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 X:S Y:S Z:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(from 1)
0.001/0.001	(sel 1 2)
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	from(X:S) -> cons(X:S,from(s(X:S)))
0.001/0.001	sel(0,cons(X:S,Y:S)) -> X:S
0.001/0.001	sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z: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 Y:S Z:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(from 1)
0.001/0.001	(sel 1 2)
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	from(X:S) -> cons(X:S,from(s(X:S)))
0.001/0.001	sel(0,cons(X:S,Y:S)) -> X:S
0.001/0.001	sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z: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	CS-TRS Processor:
0.001/0.001	R is a CS-TRS
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 Z:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(from 1)
0.001/0.001	(sel 1 2)
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	from(X:S) -> cons(X:S,from(s(X:S)))
0.001/0.001	sel(0,cons(X:S,Y:S)) -> X:S
0.001/0.001	sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S)
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	Extended u-Critical Pairs NonLHRV Processor [JLAMP21]:
0.001/0.001	->Extended u-Critical Pair:
0.001/0.001	 Rule 1 (l :-> r) => from(x4:S) -> cons(x4:S,from(s(x4:S)))
0.001/0.001	 Rule 1 (l' :-> r') => from(X:S) -> cons(X:S,from(s(X:S)))
0.001/0.001	 Var => x4:S
0.001/0.001	 Pos x4:S in l => [1]
0.001/0.001	 Sigma => {x4:S -> from(X:S)}
0.001/0.001	 s => cons(from(X:S),from(s(from(X:S))))
0.001/0.001	 t => from(cons(X:S,from(s(X:S))))
0.001/0.001	 NW => 0
0.001/0.001	
0.001/0.001	
0.001/0.001	->Extended u-Critical Pair:
0.001/0.001	 Rule 1 (l :-> r) => from(x4:S) -> cons(x4:S,from(s(x4:S)))
0.001/0.001	 Rule 2 (l' :-> r') => sel(0,cons(X:S,Y:S)) -> X:S
0.001/0.001	 Var => x4:S
0.001/0.001	 Pos x4:S in l => [1]
0.001/0.001	 Sigma => {x4:S -> sel(0,cons(X:S,Y:S))}
0.001/0.001	 s => cons(sel(0,cons(X:S,Y:S)),from(s(sel(0,cons(X:S,Y:S)))))
0.001/0.001	 t => from(X:S)
0.001/0.001	 NW => 0
0.001/0.001	
0.001/0.001	
0.001/0.001	->Extended u-Critical Pair:
0.001/0.001	 Rule 1 (l :-> r) => from(x4:S) -> cons(x4:S,from(s(x4:S)))
0.001/0.001	 Rule 3 (l' :-> r') => sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S)
0.001/0.001	 Var => x4:S
0.001/0.001	 Pos x4:S in l => [1]
0.001/0.001	 Sigma => {x4:S -> sel(s(X:S),cons(Y:S,Z:S))}
0.001/0.001	 s => cons(sel(s(X:S),cons(Y:S,Z:S)),from(s(sel(s(X:S),cons(Y:S,Z:S)))))
0.001/0.001	 t => from(sel(X:S,Z:S))
0.001/0.001	 NW => 0
0.001/0.001	
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 Z:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(from 1)
0.001/0.001	(sel 1 2)
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	from(X:S) -> cons(X:S,from(s(X:S)))
0.001/0.001	sel(0,cons(X:S,Y:S)) -> X:S
0.001/0.001	sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S)
0.001/0.001	)
0.001/0.001	Critical Pairs:
0.001/0.001	<cons(from(X:S),from(s(from(X:S)))),from(cons(X:S,from(s(X:S))))>   =>  Not trivial, Not overlay, NW0, N1
