0.00/0.13	YES
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	(VAR x y)
0.00/0.13	(THEORY 
0.00/0.13	(AC plus))
0.00/0.13	(RULES
0.00/0.13	L(T(x)) -> L(x)
0.00/0.13	L(plus(T(y),x)) -> plus(L(plus(x,y)),L(y))
0.00/0.13	T(T(x)) -> T(x)
0.00/0.13	T(plus(T(y),x)) -> plus(T(plus(x,y)),T(y))
0.00/0.13	plus(T(plus(x,y)),x) -> T(plus(x,y))
0.00/0.13	plus(T(x),x) -> T(x)
0.00/0.13	plus(x,0) -> x
0.00/0.13	plus(x,x) -> x
0.00/0.13	)
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Order Processor:
0.00/0.13	-> Rules:
0.00/0.13	 L(T(x)) -> L(x)
0.00/0.13	 L(plus(T(y),x)) -> plus(L(plus(x,y)),L(y))
0.00/0.13	 T(T(x)) -> T(x)
0.00/0.13	 T(plus(T(y),x)) -> plus(T(plus(x,y)),T(y))
0.00/0.13	 plus(T(plus(x,y)),x) -> T(plus(x,y))
0.00/0.13	 plus(T(x),x) -> T(x)
0.00/0.13	 plus(x,0) -> x
0.00/0.13	 plus(x,x) -> x
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	[L](X) = X + 1
0.00/0.13	[T](X) = 2.X + 2
0.00/0.13	[plus](X1,X2) = X1 + X2 + 1
0.00/0.13	[0] = 0
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Order Processor:
0.00/0.13	-> Rules:
0.00/0.13	 L(plus(T(y),x)) -> plus(L(plus(x,y)),L(y))
0.00/0.13	 T(T(x)) -> T(x)
0.00/0.13	 T(plus(T(y),x)) -> plus(T(plus(x,y)),T(y))
0.00/0.13	 plus(T(plus(x,y)),x) -> T(plus(x,y))
0.00/0.13	 plus(T(x),x) -> T(x)
0.00/0.13	 plus(x,0) -> x
0.00/0.13	 plus(x,x) -> x
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	[L](X) = 2.X + 2
0.00/0.13	[T](X) = 2.X + 2
0.00/0.13	[plus](X1,X2) = X1 + X2
0.00/0.13	[0] = 0
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Order Processor:
0.00/0.13	-> Rules:
0.00/0.13	 T(T(x)) -> T(x)
0.00/0.13	 T(plus(T(y),x)) -> plus(T(plus(x,y)),T(y))
0.00/0.13	 plus(T(plus(x,y)),x) -> T(plus(x,y))
0.00/0.13	 plus(T(x),x) -> T(x)
0.00/0.13	 plus(x,0) -> x
0.00/0.13	 plus(x,x) -> x
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	[L](X) = 2.X
0.00/0.13	[T](X) = 2.X + 2
0.00/0.13	[plus](X1,X2) = X1 + X2
0.00/0.13	[0] = 0
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Order Processor:
0.00/0.13	-> Rules:
0.00/0.13	 T(plus(T(y),x)) -> plus(T(plus(x,y)),T(y))
0.00/0.13	 plus(T(plus(x,y)),x) -> T(plus(x,y))
0.00/0.13	 plus(T(x),x) -> T(x)
0.00/0.13	 plus(x,0) -> x
0.00/0.13	 plus(x,x) -> x
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	[L](X) = 2.X
0.00/0.13	[T](X) = 2.X + 2
0.00/0.13	[plus](X1,X2) = X1 + X2
0.00/0.13	[0] = 0
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Order Processor:
0.00/0.13	-> Rules:
0.00/0.13	 plus(T(plus(x,y)),x) -> T(plus(x,y))
0.00/0.13	 plus(T(x),x) -> T(x)
0.00/0.13	 plus(x,0) -> x
0.00/0.13	 plus(x,x) -> x
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	[L](X) = 2.X
0.00/0.13	[T](X) = 2.X + 2
0.00/0.13	[plus](X1,X2) = X1 + X2 + 2
0.00/0.13	[0] = 0
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Order Processor:
0.00/0.13	-> Rules:
0.00/0.13	 plus(T(x),x) -> T(x)
0.00/0.13	 plus(x,0) -> x
0.00/0.13	 plus(x,x) -> x
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	[L](X) = 2.X
0.00/0.13	[T](X) = 2.X + 2
0.00/0.13	[plus](X1,X2) = X1 + X2 + 2
0.00/0.13	[0] = 0
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Order Processor:
0.00/0.13	-> Rules:
0.00/0.13	 plus(x,0) -> x
0.00/0.13	 plus(x,x) -> x
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	[L](X) = 2.X
0.00/0.13	[T](X) = 2.X
0.00/0.13	[plus](X1,X2) = X1 + X2 + 2
0.00/0.13	[0] = 2
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Order Processor:
0.00/0.13	-> Rules:
0.00/0.13	 plus(x,x) -> x
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	[L](X) = 2.X
0.00/0.13	[T](X) = 2.X
0.00/0.13	[plus](X1,X2) = X1 + X2 + 2
0.00/0.13	[0] = 0
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Dependency Pairs Processor:
0.00/0.13	-> FAxioms:
0.00/0.13	 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
0.00/0.13	 PLUS(x2,x3) = PLUS(x3,x2)
0.00/0.13	-> Pairs:
0.00/0.13	 Empty
0.00/0.13	-> EAxioms:
0.00/0.13	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.13	 plus(x2,x3) = plus(x3,x2)
0.00/0.13	-> Rules:
0.00/0.13	 Empty
0.00/0.13	-> SRules:
0.00/0.13	 PLUS(plus(x2,x3),x4) -> PLUS(x2,x3)
0.00/0.13	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	SCC Processor:
0.00/0.13	-> FAxioms:
0.00/0.13	 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
0.00/0.13	 PLUS(x2,x3) = PLUS(x3,x2)
0.00/0.13	-> Pairs:
0.00/0.13	 Empty
0.00/0.13	-> EAxioms:
0.00/0.13	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.13	 plus(x2,x3) = plus(x3,x2)
0.00/0.13	-> Rules:
0.00/0.13	 Empty
0.00/0.13	-> SRules:
0.00/0.13	 PLUS(plus(x2,x3),x4) -> PLUS(x2,x3)
0.00/0.13	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
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