0.00/0.16	YES
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	(THEORY 
0.00/0.16	(AC f))
0.00/0.16	(RULES
0.00/0.16	f(g(f(h(a),a)),a) -> f(h(a),f(a,a))
0.00/0.16	f(g(h(a)),f(b,f(b,b))) -> f(g(f(h(a),a)),a)
0.00/0.16	f(h(a),a) -> f(h(a),b)
0.00/0.16	f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	)
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	Reduction Order Processor:
0.00/0.16	-> Rules:
0.00/0.16	 f(g(f(h(a),a)),a) -> f(h(a),f(a,a))
0.00/0.16	 f(g(h(a)),f(b,f(b,b))) -> f(g(f(h(a),a)),a)
0.00/0.16	 f(h(a),a) -> f(h(a),b)
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	->Interpretation type:
0.00/0.16	 Linear
0.00/0.16	->Coefficients:
0.00/0.16	 Natural Numbers
0.00/0.16	->Dimension:
0.00/0.16	 1
0.00/0.16	->Bound:
0.00/0.16	 2
0.00/0.16	->Interpretation:
0.00/0.16	 
0.00/0.16	[f](X1,X2) = X1 + X2 + 2
0.00/0.16	[a] = 2
0.00/0.16	[b] = 2
0.00/0.16	[g](X) = X + 2
0.00/0.16	[h](X) = 2.X + 2
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	Reduction Order Processor:
0.00/0.16	-> Rules:
0.00/0.16	 f(g(h(a)),f(b,f(b,b))) -> f(g(f(h(a),a)),a)
0.00/0.16	 f(h(a),a) -> f(h(a),b)
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	->Interpretation type:
0.00/0.16	 Linear
0.00/0.16	->Coefficients:
0.00/0.16	 Natural Numbers
0.00/0.16	->Dimension:
0.00/0.16	 1
0.00/0.16	->Bound:
0.00/0.16	 2
0.00/0.16	->Interpretation:
0.00/0.16	 
0.00/0.16	[f](X1,X2) = X1 + X2 + 2
0.00/0.16	[a] = 1
0.00/0.16	[b] = 1
0.00/0.16	[g](X) = X + 2
0.00/0.16	[h](X) = 2.X + 2
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	Reduction Order Processor:
0.00/0.16	-> Rules:
0.00/0.16	 f(h(a),a) -> f(h(a),b)
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	->Interpretation type:
0.00/0.16	 Linear
0.00/0.16	->Coefficients:
0.00/0.16	 Natural Numbers
0.00/0.16	->Dimension:
0.00/0.16	 1
0.00/0.16	->Bound:
0.00/0.16	 2
0.00/0.16	->Interpretation:
0.00/0.16	 
0.00/0.16	[f](X1,X2) = X1 + X2 + 2
0.00/0.16	[a] = 1
0.00/0.16	[b] = 0
0.00/0.16	[g](X) = 2.X + 2
0.00/0.16	[h](X) = X
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	Dependency Pairs Processor:
0.00/0.16	-> FAxioms:
0.00/0.16	 F(f(x0,x1),x2) = F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) = F(x1,x0)
0.00/0.16	-> Pairs:
0.00/0.16	 F(f(h(a),g(a)),x0) -> F(f(g(h(a)),a),x0)
0.00/0.16	 F(f(h(a),g(a)),x0) -> F(g(h(a)),a)
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,x1)
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	SCC Processor:
0.00/0.16	-> FAxioms:
0.00/0.16	 F(f(x0,x1),x2) = F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) = F(x1,x0)
0.00/0.16	-> Pairs:
0.00/0.16	 F(f(h(a),g(a)),x0) -> F(f(g(h(a)),a),x0)
0.00/0.16	 F(f(h(a),g(a)),x0) -> F(g(h(a)),a)
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,x1)
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	->Strongly Connected Components:
0.00/0.16	->->Cycle:
0.00/0.16	->->-> Pairs:
0.00/0.16	 F(f(h(a),g(a)),x0) -> F(f(g(h(a)),a),x0)
0.00/0.16	 F(f(h(a),g(a)),x0) -> F(g(h(a)),a)
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> FAxioms:
0.00/0.16	 f(f(x0,x1),x2) -> f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) -> f(x1,x0)
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) -> F(x1,x0)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	->->-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,x1)
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	Reduction Pairs Processor:
0.00/0.16	-> FAxioms:
0.00/0.16	 F(f(x0,x1),x2) = F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) = F(x1,x0)
0.00/0.16	-> Pairs:
0.00/0.16	 F(f(h(a),g(a)),x0) -> F(f(g(h(a)),a),x0)
0.00/0.16	 F(f(h(a),g(a)),x0) -> F(g(h(a)),a)
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Usable Equations:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> Usable Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,x1)
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	->Interpretation type:
0.00/0.16	 Linear
0.00/0.16	->Coefficients:
0.00/0.16	 Natural Numbers
0.00/0.16	->Dimension:
0.00/0.16	 1
0.00/0.16	->Bound:
0.00/0.16	 2
0.00/0.16	->Interpretation:
0.00/0.16	 
0.00/0.16	[f](X1,X2) = X1 + X2
0.00/0.16	[a] = 2
0.00/0.16	[b] = 0
0.00/0.16	[g](X) = 2.X + 1
0.00/0.16	[h](X) = 1
0.00/0.16	[F](X1,X2) = 2.X1 + 2.X2
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	SCC Processor:
0.00/0.16	-> FAxioms:
0.00/0.16	 F(f(x0,x1),x2) = F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) = F(x1,x0)
0.00/0.16	-> Pairs:
0.00/0.16	 F(f(h(a),g(a)),x0) -> F(g(h(a)),a)
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,x1)
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	->Strongly Connected Components:
0.00/0.16	->->Cycle:
0.00/0.16	->->-> Pairs:
0.00/0.16	 F(f(h(a),g(a)),x0) -> F(g(h(a)),a)
