102.16/100.89	YES
102.16/100.89	
102.16/100.89	Problem 1: 
102.16/100.89	
102.16/100.89	(VAR v_NonEmpty:S x1:S)
102.16/100.89	(RULES
102.16/100.89	c(c(x1:S)) -> c(x1:S)
102.16/100.89	c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	n(a(x1:S)) -> c(x1:S)
102.16/100.89	n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	)
102.16/100.89	
102.16/100.89	Problem 1: 
102.16/100.89	
102.16/100.89	Dependency Pairs Processor:
102.16/100.89	-> Pairs:
102.16/100.89	 C(f(x1:S)) -> C(x1:S)
102.16/100.89	 C(f(x1:S)) -> F(n(a(c(x1:S))))
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 F(x1:S) -> C(n(a(x1:S)))
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 F(x1:S) -> N(a(x1:S))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	 N(s(x1:S)) -> F(s(s(x1:S)))
102.16/100.89	-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	
102.16/100.89	Problem 1: 
102.16/100.89	
102.16/100.89	SCC Processor:
102.16/100.89	-> Pairs:
102.16/100.89	 C(f(x1:S)) -> C(x1:S)
102.16/100.89	 C(f(x1:S)) -> F(n(a(c(x1:S))))
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 F(x1:S) -> C(n(a(x1:S)))
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 F(x1:S) -> N(a(x1:S))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	 N(s(x1:S)) -> F(s(s(x1:S)))
102.16/100.89	-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	->Strongly Connected Components:
102.16/100.89	->->Cycle:
102.16/100.89	->->-> Pairs:
102.16/100.89	 C(f(x1:S)) -> C(x1:S)
102.16/100.89	 C(f(x1:S)) -> F(n(a(c(x1:S))))
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 F(x1:S) -> C(n(a(x1:S)))
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 F(x1:S) -> N(a(x1:S))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	 N(s(x1:S)) -> F(s(s(x1:S)))
102.16/100.89	->->-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	
102.16/100.89	Problem 1: 
102.16/100.89	
102.16/100.89	Reduction Pair Processor:
102.16/100.89	-> Pairs:
102.16/100.89	 C(f(x1:S)) -> C(x1:S)
102.16/100.89	 C(f(x1:S)) -> F(n(a(c(x1:S))))
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 F(x1:S) -> C(n(a(x1:S)))
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 F(x1:S) -> N(a(x1:S))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	 N(s(x1:S)) -> F(s(s(x1:S)))
102.16/100.89	-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	-> Usable rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	->Interpretation type:
102.16/100.89	 Linear
102.16/100.89	->Coefficients:
102.16/100.89	 Natural Numbers
102.16/100.89	->Dimension:
102.16/100.89	 1
102.16/100.89	->Bound:
102.16/100.89	 2
102.16/100.89	->Interpretation:
102.16/100.89	 
102.16/100.89	[c](X) = 0
102.16/100.89	[f](X) = 2.X
102.16/100.89	[n](X) = 2.X
102.16/100.89	[a](X) = 0
102.16/100.89	[s](X) = 2
102.16/100.89	[C](X) = 2
102.16/100.89	[F](X) = X + 2
102.16/100.89	[N](X) = 2.X + 2
102.16/100.89	
102.16/100.89	Problem 1: 
102.16/100.89	
102.16/100.89	SCC Processor:
102.16/100.89	-> Pairs:
102.16/100.89	 C(f(x1:S)) -> C(x1:S)
102.16/100.89	 C(f(x1:S)) -> F(n(a(c(x1:S))))
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 F(x1:S) -> C(n(a(x1:S)))
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 F(x1:S) -> N(a(x1:S))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	->Strongly Connected Components:
102.16/100.89	->->Cycle:
102.16/100.89	->->-> Pairs:
102.16/100.89	 C(f(x1:S)) -> C(x1:S)
102.16/100.89	 C(f(x1:S)) -> F(n(a(c(x1:S))))
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 F(x1:S) -> C(n(a(x1:S)))
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 F(x1:S) -> N(a(x1:S))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	->->-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	
102.16/100.89	Problem 1: 
102.16/100.89	
102.16/100.89	Reduction Pair Processor:
102.16/100.89	-> Pairs:
102.16/100.89	 C(f(x1:S)) -> C(x1:S)
102.16/100.89	 C(f(x1:S)) -> F(n(a(c(x1:S))))
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 F(x1:S) -> C(n(a(x1:S)))
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 F(x1:S) -> N(a(x1:S))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	-> Usable rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	->Interpretation type:
