0.00/0.03	YES
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	(VAR v_NonEmpty:S f:S x:S xs:S y:S)
0.00/0.03	(RULES
0.00/0.03	app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S)
0.00/0.03	app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	app(app(filter,f:S),nil) -> nil
0.00/0.03	app(app(int,app(s,x:S)),app(s,y:S)) -> app(intlist,app(app(int,x:S),y:S))
0.00/0.03	app(app(int,app(s,x:S)),0) -> nil
0.00/0.03	app(app(int,0),app(s,y:S)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	app(app(int,0),0) -> app(app(cons,0),nil)
0.00/0.03	app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	app(app(map,f:S),nil) -> nil
0.00/0.03	app(intlist,app(app(cons,x:S),y:S)) -> app(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	app(intlist,nil) -> nil
0.00/0.03	) 
0.00/0.03	(STRATEGY INNERMOST)
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	Dependency Pairs Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 APP(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S)
0.00/0.03	 APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S)
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(app(filter2,app(f:S,x:S)),f:S),x:S)
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(filter2,app(f:S,x:S)),f:S)
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(filter2,app(f:S,x:S))
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S)
0.00/0.03	 APP(app(int,app(s,x:S)),app(s,y:S)) -> APP(app(int,x:S),y:S)
0.00/0.03	 APP(app(int,app(s,x:S)),app(s,y:S)) -> APP(intlist,app(app(int,x:S),y:S))
0.00/0.03	 APP(app(int,0),app(s,y:S)) -> APP(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 APP(app(int,0),app(s,y:S)) -> APP(app(int,app(s,0)),app(s,y:S))
0.00/0.03	 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S)
0.00/0.03	 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(cons,app(f:S,x:S))
0.00/0.03	 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S)
0.00/0.03	 APP(intlist,app(app(cons,x:S),y:S)) -> APP(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 APP(intlist,app(app(cons,x:S),y:S)) -> APP(intlist,y:S)
0.00/0.03	-> Rules:
0.00/0.03	 app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S)
0.00/0.03	 app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 app(app(filter,f:S),nil) -> nil
0.00/0.03	 app(app(int,app(s,x:S)),app(s,y:S)) -> app(intlist,app(app(int,x:S),y:S))
0.00/0.03	 app(app(int,app(s,x:S)),0) -> nil
0.00/0.03	 app(app(int,0),app(s,y:S)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 app(app(int,0),0) -> app(app(cons,0),nil)
0.00/0.03	 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 app(app(map,f:S),nil) -> nil
0.00/0.03	 app(intlist,app(app(cons,x:S),y:S)) -> app(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 app(intlist,nil) -> nil
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 APP(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S)
0.00/0.03	 APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S)
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(app(filter2,app(f:S,x:S)),f:S),x:S)
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(filter2,app(f:S,x:S)),f:S)
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(filter2,app(f:S,x:S))
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S)
0.00/0.03	 APP(app(int,app(s,x:S)),app(s,y:S)) -> APP(app(int,x:S),y:S)
0.00/0.03	 APP(app(int,app(s,x:S)),app(s,y:S)) -> APP(intlist,app(app(int,x:S),y:S))
0.00/0.03	 APP(app(int,0),app(s,y:S)) -> APP(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 APP(app(int,0),app(s,y:S)) -> APP(app(int,app(s,0)),app(s,y:S))
0.00/0.03	 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S)
0.00/0.03	 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(cons,app(f:S,x:S))
0.00/0.03	 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S)
0.00/0.03	 APP(intlist,app(app(cons,x:S),y:S)) -> APP(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 APP(intlist,app(app(cons,x:S),y:S)) -> APP(intlist,y:S)
0.00/0.03	-> Rules:
0.00/0.03	 app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S)
0.00/0.03	 app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 app(app(filter,f:S),nil) -> nil
0.00/0.03	 app(app(int,app(s,x:S)),app(s,y:S)) -> app(intlist,app(app(int,x:S),y:S))
0.00/0.03	 app(app(int,app(s,x:S)),0) -> nil
0.00/0.03	 app(app(int,0),app(s,y:S)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 app(app(int,0),0) -> app(app(cons,0),nil)
0.00/0.03	 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 app(app(map,f:S),nil) -> nil
0.00/0.03	 app(intlist,app(app(cons,x:S),y:S)) -> app(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 app(intlist,nil) -> nil
