0.50/0.61	YES
0.50/0.61	
0.50/0.61	Problem 1: 
0.50/0.61	
0.50/0.61	(VAR v_NonEmpty:S x1:S)
0.50/0.61	(RULES
0.50/0.61	a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	)
0.50/0.61	
0.50/0.61	Problem 1: 
0.50/0.61	
0.50/0.61	Dependency Pairs Processor:
0.50/0.61	-> Pairs:
0.50/0.61	 A(q1(b(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q1(b(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 A(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.61	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.61	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.61	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.61	-> Rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	
0.50/0.61	Problem 1: 
0.50/0.61	
0.50/0.61	SCC Processor:
0.50/0.61	-> Pairs:
0.50/0.61	 A(q1(b(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q1(b(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 A(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.61	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.61	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.61	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.61	-> Rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	->Strongly Connected Components:
0.50/0.61	->->Cycle:
0.50/0.61	->->-> Pairs:
0.50/0.61	 A(q1(b(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q1(b(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 A(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.61	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.61	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.61	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.61	->->-> Rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	
0.50/0.61	Problem 1: 
0.50/0.61	
0.50/0.61	Reduction Pair Processor:
0.50/0.61	-> Pairs:
0.50/0.61	 A(q1(b(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q1(b(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 A(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.61	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.61	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.61	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.61	-> Rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	-> Usable rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	->Interpretation type:
0.50/0.61	 Linear
0.50/0.61	->Coefficients:
0.50/0.61	 Natural Numbers
0.50/0.61	->Dimension:
0.50/0.61	 1
0.50/0.61	->Bound:
0.50/0.61	 2
0.50/0.61	->Interpretation:
0.50/0.61	 
0.50/0.61	[a](X) = 2.X + 2
0.50/0.61	[q0](X) = 2.X + 2
0.50/0.61	[q1](X) = 2.X + 2
0.50/0.61	[q2](X) = 2.X + 2
0.50/0.61	[q3](X) = 2.X + 2
0.50/0.61	[y](X) = 2.X + 2
0.50/0.61	[b](X) = 2.X + 2
0.50/0.61	[bl](X) = X + 1
0.50/0.61	[q4](X) = X
0.50/0.61	[x](X) = X + 1
0.50/0.61	[A](X) = 2.X
0.50/0.61	[Q0](X) = 2.X + 2
0.50/0.61	[Q1](X) = 2.X + 2
0.50/0.61	[Q2](X) = 2.X
0.50/0.61	[Q3](X) = 2.X + 2
0.50/0.61	[Y](X) = 2.X + 2
0.50/0.61	
0.50/0.61	Problem 1: 
0.50/0.61	
0.50/0.61	SCC Processor:
0.50/0.61	-> Pairs:
0.50/0.61	 A(q1(b(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 A(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.61	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.61	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.61	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.61	-> Rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	->Strongly Connected Components:
0.50/0.61	->->Cycle:
0.50/0.61	->->-> Pairs:
0.50/0.61	 A(q1(b(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 A(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.61	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.61	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.61	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.61	->->-> Rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	