102.16/100.89	 Linear
102.16/100.89	->Coefficients:
102.16/100.89	 Natural Numbers
102.16/100.89	->Dimension:
102.16/100.89	 2
102.16/100.89	->Bound:
102.16/100.89	 1
102.16/100.89	->Interpretation:
102.16/100.89	 
102.16/100.89	[c](X) = [1 0;0 0].X
102.16/100.89	[f](X) = [1 0;0 1].X + [1;0]
102.16/100.89	[n](X) = [1 1;0 1].X
102.16/100.89	[a](X) = [1 0;0 0].X
102.16/100.89	[s](X) = [0;1]
102.16/100.89	[C](X) = [1 0;1 0].X + [0;1]
102.16/100.89	[F](X) = [1 0;1 0].X + [0;1]
102.16/100.89	[N](X) = [1 1;1 1].X + [0;1]
102.16/100.89	
102.16/100.89	Problem 1: 
102.16/100.89	
102.16/100.89	SCC Processor:
102.16/100.89	-> Pairs:
102.16/100.89	 C(f(x1:S)) -> F(n(a(c(x1:S))))
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 F(x1:S) -> C(n(a(x1:S)))
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 F(x1:S) -> N(a(x1:S))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	->Strongly Connected Components:
102.16/100.89	->->Cycle:
102.16/100.89	->->-> Pairs:
102.16/100.89	 C(f(x1:S)) -> F(n(a(c(x1:S))))
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 F(x1:S) -> C(n(a(x1:S)))
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 F(x1:S) -> N(a(x1:S))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	->->-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	
102.16/100.89	Problem 1: 
102.16/100.89	
102.16/100.89	Reduction Pair Processor:
102.16/100.89	-> Pairs:
102.16/100.89	 C(f(x1:S)) -> F(n(a(c(x1:S))))
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 F(x1:S) -> C(n(a(x1:S)))
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 F(x1:S) -> N(a(x1:S))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	-> Usable rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	->Interpretation type:
102.16/100.89	 Linear
102.16/100.89	->Coefficients:
102.16/100.89	 Natural Numbers
102.16/100.89	->Dimension:
102.16/100.89	 2
102.16/100.89	->Bound:
102.16/100.89	 1
102.16/100.89	->Interpretation:
102.16/100.89	 
102.16/100.89	[c](X) = [0 0;0 1].X
102.16/100.89	[f](X) = [1 0;0 1].X + [0;1]
102.16/100.89	[n](X) = [1 0;1 1].X
102.16/100.89	[a](X) = [0 0;0 1].X
102.16/100.89	[s](X) = [1;0]
102.16/100.89	[C](X) = [0 1;0 1].X + [1;1]
102.16/100.89	[F](X) = [0 1;0 1].X + [1;1]
102.16/100.89	[N](X) = [1 1;1 1].X + [1;1]
102.16/100.89	
102.16/100.89	Problem 1: 
102.16/100.89	
102.16/100.89	SCC Processor:
102.16/100.89	-> Pairs:
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 F(x1:S) -> C(n(a(x1:S)))
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 F(x1:S) -> N(a(x1:S))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	->Strongly Connected Components:
102.16/100.89	->->Cycle:
102.16/100.89	->->-> Pairs:
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	->->-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	->->Cycle:
102.16/100.89	->->-> Pairs:
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	->->-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	
102.16/100.89	
102.16/100.89	The problem is decomposed in 2 subproblems.
102.16/100.89	
102.16/100.89	Problem 1.1: 
102.16/100.89	
102.16/100.89	Reduction Pair Processor:
102.16/100.89	-> Pairs:
102.16/100.89	 C(f(x1:S)) -> N(a(c(x1:S)))
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	-> Usable rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	->Interpretation type:
102.16/100.89	 Linear
102.16/100.89	->Coefficients:
102.16/100.89	 Natural Numbers
102.16/100.89	->Dimension:
102.16/100.89	 2
102.16/100.89	->Bound:
102.16/100.89	 1
102.16/100.89	->Interpretation:
102.16/100.89	 
102.16/100.89	[c](X) = [0 0;0 1].X
102.16/100.89	[f](X) = [1 0;0 1].X + [0;1]
102.16/100.89	[n](X) = [1 0;1 1].X
102.16/100.89	[a](X) = [0 0;0 1].X
102.16/100.89	[s](X) = [1;1]
102.16/100.89	[C](X) = [0 1;0 1].X + [0;1]
102.16/100.89	[N](X) = [0 1;1 1].X + [0;1]
102.16/100.89	
102.16/100.89	Problem 1.1: 
102.16/100.89	
102.16/100.89	SCC Processor:
102.16/100.89	-> Pairs:
102.16/100.89	 N(a(x1:S)) -> C(x1:S)
102.16/100.89	-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	->Strongly Connected Components:
102.16/100.89	 There is no strongly connected component
102.16/100.89	
102.16/100.89	The problem is finite.