0.00/0.03	->Strongly Connected Components:
0.00/0.03	->->Cycle:
0.00/0.03	->->-> Pairs:
0.00/0.03	 APP(intlist,app(app(cons,x:S),y:S)) -> APP(intlist,y:S)
0.00/0.03	->->-> Rules:
0.00/0.03	 app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S)
0.00/0.03	 app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 app(app(filter,f:S),nil) -> nil
0.00/0.03	 app(app(int,app(s,x:S)),app(s,y:S)) -> app(intlist,app(app(int,x:S),y:S))
0.00/0.03	 app(app(int,app(s,x:S)),0) -> nil
0.00/0.03	 app(app(int,0),app(s,y:S)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 app(app(int,0),0) -> app(app(cons,0),nil)
0.00/0.03	 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 app(app(map,f:S),nil) -> nil
0.00/0.03	 app(intlist,app(app(cons,x:S),y:S)) -> app(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 app(intlist,nil) -> nil
0.00/0.03	->->Cycle:
0.00/0.03	->->-> Pairs:
0.00/0.03	 APP(app(int,app(s,x:S)),app(s,y:S)) -> APP(app(int,x:S),y:S)
0.00/0.03	 APP(app(int,0),app(s,y:S)) -> APP(app(int,app(s,0)),app(s,y:S))
0.00/0.03	->->-> Rules:
0.00/0.03	 app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S)
0.00/0.03	 app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 app(app(filter,f:S),nil) -> nil
0.00/0.03	 app(app(int,app(s,x:S)),app(s,y:S)) -> app(intlist,app(app(int,x:S),y:S))
0.00/0.03	 app(app(int,app(s,x:S)),0) -> nil
0.00/0.03	 app(app(int,0),app(s,y:S)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 app(app(int,0),0) -> app(app(cons,0),nil)
0.00/0.03	 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 app(app(map,f:S),nil) -> nil
0.00/0.03	 app(intlist,app(app(cons,x:S),y:S)) -> app(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 app(intlist,nil) -> nil
0.00/0.03	->->Cycle:
0.00/0.03	->->-> Pairs:
0.00/0.03	 APP(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S)
0.00/0.03	 APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S)
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S)
0.00/0.03	 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S)
0.00/0.03	 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S)
0.00/0.03	->->-> Rules:
0.00/0.03	 app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S)
0.00/0.03	 app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 app(app(filter,f:S),nil) -> nil
0.00/0.03	 app(app(int,app(s,x:S)),app(s,y:S)) -> app(intlist,app(app(int,x:S),y:S))
0.00/0.03	 app(app(int,app(s,x:S)),0) -> nil
0.00/0.03	 app(app(int,0),app(s,y:S)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 app(app(int,0),0) -> app(app(cons,0),nil)
0.00/0.03	 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 app(app(map,f:S),nil) -> nil
0.00/0.03	 app(intlist,app(app(cons,x:S),y:S)) -> app(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 app(intlist,nil) -> nil
0.00/0.03	
0.00/0.03	
0.00/0.03	The problem is decomposed in 3 subproblems.
0.00/0.03	
0.00/0.03	Problem 1.1: 
0.00/0.03	
0.00/0.03	Subterm Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 APP(intlist,app(app(cons,x:S),y:S)) -> APP(intlist,y:S)
0.00/0.03	-> Rules:
0.00/0.03	 app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S)
0.00/0.03	 app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 app(app(filter,f:S),nil) -> nil
0.00/0.03	 app(app(int,app(s,x:S)),app(s,y:S)) -> app(intlist,app(app(int,x:S),y:S))
0.00/0.03	 app(app(int,app(s,x:S)),0) -> nil
0.00/0.03	 app(app(int,0),app(s,y:S)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 app(app(int,0),0) -> app(app(cons,0),nil)
0.00/0.03	 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 app(app(map,f:S),nil) -> nil
0.00/0.03	 app(intlist,app(app(cons,x:S),y:S)) -> app(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 app(intlist,nil) -> nil
0.00/0.03	->Projection:
0.00/0.03	 pi(APP) = 2
0.00/0.03	
0.00/0.03	Problem 1.1: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 Empty
0.00/0.03	-> Rules:
0.00/0.03	 app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S)
0.00/0.03	 app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 app(app(filter,f:S),nil) -> nil
0.00/0.03	 app(app(int,app(s,x:S)),app(s,y:S)) -> app(intlist,app(app(int,x:S),y:S))
0.00/0.03	 app(app(int,app(s,x:S)),0) -> nil
0.00/0.03	 app(app(int,0),app(s,y:S)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 app(app(int,0),0) -> app(app(cons,0),nil)
0.00/0.03	 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 app(app(map,f:S),nil) -> nil
0.00/0.03	 app(intlist,app(app(cons,x:S),y:S)) -> app(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 app(intlist,nil) -> nil
0.00/0.03	->Strongly Connected Components:
0.00/0.03	 There is no strongly connected component
0.00/0.03	
0.00/0.03	The problem is finite.
