0.001/0.001	YES
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	
0.001/0.001	
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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	(adx 1)
0.001/0.001	(hd 1)
0.001/0.001	(incr 1)
0.001/0.001	(nats)
0.001/0.001	(tl 1)
0.001/0.001	(zeros)
0.001/0.001	(0)
0.001/0.001	(cons)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(s)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	adx(cons(X:S,Y:S)) -> incr(cons(X:S,adx(Y:S)))
0.001/0.001	hd(cons(X:S,Y:S)) -> X:S
0.001/0.001	incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S))
0.001/0.001	nats -> adx(zeros)
0.001/0.001	tl(cons(X:S,Y:S)) -> Y:S
0.001/0.001	zeros -> cons(0,zeros)
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	(adx 1)
0.001/0.001	(hd 1)
0.001/0.001	(incr 1)
0.001/0.001	(nats)
0.001/0.001	(tl 1)
0.001/0.001	(zeros)
0.001/0.001	(0)
0.001/0.001	(cons)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(s)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	adx(cons(X:S,Y:S)) -> incr(cons(X:S,adx(Y:S)))
0.001/0.001	hd(cons(X:S,Y:S)) -> X:S
0.001/0.001	incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S))
0.001/0.001	nats -> adx(zeros)
0.001/0.001	tl(cons(X:S,Y:S)) -> Y:S
0.001/0.001	zeros -> cons(0,zeros)
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	(adx 1)
0.001/0.001	(hd 1)
0.001/0.001	(incr 1)
0.001/0.001	(nats)
0.001/0.001	(tl 1)
0.001/0.001	(zeros)
0.001/0.001	(0)
0.001/0.001	(cons)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(s)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	adx(cons(X:S,Y:S)) -> incr(cons(X:S,adx(Y:S)))
0.001/0.001	hd(cons(X:S,Y:S)) -> X:S
0.001/0.001	incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S))
0.001/0.001	nats -> adx(zeros)
0.001/0.001	tl(cons(X:S,Y:S)) -> Y:S
0.001/0.001	zeros -> cons(0,zeros)
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	 adx(cons(X:S,Y:S)) -> incr(cons(X:S,adx(Y:S)))
0.001/0.001	 hd(cons(X:S,Y:S)) -> X:S
0.001/0.001	 incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S))
0.001/0.001	 nats -> adx(zeros)
0.001/0.001	 tl(cons(X:S,Y:S)) -> Y:S
0.001/0.001	 zeros -> cons(0,zeros)
0.001/0.001	-> Vars:
0.001/0.001	 X, Y, X, Y, X, Y, X, Y
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X, Y], UV-RFrozen: [X, Y])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X, Y], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X, Y], UV-RFrozen: [X, Y])
0.001/0.001	 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [Y], UV-LFrozen: [X, Y], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	-> FVars:
0.001/0.001	 x3, x4, x5, x6, x7, x8, x9, x10
0.001/0.001	-> PVars:
0.001/0.001	 X: [x3, x5, x7, x9], Y: [x4, x6, x8, x10]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: adx(cons(x3:S,x4:S)) -> incr(cons(x3:S,adx(x4:S))), id: 1, possubterms: adx(cons(x3:S,x4:S))->[], cons(x3:S,x4:S)->[1])
0.001/0.001	 (rule: hd(cons(x5:S,x6:S)) -> x5:S, id: 2, possubterms: hd(cons(x5:S,x6:S))->[], cons(x5:S,x6:S)->[1])
0.001/0.001	 (rule: incr(cons(x7:S,x8:S)) -> cons(s(x7:S),incr(x8:S)), id: 3, possubterms: incr(cons(x7:S,x8:S))->[], cons(x7:S,x8:S)->[1])
0.001/0.001	 (rule: nats -> adx(zeros), id: 4, possubterms: nats->[])
0.001/0.001	 (rule: tl(cons(x9:S,x10:S)) -> x10:S, id: 5, possubterms: tl(cons(x9:S,x10:S))->[], cons(x9:S,x10:S)->[1])
0.001/0.001	 (rule: zeros -> cons(0,zeros), id: 6, possubterms: zeros->[])
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 50%CPU (0avgtext+0avgdata 8332maxresident)k
0.001/0.001	0inputs+0outputs (0major+684minor)pagefaults 0swaps