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> FAxioms:
0.00/0.16	 f(f(x0,x1),x2) -> f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) -> f(x1,x0)
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) -> F(x1,x0)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	->->-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,x1)
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	Reduction Pairs Processor:
0.00/0.16	-> FAxioms:
0.00/0.16	 F(f(x0,x1),x2) = F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) = F(x1,x0)
0.00/0.16	-> Pairs:
0.00/0.16	 F(f(h(a),g(a)),x0) -> F(g(h(a)),a)
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Usable Equations:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> Usable Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,x1)
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	->Interpretation type:
0.00/0.16	 Linear
0.00/0.16	->Coefficients:
0.00/0.16	 Natural Numbers
0.00/0.16	->Dimension:
0.00/0.16	 1
0.00/0.16	->Bound:
0.00/0.16	 2
0.00/0.16	->Interpretation:
0.00/0.16	 
0.00/0.16	[f](X1,X2) = X1 + X2 + 2
0.00/0.16	[a] = 1
0.00/0.16	[b] = 0
0.00/0.16	[g](X) = X
0.00/0.16	[h](X) = X + 1
0.00/0.16	[F](X1,X2) = 2.X1 + 2.X2
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	SCC Processor:
0.00/0.16	-> FAxioms:
0.00/0.16	 F(f(x0,x1),x2) = F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) = F(x1,x0)
0.00/0.16	-> Pairs:
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,x1)
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	->Strongly Connected Components:
0.00/0.16	->->Cycle:
0.00/0.16	->->-> Pairs:
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> FAxioms:
0.00/0.16	 f(f(x0,x1),x2) -> f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) -> f(x1,x0)
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) -> F(x1,x0)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	->->-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,x1)
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	Reduction Pairs Processor:
0.00/0.16	-> FAxioms:
0.00/0.16	 F(f(x0,x1),x2) = F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) = F(x1,x0)
0.00/0.16	-> Pairs:
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Usable Equations:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> Usable Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,x1)
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	->Interpretation type:
0.00/0.16	 Linear
0.00/0.16	->Coefficients:
0.00/0.16	 Natural Numbers
0.00/0.16	->Dimension:
0.00/0.16	 1
0.00/0.16	->Bound:
0.00/0.16	 2
0.00/0.16	->Interpretation:
0.00/0.16	 
0.00/0.16	[f](X1,X2) = X1 + X2 + 1
0.00/0.16	[a] = 1
0.00/0.16	[b] = 0
0.00/0.16	[g](X) = X + 2
0.00/0.16	[h](X) = X + 1
0.00/0.16	[F](X1,X2) = X1 + X2
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	SCC Processor:
0.00/0.16	-> FAxioms:
0.00/0.16	 F(f(x0,x1),x2) = F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) = F(x1,x0)
0.00/0.16	-> Pairs:
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	->Strongly Connected Components:
0.00/0.16	->->Cycle:
0.00/0.16	->->-> Pairs:
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> FAxioms:
0.00/0.16	 f(f(x0,x1),x2) -> f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) -> f(x1,x0)
0.00/0.16	 F(f(x0,x1),x2) -> F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) -> F(x1,x0)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	->->-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	Reduction Pairs Processor:
0.00/0.16	-> FAxioms:
0.00/0.16	 F(f(x0,x1),x2) = F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) = F(x1,x0)
0.00/0.16	-> Pairs:
0.00/0.16	 F(h(a),g(a)) -> F(g(h(a)),a)
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Usable Equations:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> Usable Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	->Interpretation type:
0.00/0.16	 Linear
0.00/0.16	->Coefficients:
0.00/0.16	 Natural Numbers
0.00/0.16	->Dimension:
0.00/0.16	 1
0.00/0.16	->Bound:
0.00/0.16	 2
0.00/0.16	->Interpretation:
0.00/0.16	 
0.00/0.16	[f](X1,X2) = X1 + X2
0.00/0.16	[a] = 2
0.00/0.16	[b] = 0
0.00/0.16	[g](X) = 2.X
0.00/0.16	[h](X) = 1
0.00/0.16	[F](X1,X2) = 2.X1 + 2.X2
0.00/0.16	
0.00/0.16	Problem 1: 
0.00/0.16	
0.00/0.16	SCC Processor:
0.00/0.16	-> FAxioms:
0.00/0.16	 F(f(x0,x1),x2) = F(x0,f(x1,x2))
0.00/0.16	 F(x0,x1) = F(x1,x0)
0.00/0.16	-> Pairs:
0.00/0.16	 Empty
0.00/0.16	-> EAxioms:
0.00/0.16	 f(f(x0,x1),x2) = f(x0,f(x1,x2))
0.00/0.16	 f(x0,x1) = f(x1,x0)
0.00/0.16	-> Rules:
0.00/0.16	 f(h(a),g(a)) -> f(g(h(a)),a)
0.00/0.16	-> SRules:
0.00/0.16	 F(x0,f(x1,x2)) -> F(x1,x2)
0.00/0.16	->Strongly Connected Components:
0.00/0.16	 There is no strongly connected component
0.00/0.16	
0.00/0.16	The problem is finite.
0.00/0.17	EOF