0.34/0.35	YES
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	(VAR X Y Z x y)
0.34/0.35	(THEORY 
0.34/0.35	(AC app)
0.34/0.35	(C max'))
0.34/0.35	(RULES
0.34/0.35	1 -> s(0)
0.34/0.35	2 -> s(1)
0.34/0.35	3 -> s(2)
0.34/0.35	4 -> s(3)
0.34/0.35	5 -> s(4)
0.34/0.35	6 -> s(5)
0.34/0.35	7 -> s(6)
0.34/0.35	8 -> s(7)
0.34/0.35	9 -> s(8)
0.34/0.35	app(empty,X) -> X
0.34/0.35	max(app(singl(x),Y)) -> max2(x,Y)
0.34/0.35	max(singl(x)) -> x
0.34/0.35	max'(0,x) -> x
0.34/0.35	max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	max2(x,empty) -> x
0.34/0.35	max2(x,singl(y)) -> max'(x,y)
0.34/0.35	)
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 1 -> s(0)
0.34/0.35	 2 -> s(1)
0.34/0.35	 3 -> s(2)
0.34/0.35	 4 -> s(3)
0.34/0.35	 5 -> s(4)
0.34/0.35	 6 -> s(5)
0.34/0.35	 7 -> s(6)
0.34/0.35	 8 -> s(7)
0.34/0.35	 9 -> s(8)
0.34/0.35	 app(empty,X) -> X
0.34/0.35	 max(app(singl(x),Y)) -> max2(x,Y)
0.34/0.35	 max(singl(x)) -> x
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 2
0.34/0.35	[2] = 2
0.34/0.35	[3] = 2
0.34/0.35	[4] = 2
0.34/0.35	[5] = 2
0.34/0.35	[6] = 2
0.34/0.35	[7] = 2
0.34/0.35	[8] = 2
0.34/0.35	[9] = 2
0.34/0.35	[app](X1,X2) = X1 + X2
0.34/0.35	[max](X) = 2.X + 1
0.34/0.35	[max'](X1,X2) = X1 + X2
0.34/0.35	[max2](X1,X2) = 2.X1 + 2.X2 + 2
0.34/0.35	[0] = 1
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = X
0.34/0.35	[singl](X) = X + 2
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 2 -> s(1)
0.34/0.35	 3 -> s(2)
0.34/0.35	 4 -> s(3)
0.34/0.35	 5 -> s(4)
0.34/0.35	 6 -> s(5)
0.34/0.35	 7 -> s(6)
0.34/0.35	 8 -> s(7)
0.34/0.35	 9 -> s(8)
0.34/0.35	 app(empty,X) -> X
0.34/0.35	 max(app(singl(x),Y)) -> max2(x,Y)
0.34/0.35	 max(singl(x)) -> x
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 1
0.34/0.35	[3] = 1
0.34/0.35	[4] = 1
0.34/0.35	[5] = 1
0.34/0.35	[6] = 1
0.34/0.35	[7] = 1
0.34/0.35	[8] = 2
0.34/0.35	[9] = 2
0.34/0.35	[app](X1,X2) = X1 + X2 + 2
0.34/0.35	[max](X) = 2.X + 2
0.34/0.35	[max'](X1,X2) = X1 + X2 + 1
0.34/0.35	[max2](X1,X2) = 2.X1 + 2.X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = X
0.34/0.35	[singl](X) = 2.X
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 3 -> s(2)
0.34/0.35	 4 -> s(3)
0.34/0.35	 5 -> s(4)
0.34/0.35	 6 -> s(5)
0.34/0.35	 7 -> s(6)
0.34/0.35	 8 -> s(7)
0.34/0.35	 9 -> s(8)
0.34/0.35	 app(empty,X) -> X
0.34/0.35	 max(app(singl(x),Y)) -> max2(x,Y)
0.34/0.35	 max(singl(x)) -> x
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 1
0.34/0.35	[3] = 2
0.34/0.35	[4] = 2
0.34/0.35	[5] = 2
0.34/0.35	[6] = 2
0.34/0.35	[7] = 2
0.34/0.35	[8] = 2
0.34/0.35	[9] = 2
0.34/0.35	[app](X1,X2) = X1 + X2
0.34/0.35	[max](X) = 2.X + 2
0.34/0.35	[max'](X1,X2) = X1 + X2 + 1
0.34/0.35	[max2](X1,X2) = 2.X1 + 2.X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = X
0.34/0.35	[singl](X) = 2.X + 1
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 4 -> s(3)