0.50/0.61	Problem 1: 
0.50/0.61	
0.50/0.61	Reduction Pair Processor:
0.50/0.61	-> Pairs:
0.50/0.61	 A(q1(b(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 A(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.61	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.61	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.61	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.61	-> Rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	-> Usable rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	->Interpretation type:
0.50/0.61	 Linear
0.50/0.61	->Coefficients:
0.50/0.61	 Natural Numbers
0.50/0.61	->Dimension:
0.50/0.61	 1
0.50/0.61	->Bound:
0.50/0.61	 2
0.50/0.61	->Interpretation:
0.50/0.61	 
0.50/0.61	[a](X) = 2.X + 2
0.50/0.61	[q0](X) = 2.X + 2
0.50/0.61	[q1](X) = 2.X + 2
0.50/0.61	[q2](X) = 2.X + 2
0.50/0.61	[q3](X) = 2.X + 2
0.50/0.61	[y](X) = 2.X + 2
0.50/0.61	[b](X) = 2.X + 2
0.50/0.61	[bl](X) = 2.X + 2
0.50/0.61	[q4](X) = 2.X + 1
0.50/0.61	[x](X) = 2.X + 2
0.50/0.61	[A](X) = 2.X + 1
0.50/0.61	[Q0](X) = 2.X + 2
0.50/0.61	[Q1](X) = 2.X + 2
0.50/0.61	[Q2](X) = 2.X
0.50/0.61	[Q3](X) = 2.X + 1
0.50/0.61	[Y](X) = 2.X
0.50/0.61	
0.50/0.61	Problem 1: 
0.50/0.61	
0.50/0.61	SCC Processor:
0.50/0.61	-> Pairs:
0.50/0.61	 A(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.61	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.61	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.61	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.61	-> Rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	->Strongly Connected Components:
0.50/0.61	->->Cycle:
0.50/0.61	->->-> Pairs:
0.50/0.61	 A(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.61	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.61	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.61	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.61	->->-> Rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	
0.50/0.61	Problem 1: 
0.50/0.61	
0.50/0.61	Reduction Pair Processor:
0.50/0.61	-> Pairs:
0.50/0.61	 A(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.61	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.61	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.61	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.61	-> Rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	-> Usable rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	->Interpretation type:
0.50/0.61	 Linear
0.50/0.61	->Coefficients:
0.50/0.61	 Natural Numbers
0.50/0.61	->Dimension:
0.50/0.61	 1
0.50/0.61	->Bound:
0.50/0.61	 2
0.50/0.61	->Interpretation:
0.50/0.61	 
0.50/0.61	[a](X) = 1
0.50/0.61	[q0](X) = 2.X + 2
0.50/0.61	[q1](X) = 1
0.50/0.61	[q2](X) = X
0.50/0.61	[q3](X) = 2.X
0.50/0.61	[y](X) = 0
0.50/0.61	[b](X) = 2.X + 2
0.50/0.61	[bl](X) = 0
0.50/0.61	[q4](X) = 2.X + 2
0.50/0.61	[x](X) = 2
0.50/0.61	[A](X) = 2
0.50/0.61	[Q0](X) = 2
0.50/0.61	[Q1](X) = 2
0.50/0.61	[Q2](X) = 2.X
0.50/0.61	[Q3](X) = 2
0.50/0.61	[Y](X) = 1
0.50/0.61	
0.50/0.61	Problem 1: 
0.50/0.61	
0.50/0.61	SCC Processor:
0.50/0.61	-> Pairs:
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.61	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.61	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.61	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.61	-> Rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	->Strongly Connected Components:
0.50/0.61	->->Cycle:
0.50/0.61	->->-> Pairs:
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.61	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.61	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.61	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.61	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.61	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.61	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.61	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.61	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.61	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.61	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.61	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.61	->->-> Rules:
