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 X:S XS:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(head 1)
0.001/0.001	(incr 1)
0.001/0.001	(nats)
0.001/0.001	(odds)
0.001/0.001	(pairs)
0.001/0.001	(tail 1)
0.001/0.001	(0)
0.001/0.001	(cons 1)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(s 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	head(cons(X:S,XS:S)) -> X:S
0.001/0.001	incr(cons(X:S,XS:S)) -> cons(s(X:S),incr(XS:S))
0.001/0.001	nats -> cons(0,incr(nats))
0.001/0.001	odds -> incr(pairs)
0.001/0.001	pairs -> cons(0,incr(odds))
0.001/0.001	tail(cons(X:S,XS:S)) -> XS: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 XS:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(head 1)
0.001/0.001	(incr 1)
0.001/0.001	(nats)
0.001/0.001	(odds)
0.001/0.001	(pairs)
0.001/0.001	(tail 1)
0.001/0.001	(0)
0.001/0.001	(cons 1)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(s 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	head(cons(X:S,XS:S)) -> X:S
0.001/0.001	incr(cons(X:S,XS:S)) -> cons(s(X:S),incr(XS:S))
0.001/0.001	nats -> cons(0,incr(nats))
0.001/0.001	odds -> incr(pairs)
0.001/0.001	pairs -> cons(0,incr(odds))
0.001/0.001	tail(cons(X:S,XS:S)) -> XS: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 XS:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(head 1)
0.001/0.001	(incr 1)
0.001/0.001	(nats)
0.001/0.001	(odds)
0.001/0.001	(pairs)
0.001/0.001	(tail 1)
0.001/0.001	(0)
0.001/0.001	(cons 1)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(s 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	head(cons(X:S,XS:S)) -> X:S
0.001/0.001	incr(cons(X:S,XS:S)) -> cons(s(X:S),incr(XS:S))
0.001/0.001	nats -> cons(0,incr(nats))
0.001/0.001	odds -> incr(pairs)
0.001/0.001	pairs -> cons(0,incr(odds))
0.001/0.001	tail(cons(X:S,XS:S)) -> XS: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	 head(cons(X:S,XS:S)) -> X:S
0.001/0.001	 incr(cons(X:S,XS:S)) -> cons(s(X:S),incr(XS:S))
0.001/0.001	 nats -> cons(0,incr(nats))
0.001/0.001	 odds -> incr(pairs)
0.001/0.001	 pairs -> cons(0,incr(odds))
0.001/0.001	 tail(cons(X:S,XS:S)) -> XS:S
0.001/0.001	-> Vars:
0.001/0.001	 X, XS, X, XS, X, XS
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [XS], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [XS], UV-RFrozen: [XS])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
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: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 6, UV-LActive: [X], UV-RActive: [XS], UV-LFrozen: [XS], 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, x5, x7], XS: [x4, x6, x8]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: head(cons(x3:S,x4:S)) -> x3:S, id: 1, possubterms: head(cons(x3:S,x4:S))->[], cons(x3:S,x4:S)->[1])
0.001/0.001	 (rule: incr(cons(x5:S,x6:S)) -> cons(s(x5:S),incr(x6:S)), id: 2, possubterms: incr(cons(x5:S,x6:S))->[], cons(x5:S,x6:S)->[1])
0.001/0.001	 (rule: nats -> cons(0,incr(nats)), id: 3, possubterms: nats->[])
0.001/0.001	 (rule: odds -> incr(pairs), id: 4, possubterms: odds->[])
0.001/0.001	 (rule: pairs -> cons(0,incr(odds)), id: 5, possubterms: pairs->[])
0.001/0.001	 (rule: tail(cons(x7:S,x8:S)) -> x8:S, id: 6, possubterms: tail(cons(x7:S,x8:S))->[], cons(x7:S,x8:S)->[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 46%CPU (0avgtext+0avgdata 8536maxresident)k
0.001/0.001	0inputs+0outputs (0major+676minor)pagefaults 0swaps