0.00/0.01	YES
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	(VAR v_NonEmpty:S x:S y:S ys:S zs1:S zs2:S)
0.00/0.01	(RULES
0.00/0.01	le(0,y:S) -> ttrue
0.00/0.01	le(s(x:S),0) -> ffalse
0.00/0.01	le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.01	split(x:S,cons(y:S,ys:S)) -> tp2(cons(y:S,zs1:S),zs2:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ffalse
0.00/0.01	split(x:S,cons(y:S,ys:S)) -> tp2(zs1:S,cons(y:S,zs2:S)) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ttrue
0.00/0.01	split(x:S,nil) -> tp2(nil,nil)
0.00/0.01	)
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	Valid CTRS Processor:
0.00/0.01	-> Rules:
0.00/0.01	 le(0,y:S) -> ttrue
0.00/0.01	 le(s(x:S),0) -> ffalse
0.00/0.01	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(cons(y:S,zs1:S),zs2:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ffalse
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(zs1:S,cons(y:S,zs2:S)) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ttrue
0.00/0.01	 split(x:S,nil) -> tp2(nil,nil)
0.00/0.01	-> The system is a deterministic 3-CTRS.
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	Dependency Pairs Processor:
0.00/0.01	
0.00/0.01	Conditional Termination Problem 1:
0.00/0.01	-> Pairs:
0.00/0.01	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
0.00/0.01	-> QPairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 le(0,y:S) -> ttrue
0.00/0.01	 le(s(x:S),0) -> ffalse
0.00/0.01	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(cons(y:S,zs1:S),zs2:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ffalse
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(zs1:S,cons(y:S,zs2:S)) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ttrue
0.00/0.01	 split(x:S,nil) -> tp2(nil,nil)
0.00/0.01	
0.00/0.01	Conditional Termination Problem 2:
0.00/0.01	-> Pairs:
0.00/0.01	 SPLIT(x:S,cons(y:S,ys:S)) -> LE(x:S,y:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S)
0.00/0.01	 SPLIT(x:S,cons(y:S,ys:S)) -> SPLIT(x:S,ys:S)
0.00/0.01	-> QPairs:
0.00/0.01	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
0.00/0.01	-> Rules:
0.00/0.01	 le(0,y:S) -> ttrue
0.00/0.01	 le(s(x:S),0) -> ffalse
0.00/0.01	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(cons(y:S,zs1:S),zs2:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ffalse
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(zs1:S,cons(y:S,zs2:S)) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ttrue
0.00/0.01	 split(x:S,nil) -> tp2(nil,nil)
0.00/0.01	
0.00/0.01	
0.00/0.01	The problem is decomposed in 2 subproblems.
0.00/0.01	
0.00/0.01	Problem 1.1: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
0.00/0.01	-> QPairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 le(0,y:S) -> ttrue
0.00/0.01	 le(s(x:S),0) -> ffalse
0.00/0.01	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(cons(y:S,zs1:S),zs2:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ffalse
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(zs1:S,cons(y:S,zs2:S)) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ttrue
0.00/0.01	 split(x:S,nil) -> tp2(nil,nil)
0.00/0.01	->Strongly Connected Components:
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
0.00/0.01	-> QPairs:
0.00/0.01	 Empty
0.00/0.01	->->-> Rules:
0.00/0.01	 le(0,y:S) -> ttrue
0.00/0.01	 le(s(x:S),0) -> ffalse
0.00/0.01	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(cons(y:S,zs1:S),zs2:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ffalse
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(zs1:S,cons(y:S,zs2:S)) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ttrue
0.00/0.01	 split(x:S,nil) -> tp2(nil,nil)
0.00/0.01	
0.00/0.01	Problem 1.1: 
0.00/0.01	
0.00/0.01	Conditional Subterm Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
0.00/0.01	-> QPairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 le(0,y:S) -> ttrue
0.00/0.01	 le(s(x:S),0) -> ffalse
0.00/0.01	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(cons(y:S,zs1:S),zs2:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ffalse
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(zs1:S,cons(y:S,zs2:S)) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ttrue
0.00/0.01	 split(x:S,nil) -> tp2(nil,nil)
0.00/0.01	->Projection:
0.00/0.01	 pi(LE) = 1
0.00/0.01	
0.00/0.01	Problem 1.1: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 Empty
0.00/0.01	-> QPairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 le(0,y:S) -> ttrue
0.00/0.01	 le(s(x:S),0) -> ffalse
0.00/0.01	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(cons(y:S,zs1:S),zs2:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ffalse
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(zs1:S,cons(y:S,zs2:S)) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ttrue
0.00/0.01	 split(x:S,nil) -> tp2(nil,nil)
0.00/0.01	->Strongly Connected Components:
0.00/0.01	 There is no strongly connected component
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.01	
0.00/0.01	Problem 1.2: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 SPLIT(x:S,cons(y:S,ys:S)) -> LE(x:S,y:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S)
0.00/0.01	 SPLIT(x:S,cons(y:S,ys:S)) -> SPLIT(x:S,ys:S)
0.00/0.01	-> QPairs:
0.00/0.01	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
0.00/0.01	-> Rules:
0.00/0.01	 le(0,y:S) -> ttrue
0.00/0.01	 le(s(x:S),0) -> ffalse
0.00/0.01	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(cons(y:S,zs1:S),zs2:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ffalse
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(zs1:S,cons(y:S,zs2:S)) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ttrue
0.00/0.01	 split(x:S,nil) -> tp2(nil,nil)
0.00/0.01	->Strongly Connected Components:
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 SPLIT(x:S,cons(y:S,ys:S)) -> SPLIT(x:S,ys:S)
0.00/0.01	-> QPairs:
0.00/0.01	 Empty
0.00/0.01	->->-> Rules:
0.00/0.01	 le(0,y:S) -> ttrue
0.00/0.01	 le(s(x:S),0) -> ffalse
0.00/0.01	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(cons(y:S,zs1:S),zs2:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ffalse
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(zs1:S,cons(y:S,zs2:S)) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ttrue
0.00/0.01	 split(x:S,nil) -> tp2(nil,nil)
0.00/0.01	
0.00/0.01	Problem 1.2: 
0.00/0.01	
0.00/0.01	Conditional Subterm Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 SPLIT(x:S,cons(y:S,ys:S)) -> SPLIT(x:S,ys:S)
0.00/0.01	-> QPairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 le(0,y:S) -> ttrue
0.00/0.01	 le(s(x:S),0) -> ffalse
0.00/0.01	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(cons(y:S,zs1:S),zs2:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ffalse
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(zs1:S,cons(y:S,zs2:S)) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ttrue
0.00/0.01	 split(x:S,nil) -> tp2(nil,nil)
0.00/0.01	->Projection:
0.00/0.01	 pi(SPLIT) = 2
0.00/0.01	
0.00/0.01	Problem 1.2: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 Empty
0.00/0.01	-> QPairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 le(0,y:S) -> ttrue
0.00/0.01	 le(s(x:S),0) -> ffalse
0.00/0.01	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(cons(y:S,zs1:S),zs2:S) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ffalse
0.00/0.01	 split(x:S,cons(y:S,ys:S)) -> tp2(zs1:S,cons(y:S,zs2:S)) | split(x:S,ys:S) ->* tp2(zs1:S,zs2:S), le(x:S,y:S) ->* ttrue
0.00/0.01	 split(x:S,nil) -> tp2(nil,nil)
0.00/0.01	->Strongly Connected Components:
0.00/0.01	 There is no strongly connected component
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.02	EOF