0.34/0.35	 5 -> s(4)
0.34/0.35	 6 -> s(5)
0.34/0.35	 7 -> s(6)
0.34/0.35	 8 -> s(7)
0.34/0.35	 9 -> s(8)
0.34/0.35	 app(empty,X) -> X
0.34/0.35	 max(app(singl(x),Y)) -> max2(x,Y)
0.34/0.35	 max(singl(x)) -> x
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 1
0.34/0.35	[4] = 2
0.34/0.35	[5] = 2
0.34/0.35	[6] = 2
0.34/0.35	[7] = 2
0.34/0.35	[8] = 2
0.34/0.35	[9] = 2
0.34/0.35	[app](X1,X2) = X1 + X2 + 2
0.34/0.35	[max](X) = X + 2
0.34/0.35	[max'](X1,X2) = X1 + X2
0.34/0.35	[max2](X1,X2) = X1 + X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = X
0.34/0.35	[singl](X) = X
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 5 -> s(4)
0.34/0.35	 6 -> s(5)
0.34/0.35	 7 -> s(6)
0.34/0.35	 8 -> s(7)
0.34/0.35	 9 -> s(8)
0.34/0.35	 app(empty,X) -> X
0.34/0.35	 max(app(singl(x),Y)) -> max2(x,Y)
0.34/0.35	 max(singl(x)) -> x
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 1
0.34/0.35	[6] = 1
0.34/0.35	[7] = 1
0.34/0.35	[8] = 1
0.34/0.35	[9] = 1
0.34/0.35	[app](X1,X2) = X1 + X2 + 1
0.34/0.35	[max](X) = 2.X + 2
0.34/0.35	[max'](X1,X2) = X1 + X2
0.34/0.35	[max2](X1,X2) = 2.X1 + 2.X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = X
0.34/0.35	[singl](X) = 2.X + 2
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 6 -> s(5)
0.34/0.35	 7 -> s(6)
0.34/0.35	 8 -> s(7)
0.34/0.35	 9 -> s(8)
0.34/0.35	 app(empty,X) -> X
0.34/0.35	 max(app(singl(x),Y)) -> max2(x,Y)
0.34/0.35	 max(singl(x)) -> x
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 0
0.34/0.35	[6] = 1
0.34/0.35	[7] = 2
0.34/0.35	[8] = 2
0.34/0.35	[9] = 2
0.34/0.35	[app](X1,X2) = X1 + X2 + 2
0.34/0.35	[max](X) = X + 2
0.34/0.35	[max'](X1,X2) = X1 + X2
0.34/0.35	[max2](X1,X2) = X1 + X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = X
0.34/0.35	[singl](X) = X
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 7 -> s(6)
0.34/0.35	 8 -> s(7)
0.34/0.35	 9 -> s(8)
0.34/0.35	 app(empty,X) -> X
0.34/0.35	 max(app(singl(x),Y)) -> max2(x,Y)
0.34/0.35	 max(singl(x)) -> x
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 0
0.34/0.35	[6] = 1
0.34/0.35	[7] = 2
0.34/0.35	[8] = 2
0.34/0.35	[9] = 2
0.34/0.35	[app](X1,X2) = X1 + X2 + 1
0.34/0.35	[max](X) = 2.X + 2
0.34/0.35	[max'](X1,X2) = X1 + X2 + 1
0.34/0.35	[max2](X1,X2) = 2.X1 + 2.X2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = X
0.34/0.35	[singl](X) = X + 1
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 8 -> s(7)
0.34/0.35	 9 -> s(8)
0.34/0.35	 app(empty,X) -> X
0.34/0.35	 max(app(singl(x),Y)) -> max2(x,Y)
0.34/0.35	 max(singl(x)) -> x
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 0
0.34/0.35	[6] = 0
0.34/0.35	[7] = 0
0.34/0.35	[8] = 1
0.34/0.35	[9] = 2
0.34/0.35	[app](X1,X2) = X1 + X2 + 2
0.34/0.35	[max](X) = X + 2
0.34/0.35	[max'](X1,X2) = X1 + X2
0.34/0.35	[max2](X1,X2) = X1 + X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = 2.X
