0.00/0.05	YES
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	(VAR v_NonEmpty:S x1:S)
0.00/0.05	(RULES
0.00/0.05	0(x1:S) -> 1(x1:S)
0.00/0.05	4(5(4(5(x1:S)))) -> 4(4(5(5(x1:S))))
0.00/0.05	5(5(5(5(5(5(4(4(4(4(4(4(x1:S)))))))))))) -> 2(x1:S)
0.00/0.05	)
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	Dependency Pairs Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 4#(5(4(5(x1:S)))) -> 4#(4(5(5(x1:S))))
0.00/0.05	 4#(5(4(5(x1:S)))) -> 4#(5(5(x1:S)))
0.00/0.05	 4#(5(4(5(x1:S)))) -> 5#(5(x1:S))
0.00/0.05	-> Rules:
0.00/0.05	 0(x1:S) -> 1(x1:S)
0.00/0.05	 4(5(4(5(x1:S)))) -> 4(4(5(5(x1:S))))
0.00/0.05	 5(5(5(5(5(5(4(4(4(4(4(4(x1:S)))))))))))) -> 2(x1:S)
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	SCC Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 4#(5(4(5(x1:S)))) -> 4#(4(5(5(x1:S))))
0.00/0.05	 4#(5(4(5(x1:S)))) -> 4#(5(5(x1:S)))
0.00/0.05	 4#(5(4(5(x1:S)))) -> 5#(5(x1:S))
0.00/0.05	-> Rules:
0.00/0.05	 0(x1:S) -> 1(x1:S)
0.00/0.05	 4(5(4(5(x1:S)))) -> 4(4(5(5(x1:S))))
0.00/0.05	 5(5(5(5(5(5(4(4(4(4(4(4(x1:S)))))))))))) -> 2(x1:S)
0.00/0.05	->Strongly Connected Components:
0.00/0.05	->->Cycle:
0.00/0.05	->->-> Pairs:
0.00/0.05	 4#(5(4(5(x1:S)))) -> 4#(4(5(5(x1:S))))
0.00/0.05	 4#(5(4(5(x1:S)))) -> 4#(5(5(x1:S)))
0.00/0.05	->->-> Rules:
0.00/0.05	 0(x1:S) -> 1(x1:S)
0.00/0.05	 4(5(4(5(x1:S)))) -> 4(4(5(5(x1:S))))
0.00/0.05	 5(5(5(5(5(5(4(4(4(4(4(4(x1:S)))))))))))) -> 2(x1:S)
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	Reduction Pair Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 4#(5(4(5(x1:S)))) -> 4#(4(5(5(x1:S))))
0.00/0.05	 4#(5(4(5(x1:S)))) -> 4#(5(5(x1:S)))
0.00/0.05	-> Rules:
0.00/0.05	 0(x1:S) -> 1(x1:S)
0.00/0.05	 4(5(4(5(x1:S)))) -> 4(4(5(5(x1:S))))
0.00/0.05	 5(5(5(5(5(5(4(4(4(4(4(4(x1:S)))))))))))) -> 2(x1:S)
0.00/0.05	-> Usable rules:
0.00/0.05	 4(5(4(5(x1:S)))) -> 4(4(5(5(x1:S))))
0.00/0.05	 5(5(5(5(5(5(4(4(4(4(4(4(x1:S)))))))))))) -> 2(x1:S)
0.00/0.05	->Interpretation type:
0.00/0.05	 Linear
0.00/0.05	->Coefficients:
0.00/0.05	 Natural Numbers
0.00/0.05	->Dimension:
0.00/0.05	 1
0.00/0.05	->Bound:
0.00/0.05	 2
0.00/0.05	->Interpretation:
0.00/0.05	 
0.00/0.05	[4](X) = X + 2
0.00/0.05	[5](X) = 2.X + 2
0.00/0.05	[2](X) = X + 1
0.00/0.05	[4#](X) = 2.X
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	SCC Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 4#(5(4(5(x1:S)))) -> 4#(5(5(x1:S)))
0.00/0.05	-> Rules:
0.00/0.05	 0(x1:S) -> 1(x1:S)
0.00/0.05	 4(5(4(5(x1:S)))) -> 4(4(5(5(x1:S))))
0.00/0.05	 5(5(5(5(5(5(4(4(4(4(4(4(x1:S)))))))))))) -> 2(x1:S)
0.00/0.05	->Strongly Connected Components:
0.00/0.05	->->Cycle:
0.00/0.05	->->-> Pairs:
0.00/0.05	 4#(5(4(5(x1:S)))) -> 4#(5(5(x1:S)))
0.00/0.05	->->-> Rules:
0.00/0.05	 0(x1:S) -> 1(x1:S)
0.00/0.05	 4(5(4(5(x1:S)))) -> 4(4(5(5(x1:S))))
0.00/0.05	 5(5(5(5(5(5(4(4(4(4(4(4(x1:S)))))))))))) -> 2(x1:S)
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	Reduction Pair Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 4#(5(4(5(x1:S)))) -> 4#(5(5(x1:S)))
0.00/0.05	-> Rules:
0.00/0.05	 0(x1:S) -> 1(x1:S)
0.00/0.05	 4(5(4(5(x1:S)))) -> 4(4(5(5(x1:S))))
0.00/0.05	 5(5(5(5(5(5(4(4(4(4(4(4(x1:S)))))))))))) -> 2(x1:S)
0.00/0.05	-> Usable rules:
0.00/0.05	 5(5(5(5(5(5(4(4(4(4(4(4(x1:S)))))))))))) -> 2(x1:S)
0.00/0.05	->Interpretation type:
0.00/0.05	 Linear
0.00/0.05	->Coefficients:
0.00/0.05	 Natural Numbers
0.00/0.05	->Dimension:
0.00/0.05	 1
0.00/0.05	->Bound:
0.00/0.05	 2
0.00/0.05	->Interpretation:
0.00/0.05	 
0.00/0.05	[4](X) = 2.X + 2
0.00/0.05	[5](X) = 2.X
0.00/0.05	[2](X) = 2
0.00/0.05	[4#](X) = 2.X
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	SCC Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 Empty
0.00/0.05	-> Rules:
0.00/0.05	 0(x1:S) -> 1(x1:S)
0.00/0.05	 4(5(4(5(x1:S)))) -> 4(4(5(5(x1:S))))
0.00/0.05	 5(5(5(5(5(5(4(4(4(4(4(4(x1:S)))))))))))) -> 2(x1:S)
0.00/0.05	->Strongly Connected Components:
0.00/0.05	 There is no strongly connected component
0.00/0.05	
0.00/0.05	The problem is finite.
0.00/0.05	EOF