0.001/0.001	YES
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 Y:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f)
0.001/0.001	(if 1)
0.001/0.001	(c)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(ffalse)
0.001/0.001	(ftrue)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f(X:S:S) -> if(X:S:S,c,f(ftrue))
0.001/0.001	if(ffalse,X:S:S,Y:S:S) -> Y:S:S
0.001/0.001	if(ftrue,X:S:S,Y:S:S) -> X:S: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 v_NonEmpty:S:S X:S:S Y:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f)
0.001/0.001	(if 1)
0.001/0.001	(c)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(ffalse)
0.001/0.001	(ftrue)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f(X:S:S) -> if(X:S:S,c,f(ftrue))
0.001/0.001	if(ffalse,X:S:S,Y:S:S) -> Y:S:S
0.001/0.001	if(ftrue,X:S:S,Y:S:S) -> X:S: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 v_NonEmpty:S:S X:S:S Y:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f)
0.001/0.001	(if 1)
0.001/0.001	(c)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(ffalse)
0.001/0.001	(ftrue)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f(X:S:S) -> if(X:S:S,c,f(ftrue))
0.001/0.001	if(ffalse,X:S:S,Y:S:S) -> Y:S:S
0.001/0.001	if(ftrue,X:S:S,Y:S:S) -> X:S: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(X:S:S) -> if(X:S:S,c,f(ftrue))
0.001/0.001	 if(ffalse,X:S:S,Y:S:S) -> Y:S:S
0.001/0.001	 if(ftrue,X:S:S,Y:S:S) -> X:S:S
0.001/0.001	-> Vars:
0.001/0.001	 X:S, X:S, Y:S, X:S, Y:S
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [])
0.001/0.001	-> FVars:
0.001/0.001	 x4, x5, x6, x7, x8
0.001/0.001	-> PVars:
0.001/0.001	 X:S: [x4, x5, x7], Y:S: [x6, x8]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: f(x4:S) -> if(x4:S,c,f(ftrue)), id: 1, possubterms: f(x4:S)->[])
0.001/0.001	 (rule: if(ffalse,x5:S,x6:S) -> x6:S, id: 2, possubterms: if(ffalse,x5:S,x6:S)->[], ffalse->[1])
0.001/0.001	 (rule: if(ftrue,x7:S,x8:S) -> x7:S, id: 3, possubterms: if(ftrue,x7:S,x8:S)->[], ftrue->[1])
0.001/0.001	
0.001/0.001	-> Unifications:
0.001/0.001	
0.001/0.001	
0.001/0.001	-> Critical pairs info:
0.001/0.001	
0.001/0.001	
0.001/0.001	-> Problem conclusions:
0.001/0.001	 Left linear, Right linear, Linear
0.001/0.001	 Weakly orthogonal, Almost orthogonal, Orthogonal
0.001/0.001	 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	The problem is joinable.
0.001/0.001	0.00user 0.00system 0:00.01elapsed 41%CPU (0avgtext+0avgdata 8372maxresident)k
0.001/0.001	8inputs+0outputs (0major+658minor)pagefaults 0swaps