0.00/0.18	YES
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	(VAR x y)
0.00/0.18	(THEORY 
0.00/0.18	(AC plus))
0.00/0.18	(RULES
0.00/0.18	double(x) -> plus(x,x)
0.00/0.18	plus(x,0) -> x
0.00/0.18	plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	)
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Reduction Order Processor:
0.00/0.18	-> Rules:
0.00/0.18	 double(x) -> plus(x,x)
0.00/0.18	 plus(x,0) -> x
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 Natural Numbers
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[double](X) = 2.X + 2
0.00/0.18	[plus](X1,X2) = X1 + X2
0.00/0.18	[0] = 0
0.00/0.18	[s](X) = X + 2
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Reduction Order Processor:
0.00/0.18	-> Rules:
0.00/0.18	 plus(x,0) -> x
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 Natural Numbers
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[double](X) = 2.X
0.00/0.18	[plus](X1,X2) = X1 + X2 + 2
0.00/0.18	[0] = 2
0.00/0.18	[s](X) = X + 1
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Dependency Pairs Processor:
0.00/0.18	-> FAxioms:
0.00/0.18	 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) = PLUS(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(x,y)
0.00/0.18	 PLUS(x,s(y)) -> PLUS(x,y)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(plus(x2,x3),x4) -> PLUS(x2,x3)
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> FAxioms:
0.00/0.18	 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) = PLUS(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(x,y)
0.00/0.18	 PLUS(x,s(y)) -> PLUS(x,y)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(plus(x2,x3),x4) -> PLUS(x2,x3)
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(x,y)
0.00/0.18	 PLUS(x,s(y)) -> PLUS(x,y)
0.00/0.18	-> FAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) -> plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) -> plus(x3,x2)
0.00/0.18	 PLUS(plus(x2,x3),x4) -> PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) -> PLUS(x3,x2)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	->->-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(plus(x2,x3),x4) -> PLUS(x2,x3)
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Reduction Pairs Processor:
0.00/0.18	-> FAxioms:
0.00/0.18	 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) = PLUS(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(x,y)
0.00/0.18	 PLUS(x,s(y)) -> PLUS(x,y)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Usable Equations:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> Usable Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(plus(x2,x3),x4) -> PLUS(x2,x3)
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 Natural Numbers
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[double](X) = 0
0.00/0.18	[plus](X1,X2) = X1 + X2 + 2
0.00/0.18	[0] = 0
0.00/0.18	[s](X) = X
0.00/0.18	[PLUS](X1,X2) = 2.X1 + 2.X2
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> FAxioms:
0.00/0.18	 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) = PLUS(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	 PLUS(x,s(y)) -> PLUS(x,y)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(plus(x2,x3),x4) -> PLUS(x2,x3)
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	 PLUS(x,s(y)) -> PLUS(x,y)
0.00/0.18	-> FAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) -> plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) -> plus(x3,x2)
0.00/0.18	 PLUS(plus(x2,x3),x4) -> PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) -> PLUS(x3,x2)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	->->-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(plus(x2,x3),x4) -> PLUS(x2,x3)
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Reduction Pairs Processor:
0.00/0.18	-> FAxioms:
0.00/0.18	 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) = PLUS(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	 PLUS(x,s(y)) -> PLUS(x,y)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Usable Equations:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> Usable Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(plus(x2,x3),x4) -> PLUS(x2,x3)
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 Natural Numbers
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[double](X) = 0
0.00/0.18	[plus](X1,X2) = X1 + X2 + 2
0.00/0.18	[0] = 0
0.00/0.18	[s](X) = X + 1
0.00/0.18	[PLUS](X1,X2) = 2.X1 + 2.X2
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> FAxioms:
0.00/0.18	 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) = PLUS(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	 PLUS(x,s(y)) -> PLUS(x,y)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	 PLUS(x,s(y)) -> PLUS(x,y)
0.00/0.18	-> FAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) -> plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) -> plus(x3,x2)
0.00/0.18	 PLUS(plus(x2,x3),x4) -> PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) -> PLUS(x3,x2)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	->->-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Reduction Pairs Processor:
0.00/0.18	-> FAxioms:
0.00/0.18	 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) = PLUS(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	 PLUS(x,s(y)) -> PLUS(x,y)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Usable Equations:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> Usable Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 Natural Numbers
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[double](X) = 0
0.00/0.18	[plus](X1,X2) = X1 + X2 + 1
0.00/0.18	[0] = 0
0.00/0.18	[s](X) = X + 2
0.00/0.18	[PLUS](X1,X2) = 2.X1 + 2.X2
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> FAxioms:
0.00/0.18	 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) = PLUS(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	-> FAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) -> plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) -> plus(x3,x2)
0.00/0.18	 PLUS(plus(x2,x3),x4) -> PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) -> PLUS(x3,x2)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	->->-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Reduction Pairs Processor:
0.00/0.18	-> FAxioms:
0.00/0.18	 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) = PLUS(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 PLUS(plus(x,s(y)),x2) -> PLUS(s(plus(x,y)),x2)
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Usable Equations:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> Usable Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 Natural Numbers
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[double](X) = 0
0.00/0.18	[plus](X1,X2) = X1 + X2 + 1
0.00/0.18	[0] = 0
0.00/0.18	[s](X) = 0
0.00/0.18	[PLUS](X1,X2) = 2.X1 + 2.X2
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> FAxioms:
0.00/0.18	 PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4))
0.00/0.18	 PLUS(x2,x3) = PLUS(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 Empty
0.00/0.18	-> EAxioms:
0.00/0.18	 plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4))
0.00/0.18	 plus(x2,x3) = plus(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 plus(x,s(y)) -> s(plus(x,y))
0.00/0.18	-> SRules:
0.00/0.18	 PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4)
0.00/0.18	->Strongly Connected Components:
0.00/0.18	 There is no strongly connected component
0.00/0.18	
0.00/0.18	The problem is finite.
0.00/0.18	EOF