0.00/0.03	
0.00/0.03	Problem 1.2: 
0.00/0.03	
0.00/0.03	Subterm Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 APP(app(int,app(s,x:S)),app(s,y:S)) -> APP(app(int,x:S),y:S)
0.00/0.03	 APP(app(int,0),app(s,y:S)) -> APP(app(int,app(s,0)),app(s,y:S))
0.00/0.03	-> Rules:
0.00/0.03	 app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S)
0.00/0.03	 app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 app(app(filter,f:S),nil) -> nil
0.00/0.03	 app(app(int,app(s,x:S)),app(s,y:S)) -> app(intlist,app(app(int,x:S),y:S))
0.00/0.03	 app(app(int,app(s,x:S)),0) -> nil
0.00/0.03	 app(app(int,0),app(s,y:S)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 app(app(int,0),0) -> app(app(cons,0),nil)
0.00/0.03	 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 app(app(map,f:S),nil) -> nil
0.00/0.03	 app(intlist,app(app(cons,x:S),y:S)) -> app(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 app(intlist,nil) -> nil
0.00/0.03	->Projection:
0.00/0.03	 pi(APP) = 2
0.00/0.03	
0.00/0.03	Problem 1.2: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 APP(app(int,0),app(s,y:S)) -> APP(app(int,app(s,0)),app(s,y:S))
0.00/0.03	-> Rules:
0.00/0.03	 app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S)
0.00/0.03	 app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 app(app(filter,f:S),nil) -> nil
0.00/0.03	 app(app(int,app(s,x:S)),app(s,y:S)) -> app(intlist,app(app(int,x:S),y:S))
0.00/0.03	 app(app(int,app(s,x:S)),0) -> nil
0.00/0.03	 app(app(int,0),app(s,y:S)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 app(app(int,0),0) -> app(app(cons,0),nil)
0.00/0.03	 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 app(app(map,f:S),nil) -> nil
0.00/0.03	 app(intlist,app(app(cons,x:S),y:S)) -> app(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 app(intlist,nil) -> nil
0.00/0.03	->Strongly Connected Components:
0.00/0.03	 There is no strongly connected component
0.00/0.03	
0.00/0.03	The problem is finite.
0.00/0.03	
0.00/0.03	Problem 1.3: 
0.00/0.03	
0.00/0.03	Subterm Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 APP(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S)
0.00/0.03	 APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S)
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S)
0.00/0.03	 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S)
0.00/0.03	 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S)
0.00/0.03	-> Rules:
0.00/0.03	 app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S)
0.00/0.03	 app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 app(app(filter,f:S),nil) -> nil
0.00/0.03	 app(app(int,app(s,x:S)),app(s,y:S)) -> app(intlist,app(app(int,x:S),y:S))
0.00/0.03	 app(app(int,app(s,x:S)),0) -> nil
0.00/0.03	 app(app(int,0),app(s,y:S)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 app(app(int,0),0) -> app(app(cons,0),nil)
0.00/0.03	 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 app(app(map,f:S),nil) -> nil
0.00/0.03	 app(intlist,app(app(cons,x:S),y:S)) -> app(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 app(intlist,nil) -> nil
0.00/0.03	->Projection:
0.00/0.03	 pi(APP) = 2
0.00/0.03	
0.00/0.03	Problem 1.3: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 APP(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S)
0.00/0.03	 APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S)
0.00/0.03	-> Rules:
0.00/0.03	 app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S)
0.00/0.03	 app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S))
0.00/0.03	 app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S)
0.00/0.03	 app(app(filter,f:S),nil) -> nil
0.00/0.03	 app(app(int,app(s,x:S)),app(s,y:S)) -> app(intlist,app(app(int,x:S),y:S))
0.00/0.03	 app(app(int,app(s,x:S)),0) -> nil
0.00/0.03	 app(app(int,0),app(s,y:S)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y:S)))
0.00/0.03	 app(app(int,0),0) -> app(app(cons,0),nil)
0.00/0.03	 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
0.00/0.03	 app(app(map,f:S),nil) -> nil
0.00/0.03	 app(intlist,app(app(cons,x:S),y:S)) -> app(app(cons,app(s,x:S)),app(intlist,y:S))
0.00/0.03	 app(intlist,nil) -> nil
0.00/0.03	->Strongly Connected Components:
0.00/0.03	 There is no strongly connected component
0.00/0.03	
0.00/0.03	The problem is finite.
0.00/0.03	EOF