102.16/100.89	
102.16/100.89	Problem 1.2: 
102.16/100.89	
102.16/100.89	Reduction Pair Processor:
102.16/100.89	-> Pairs:
102.16/100.89	 F(x1:S) -> N(c(n(a(x1:S))))
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	-> Usable rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.89	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.89	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.89	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.89	 n(a(x1:S)) -> c(x1:S)
102.16/100.89	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.89	->Interpretation type:
102.16/100.89	 Linear
102.16/100.89	->Coefficients:
102.16/100.89	 Natural Numbers
102.16/100.89	->Dimension:
102.16/100.89	 2
102.16/100.89	->Bound:
102.16/100.89	 1
102.16/100.89	->Interpretation:
102.16/100.89	 
102.16/100.89	[c](X) = [0 0;0 1].X
102.16/100.89	[f](X) = [1 0;0 1].X + [0;1]
102.16/100.89	[n](X) = [1 0;1 1].X
102.16/100.89	[a](X) = [0 0;0 1].X
102.16/100.89	[s](X) = [1;1]
102.16/100.89	[F](X) = [0 1;0 1].X + [1;1]
102.16/100.89	[N](X) = [1 1;1 1].X
102.16/100.89	
102.16/100.89	Problem 1.2: 
102.16/100.89	
102.16/100.89	SCC Processor:
102.16/100.89	-> Pairs:
102.16/100.89	 N(f(x1:S)) -> F(n(x1:S))
102.16/100.89	 N(f(x1:S)) -> N(x1:S)
102.16/100.89	-> Rules:
102.16/100.89	 c(c(x1:S)) -> c(x1:S)
102.16/100.90	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.90	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.90	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.90	 n(a(x1:S)) -> c(x1:S)
102.16/100.90	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.90	->Strongly Connected Components:
102.16/100.90	->->Cycle:
102.16/100.90	->->-> Pairs:
102.16/100.90	 N(f(x1:S)) -> N(x1:S)
102.16/100.90	->->-> Rules:
102.16/100.90	 c(c(x1:S)) -> c(x1:S)
102.16/100.90	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.90	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.90	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.90	 n(a(x1:S)) -> c(x1:S)
102.16/100.90	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.90	
102.16/100.90	Problem 1.2: 
102.16/100.90	
102.16/100.90	Subterm Processor:
102.16/100.90	-> Pairs:
102.16/100.90	 N(f(x1:S)) -> N(x1:S)
102.16/100.90	-> Rules:
102.16/100.90	 c(c(x1:S)) -> c(x1:S)
102.16/100.90	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.90	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.90	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.90	 n(a(x1:S)) -> c(x1:S)
102.16/100.90	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.90	->Projection:
102.16/100.90	 pi(N) = 1
102.16/100.90	
102.16/100.90	Problem 1.2: 
102.16/100.90	
102.16/100.90	SCC Processor:
102.16/100.90	-> Pairs:
102.16/100.90	 Empty
102.16/100.90	-> Rules:
102.16/100.90	 c(c(x1:S)) -> c(x1:S)
102.16/100.90	 c(f(x1:S)) -> f(n(a(c(x1:S))))
102.16/100.90	 f(x1:S) -> n(c(n(a(x1:S))))
102.16/100.90	 n(f(x1:S)) -> f(n(x1:S))
102.16/100.90	 n(a(x1:S)) -> c(x1:S)
102.16/100.90	 n(s(x1:S)) -> f(s(s(x1:S)))
102.16/100.90	->Strongly Connected Components:
102.16/100.90	 There is no strongly connected component
102.16/100.90	
102.16/100.90	The problem is finite.
102.16/100.90	EOF