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	(first 1 2)
0.001/0.001	(from 1)
0.001/0.001	(0)
0.001/0.001	(cons 1)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(nil)
0.001/0.001	(s 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	first(0,X:S) -> nil
0.001/0.001	first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S))
0.001/0.001	from(X:S) -> cons(X:S,from(s(X: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	(first 1 2)
0.001/0.001	(from 1)
0.001/0.001	(0)
0.001/0.001	(cons 1)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(nil)
0.001/0.001	(s 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	first(0,X:S) -> nil
0.001/0.001	first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S))
0.001/0.001	from(X:S) -> cons(X:S,from(s(X: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	(first 1 2)
0.001/0.001	(from 1)
0.001/0.001	(0)
0.001/0.001	(cons 1)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(nil)
0.001/0.001	(s 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	first(0,X:S) -> nil
0.001/0.001	first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S))
0.001/0.001	from(X:S) -> cons(X:S,from(s(X: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) => first(s(x5:S),cons(x6:S,x7:S)) -> cons(x6:S,first(x5:S,x7:S))
0.001/0.001	 Rule 2 (l' :-> r') => first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S))
0.001/0.001	 Var => x5:S
0.001/0.001	 Pos x5:S in l => [1,1]
0.001/0.001	 Sigma => {x5:S -> first(s(X:S),cons(Y:S,Z:S))}
0.001/0.001	 s => cons(x6:S,first(first(s(X:S),cons(Y:S,Z:S)),x7:S))
0.001/0.001	 t => first(s(cons(Y:S,first(X:S,Z:S))),cons(x6:S,x7:S))
0.001/0.001	 NW => 1
0.001/0.001	
0.001/0.001	
0.001/0.001	->Extended u-Critical Pair:
0.001/0.001	 Rule 1 (l :-> r) => first(s(x5:S),cons(x6:S,x7:S)) -> cons(x6:S,first(x5:S,x7:S))
0.001/0.001	 Rule 3 (l' :-> r') => from(X:S) -> cons(X:S,from(s(X:S)))
0.001/0.001	 Var => x5:S
0.001/0.001	 Pos x5:S in l => [1,1]
0.001/0.001	 Sigma => {x5:S -> from(X:S)}
0.001/0.001	 s => cons(x6:S,first(from(X:S),x7:S))
0.001/0.001	 t => first(s(cons(X:S,from(s(X:S)))),cons(x6:S,x7:S))
0.001/0.001	 NW => 1
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(x8:S) -> cons(x8:S,from(s(x8:S)))
0.001/0.001	 Rule 3 (l' :-> r') => from(X:S) -> cons(X:S,from(s(X:S)))
0.001/0.001	 Var => x8:S
0.001/0.001	 Pos x8:S in l => [1]
0.001/0.001	 Sigma => {x8: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	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	(first 1 2)
0.001/0.001	(from 1)
0.001/0.001	(0)
0.001/0.001	(cons 1)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(nil)
0.001/0.001	(s 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	first(0,X:S) -> nil
0.001/0.001	first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S))
0.001/0.001	from(X:S) -> cons(X:S,from(s(X:S)))
0.001/0.001	)
0.001/0.001	Critical Pairs:
0.001/0.001	<cons(x6:S,first(first(s(X:S),cons(Y:S,Z:S)),x7:S)),first(s(cons(Y:S,first(X:S,Z:S))),cons(x6:S,x7:S))>   =>  Not trivial, Not overlay, NW1, N1
0.001/0.001	<cons(x6:S,first(from(X:S),x7:S)),first(s(cons(X:S,from(s(X:S)))),cons(x6:S,x7:S))>   =>  Not trivial, Not overlay, NW1, N2
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, 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	 first(0,X:S) -> nil
0.001/0.001	 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S))
0.001/0.001	 from(X:S) -> cons(X:S,from(s(X:S)))
0.001/0.001	-> Vars:
0.001/0.001	 X, X, Y, Z, X
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [X], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [X, Y], UV-RActive: [Y], UV-LFrozen: [Z], UV-RFrozen: [X, Z])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [], UV-RFrozen: [X])
0.001/0.001	-> FVars:
0.001/0.001	 x4, x5, x6, x7, x8
0.001/0.001	-> PVars:
0.001/0.001	 X: [x4, x5, x8], Y: [x6], Z: [x7]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: first(0,x4:S) -> nil, id: 1, possubterms: first(0,x4:S)->[], 0->[1])
0.001/0.001	 (rule: first(s(x5:S),cons(x6:S,x7:S)) -> cons(x6:S,first(x5:S,x7:S)), id: 2, possubterms: first(s(x5:S),cons(x6:S,x7:S))->[], s(x5:S)->[1], cons(x6:S,x7:S)->[2])
0.001/0.001	 (rule: from(x8:S) -> cons(x8:S,from(s(x8:S))), id: 3, possubterms: from(x8: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	<cons(Y:S,first(from(X:S),Z:S)),first(s(cons(X:S,from(s(X:S)))),cons(Y:S,Z:S))>   =>  Not trivial, Not overlay, NW1, N1
0.001/0.001	<cons(Y:S,first(first(s(X:S),cons(Y:S,Z:S)),Z:S)),first(s(cons(Y:S,first(X:S,Z:S))),cons(Y:S,Z:S))>   =>  Not trivial, Not overlay, NW1, N2
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, 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(Y:S,first(from(X:S),Z:S))
0.001/0.001	Nodes: [0]
0.001/0.001	Edges: []
0.001/0.001	ID: 0 => ('cons(Y:S,first(from(X:S),Z:S))', D0)
0.001/0.001	t: first(s(cons(X:S,from(s(X:S)))),cons(Y:S,Z:S))
0.001/0.001	Nodes: [0,1]
0.001/0.001	Edges: [(0,1)]
0.001/0.001	ID: 0 => ('first(s(cons(X:S,from(s(X:S)))),cons(Y:S,Z:S))', D0)
0.001/0.001	ID: 1 => ('cons(Y:S,first(cons(X:S,from(s(X:S))),Z:S))', D1, R2, P[], S{x5:S -> cons(X:S,from(s(X:S))), x6:S -> Y:S, x7:S -> Z:S}), NR: 'cons(Y:S,first(cons(X:S,from(s(X:S))),Z:S))'
0.001/0.001	cons(Y:S,first(from(X:S),Z:S)) ->* no union *<- first(s(cons(X:S,from(s(X:S)))),cons(Y:S,Z:S))
0.001/0.001	"Not joinable"
0.001/0.001	
0.001/0.001	The problem is not joinable.
0.001/0.001	0.01user 0.00system 0:00.01elapsed 76%CPU (0avgtext+0avgdata 9704maxresident)k
0.001/0.001	0inputs+0outputs (0major+776minor)pagefaults 0swaps