0.34/0.35	[singl](X) = X
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 9 -> s(8)
0.34/0.35	 app(empty,X) -> X
0.34/0.35	 max(app(singl(x),Y)) -> max2(x,Y)
0.34/0.35	 max(singl(x)) -> x
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 0
0.34/0.35	[6] = 0
0.34/0.35	[7] = 0
0.34/0.35	[8] = 0
0.34/0.35	[9] = 2
0.34/0.35	[app](X1,X2) = X1 + X2 + 2
0.34/0.35	[max](X) = X + 2
0.34/0.35	[max'](X1,X2) = X1 + X2
0.34/0.35	[max2](X1,X2) = X1 + X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = 2.X
0.34/0.35	[singl](X) = X
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 app(empty,X) -> X
0.34/0.35	 max(app(singl(x),Y)) -> max2(x,Y)
0.34/0.35	 max(singl(x)) -> x
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 0
0.34/0.35	[6] = 0
0.34/0.35	[7] = 0
0.34/0.35	[8] = 0
0.34/0.35	[9] = 0
0.34/0.35	[app](X1,X2) = X1 + X2 + 2
0.34/0.35	[max](X) = 2.X + 2
0.34/0.35	[max'](X1,X2) = X1 + X2 + 2
0.34/0.35	[max2](X1,X2) = 2.X1 + 2.X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 2
0.34/0.35	[s](X) = 2.X + 2
0.34/0.35	[singl](X) = 2.X
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 max(app(singl(x),Y)) -> max2(x,Y)
0.34/0.35	 max(singl(x)) -> x
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 0
0.34/0.35	[6] = 0
0.34/0.35	[7] = 0
0.34/0.35	[8] = 0
0.34/0.35	[9] = 0
0.34/0.35	[app](X1,X2) = X1 + X2 + 1
0.34/0.35	[max](X) = 2.X + 2
0.34/0.35	[max'](X1,X2) = X1 + X2
0.34/0.35	[max2](X1,X2) = 2.X1 + 2.X2 + 1
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = 2.X + 2
0.34/0.35	[singl](X) = 2.X
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 max(singl(x)) -> x
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 0
0.34/0.35	[6] = 0
0.34/0.35	[7] = 0
0.34/0.35	[8] = 0
0.34/0.35	[9] = 0
0.34/0.35	[app](X1,X2) = X1 + X2 + 2
0.34/0.35	[max](X) = X + 2
0.34/0.35	[max'](X1,X2) = X1 + X2 + 2
0.34/0.35	[max2](X1,X2) = 2.X1 + 2.X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = 2.X + 2
0.34/0.35	[singl](X) = 2.X
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 max'(0,x) -> x
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 0
0.34/0.35	[6] = 0
0.34/0.35	[7] = 0
0.34/0.35	[8] = 0
0.34/0.35	[9] = 0
0.34/0.35	[app](X1,X2) = X1 + X2 + 2
0.34/0.35	[max](X) = 2.X
0.34/0.35	[max'](X1,X2) = X1 + X2 + 2
0.34/0.35	[max2](X1,X2) = X1 + 2.X2 + 2
0.34/0.35	[0] = 1
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = 2.X + 2
0.34/0.35	[singl](X) = 2.X
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 max'(s(x),s(y)) -> s(max'(x,y))
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 0
0.34/0.35	[6] = 0
0.34/0.35	[7] = 0
0.34/0.35	[8] = 0
0.34/0.35	[9] = 0
0.34/0.35	[app](X1,X2) = X1 + X2
0.34/0.35	[max](X) = 2.X
0.34/0.35	[max'](X1,X2) = X1 + X2
0.34/0.35	[max2](X1,X2) = 2.X1 + 2.X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = 2.X + 2
0.34/0.35	[singl](X) = 2.X + 2
