0.00/0.40	YES
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	(THEORY 
0.00/0.40	(AC ac1 ac2))
0.00/0.40	(RULES
0.00/0.40	ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	)
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	Dependency Pairs Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC1(ac1(b,f(ac2(a,c))),x0)
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC2(a,c)
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	SCC Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC1(ac1(b,f(ac2(a,c))),x0)
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC2(a,c)
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Strongly Connected Components:
0.00/0.40	->->Cycle:
0.00/0.40	->->-> Pairs:
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC1(ac1(b,f(ac2(a,c))),x0)
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC2(a,c)
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> FAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) -> ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) -> ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) -> ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) -> ac2(x1,x0)
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) -> AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) -> AC2(x1,x0)
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	->->-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	Reduction Pairs Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC1(ac1(b,f(ac2(a,c))),x0)
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC2(a,c)
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Usable Equations:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> Usable Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Interpretation type:
0.00/0.40	 Linear
0.00/0.40	->Coefficients:
0.00/0.40	 Natural Numbers
0.00/0.40	->Dimension:
0.00/0.40	 1
0.00/0.40	->Bound:
0.00/0.40	 2
0.00/0.40	->Interpretation:
0.00/0.40	 
0.00/0.40	[ac1](X1,X2) = X1 + X2 + 1
0.00/0.40	[ac2](X1,X2) = X1 + X2 + 2
0.00/0.40	[a] = 0
0.00/0.40	[b] = 2
0.00/0.40	[c] = 2
0.00/0.40	[f](X) = 2
0.00/0.40	[AC1](X1,X2) = X1 + X2 + 1
0.00/0.40	[AC2](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	SCC Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC2(a,c)
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Strongly Connected Components:
0.00/0.40	->->Cycle:
0.00/0.40	->->-> Pairs:
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC2(a,c)
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> FAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) -> ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) -> ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) -> ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) -> ac2(x1,x0)
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) -> AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) -> AC2(x1,x0)
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	->->-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	Reduction Pairs Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC2(a,c)
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Usable Equations:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> Usable Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Interpretation type:
0.00/0.40	 Linear
0.00/0.40	->Coefficients:
0.00/0.40	 Natural Numbers
0.00/0.40	->Dimension:
0.00/0.40	 1
0.00/0.40	->Bound:
0.00/0.40	 2
0.00/0.40	->Interpretation:
0.00/0.40	 
0.00/0.40	[ac1](X1,X2) = X1 + X2 + 2
0.00/0.40	[ac2](X1,X2) = X1 + X2 + 2
0.00/0.40	[a] = 2
0.00/0.40	[b] = 2
0.00/0.40	[c] = 1
0.00/0.40	[f](X) = 2
0.00/0.40	[AC1](X1,X2) = X1 + X2 + 2
0.00/0.40	[AC2](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	SCC Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC2(a,c)
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Strongly Connected Components:
0.00/0.40	->->Cycle:
0.00/0.40	->->-> Pairs:
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC2(a,c)
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> FAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) -> ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) -> ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) -> ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) -> ac2(x1,x0)
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) -> AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) -> AC2(x1,x0)
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	->->-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	Reduction Pairs Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(ac1(a,ac2(b,c)),x0) -> AC2(a,c)
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Usable Equations:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> Usable Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Interpretation type:
0.00/0.40	 Linear
0.00/0.40	->Coefficients:
0.00/0.40	 Natural Numbers
0.00/0.40	->Dimension:
0.00/0.40	 1
0.00/0.40	->Bound:
0.00/0.40	 2
0.00/0.40	->Interpretation:
0.00/0.40	 
0.00/0.40	[ac1](X1,X2) = X1 + X2 + 2
0.00/0.40	[ac2](X1,X2) = X1 + X2 + 2
0.00/0.40	[a] = 0
0.00/0.40	[b] = 2
0.00/0.40	[c] = 0
0.00/0.40	[f](X) = 2
0.00/0.40	[AC1](X1,X2) = 1
0.00/0.40	[AC2](X1,X2) = 2.X1 + 2.X2
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	SCC Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Strongly Connected Components:
