0.00/0.37	YES
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	(VAR v_NonEmpty:S x1:S)
0.00/0.37	(RULES
0.00/0.37	#(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	#(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	#(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	#(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	#(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	)
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Dependency Pairs Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(0(0(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(0(0(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(0(0(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	->->-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(0(0(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[#](X) = 2.X + 2
0.00/0.37	[0](X) = 2.X + 2
0.00/0.37	[1](X) = 2.X + 2
0.00/0.37	[$](X) = 2.X + 2
0.00/0.37	[*](X) = 2.X + 2
0.00/0.37	[##](X) = 2.X + 2
0.00/0.37	[0#](X) = X + 2
0.00/0.37	[1#](X) = 2.X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	->->-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[#](X) = 2.X + 1
0.00/0.37	[0](X) = 2.X + 1
0.00/0.37	[1](X) = 2.X + 1
0.00/0.37	[$](X) = 1
0.00/0.37	[*](X) = 2.X + 1
0.00/0.37	[##](X) = 2.X + 1
0.00/0.37	[0#](X) = X + 2
0.00/0.37	[1#](X) = 2.X
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	->->-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[#](X) = X
0.00/0.37	[0](X) = X + 1
0.00/0.37	[1](X) = X + 1
0.00/0.37	[$](X) = 2.X + 2
0.00/0.37	[*](X) = X
0.00/0.37	[##](X) = X + 1
0.00/0.37	[0#](X) = X + 2
0.00/0.37	[1#](X) = X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	->->-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(0(0(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[#](X) = 2.X + 2
0.00/0.37	[0](X) = 2.X + 2
0.00/0.37	[1](X) = 2.X + 2
0.00/0.37	[$](X) = 2.X + 1
0.00/0.37	[*](X) = 2.X + 2
0.00/0.37	[##](X) = 2.X + 2
0.00/0.37	[0#](X) = X + 2
0.00/0.37	[1#](X) = 2.X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	->->-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[#](X) = 2.X + 2
0.00/0.37	[0](X) = 2.X + 2
0.00/0.37	[1](X) = 2.X + 2
0.00/0.37	[$](X) = 2.X + 2
0.00/0.37	[*](X) = 2.X + 2
0.00/0.37	[##](X) = 2.X + 2
0.00/0.37	[0#](X) = 2.X + 1
0.00/0.37	[1#](X) = 2.X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	->->-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(1(1(x1:S)))) -> ##(x1:S)
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[#](X) = 2.X + 2
0.00/0.37	[0](X) = 2.X + 2
0.00/0.37	[1](X) = 2.X + 2
0.00/0.37	[$](X) = X + 2
0.00/0.37	[*](X) = 2.X + 2
0.00/0.37	[##](X) = 2.X + 2
0.00/0.37	[0#](X) = 2.X + 2
0.00/0.37	[1#](X) = 2.X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	->->-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(#(#(x1:S)))
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[#](X) = 2.X + 2
0.00/0.37	[0](X) = 2.X + 2
0.00/0.37	[1](X) = 2.X + 2
0.00/0.37	[$](X) = 2.X + 2
0.00/0.37	[*](X) = 2.X + 2
0.00/0.37	[##](X) = 2.X
0.00/0.37	[0#](X) = 2.X
0.00/0.37	[1#](X) = 2.X
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	->->-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 ##(#(1(1(x1:S)))) -> 1#(1(#(#(x1:S))))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[#](X) = 2.X + 2
0.00/0.37	[0](X) = 2.X + 2
0.00/0.37	[1](X) = 2.X + 2
0.00/0.37	[$](X) = 2.X + 2
0.00/0.37	[*](X) = 2.X + 2
0.00/0.37	[##](X) = 2.X + 2
0.00/0.37	[0#](X) = X + 2
0.00/0.37	[1#](X) = 2.X + 1
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(#(x1:S))
0.00/0.37	 1#(1(*(*(x1:S)))) -> ##(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	->->-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(1(x1:S))
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[#](X) = 2.X + 2
0.00/0.37	[0](X) = 2.X + 2
0.00/0.37	[1](X) = 2.X + 2
0.00/0.37	[$](X) = X + 1
0.00/0.37	[*](X) = 2.X + 2
0.00/0.37	[0#](X) = 2.X + 1
0.00/0.37	[1#](X) = 2.X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	->->-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 0#(0(*(*(x1:S)))) -> 1#(x1:S)
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[#](X) = 2.X + 2
0.00/0.37	[0](X) = X
0.00/0.37	[1](X) = X
0.00/0.37	[$](X) = 2.X
0.00/0.37	[*](X) = 2.X + 2
0.00/0.37	[0#](X) = X + 1
0.00/0.37	[1#](X) = 2.X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(#(#(x1:S)))
0.00/0.37	 1#(1(*(*(x1:S)))) -> 0#(0(#(#(x1:S))))
0.00/0.37	-> Rules:
0.00/0.37	 #(#(#(#(x1:S)))) -> #(#(x1:S))
0.00/0.37	 #(#(0(0(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	 #(#(1(1(x1:S)))) -> 1(1(#(#(x1:S))))
0.00/0.37	 #(#($($(x1:S)))) -> *(*($($(x1:S))))
0.00/0.37	 #(#(*(*(x1:S)))) -> *(*(x1:S))
0.00/0.37	 0(0(*(*(x1:S)))) -> *(*(1(1(x1:S))))
0.00/0.37	 1(1(*(*(x1:S)))) -> 0(0(#(#(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	 There is no strongly connected component
0.00/0.37	
0.00/0.37	The problem is finite.
0.00/0.37	EOF