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 max2(x,app(singl(y),Z)) -> max2(max'(x,y),Z)
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 0
0.34/0.35	[6] = 0
0.34/0.35	[7] = 0
0.34/0.35	[8] = 0
0.34/0.35	[9] = 0
0.34/0.35	[app](X1,X2) = X1 + X2 + 2
0.34/0.35	[max](X) = 2.X
0.34/0.35	[max'](X1,X2) = X1 + X2
0.34/0.35	[max2](X1,X2) = 2.X1 + 2.X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = 2.X
0.34/0.35	[singl](X) = 2.X
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 max2(x,empty) -> x
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 0
0.34/0.35	[6] = 0
0.34/0.35	[7] = 0
0.34/0.35	[8] = 0
0.34/0.35	[9] = 0
0.34/0.35	[app](X1,X2) = X1 + X2 + 2
0.34/0.35	[max](X) = 2.X
0.34/0.35	[max'](X1,X2) = 2.X1 + 2.X2 + 2
0.34/0.35	[max2](X1,X2) = 2.X1 + 2.X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = 2.X
0.34/0.35	[singl](X) = X
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Reduction Order Processor:
0.34/0.35	-> Rules:
0.34/0.35	 max2(x,singl(y)) -> max'(x,y)
0.34/0.35	->Interpretation type:
0.34/0.35	 Linear
0.34/0.35	->Coefficients:
0.34/0.35	 Natural Numbers
0.34/0.35	->Dimension:
0.34/0.35	 1
0.34/0.35	->Bound:
0.34/0.35	 2
0.34/0.35	->Interpretation:
0.34/0.35	 
0.34/0.35	[1] = 0
0.34/0.35	[2] = 0
0.34/0.35	[3] = 0
0.34/0.35	[4] = 0
0.34/0.35	[5] = 0
0.34/0.35	[6] = 0
0.34/0.35	[7] = 0
0.34/0.35	[8] = 0
0.34/0.35	[9] = 0
0.34/0.35	[app](X1,X2) = X1 + X2 + 1
0.34/0.35	[max](X) = 2.X
0.34/0.35	[max'](X1,X2) = 2.X1 + 2.X2 + 2
0.34/0.35	[max2](X1,X2) = 2.X1 + 2.X2 + 2
0.34/0.35	[0] = 0
0.34/0.35	[empty] = 0
0.34/0.35	[s](X) = 2.X
0.34/0.35	[singl](X) = 2.X + 2
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	Dependency Pairs Processor:
0.34/0.35	-> FAxioms:
0.34/0.35	 APP(app(x5,x6),x7) = APP(x5,app(x6,x7))
0.34/0.35	 APP(x5,x6) = APP(x6,x5)
0.34/0.35	 MAX'(x5,x6) = MAX'(x6,x5)
0.34/0.35	-> Pairs:
0.34/0.35	 Empty
0.34/0.35	-> EAxioms:
0.34/0.35	 app(app(x5,x6),x7) = app(x5,app(x6,x7))
0.34/0.35	 app(x5,x6) = app(x6,x5)
0.34/0.35	 max'(x5,x6) = max'(x6,x5)
0.34/0.35	-> Rules:
0.34/0.35	 Empty
0.34/0.35	-> SRules:
0.34/0.35	 APP(app(x5,x6),x7) -> APP(x5,x6)
0.34/0.35	 APP(x5,app(x6,x7)) -> APP(x6,x7)
0.34/0.35	
0.34/0.35	Problem 1: 
0.34/0.35	
0.34/0.35	SCC Processor:
0.34/0.35	-> FAxioms:
0.34/0.35	 APP(app(x5,x6),x7) = APP(x5,app(x6,x7))
0.34/0.35	 APP(x5,x6) = APP(x6,x5)
0.34/0.35	 MAX'(x5,x6) = MAX'(x6,x5)
0.34/0.35	-> Pairs:
0.34/0.35	 Empty
0.34/0.35	-> EAxioms:
0.34/0.35	 app(app(x5,x6),x7) = app(x5,app(x6,x7))
0.34/0.35	 app(x5,x6) = app(x6,x5)
0.34/0.35	 max'(x5,x6) = max'(x6,x5)
0.34/0.35	-> Rules:
0.34/0.35	 Empty
0.34/0.35	-> SRules:
0.34/0.35	 APP(app(x5,x6),x7) -> APP(x5,x6)
0.34/0.35	 APP(x5,app(x6,x7)) -> APP(x6,x7)
0.34/0.35	->Strongly Connected Components:
0.34/0.35	 There is no strongly connected component
0.34/0.35	
0.34/0.35	The problem is finite.
0.34/0.35	EOF