0.00/0.12	YES
0.00/0.12	
0.00/0.12	Problem 1: 
0.00/0.12	
0.00/0.12	(VAR v_NonEmpty:S x1:S)
0.00/0.12	(RULES
0.00/0.12	0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.12	0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.12	1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.12	1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.12	1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.12	1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.12	1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.12	)
0.00/0.12	
0.00/0.12	Problem 1: 
0.00/0.12	
0.00/0.12	Dependency Pairs Processor:
0.00/0.12	-> Pairs:
0.00/0.12	 0#(q1(x1:S)) -> 1#(x1:S)
0.00/0.12	 1#(q0(0(x1:S))) -> 0#(0(q1(x1:S)))
0.00/0.12	 1#(q0(0(x1:S))) -> 0#(q1(x1:S))
0.00/0.12	 1#(q0(1(x1:S))) -> 0#(1(q1(x1:S)))
0.00/0.12	 1#(q0(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.12	 1#(q1(0(x1:S))) -> 0#(q1(x1:S))
0.00/0.12	 1#(q1(0(x1:S))) -> 1#(0(q1(x1:S)))
0.00/0.12	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.12	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.12	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.12	-> Rules:
0.00/0.12	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.12	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.12	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.12	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.12	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.12	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.12	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.12	
0.00/0.12	Problem 1: 
0.00/0.12	
0.00/0.12	SCC Processor:
0.00/0.12	-> Pairs:
0.00/0.12	 0#(q1(x1:S)) -> 1#(x1:S)
0.00/0.12	 1#(q0(0(x1:S))) -> 0#(0(q1(x1:S)))
0.00/0.12	 1#(q0(0(x1:S))) -> 0#(q1(x1:S))
0.00/0.12	 1#(q0(1(x1:S))) -> 0#(1(q1(x1:S)))
0.00/0.12	 1#(q0(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.12	 1#(q1(0(x1:S))) -> 0#(q1(x1:S))
0.00/0.12	 1#(q1(0(x1:S))) -> 1#(0(q1(x1:S)))
0.00/0.12	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.12	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.12	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.12	-> Rules:
0.00/0.12	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.12	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.12	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.12	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.12	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.12	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.12	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.12	->Strongly Connected Components:
0.00/0.12	->->Cycle:
0.00/0.12	->->-> Pairs:
0.00/0.12	 0#(q1(x1:S)) -> 1#(x1:S)
0.00/0.12	 1#(q0(0(x1:S))) -> 0#(0(q1(x1:S)))
0.00/0.12	 1#(q0(0(x1:S))) -> 0#(q1(x1:S))
0.00/0.12	 1#(q0(1(x1:S))) -> 0#(1(q1(x1:S)))
0.00/0.12	 1#(q0(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.12	 1#(q1(0(x1:S))) -> 0#(q1(x1:S))
0.00/0.12	 1#(q1(0(x1:S))) -> 1#(0(q1(x1:S)))
0.00/0.12	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.12	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.12	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.12	->->-> Rules:
0.00/0.12	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.12	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.12	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.12	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.12	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.12	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.12	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.12	
0.00/0.12	Problem 1: 
0.00/0.12	
0.00/0.12	Reduction Pair Processor:
0.00/0.12	-> Pairs:
0.00/0.12	 0#(q1(x1:S)) -> 1#(x1:S)
0.00/0.12	 1#(q0(0(x1:S))) -> 0#(0(q1(x1:S)))
0.00/0.12	 1#(q0(0(x1:S))) -> 0#(q1(x1:S))
0.00/0.12	 1#(q0(1(x1:S))) -> 0#(1(q1(x1:S)))
0.00/0.12	 1#(q0(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.12	 1#(q1(0(x1:S))) -> 0#(q1(x1:S))
0.00/0.12	 1#(q1(0(x1:S))) -> 1#(0(q1(x1:S)))
0.00/0.12	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.12	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.12	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.12	-> Rules:
