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 z:S)
0.00/0.01	(RULES
0.00/0.01	f(c(x:S),x:S,y:S) -> c(y:S)
0.00/0.01	f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S))
0.00/0.01	f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S))
0.00/0.01	g(x:S,y:S) -> x:S
0.00/0.01	g(x:S,y:S) -> y:S
0.00/0.01	) 
0.00/0.01	(STRATEGY INNERMOST)
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	-> Pairs:
0.00/0.01	 F(s(x:S),y:S,z:S) -> F(x:S,s(c(y:S)),c(z:S))
0.00/0.01	 F(x:S,c(x:S),c(y:S)) -> F(y:S,x:S,y:S)
0.00/0.01	 F(x:S,c(x:S),c(y:S)) -> F(y:S,y:S,f(y:S,x:S,y:S))
0.00/0.01	-> Rules:
0.00/0.01	 f(c(x:S),x:S,y:S) -> c(y:S)
0.00/0.01	 f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S))
0.00/0.01	 f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S))
0.00/0.01	 g(x:S,y:S) -> x:S
0.00/0.01	 g(x:S,y:S) -> y:S
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 F(s(x:S),y:S,z:S) -> F(x:S,s(c(y:S)),c(z:S))
0.00/0.01	 F(x:S,c(x:S),c(y:S)) -> F(y:S,x:S,y:S)
0.00/0.01	 F(x:S,c(x:S),c(y:S)) -> F(y:S,y:S,f(y:S,x:S,y:S))
0.00/0.01	-> Rules:
0.00/0.01	 f(c(x:S),x:S,y:S) -> c(y:S)
0.00/0.01	 f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S))
0.00/0.01	 f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S))
0.00/0.01	 g(x:S,y:S) -> x:S
0.00/0.01	 g(x:S,y:S) -> y:S
0.00/0.01	->Strongly Connected Components:
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 F(s(x:S),y:S,z:S) -> F(x:S,s(c(y:S)),c(z:S))
0.00/0.01	->->-> Rules:
0.00/0.01	 f(c(x:S),x:S,y:S) -> c(y:S)
0.00/0.01	 f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S))
0.00/0.01	 f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S))
0.00/0.01	 g(x:S,y:S) -> x:S
0.00/0.01	 g(x:S,y:S) -> y:S
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 F(x:S,c(x:S),c(y:S)) -> F(y:S,x:S,y:S)
0.00/0.01	->->-> Rules:
0.00/0.01	 f(c(x:S),x:S,y:S) -> c(y:S)
0.00/0.01	 f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S))
0.00/0.01	 f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S))
0.00/0.01	 g(x:S,y:S) -> x:S
0.00/0.01	 g(x:S,y:S) -> y:S
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	Subterm Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 F(s(x:S),y:S,z:S) -> F(x:S,s(c(y:S)),c(z:S))
0.00/0.01	-> Rules:
0.00/0.01	 f(c(x:S),x:S,y:S) -> c(y:S)
0.00/0.01	 f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S))
0.00/0.01	 f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S))
0.00/0.01	 g(x:S,y:S) -> x:S
0.00/0.01	 g(x:S,y:S) -> y:S
0.00/0.01	->Projection:
0.00/0.01	 pi(F) = 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	-> Rules:
0.00/0.01	 f(c(x:S),x:S,y:S) -> c(y:S)
0.00/0.01	 f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S))
0.00/0.01	 f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S))
0.00/0.01	 g(x:S,y:S) -> x:S
0.00/0.01	 g(x:S,y:S) -> y:S
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	Subterm Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 F(x:S,c(x:S),c(y:S)) -> F(y:S,x:S,y:S)
0.00/0.01	-> Rules:
0.00/0.01	 f(c(x:S),x:S,y:S) -> c(y:S)
0.00/0.01	 f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S))
0.00/0.01	 f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S))
0.00/0.01	 g(x:S,y:S) -> x:S
0.00/0.01	 g(x:S,y:S) -> y:S
0.00/0.01	->Projection:
0.00/0.01	 pi(F) = 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	-> Rules:
0.00/0.01	 f(c(x:S),x:S,y:S) -> c(y:S)
0.00/0.01	 f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S))
0.00/0.01	 f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S))
0.00/0.01	 g(x:S,y:S) -> x:S
0.00/0.01	 g(x:S,y:S) -> y:S
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	EOF