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 f))
0.00/0.18	(RULES
0.00/0.18	f(g(f(h(x),x)),x) -> f(h(x),f(x,x))
0.00/0.18	f(g(g(x)),x) -> f(g(x),g(x))
0.00/0.18	f(g(h(x)),f(x,f(x,y))) -> f(g(f(h(x),y)),x)
0.00/0.18	f(h(x),g(x)) -> f(g(h(x)),x)
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	 f(g(f(h(x),x)),x) -> f(h(x),f(x,x))
0.00/0.18	 f(g(g(x)),x) -> f(g(x),g(x))
0.00/0.18	 f(g(h(x)),f(x,f(x,y))) -> f(g(f(h(x),y)),x)
0.00/0.18	 f(h(x),g(x)) -> f(g(h(x)),x)
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	[f](X1,X2) = X1 + X2 + 2
0.00/0.18	[g](X) = X + 1
0.00/0.18	[h](X) = 2.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	 f(g(g(x)),x) -> f(g(x),g(x))
0.00/0.18	 f(g(h(x)),f(x,f(x,y))) -> f(g(f(h(x),y)),x)
0.00/0.18	 f(h(x),g(x)) -> f(g(h(x)),x)
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	[f](X1,X2) = X1 + X2 + 1
0.00/0.18	[g](X) = X + 1
0.00/0.18	[h](X) = 2.X
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	 f(g(g(x)),x) -> f(g(x),g(x))
0.00/0.18	 f(h(x),g(x)) -> f(g(h(x)),x)
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	[f](X1,X2) = X1 + X2 + 1
0.00/0.18	[g](X) = 2.X + 2
0.00/0.18	[h](X) = X
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	 F(f(x2,x3),x4) = F(x2,f(x3,x4))
0.00/0.18	 F(x2,x3) = F(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 F(f(h(x),g(x)),x2) -> F(f(g(h(x)),x),x2)
0.00/0.18	 F(f(h(x),g(x)),x2) -> F(g(h(x)),x)
0.00/0.18	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.18	-> EAxioms:
0.00/0.18	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.18	 f(x2,x3) = f(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.18	-> SRules:
0.00/0.18	 F(f(x2,x3),x4) -> F(x2,x3)
0.00/0.18	 F(x2,f(x3,x4)) -> F(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	 F(f(x2,x3),x4) = F(x2,f(x3,x4))
0.00/0.18	 F(x2,x3) = F(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 F(f(h(x),g(x)),x2) -> F(f(g(h(x)),x),x2)
0.00/0.18	 F(f(h(x),g(x)),x2) -> F(g(h(x)),x)
0.00/0.18	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.18	-> EAxioms:
0.00/0.18	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.18	 f(x2,x3) = f(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.18	-> SRules:
0.00/0.18	 F(f(x2,x3),x4) -> F(x2,x3)
0.00/0.18	 F(x2,f(x3,x4)) -> F(x3,x4)
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 F(f(h(x),g(x)),x2) -> F(f(g(h(x)),x),x2)
0.00/0.18	 F(f(h(x),g(x)),x2) -> F(g(h(x)),x)
0.00/0.18	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.18	-> FAxioms:
0.00/0.18	 f(f(x2,x3),x4) -> f(x2,f(x3,x4))
0.00/0.18	 f(x2,x3) -> f(x3,x2)
0.00/0.18	 F(f(x2,x3),x4) -> F(x2,f(x3,x4))
0.00/0.18	 F(x2,x3) -> F(x3,x2)
0.00/0.18	-> EAxioms:
0.00/0.18	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.18	 f(x2,x3) = f(x3,x2)
0.00/0.18	->->-> Rules:
0.00/0.18	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.18	-> SRules:
0.00/0.18	 F(f(x2,x3),x4) -> F(x2,x3)
0.00/0.18	 F(x2,f(x3,x4)) -> F(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	 F(f(x2,x3),x4) = F(x2,f(x3,x4))
0.00/0.18	 F(x2,x3) = F(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 F(f(h(x),g(x)),x2) -> F(f(g(h(x)),x),x2)
0.00/0.18	 F(f(h(x),g(x)),x2) -> F(g(h(x)),x)
0.00/0.18	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.18	-> EAxioms:
0.00/0.18	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.18	 f(x2,x3) = f(x3,x2)
0.00/0.18	-> Usable Equations:
0.00/0.18	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.18	 f(x2,x3) = f(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.18	-> Usable Rules:
0.00/0.18	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.18	-> SRules:
