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 Z:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(first 1 2)
0.001/0.001	(from)
0.001/0.001	(cons)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(nil)
0.001/0.001	(num0)
0.001/0.001	(s)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	first(num0,X:S:S) -> nil
0.001/0.001	first(s(X:S:S),cons(Y:S:S,Z:S:S)) -> cons(Y:S:S,first(X:S:S,Z:S:S))
0.001/0.001	from(X:S:S) -> cons(X:S:S,from(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 Z:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(first 1 2)
0.001/0.001	(from)
0.001/0.001	(cons)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(nil)
0.001/0.001	(num0)
0.001/0.001	(s)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	first(num0,X:S:S) -> nil
0.001/0.001	first(s(X:S:S),cons(Y:S:S,Z:S:S)) -> cons(Y:S:S,first(X:S:S,Z:S:S))
0.001/0.001	from(X:S:S) -> cons(X:S:S,from(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 Z:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(first 1 2)
0.001/0.001	(from)
0.001/0.001	(cons)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(nil)
0.001/0.001	(num0)
0.001/0.001	(s)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	first(num0,X:S:S) -> nil
0.001/0.001	first(s(X:S:S),cons(Y:S:S,Z:S:S)) -> cons(Y:S:S,first(X:S:S,Z:S:S))
0.001/0.001	from(X:S:S) -> cons(X:S:S,from(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	 first(num0,X:S:S) -> nil
0.001/0.001	 first(s(X:S:S),cons(Y:S:S,Z:S:S)) -> cons(Y:S:S,first(X:S:S,Z:S:S))
0.001/0.001	 from(X:S:S) -> cons(X:S:S,from(s(X:S:S)))
0.001/0.001	-> Vars:
0.001/0.001	 X:S, X:S, Y:S, Z:S, X:S
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [X:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, Y:S, Z:S], UV-RFrozen: [X:S, Y:S, Z:S])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S], UV-RFrozen: [X:S])
0.001/0.001	-> FVars:
0.001/0.001	 x5, x6, x7, x8, x9
0.001/0.001	-> PVars:
0.001/0.001	 X:S: [x5, x6, x9], Y:S: [x7], Z:S: [x8]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: first(num0,x5:S) -> nil, id: 1, possubterms: first(num0,x5:S)->[], num0->[1])
0.001/0.001	 (rule: first(s(x6:S),cons(x7:S,x8:S)) -> cons(x7:S,first(x6:S,x8:S)), id: 2, possubterms: first(s(x6:S),cons(x7:S,x8:S))->[], s(x6:S)->[1], cons(x7:S,x8:S)->[2])
0.001/0.001	 (rule: from(x9:S) -> cons(x9:S,from(s(x9:S))), id: 3, possubterms: from(x9:S)->[])
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, Not right linear, Not 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 37%CPU (0avgtext+0avgdata 8416maxresident)k
0.001/0.001	8inputs+0outputs (0major+658minor)pagefaults 0swaps