: {x5:S -> g_1(x:S:S)}, l': f_0(g_1(x:S:S)), r: b_0, r': f_1(f_0(g_1(x:S:S))))
0.005/0.005	(R4 unifies with R3 at p: [1], l: f_1(f_1(x6:S)), lp: f_1(x6:S), sig: {x6:S -> f_0(x:S:S)}, l': f_1(f_0(x:S:S)), r: b_0, r': b_0)
0.005/0.005	(R4 unifies with R4 at p: [1], l: f_1(f_1(x6:S)), lp: f_1(x6:S), sig: {x6:S -> f_1(x:S:S)}, l': f_1(f_1(x:S:S)), r: b_0, r': b_0)
0.005/0.005	(R4 unifies with R5 at p: [1], l: f_1(f_1(x6:S)), lp: f_1(x6:S), sig: {x6:S -> g_1(a_0)}, l': f_1(g_1(a_0)), r: b_0, r': f_0(s_0(g_1(b_0))))
0.005/0.005	(R5 unifies with R6 at p: [1], l: f_1(g_1(a_0)), lp: g_1(a_0), sig: {x:S:S -> a_0}, l': g_1(x:S:S), r: f_0(s_0(g_1(b_0))), r': f_1(g_1(x:S:S)))
0.005/0.005	(R7 unifies with R6 at p: [1], l: s_0(g_1(x8:S)), lp: g_1(x8:S), sig: {x8:S -> x:S:S}, l': g_1(x:S:S), r: s_0(f_0(g_1(x8:S))), r': f_1(g_1(x:S:S)))
0.005/0.005	
0.005/0.005	-> Critical pairs info:
0.005/0.005	<f_1(f_1(g_1(a_0))),f_0(s_0(g_1(b_0)))>   =>  Not trivial, Not overlay, NW0, N1
0.005/0.005	<f_1(b_0),b_0>   =>  Not trivial, Not overlay, NW0, N2
0.005/0.005	<f_1(f_1(f_0(g_1(x:S:S)))),b_0>   =>  Not trivial, Not overlay, NW0, N3
0.005/0.005	<s_0(f_1(g_1(x:S:S))),s_0(f_0(g_1(x:S:S)))>   =>  Not trivial, Not overlay, NW0, N4
0.005/0.005	<f_0(f_1(g_1(x:S:S))),f_1(f_0(g_1(x:S:S)))>   =>  Not trivial, Not overlay, NW0, N5
0.005/0.005	<*top*_0(f_1(g_1(x:S:S))),*top*_0(f_0(g_1(x:S:S)))>   =>  Not trivial, Not overlay, NW0, N6
0.005/0.005	<f_1(f_0(s_0(g_1(b_0)))),b_0>   =>  Not trivial, Not overlay, NW0, N7
0.005/0.005	<f_1(b_0),b_0>   =>  Not trivial, Not overlay, NW0, N8
0.005/0.005	
0.005/0.005	-> Problem conclusions:
0.005/0.005	 Left linear, Right linear, Linear
0.005/0.005	 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
0.005/0.005	 Not Huet-Levy confluent, Not Newman confluent
0.005/0.005	 R is a TRS
0.005/0.005	
0.005/0.005	
0.005/0.005	Problem 1:
0.005/0.005	Different Normal CP Terms Processor:
0.005/0.005	<f_1(b_0),b_0>   =>  Not trivial, Not overlay, NW0, N2, Normal and not trivial cp
0.005/0.005	
0.005/0.005	The problem is not joinable.
0.005/0.005	0.04user 0.00system 0:00.05elapsed 82%CPU (0avgtext+0avgdata 10976maxresident)k
0.005/0.005	8inputs+0outputs (0major+1045minor)pagefaults 0swaps