0.00/0.12	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.12	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.12	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.12	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.12	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.12	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.12	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.12	-> Usable rules:
0.00/0.12	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.12	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.12	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.12	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.12	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.12	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.12	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.12	->Interpretation type:
0.00/0.12	 Linear
0.00/0.12	->Coefficients:
0.00/0.12	 Natural Numbers
0.00/0.12	->Dimension:
0.00/0.12	 1
0.00/0.12	->Bound:
0.00/0.12	 2
0.00/0.12	->Interpretation:
0.00/0.12	 
0.00/0.12	[0](X) = 2.X + 2
0.00/0.12	[1](X) = 2.X + 1
0.00/0.12	[q0](X) = 2.X + 2
0.00/0.12	[q1](X) = 2.X + 1
0.00/0.12	[q2](X) = 2.X + 2
0.00/0.12	[0#](X) = X + 2
0.00/0.12	[1#](X) = 2.X + 2
0.00/0.12	
0.00/0.12	Problem 1: 
0.00/0.12	
0.00/0.12	SCC Processor:
0.00/0.12	-> Pairs:
0.00/0.12	 1#(q0(0(x1:S))) -> 0#(0(q1(x1:S)))
0.00/0.12	 1#(q0(0(x1:S))) -> 0#(q1(x1:S))
0.00/0.12	 1#(q0(1(x1:S))) -> 0#(1(q1(x1:S)))
0.00/0.12	 1#(q0(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.12	 1#(q1(0(x1:S))) -> 0#(q1(x1:S))
0.00/0.12	 1#(q1(0(x1:S))) -> 1#(0(q1(x1:S)))
0.00/0.12	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.12	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.12	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.12	-> Rules:
0.00/0.12	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.12	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.12	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.12	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.12	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.12	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.12	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.12	->Strongly Connected Components:
0.00/0.12	->->Cycle:
0.00/0.12	->->-> Pairs:
0.00/0.12	 1#(q0(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.12	 1#(q1(0(x1:S))) -> 1#(0(q1(x1:S)))
0.00/0.12	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.12	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.12	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.12	->->-> Rules:
0.00/0.12	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.12	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.12	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.12	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Pair Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 1#(q0(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.13	 1#(q1(0(x1:S))) -> 1#(0(q1(x1:S)))
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.13	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.13	-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	-> Usable rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	->Interpretation type:
0.00/0.13	 Linear
0.00/0.13	->Coefficients:
0.00/0.13	 Natural Numbers
0.00/0.13	->Dimension:
0.00/0.13	 1
0.00/0.13	->Bound:
0.00/0.13	 2
0.00/0.13	->Interpretation:
0.00/0.13	 
0.00/0.13	[0](X) = 2.X + 1
0.00/0.13	[1](X) = 2.X
0.00/0.13	[q0](X) = 2.X + 1
0.00/0.13	[q1](X) = 2.X
0.00/0.13	[q2](X) = 2.X + 1
0.00/0.13	[1#](X) = X
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	SCC Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 1#(q1(0(x1:S))) -> 1#(0(q1(x1:S)))
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.13	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.13	-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	->Strongly Connected Components:
0.00/0.13	->->Cycle:
0.00/0.13	->->-> Pairs:
0.00/0.13	 1#(q1(0(x1:S))) -> 1#(0(q1(x1:S)))
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.13	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.13	->->-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Pair Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 1#(q1(0(x1:S))) -> 1#(0(q1(x1:S)))