0.001/0.001	<cons(sel(0,cons(X:S,Y:S)),from(s(sel(0,cons(X:S,Y:S))))),from(X:S)>   =>  Not trivial, Not overlay, NW0, N2
0.001/0.001	<cons(sel(s(X:S),cons(Y:S,Z:S)),from(s(sel(s(X:S),cons(Y:S,Z:S))))),from(sel(X:S,Z:S))>   =>  Not trivial, Not overlay, NW0, N3
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	Huet Levy Processor:
0.001/0.001	-> Rules:
0.001/0.001	 from(X:S) -> cons(X:S,from(s(X:S)))
0.001/0.001	 sel(0,cons(X:S,Y:S)) -> X:S
0.001/0.001	 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S)
0.001/0.001	-> Vars:
0.001/0.001	 X, X, Y, X, Y, Z
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: [X])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [Y], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [X, Y], UV-RActive: [X, Z], UV-LFrozen: [Z], UV-RFrozen: [])
0.001/0.001	-> FVars:
0.001/0.001	 x4, x5, x6, x7, x8, x9
0.001/0.001	-> PVars:
0.001/0.001	 X: [x4, x5, x7], Y: [x6, x8], Z: [x9]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: from(x4:S) -> cons(x4:S,from(s(x4:S))), id: 1, possubterms: from(x4:S)->[])
0.001/0.001	 (rule: sel(0,cons(x5:S,x6:S)) -> x5:S, id: 2, possubterms: sel(0,cons(x5:S,x6:S))->[], 0->[1], cons(x5:S,x6:S)->[2])
0.001/0.001	 (rule: sel(s(x7:S),cons(x8:S,x9:S)) -> sel(x7:S,x9:S), id: 3, possubterms: sel(s(x7:S),cons(x8:S,x9:S))->[], s(x7:S)->[1], cons(x8:S,x9:S)->[2])
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	<cons(from(X:S),from(s(from(X:S)))),from(cons(X:S,from(s(X:S))))>   =>  Not trivial, Not overlay, NW0, N1
0.001/0.001	<cons(sel(0,cons(X:S,Y:S)),from(s(sel(0,cons(X:S,Y:S))))),from(X:S)>   =>  Not trivial, Not overlay, NW0, N2
0.001/0.001	<cons(sel(s(X:S),cons(Y:S,Z:S)),from(s(sel(s(X:S),cons(Y:S,Z:S))))),from(sel(X:S,Z:S))>   =>  Not trivial, Not overlay, NW0, N3
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	 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, Not left-homogeneous u-replacing variables
0.001/0.001	
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	No Convergence Brute Force Processor:
0.001/0.001	-> Rewritings:
0.001/0.001	s: cons(from(X:S),from(s(from(X:S))))
0.001/0.001	Nodes: [0,1]
0.001/0.001	Edges: [(0,1)]
0.001/0.001	ID: 0 => ('cons(from(X:S),from(s(from(X:S))))', D0)
0.001/0.001	ID: 1 => ('cons(cons(X:S,from(s(X:S))),from(s(from(X:S))))', D1, R1, P[1], S{x4:S -> X:S}), NR: 'cons(X:S,from(s(X:S)))'
0.001/0.001	t: from(cons(X:S,from(s(X:S))))
0.001/0.001	Nodes: [0,1]
0.001/0.001	Edges: [(0,1)]
0.001/0.001	ID: 0 => ('from(cons(X:S,from(s(X:S))))', D0)
0.001/0.001	ID: 1 => ('cons(cons(X:S,from(s(X:S))),from(s(cons(X:S,from(s(X:S))))))', D1, R1, P[], S{x4:S -> cons(X:S,from(s(X:S)))}), NR: 'cons(cons(X:S,from(s(X:S))),from(s(cons(X:S,from(s(X:S))))))'
0.001/0.001	cons(from(X:S),from(s(from(X:S)))) ->* no union *<- from(cons(X:S,from(s(X:S))))
0.001/0.001	"Not joinable"
0.001/0.001	
0.001/0.001	The problem is not joinable.
0.001/0.001	0.00user 0.00system 0:00.01elapsed 66%CPU (0avgtext+0avgdata 9088maxresident)k
0.001/0.001	0inputs+0outputs (0major+724minor)pagefaults 0swaps