0.00/0.40	->->Cycle:
0.00/0.40	->->-> Pairs:
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> FAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) -> ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) -> ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) -> ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) -> ac2(x1,x0)
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) -> AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) -> AC2(x1,x0)
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	->->-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	Reduction Pairs Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Usable Equations:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> Usable Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,x1)
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Interpretation type:
0.00/0.40	 Linear
0.00/0.40	->Coefficients:
0.00/0.40	 Natural Numbers
0.00/0.40	->Dimension:
0.00/0.40	 1
0.00/0.40	->Bound:
0.00/0.40	 2
0.00/0.40	->Interpretation:
0.00/0.40	 
0.00/0.40	[ac1](X1,X2) = X1 + X2 + 2
0.00/0.40	[ac2](X1,X2) = X1 + X2
0.00/0.40	[a] = 2
0.00/0.40	[b] = 2
0.00/0.40	[c] = 0
0.00/0.40	[f](X) = 1
0.00/0.40	[AC1](X1,X2) = 2.X1 + 2.X2 + 1
0.00/0.40	[AC2](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	SCC Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Strongly Connected Components:
0.00/0.40	->->Cycle:
0.00/0.40	->->-> Pairs:
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> FAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) -> ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) -> ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) -> ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) -> ac2(x1,x0)
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) -> AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) -> AC2(x1,x0)
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	->->-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	Reduction Pairs Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(a,ac2(b,c)) -> AC1(b,f(ac2(a,c)))
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Usable Equations:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> Usable Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Interpretation type:
0.00/0.40	 Linear
0.00/0.40	->Coefficients:
0.00/0.40	 Natural Numbers
0.00/0.40	->Dimension:
0.00/0.40	 1
0.00/0.40	->Bound:
0.00/0.40	 2
0.00/0.40	->Interpretation:
0.00/0.40	 
0.00/0.40	[ac1](X1,X2) = X1 + X2
0.00/0.40	[ac2](X1,X2) = X1 + X2 + 1
0.00/0.40	[a] = 2
0.00/0.40	[b] = 2
0.00/0.40	[c] = 2
0.00/0.40	[f](X) = 2
0.00/0.40	[AC1](X1,X2) = 2.X1 + 2.X2 + 1
0.00/0.40	[AC2](X1,X2) = 2.X1 + 2.X2 + 1
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	SCC Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Strongly Connected Components:
0.00/0.40	->->Cycle:
0.00/0.40	->->-> Pairs:
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> FAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) -> ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) -> ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) -> ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) -> ac2(x1,x0)
0.00/0.40	 AC1(ac1(x0,x1),x2) -> AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) -> AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) -> AC2(x1,x0)
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	->->-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	Reduction Pairs Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC1(a,ac2(b,c)) -> AC2(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Usable Equations:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> Usable Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Interpretation type:
0.00/0.40	 Linear
0.00/0.40	->Coefficients:
0.00/0.40	 Natural Numbers
0.00/0.40	->Dimension:
0.00/0.40	 1
0.00/0.40	->Bound:
0.00/0.40	 2
0.00/0.40	->Interpretation:
0.00/0.40	 
0.00/0.40	[ac1](X1,X2) = X1 + X2 + 2
0.00/0.40	[ac2](X1,X2) = X1 + X2 + 1
0.00/0.40	[a] = 2
0.00/0.40	[b] = 2
0.00/0.40	[c] = 1
0.00/0.40	[f](X) = 2
0.00/0.40	[AC1](X1,X2) = 2.X1 + 2.X2 + 1
0.00/0.40	[AC2](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	SCC Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC1(ac1(x0,x1),x2) = AC1(x0,ac1(x1,x2))
0.00/0.40	 AC1(x0,x1) = AC1(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC1(a,c)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC1(a,c)
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC1(x0,ac1(x1,x2)) -> AC1(x1,x2)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Strongly Connected Components:
0.00/0.40	->->Cycle:
0.00/0.40	->->-> Pairs:
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> FAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) -> ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) -> ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) -> ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) -> ac2(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) -> AC2(x1,x0)
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	->->-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	Reduction Pairs Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(ac2(b,f(ac1(a,c))),x0)