0.50/0.61	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.61	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.61	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.61	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.61	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.61	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.61	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.61	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.61	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.61	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.61	
0.50/0.61	Problem 1: 
0.50/0.61	
0.50/0.61	Reduction Pair Processor:
0.50/0.61	-> Pairs:
0.50/0.61	 A(q2(a(x1:S))) -> A(a(x1:S))
0.50/0.61	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.61	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.62	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	-> Usable rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Interpretation type:
0.50/0.62	 Linear
0.50/0.62	->Coefficients:
0.50/0.62	 Natural Numbers
0.50/0.62	->Dimension:
0.50/0.62	 1
0.50/0.62	->Bound:
0.50/0.62	 2
0.50/0.62	->Interpretation:
0.50/0.62	 
0.50/0.62	[a](X) = 2.X
0.50/0.62	[q0](X) = X + 1
0.50/0.62	[q1](X) = 2.X
0.50/0.62	[q2](X) = X + 1
0.50/0.62	[q3](X) = X
0.50/0.62	[y](X) = 2.X + 2
0.50/0.62	[b](X) = 2.X + 2
0.50/0.62	[bl](X) = 2.X + 2
0.50/0.62	[q4](X) = X
0.50/0.62	[x](X) = X + 1
0.50/0.62	[A](X) = 2.X
0.50/0.62	[Q0](X) = X + 1
0.50/0.62	[Q1](X) = 2.X + 1
0.50/0.62	[Q2](X) = X
0.50/0.62	[Q3](X) = 2.X + 2
0.50/0.62	[Y](X) = 2.X
0.50/0.62	
0.50/0.62	Problem 1: 
0.50/0.62	
0.50/0.62	SCC Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.62	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.62	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Strongly Connected Components:
0.50/0.62	->->Cycle:
0.50/0.62	->->-> Pairs:
0.50/0.62	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.62	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.62	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	->->-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	
0.50/0.62	Problem 1: 
0.50/0.62	
0.50/0.62	Reduction Pair Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 A(q2(a(x1:S))) -> Q2(a(a(x1:S)))
0.50/0.62	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.62	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	-> Usable rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Interpretation type:
0.50/0.62	 Linear
0.50/0.62	->Coefficients:
0.50/0.62	 Natural Numbers
0.50/0.62	->Dimension:
0.50/0.62	 1
0.50/0.62	->Bound:
0.50/0.62	 2
0.50/0.62	->Interpretation:
0.50/0.62	 
0.50/0.62	[a](X) = 0
0.50/0.62	[q0](X) = 2.X + 2
0.50/0.62	[q1](X) = 2
0.50/0.62	[q2](X) = X
0.50/0.62	[q3](X) = 2.X + 2
0.50/0.62	[y](X) = 1
0.50/0.62	[b](X) = 2.X + 2
0.50/0.62	[bl](X) = 2.X + 2
0.50/0.62	[q4](X) = 2.X + 2
0.50/0.62	[x](X) = 1
0.50/0.62	[A](X) = 1
0.50/0.62	[Q0](X) = 2
0.50/0.62	[Q1](X) = 2
0.50/0.62	[Q2](X) = 2.X
0.50/0.62	[Q3](X) = 2
0.50/0.62	[Y](X) = 2
0.50/0.62	
0.50/0.62	Problem 1: 
0.50/0.62	
0.50/0.62	SCC Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.62	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Strongly Connected Components:
0.50/0.62	->->Cycle:
0.50/0.62	->->-> Pairs:
0.50/0.62	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.62	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	->->-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	
0.50/0.62	Problem 1: 
0.50/0.62	
