0.85/0.98	YES
0.85/0.98	
0.85/0.98	Problem 1: 
0.85/0.98	
0.85/0.98	(VAR v_NonEmpty:S x1:S)
0.85/0.98	(RULES
0.85/0.98	f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	)
0.85/0.98	
0.85/0.98	Problem 1: 
0.85/0.98	
0.85/0.98	Dependency Pairs Processor:
0.85/0.98	-> Pairs:
0.85/0.98	 F(f(g(x1:S))) -> F(x1:S)
0.85/0.98	 F(f(g(x1:S))) -> G(f(x1:S))
0.85/0.98	 G(g(x1:S)) -> F(g(x1:S))
0.85/0.98	 G(g(x1:S)) -> G(f(g(x1:S)))
0.85/0.98	 G(c(x1:S)) -> G(f(c(x1:S)))
0.85/0.98	-> Rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	
0.85/0.98	Problem 1: 
0.85/0.98	
0.85/0.98	SCC Processor:
0.85/0.98	-> Pairs:
0.85/0.98	 F(f(g(x1:S))) -> F(x1:S)
0.85/0.98	 F(f(g(x1:S))) -> G(f(x1:S))
0.85/0.98	 G(g(x1:S)) -> F(g(x1:S))
0.85/0.98	 G(g(x1:S)) -> G(f(g(x1:S)))
0.85/0.98	 G(c(x1:S)) -> G(f(c(x1:S)))
0.85/0.98	-> Rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	->Strongly Connected Components:
0.85/0.98	->->Cycle:
0.85/0.98	->->-> Pairs:
0.85/0.98	 F(f(g(x1:S))) -> F(x1:S)
0.85/0.98	 F(f(g(x1:S))) -> G(f(x1:S))
0.85/0.98	 G(g(x1:S)) -> F(g(x1:S))
0.85/0.98	 G(g(x1:S)) -> G(f(g(x1:S)))
0.85/0.98	->->-> Rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	
0.85/0.98	Problem 1: 
0.85/0.98	
0.85/0.98	Reduction Pair Processor:
0.85/0.98	-> Pairs:
0.85/0.98	 F(f(g(x1:S))) -> F(x1:S)
0.85/0.98	 F(f(g(x1:S))) -> G(f(x1:S))
0.85/0.98	 G(g(x1:S)) -> F(g(x1:S))
0.85/0.98	 G(g(x1:S)) -> G(f(g(x1:S)))
0.85/0.98	-> Rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	-> Usable rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	->Interpretation type:
0.85/0.98	 Linear
0.85/0.98	->Coefficients:
0.85/0.98	 Natural Numbers
0.85/0.98	->Dimension:
0.85/0.98	 1
0.85/0.98	->Bound:
0.85/0.98	 2
0.85/0.98	->Interpretation:
0.85/0.98	 
0.85/0.98	[f](X) = X
0.85/0.98	[g](X) = 2.X + 2
0.85/0.98	[c](X) = 2.X + 2
0.85/0.98	[F](X) = X
0.85/0.98	[G](X) = X
0.85/0.98	
0.85/0.98	Problem 1: 
0.85/0.98	
0.85/0.98	SCC Processor:
0.85/0.98	-> Pairs:
0.85/0.98	 F(f(g(x1:S))) -> G(f(x1:S))
0.85/0.98	 G(g(x1:S)) -> F(g(x1:S))
0.85/0.98	 G(g(x1:S)) -> G(f(g(x1:S)))
0.85/0.98	-> Rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	->Strongly Connected Components:
0.85/0.98	->->Cycle:
0.85/0.98	->->-> Pairs:
0.85/0.98	 F(f(g(x1:S))) -> G(f(x1:S))
0.85/0.98	 G(g(x1:S)) -> F(g(x1:S))
0.85/0.98	 G(g(x1:S)) -> G(f(g(x1:S)))
0.85/0.98	->->-> Rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	
0.85/0.98	Problem 1: 
0.85/0.98	
0.85/0.98	Reduction Pair Processor:
0.85/0.98	-> Pairs:
0.85/0.98	 F(f(g(x1:S))) -> G(f(x1:S))
0.85/0.98	 G(g(x1:S)) -> F(g(x1:S))
0.85/0.98	 G(g(x1:S)) -> G(f(g(x1:S)))
0.85/0.98	-> Rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	-> Usable rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	->Interpretation type:
0.85/0.98	 Linear
0.85/0.98	->Coefficients:
0.85/0.98	 Natural Numbers
0.85/0.98	->Dimension:
0.85/0.98	 1
0.85/0.98	->Bound:
0.85/0.98	 2
0.85/0.98	->Interpretation:
0.85/0.98	 
0.85/0.98	[f](X) = X
0.85/0.98	[g](X) = 2.X + 1
0.85/0.98	[c](X) = 0
0.85/0.98	[F](X) = X + 1
0.85/0.98	[G](X) = 2.X + 1
0.85/0.98	
0.85/0.98	Problem 1: 
0.85/0.98	
0.85/0.98	SCC Processor:
0.85/0.98	-> Pairs:
0.85/0.98	 G(g(x1:S)) -> F(g(x1:S))
0.85/0.98	 G(g(x1:S)) -> G(f(g(x1:S)))
0.85/0.98	-> Rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	->Strongly Connected Components:
0.85/0.98	->->Cycle:
0.85/0.98	->->-> Pairs:
0.85/0.98	 G(g(x1:S)) -> G(f(g(x1:S)))
0.85/0.98	->->-> Rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	
0.85/0.98	Problem 1: 
0.85/0.98	
0.85/0.98	Reduction Pair Processor:
0.85/0.98	-> Pairs:
0.85/0.98	 G(g(x1:S)) -> G(f(g(x1:S)))
0.85/0.98	-> Rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	-> Usable rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	->Interpretation type:
0.85/0.98	 Linear
0.85/0.98	->Coefficients:
0.85/0.98	 Natural Numbers
0.85/0.98	->Dimension:
0.85/0.98	 2
0.85/0.98	->Bound:
0.85/0.98	 1
0.85/0.98	->Interpretation:
0.85/0.98	 
0.85/0.98	[f](X) = [0 1;1 0].X
0.85/0.98	[g](X) = [1 1;0 0].X + [1;0]
0.85/0.98	[c](X) = [1 1;1 1].X + [1;1]
0.85/0.98	[G](X) = [1 0;1 1].X
0.85/0.98	
0.85/0.98	Problem 1: 
0.85/0.98	
0.85/0.98	SCC Processor:
0.85/0.98	-> Pairs:
0.85/0.98	 Empty
0.85/0.98	-> Rules:
0.85/0.98	 f(f(g(x1:S))) -> g(f(x1:S))
0.85/0.98	 g(f(c(x1:S))) -> g(f(f(c(x1:S))))
0.85/0.98	 g(g(x1:S)) -> g(f(g(x1:S)))
0.85/0.98	 g(c(x1:S)) -> g(f(c(x1:S)))
0.85/0.98	->Strongly Connected Components:
0.85/0.98	 There is no strongly connected component
0.85/0.98	
0.85/0.98	The problem is finite.
0.85/0.99	EOF