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 y:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f_1)
0.001/0.001	(g_1)
0.001/0.001	(a_0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(i_0 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f_1(x:S,i_0(g_1(x:S))) -> a_0
0.001/0.001	f_1(x:S,i_0(x:S)) -> f_1(x:S,x:S)
0.001/0.001	f_1(x:S,x:S) -> f_1(i_0(x:S),g_1(g_1(x:S)))
0.001/0.001	f_1(x:S,y:S) -> x:S
0.001/0.001	g_1(x:S) -> i_0(x:S)
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 y:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f_1)
0.001/0.001	(g_1)
0.001/0.001	(a_0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(i_0 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f_1(x:S,i_0(g_1(x:S))) -> a_0
0.001/0.001	f_1(x:S,i_0(x:S)) -> f_1(x:S,x:S)
0.001/0.001	f_1(x:S,x:S) -> f_1(i_0(x:S),g_1(g_1(x:S)))
0.001/0.001	f_1(x:S,y:S) -> x:S
0.001/0.001	g_1(x:S) -> i_0(x:S)
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 y:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f_1)
0.001/0.001	(g_1)
0.001/0.001	(a_0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(i_0 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f_1(x:S,i_0(g_1(x:S))) -> a_0
0.001/0.001	f_1(x:S,i_0(x:S)) -> f_1(x:S,x:S)
0.001/0.001	f_1(x:S,x:S) -> f_1(i_0(x:S),g_1(g_1(x:S)))
0.001/0.001	f_1(x:S,y:S) -> x:S
0.001/0.001	g_1(x:S) -> i_0(x:S)
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	 f_1(x:S,i_0(g_1(x:S))) -> a_0
0.001/0.001	 f_1(x:S,i_0(x:S)) -> f_1(x:S,x:S)
0.001/0.001	 f_1(x:S,x:S) -> f_1(i_0(x:S),g_1(g_1(x:S)))
0.001/0.001	 f_1(x:S,y:S) -> x:S
0.001/0.001	 g_1(x:S) -> i_0(x:S)
0.001/0.001	-> Vars:
0.001/0.001	 x, x, x, x, y, x
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x], UV-RFrozen: [x])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x], UV-RFrozen: [x])
0.001/0.001	 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [x], UV-LFrozen: [x, y], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [x], UV-LFrozen: [x], UV-RFrozen: [])
0.001/0.001	-> FVars:
0.001/0.001	 x3, x4, x5, x6, x7, x8
0.001/0.001	-> PVars:
0.001/0.001	 x: [x3, x4, x5, x6, x8], y: [x7]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: f_1(x3:S,i_0(g_1(x3:S))) -> a_0, id: 1, possubterms: f_1(x3:S,i_0(g_1(x3:S)))->[])
0.001/0.001	 (rule: f_1(x4:S,i_0(x4:S)) -> f_1(x4:S,x4:S), id: 2, possubterms: f_1(x4:S,i_0(x4:S))->[])
0.001/0.001	 (rule: f_1(x5:S,x5:S) -> f_1(i_0(x5:S),g_1(g_1(x5:S))), id: 3, possubterms: f_1(x5:S,x5:S)->[])
0.001/0.001	 (rule: f_1(x6:S,x7:S) -> x6:S, id: 4, possubterms: f_1(x6:S,x7:S)->[])
0.001/0.001	 (rule: g_1(x8:S) -> i_0(x8:S), id: 5, possubterms: g_1(x8:S)->[])
0.001/0.001	
0.001/0.001	-> Unifications:
0.001/0.001	(R4 unifies with R1 at p: [], l: f_1(x6:S,x7:S), lp: f_1(x6:S,x7:S), sig: {x6:S -> x:S,x7:S -> i_0(g_1(x:S))}, l': f_1(x:S,i_0(g_1(x:S))), r: x6:S, r': a_0)
0.001/0.001	(R4 unifies with R2 at p: [], l: f_1(x6:S,x7:S), lp: f_1(x6:S,x7:S), sig: {x6:S -> x:S,x7:S -> i_0(x:S)}, l': f_1(x:S,i_0(x:S)), r: x6:S, r': f_1(x:S,x:S))
0.001/0.001	(R4 unifies with R3 at p: [], l: f_1(x6:S,x7:S), lp: f_1(x6:S,x7:S), sig: {x6:S -> x:S,x7:S -> x:S}, l': f_1(x:S,x:S), r: x6:S, r': f_1(i_0(x:S),g_1(g_1(x:S))))
0.001/0.001	
0.001/0.001	-> Critical pairs info:
0.001/0.001	<a_0,x:S>   =>  Not trivial, Overlay, NW0, N1
0.001/0.001	<f_1(x:S,x:S),x:S>   =>  Not trivial, Overlay, NW0, N2
0.001/0.001	<f_1(i_0(x:S),g_1(g_1(x:S))),x:S>   =>  Not trivial, Overlay, NW0, N3
0.001/0.001	
0.001/0.001	-> Problem conclusions:
0.001/0.001	 Not left linear, Not right linear, Not 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	<a_0,x:S>   =>  Not trivial, 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 33%CPU (0avgtext+0avgdata 8848maxresident)k
0.001/0.001	0inputs+0outputs (0major+708minor)pagefaults 0swaps