0.50/0.62	Reduction Pair Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 A(q2(y(x1:S))) -> A(y(x1:S))
0.50/0.62	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	-> Usable rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Interpretation type:
0.50/0.62	 Linear
0.50/0.62	->Coefficients:
0.50/0.62	 Natural Numbers
0.50/0.62	->Dimension:
0.50/0.62	 1
0.50/0.62	->Bound:
0.50/0.62	 2
0.50/0.62	->Interpretation:
0.50/0.62	 
0.50/0.62	[a](X) = 2.X + 2
0.50/0.62	[q0](X) = 2.X + 2
0.50/0.62	[q1](X) = 2.X + 2
0.50/0.62	[q2](X) = 2.X + 2
0.50/0.62	[q3](X) = 2.X + 2
0.50/0.62	[y](X) = 2.X + 2
0.50/0.62	[b](X) = 2.X + 2
0.50/0.62	[bl](X) = 2.X
0.50/0.62	[q4](X) = X + 1
0.50/0.62	[x](X) = 2.X + 2
0.50/0.62	[A](X) = 2.X
0.50/0.62	[Q0](X) = 2.X + 2
0.50/0.62	[Q1](X) = 2.X + 2
0.50/0.62	[Q2](X) = 2.X
0.50/0.62	[Q3](X) = 2.X + 2
0.50/0.62	[Y](X) = 2.X + 2
0.50/0.62	
0.50/0.62	Problem 1: 
0.50/0.62	
0.50/0.62	SCC Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Strongly Connected Components:
0.50/0.62	->->Cycle:
0.50/0.62	->->-> Pairs:
0.50/0.62	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	->->-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	
0.50/0.62	Problem 1: 
0.50/0.62	
0.50/0.62	Reduction Pair Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 A(q2(y(x1:S))) -> Q2(a(y(x1:S)))
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	-> Usable rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Interpretation type:
0.50/0.62	 Linear
0.50/0.62	->Coefficients:
0.50/0.62	 Natural Numbers
0.50/0.62	->Dimension:
0.50/0.62	 1
0.50/0.62	->Bound:
0.50/0.62	 2
0.50/0.62	->Interpretation:
0.50/0.62	 
0.50/0.62	[a](X) = 2.X
0.50/0.62	[q0](X) = 2.X + 2
0.50/0.62	[q1](X) = 2.X
0.50/0.62	[q2](X) = 2.X + 2
0.50/0.62	[q3](X) = 2.X
0.50/0.62	[y](X) = 2.X + 1
0.50/0.62	[b](X) = 2.X + 2
0.50/0.62	[bl](X) = X + 2
0.50/0.62	[q4](X) = X + 2
0.50/0.62	[x](X) = X + 2
0.50/0.62	[A](X) = 2.X + 2
0.50/0.62	[Q0](X) = 2.X + 2
0.50/0.62	[Q1](X) = 2.X + 2
0.50/0.62	[Q2](X) = 2.X + 2
0.50/0.62	[Q3](X) = 2.X + 2
0.50/0.62	[Y](X) = 2.X + 2
0.50/0.62	
0.50/0.62	Problem 1: 
0.50/0.62	
0.50/0.62	SCC Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> A(q1(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Strongly Connected Components:
0.50/0.62	->->Cycle:
0.50/0.62	->->-> Pairs:
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	->->-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	
0.50/0.62	Problem 1: 
0.50/0.62	
0.50/0.62	Reduction Pair Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Q0(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	-> Usable rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Interpretation type:
0.50/0.62	 Linear
0.50/0.62	->Coefficients:
0.50/0.62	 Natural Numbers
0.50/0.62	->Dimension:
0.50/0.62	 1
0.50/0.62	->Bound:
0.50/0.62	 2
0.50/0.62	->Interpretation:
0.50/0.62	 
0.50/0.62	[a](X) = X
0.50/0.62	[q0](X) = X + 2
0.50/0.62	[q1](X) = 2.X
0.50/0.62	[q2](X) = 2.X
0.50/0.62	[q3](X) = 2
0.50/0.62	[y](X) = 0
0.50/0.62	[b](X) = 2.X + 2
0.50/0.62	[bl](X) = 2.X
0.50/0.62	[q4](X) = 1
0.50/0.62	[x](X) = 2
0.50/0.62	[Q0](X) = 1
0.50/0.62	[Q1](X) = 0
0.50/0.62	[Q2](X) = 2.X
0.50/0.62	[Q3](X) = 1
0.50/0.62	[Y](X) = 0
0.50/0.62	
0.50/0.62	Problem 1: 
0.50/0.62	
0.50/0.62	SCC Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Y(q1(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Strongly Connected Components:
0.50/0.62	->->Cycle:
0.50/0.62	->->-> Pairs:
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	->->-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->->Cycle:
0.50/0.62	->->-> Pairs:
0.50/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.50/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.50/0.62	->->-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	
0.50/0.62	
0.50/0.62	The problem is decomposed in 2 subproblems.