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Usable Equations:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> Usable Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Interpretation type:
0.00/0.40	 Linear
0.00/0.40	->Coefficients:
0.00/0.40	 Natural Numbers
0.00/0.40	->Dimension:
0.00/0.40	 1
0.00/0.40	->Bound:
0.00/0.40	 2
0.00/0.40	->Interpretation:
0.00/0.40	 
0.00/0.40	[ac1](X1,X2) = 0
0.00/0.40	[ac2](X1,X2) = X1 + X2 + 1
0.00/0.40	[a] = 2
0.00/0.40	[b] = 0
0.00/0.40	[c] = 0
0.00/0.40	[f](X) = 0
0.00/0.40	[AC1](X1,X2) = 0
0.00/0.40	[AC2](X1,X2) = 2.X1 + 2.X2
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	SCC Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Strongly Connected Components:
0.00/0.40	->->Cycle:
0.00/0.40	->->-> Pairs:
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> FAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) -> ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) -> ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) -> ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) -> ac2(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) -> AC2(x1,x0)
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	->->-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	Reduction Pairs Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC2(ac2(a,ac1(b,c)),x0) -> AC2(b,f(ac1(a,c)))
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Usable Equations:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> Usable Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Interpretation type:
0.00/0.40	 Linear
0.00/0.40	->Coefficients:
0.00/0.40	 Natural Numbers
0.00/0.40	->Dimension:
0.00/0.40	 1
0.00/0.40	->Bound:
0.00/0.40	 2
0.00/0.40	->Interpretation:
0.00/0.40	 
0.00/0.40	[ac1](X1,X2) = X1 + X2 + 2
0.00/0.40	[ac2](X1,X2) = X1 + X2 + 1
0.00/0.40	[a] = 0
0.00/0.40	[b] = 1
0.00/0.40	[c] = 2
0.00/0.40	[f](X) = 2
0.00/0.40	[AC1](X1,X2) = 0
0.00/0.40	[AC2](X1,X2) = 2.X1 + 2.X2
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	SCC Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Strongly Connected Components:
0.00/0.40	->->Cycle:
0.00/0.40	->->-> Pairs:
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> FAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) -> ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) -> ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) -> ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) -> ac2(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) -> AC2(x1,x0)
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	->->-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	Reduction Pairs Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Usable Equations:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> Usable Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,x1)
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Interpretation type:
0.00/0.40	 Linear
0.00/0.40	->Coefficients:
0.00/0.40	 Natural Numbers
0.00/0.40	->Dimension:
0.00/0.40	 1
0.00/0.40	->Bound:
0.00/0.40	 2
0.00/0.40	->Interpretation:
0.00/0.40	 
0.00/0.40	[ac1](X1,X2) = 1
0.00/0.40	[ac2](X1,X2) = X1 + X2 + 2
0.00/0.40	[a] = 1
0.00/0.40	[b] = 0
0.00/0.40	[c] = 0
0.00/0.40	[f](X) = 2.X
0.00/0.40	[AC1](X1,X2) = 0
0.00/0.40	[AC2](X1,X2) = 2.X1 + 2.X2
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	SCC Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Strongly Connected Components:
0.00/0.40	->->Cycle:
0.00/0.40	->->-> Pairs:
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> FAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) -> ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) -> ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) -> ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) -> ac2(x1,x0)
0.00/0.40	 AC2(ac2(x0,x1),x2) -> AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) -> AC2(x1,x0)
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	->->-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	Reduction Pairs Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 AC2(a,ac1(b,c)) -> AC2(b,f(ac1(a,c)))
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Usable Equations:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> Usable Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Interpretation type:
0.00/0.40	 Linear
0.00/0.40	->Coefficients:
0.00/0.40	 Natural Numbers
0.00/0.40	->Dimension:
0.00/0.40	 1
0.00/0.40	->Bound:
0.00/0.40	 2
0.00/0.40	->Interpretation:
0.00/0.40	 
0.00/0.40	[ac1](X1,X2) = 0
0.00/0.40	[ac2](X1,X2) = X1 + X2 + 1
0.00/0.40	[a] = 2
0.00/0.40	[b] = 0
0.00/0.40	[c] = 0
0.00/0.40	[f](X) = 2.X + 1
0.00/0.40	[AC1](X1,X2) = 0
0.00/0.40	[AC2](X1,X2) = 2.X1 + 2.X2
0.00/0.40	
0.00/0.40	Problem 1: 
0.00/0.40	
0.00/0.40	SCC Processor:
0.00/0.40	-> FAxioms:
0.00/0.40	 AC2(ac2(x0,x1),x2) = AC2(x0,ac2(x1,x2))
0.00/0.40	 AC2(x0,x1) = AC2(x1,x0)
0.00/0.40	-> Pairs:
0.00/0.40	 Empty
0.00/0.40	-> EAxioms:
0.00/0.40	 ac1(ac1(x0,x1),x2) = ac1(x0,ac1(x1,x2))
0.00/0.40	 ac1(x0,x1) = ac1(x1,x0)
0.00/0.40	 ac2(ac2(x0,x1),x2) = ac2(x0,ac2(x1,x2))
0.00/0.40	 ac2(x0,x1) = ac2(x1,x0)
0.00/0.40	-> Rules:
0.00/0.40	 ac1(a,ac2(b,c)) -> ac1(b,f(ac2(a,c)))
0.00/0.40	 ac2(a,ac1(b,c)) -> ac2(b,f(ac1(a,c)))
0.00/0.40	-> SRules:
0.00/0.40	 AC2(x0,ac2(x1,x2)) -> AC2(x1,x2)
0.00/0.40	->Strongly Connected Components:
0.00/0.40	 There is no strongly connected component
0.00/0.40	
0.00/0.40	The problem is finite.
0.00/0.40	EOF