0.00/0.18	 F(f(x2,x3),x4) -> F(x2,x3)
0.00/0.18	 F(x2,f(x3,x4)) -> F(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	[f](X1,X2) = X1 + X2
0.00/0.18	[g](X) = 0
0.00/0.18	[h](X) = 2.X + 1
0.00/0.18	[F](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	 F(f(x2,x3),x4) = F(x2,f(x3,x4))
0.00/0.18	 F(x2,x3) = F(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 F(f(h(x),g(x)),x2) -> F(g(h(x)),x)
0.00/0.18	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.18	-> EAxioms:
0.00/0.18	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.18	 f(x2,x3) = f(x3,x2)
0.00/0.18	-> Rules:
0.00/0.18	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.18	-> SRules:
0.00/0.18	 F(f(x2,x3),x4) -> F(x2,x3)
0.00/0.18	 F(x2,f(x3,x4)) -> F(x3,x4)
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 F(f(h(x),g(x)),x2) -> F(g(h(x)),x)
0.00/0.18	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.18	-> FAxioms:
0.00/0.18	 f(f(x2,x3),x4) -> f(x2,f(x3,x4))
0.00/0.18	 f(x2,x3) -> f(x3,x2)
0.00/0.18	 F(f(x2,x3),x4) -> F(x2,f(x3,x4))
0.00/0.18	 F(x2,x3) -> F(x3,x2)
0.00/0.18	-> EAxioms:
0.00/0.18	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.18	 f(x2,x3) = f(x3,x2)
0.00/0.18	->->-> Rules:
0.00/0.18	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.18	-> SRules:
0.00/0.18	 F(f(x2,x3),x4) -> F(x2,x3)
0.00/0.18	 F(x2,f(x3,x4)) -> F(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	 F(f(x2,x3),x4) = F(x2,f(x3,x4))
0.00/0.18	 F(x2,x3) = F(x3,x2)
0.00/0.18	-> Pairs:
0.00/0.18	 F(f(h(x),g(x)),x2) -> F(g(h(x)),x)
0.00/0.18	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.18	-> EAxioms:
0.00/0.18	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) = f(x3,x2)
0.00/0.19	-> Usable Equations:
0.00/0.19	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) = f(x3,x2)
0.00/0.19	-> Rules:
0.00/0.19	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.19	-> Usable Rules:
0.00/0.19	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.19	-> SRules:
0.00/0.19	 F(f(x2,x3),x4) -> F(x2,x3)
0.00/0.19	 F(x2,f(x3,x4)) -> F(x3,x4)
0.00/0.19	->Interpretation type:
0.00/0.19	 Linear
0.00/0.19	->Coefficients:
0.00/0.19	 Natural Numbers
0.00/0.19	->Dimension:
0.00/0.19	 1
0.00/0.19	->Bound:
0.00/0.19	 2
0.00/0.19	->Interpretation:
0.00/0.19	 
0.00/0.19	[f](X1,X2) = X1 + X2 + 1
0.00/0.19	[g](X) = 2.X + 1
0.00/0.19	[h](X) = 0
0.00/0.19	[F](X1,X2) = 2.X1 + 2.X2
0.00/0.19	
0.00/0.19	Problem 1: 
0.00/0.19	
0.00/0.19	SCC Processor:
0.00/0.19	-> FAxioms:
0.00/0.19	 F(f(x2,x3),x4) = F(x2,f(x3,x4))
0.00/0.19	 F(x2,x3) = F(x3,x2)
0.00/0.19	-> Pairs:
0.00/0.19	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.19	-> EAxioms:
0.00/0.19	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) = f(x3,x2)
0.00/0.19	-> Rules:
0.00/0.19	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.19	-> SRules:
0.00/0.19	 F(f(x2,x3),x4) -> F(x2,x3)
0.00/0.19	 F(x2,f(x3,x4)) -> F(x3,x4)
0.00/0.19	->Strongly Connected Components:
0.00/0.19	->->Cycle:
0.00/0.19	->->-> Pairs:
0.00/0.19	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.19	-> FAxioms:
0.00/0.19	 f(f(x2,x3),x4) -> f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) -> f(x3,x2)
0.00/0.19	 F(f(x2,x3),x4) -> F(x2,f(x3,x4))
0.00/0.19	 F(x2,x3) -> F(x3,x2)
0.00/0.19	-> EAxioms:
0.00/0.19	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) = f(x3,x2)
0.00/0.19	->->-> Rules:
0.00/0.19	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.19	-> SRules:
0.00/0.19	 F(f(x2,x3),x4) -> F(x2,x3)
0.00/0.19	 F(x2,f(x3,x4)) -> F(x3,x4)
0.00/0.19	
0.00/0.19	Problem 1: 
0.00/0.19	
0.00/0.19	Reduction Pairs Processor:
