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 v_NonEmpty:S:S x:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f_1)
0.001/0.001	(g_1 1)
0.001/0.001	(a_0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f_1(x:S:S) -> g_1(f_1(x:S:S))
0.001/0.001	g_1(f_1(x:S:S)) -> x:S:S
0.001/0.001	g_1(x:S:S) -> a_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 v_NonEmpty:S:S x:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f_1)
0.001/0.001	(g_1 1)
0.001/0.001	(a_0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f_1(x:S:S) -> g_1(f_1(x:S:S))
0.001/0.001	g_1(f_1(x:S:S)) -> x:S:S
0.001/0.001	g_1(x:S:S) -> a_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 v_NonEmpty:S:S x:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f_1)
0.001/0.001	(g_1 1)
0.001/0.001	(a_0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f_1(x:S:S) -> g_1(f_1(x:S:S))
0.001/0.001	g_1(f_1(x:S:S)) -> x:S:S
0.001/0.001	g_1(x:S:S) -> a_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	 f_1(x:S:S) -> g_1(f_1(x:S:S))
0.001/0.001	 g_1(f_1(x:S:S)) -> x:S:S
0.001/0.001	 g_1(x:S:S) -> a_0
0.001/0.001	-> Vars:
0.001/0.001	 x:S, x:S, x:S
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [x:S], UV-RFrozen: [x:S])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [x:S], UV-LFrozen: [x:S], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [x:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	-> FVars:
0.001/0.001	 x3, x4, x5
0.001/0.001	-> PVars:
0.001/0.001	 x:S: [x3, x4, x5]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: f_1(x3:S) -> g_1(f_1(x3:S)), id: 1, possubterms: f_1(x3:S)->[])
0.001/0.001	 (rule: g_1(f_1(x4:S)) -> x4:S, id: 2, possubterms: g_1(f_1(x4:S))->[], f_1(x4:S)->[1])
0.001/0.001	 (rule: g_1(x5:S) -> a_0, id: 3, possubterms: g_1(x5:S)->[])
0.001/0.001	
0.001/0.001	-> Unifications:
0.001/0.001	(R2 unifies with R1 at p: [1], l: g_1(f_1(x4:S)), lp: f_1(x4:S), sig: {x4:S -> x:S:S}, l': f_1(x:S:S), r: x4:S, r': g_1(f_1(x:S:S)))
0.001/0.001	(R3 unifies with R2 at p: [], l: g_1(x5:S), lp: g_1(x5:S), sig: {x5:S -> f_1(x:S:S)}, l': g_1(f_1(x:S:S)), r: a_0, r': x:S:S)
0.001/0.001	
0.001/0.001	-> Critical pairs info:
0.001/0.001	<g_1(g_1(f_1(x:S:S))),x:S:S>   =>  Not trivial, Not overlay, NW0, N1
0.001/0.001	<x:S:S,a_0>   =>  Not trivial, Overlay, NW0, N2
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	<x:S:S,a_0>   =>  Not trivial, Overlay, NW0, N2, 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 36%CPU (0avgtext+0avgdata 9716maxresident)k
0.001/0.001	8inputs+0outputs (0major+746minor)pagefaults 0swaps