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.13	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.13	-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	-> Usable rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	->Interpretation type:
0.00/0.13	 Linear
0.00/0.13	->Coefficients:
0.00/0.13	 Natural Numbers
0.00/0.13	->Dimension:
0.00/0.13	 1
0.00/0.13	->Bound:
0.00/0.13	 2
0.00/0.13	->Interpretation:
0.00/0.13	 
0.00/0.13	[0](X) = 2.X + 2
0.00/0.13	[1](X) = 2.X
0.00/0.13	[q0](X) = 2.X + 2
0.00/0.13	[q1](X) = 2.X
0.00/0.13	[q2](X) = 2.X + 2
0.00/0.13	[1#](X) = X
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	SCC Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.13	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.13	-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	->Strongly Connected Components:
0.00/0.13	->->Cycle:
0.00/0.13	->->-> Pairs:
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.13	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.13	->->-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Pair Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(1(q1(x1:S)))
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.13	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.13	-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	-> Usable rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	->Interpretation type:
0.00/0.13	 Linear
0.00/0.13	->Coefficients:
0.00/0.13	 Natural Numbers
0.00/0.13	->Dimension:
0.00/0.13	 1
0.00/0.13	->Bound:
0.00/0.13	 2
0.00/0.13	->Interpretation:
0.00/0.13	 
0.00/0.13	[0](X) = X + 2
0.00/0.13	[1](X) = 2.X + 2
0.00/0.13	[q0](X) = X + 1
0.00/0.13	[q1](X) = 2.X + 1
0.00/0.13	[q2](X) = X + 1
0.00/0.13	[1#](X) = 2.X
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	SCC Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.13	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.13	-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	->Strongly Connected Components:
0.00/0.13	->->Cycle:
0.00/0.13	->->-> Pairs:
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.13	->->-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	->->Cycle:
0.00/0.13	->->-> Pairs:
0.00/0.13	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.13	->->-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	
0.00/0.13	
0.00/0.13	The problem is decomposed in 2 subproblems.
0.00/0.13	
0.00/0.13	Problem 1.1: 
0.00/0.13	
0.00/0.13	Reduction Pair Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 1#(q1(1(x1:S))) -> 1#(q1(x1:S))
0.00/0.13	-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	-> Usable rules:
0.00/0.13	 Empty
0.00/0.13	->Interpretation type:
0.00/0.13	 Linear
0.00/0.13	->Coefficients:
0.00/0.13	 Natural Numbers
0.00/0.13	->Dimension:
0.00/0.13	 1
0.00/0.13	->Bound:
0.00/0.13	 2
0.00/0.13	->Interpretation:
0.00/0.13	 
0.00/0.13	[1](X) = 2.X + 2
0.00/0.13	[q1](X) = 2.X
0.00/0.13	[1#](X) = 2.X
0.00/0.13	
0.00/0.13	Problem 1.1: 
0.00/0.13	
0.00/0.13	SCC Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 Empty
0.00/0.13	-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	->Strongly Connected Components:
0.00/0.13	 There is no strongly connected component
0.00/0.13	
0.00/0.13	The problem is finite.
0.00/0.13	
0.00/0.13	Problem 1.2: 
0.00/0.13	
0.00/0.13	Subterm Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 1#(q2(x1:S)) -> 1#(x1:S)
0.00/0.13	-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	->Projection:
0.00/0.13	 pi(1#) = 1
0.00/0.13	
0.00/0.13	Problem 1.2: 
0.00/0.13	
0.00/0.13	SCC Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 Empty
0.00/0.13	-> Rules:
0.00/0.13	 0(q1(x1:S)) -> q2(1(x1:S))
0.00/0.13	 0(q2(x1:S)) -> 0(q0(x1:S))
0.00/0.13	 1(q0(0(x1:S))) -> 0(0(q1(x1:S)))
0.00/0.13	 1(q0(1(x1:S))) -> 0(1(q1(x1:S)))
0.00/0.13	 1(q1(0(x1:S))) -> 1(0(q1(x1:S)))
0.00/0.13	 1(q1(1(x1:S))) -> 1(1(q1(x1:S)))
0.00/0.13	 1(q2(x1:S)) -> q2(1(x1:S))
0.00/0.13	->Strongly Connected Components:
0.00/0.13	 There is no strongly connected component
0.00/0.13	
0.00/0.13	The problem is finite.
0.00/0.13	EOF