0.00/0.19	-> FAxioms:
0.00/0.19	 F(f(x2,x3),x4) = F(x2,f(x3,x4))
0.00/0.19	 F(x2,x3) = F(x3,x2)
0.00/0.19	-> Pairs:
0.00/0.19	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.19	-> EAxioms:
0.00/0.19	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) = f(x3,x2)
0.00/0.19	-> Usable Equations:
0.00/0.19	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) = f(x3,x2)
0.00/0.19	-> Rules:
0.00/0.19	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.19	-> Usable Rules:
0.00/0.19	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.19	-> SRules:
0.00/0.19	 F(f(x2,x3),x4) -> F(x2,x3)
0.00/0.19	 F(x2,f(x3,x4)) -> F(x3,x4)
0.00/0.19	->Interpretation type:
0.00/0.19	 Linear
0.00/0.19	->Coefficients:
0.00/0.19	 Natural Numbers
0.00/0.19	->Dimension:
0.00/0.19	 1
0.00/0.19	->Bound:
0.00/0.19	 2
0.00/0.19	->Interpretation:
0.00/0.19	 
0.00/0.19	[f](X1,X2) = X1 + X2 + 1
0.00/0.19	[g](X) = 2.X
0.00/0.19	[h](X) = X
0.00/0.19	[F](X1,X2) = 2.X1 + 2.X2
0.00/0.19	
0.00/0.19	Problem 1: 
0.00/0.19	
0.00/0.19	SCC Processor:
0.00/0.19	-> FAxioms:
0.00/0.19	 F(f(x2,x3),x4) = F(x2,f(x3,x4))
0.00/0.19	 F(x2,x3) = F(x3,x2)
0.00/0.19	-> Pairs:
0.00/0.19	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.19	-> EAxioms:
0.00/0.19	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) = f(x3,x2)
0.00/0.19	-> Rules:
0.00/0.19	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.19	-> SRules:
0.00/0.19	 F(x2,f(x3,x4)) -> F(x3,x4)
0.00/0.19	->Strongly Connected Components:
0.00/0.19	->->Cycle:
0.00/0.19	->->-> Pairs:
0.00/0.19	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.19	-> FAxioms:
0.00/0.19	 f(f(x2,x3),x4) -> f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) -> f(x3,x2)
0.00/0.19	 F(f(x2,x3),x4) -> F(x2,f(x3,x4))
0.00/0.19	 F(x2,x3) -> F(x3,x2)
0.00/0.19	-> EAxioms:
0.00/0.19	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) = f(x3,x2)
0.00/0.19	->->-> Rules:
0.00/0.19	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.19	-> SRules:
0.00/0.19	 F(x2,f(x3,x4)) -> F(x3,x4)
0.00/0.19	
0.00/0.19	Problem 1: 
0.00/0.19	
0.00/0.19	Reduction Pairs Processor:
0.00/0.19	-> FAxioms:
0.00/0.19	 F(f(x2,x3),x4) = F(x2,f(x3,x4))
0.00/0.19	 F(x2,x3) = F(x3,x2)
0.00/0.19	-> Pairs:
0.00/0.19	 F(h(x),g(x)) -> F(g(h(x)),x)
0.00/0.19	-> EAxioms:
0.00/0.19	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) = f(x3,x2)
0.00/0.19	-> Usable Equations:
0.00/0.19	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) = f(x3,x2)
0.00/0.19	-> Rules:
0.00/0.19	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.19	-> Usable Rules:
0.00/0.19	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.19	-> SRules:
0.00/0.19	 F(x2,f(x3,x4)) -> F(x3,x4)
0.00/0.19	->Interpretation type:
0.00/0.19	 Linear
0.00/0.19	->Coefficients:
0.00/0.19	 Natural Numbers
0.00/0.19	->Dimension:
0.00/0.19	 1
0.00/0.19	->Bound:
0.00/0.19	 2
0.00/0.19	->Interpretation:
0.00/0.19	 
0.00/0.19	[f](X1,X2) = X1 + X2
0.00/0.19	[g](X) = 2
0.00/0.19	[h](X) = 2.X + 2
0.00/0.19	[F](X1,X2) = 2.X1 + 2.X2
0.00/0.19	
0.00/0.19	Problem 1: 
0.00/0.19	
0.00/0.19	SCC Processor:
0.00/0.19	-> FAxioms:
0.00/0.19	 F(f(x2,x3),x4) = F(x2,f(x3,x4))
0.00/0.19	 F(x2,x3) = F(x3,x2)
0.00/0.19	-> Pairs:
0.00/0.19	 Empty
0.00/0.19	-> EAxioms:
0.00/0.19	 f(f(x2,x3),x4) = f(x2,f(x3,x4))
0.00/0.19	 f(x2,x3) = f(x3,x2)
0.00/0.19	-> Rules:
0.00/0.19	 f(h(x),g(x)) -> f(g(h(x)),x)
0.00/0.19	-> SRules:
0.00/0.19	 F(x2,f(x3,x4)) -> F(x3,x4)
0.00/0.19	->Strongly Connected Components:
0.00/0.19	 There is no strongly connected component
0.00/0.19	
0.00/0.19	The problem is finite.
0.00/0.19	EOF