0.50/0.62	
0.50/0.62	Problem 1.1: 
0.50/0.62	
0.50/0.62	Reduction Pair Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Q0(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	-> Usable rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Interpretation type:
0.50/0.62	 Linear
0.50/0.62	->Coefficients:
0.50/0.62	 Natural Numbers
0.50/0.62	->Dimension:
0.50/0.62	 1
0.50/0.62	->Bound:
0.50/0.62	 2
0.50/0.62	->Interpretation:
0.50/0.62	 
0.50/0.62	[a](X) = 2.X + 2
0.50/0.62	[q0](X) = X
0.50/0.62	[q1](X) = X
0.50/0.62	[q2](X) = X
0.50/0.62	[q3](X) = X
0.50/0.62	[y](X) = 2.X + 1
0.50/0.62	[b](X) = 2.X + 2
0.50/0.62	[bl](X) = X + 2
0.50/0.62	[q4](X) = 0
0.50/0.62	[x](X) = 2.X + 2
0.50/0.62	[Q0](X) = 2.X + 1
0.50/0.62	[Q2](X) = X + 1
0.50/0.62	[Q3](X) = 2.X + 1
0.50/0.62	[Y](X) = 2.X + 2
0.50/0.62	
0.50/0.62	Problem 1.1: 
0.50/0.62	
0.50/0.62	SCC Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	 Q3(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Strongly Connected Components:
0.50/0.62	->->Cycle:
0.50/0.62	->->-> Pairs:
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	->->-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->->Cycle:
0.50/0.62	->->-> Pairs:
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	->->-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	
0.50/0.62	
0.50/0.62	The problem is decomposed in 2 subproblems.
0.50/0.62	
0.50/0.62	Problem 1.1.1: 
0.50/0.62	
0.50/0.62	Reduction Pair Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Q0(y(x1:S)) -> Y(q3(x1:S))
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	-> Usable rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Interpretation type:
0.50/0.62	 Linear
0.50/0.62	->Coefficients:
0.50/0.62	 Natural Numbers
0.50/0.62	->Dimension:
0.50/0.62	 1
0.50/0.62	->Bound:
0.50/0.62	 2
0.50/0.62	->Interpretation:
0.50/0.62	 
0.50/0.62	[a](X) = 2.X + 2
0.50/0.62	[q0](X) = 2.X
0.50/0.62	[q1](X) = 2.X + 2
0.50/0.62	[q2](X) = 2.X + 2
0.50/0.62	[q3](X) = 0
0.50/0.62	[y](X) = X
0.50/0.62	[b](X) = X + 1
0.50/0.62	[bl](X) = 2.X
0.50/0.62	[q4](X) = 0
0.50/0.62	[x](X) = 1
0.50/0.62	[Q0](X) = 2
0.50/0.62	[Q2](X) = 2
0.50/0.62	[Y](X) = 2.X + 1
0.50/0.62	
0.50/0.62	Problem 1.1.1: 
0.50/0.62	
0.50/0.62	SCC Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Q2(x(x1:S)) -> Q0(x1:S)
0.50/0.62	 Y(q1(b(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Q2(y(a(x1:S)))
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Q2(y(y(x1:S)))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Strongly Connected Components:
0.50/0.62	->->Cycle:
0.50/0.62	->->-> Pairs:
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	->->-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	
0.50/0.62	Problem 1.1.1: 
0.50/0.62	
0.50/0.62	Reduction Pair Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Y(q1(b(x1:S))) -> Y(y(x1:S))
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	-> Usable rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Interpretation type:
0.50/0.62	 Linear
0.50/0.62	->Coefficients:
0.50/0.62	 Natural Numbers
0.50/0.62	->Dimension:
0.50/0.62	 1
0.50/0.62	->Bound:
0.50/0.62	 2
0.50/0.62	->Interpretation:
0.50/0.62	 
0.50/0.62	[a](X) = 2.X + 2
0.50/0.62	[q0](X) = 2.X + 2
0.50/0.62	[q1](X) = 2.X + 2
0.50/0.62	[q2](X) = 2.X + 2
0.50/0.62	[q3](X) = 2.X + 2
0.50/0.62	[y](X) = 2.X + 2
0.50/0.62	[b](X) = 2.X + 2
0.50/0.62	[bl](X) = 2.X + 2
0.50/0.62	[q4](X) = 2.X + 2
0.50/0.62	[x](X) = 2.X + 2
0.50/0.62	[Y](X) = 2.X
0.50/0.62	
0.50/0.62	Problem 1.1.1: 
0.50/0.62	
0.50/0.62	SCC Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Strongly Connected Components:
0.50/0.62	->->Cycle:
0.50/0.62	->->-> Pairs:
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	->->-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	
0.50/0.62	Problem 1.1.1: 
0.50/0.62	
0.50/0.62	Subterm Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Y(q1(b(x1:S))) -> Y(x1:S)
0.50/0.62	 Y(q2(a(x1:S))) -> Y(a(x1:S))
0.50/0.62	 Y(q2(y(x1:S))) -> Y(y(x1:S))
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Projection:
0.50/0.62	 pi(Y) = 1
0.50/0.62	
0.50/0.62	Problem 1.1.1: 
0.50/0.62	
0.50/0.62	SCC Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Empty
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Strongly Connected Components:
0.50/0.62	 There is no strongly connected component
0.50/0.62	
0.50/0.62	The problem is finite.
0.50/0.62	
0.50/0.62	Problem 1.1.2: 
0.50/0.62	
0.50/0.62	Subterm Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Q3(y(x1:S)) -> Q3(x1:S)
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	->Projection:
0.50/0.62	 pi(Q3) = 1
0.50/0.62	
0.50/0.62	Problem 1.1.2: 
0.50/0.62	
0.50/0.62	SCC Processor:
0.50/0.62	-> Pairs:
0.50/0.62	 Empty
0.50/0.62	-> Rules:
0.50/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.50/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.50/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.50/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.50/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.50/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.50/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.50/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.50/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.50/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.50/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.60/0.62	->Strongly Connected Components:
0.60/0.62	 There is no strongly connected component
0.60/0.62	
0.60/0.62	The problem is finite.
0.60/0.62	
0.60/0.62	Problem 1.2: 
0.60/0.62	
0.60/0.62	Subterm Processor:
0.60/0.62	-> Pairs:
0.60/0.62	 Q1(a(x1:S)) -> Q1(x1:S)
0.60/0.62	 Q1(y(x1:S)) -> Q1(x1:S)
0.60/0.62	-> Rules:
0.60/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.60/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.60/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.60/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.60/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.60/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.60/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.60/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.60/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.60/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.60/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.60/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.60/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.60/0.62	->Projection:
0.60/0.62	 pi(Q1) = 1
0.60/0.62	
0.60/0.62	Problem 1.2: 
0.60/0.62	
0.60/0.62	SCC Processor:
0.60/0.62	-> Pairs:
0.60/0.62	 Empty
0.60/0.62	-> Rules:
0.60/0.62	 a(q1(b(x1:S))) -> q2(a(y(x1:S)))
0.60/0.62	 a(q2(a(x1:S))) -> q2(a(a(x1:S)))
0.60/0.62	 a(q2(y(x1:S))) -> q2(a(y(x1:S)))
0.60/0.62	 q0(a(x1:S)) -> x(q1(x1:S))
0.60/0.62	 q0(y(x1:S)) -> y(q3(x1:S))
0.60/0.62	 q1(a(x1:S)) -> a(q1(x1:S))
0.60/0.62	 q1(y(x1:S)) -> y(q1(x1:S))
0.60/0.62	 q2(x(x1:S)) -> x(q0(x1:S))
0.60/0.62	 q3(y(x1:S)) -> y(q3(x1:S))
0.60/0.62	 q3(bl(x1:S)) -> bl(q4(x1:S))
0.60/0.62	 y(q1(b(x1:S))) -> q2(y(y(x1:S)))
0.60/0.62	 y(q2(a(x1:S))) -> q2(y(a(x1:S)))
0.60/0.62	 y(q2(y(x1:S))) -> q2(y(y(x1:S)))
0.60/0.62	->Strongly Connected Components:
0.60/0.62	 There is no strongly connected component
0.60/0.62	
0.60/0.62	The problem is finite.
0.60/0.62	EOF