30.38/30.47	YES
30.38/30.47	
30.38/30.47	Problem 1: 
30.38/30.47	
30.38/30.47	(VAR X Y Z x y)
30.38/30.47	(THEORY 
30.38/30.47	(AC union))
30.38/30.47	(RULES
30.38/30.47	max(union(singl(s(x)),singl(s(y)))) -> s(max(union(singl(x),singl(y))))
30.38/30.47	max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	max(union(singl(x),singl(0))) -> x
30.38/30.47	max(singl(x)) -> x
30.38/30.47	union(empty,X) -> X
30.38/30.47	)
30.38/30.47	
30.38/30.47	Problem 1: 
30.38/30.47	
30.38/30.47	Reduction Order Processor:
30.38/30.47	-> Rules:
30.38/30.47	 max(union(singl(s(x)),singl(s(y)))) -> s(max(union(singl(x),singl(y))))
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(union(singl(x),singl(0))) -> x
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	 union(empty,X) -> X
30.38/30.47	->Interpretation type:
30.38/30.47	 Linear
30.38/30.47	->Coefficients:
30.38/30.47	 Natural Numbers
30.38/30.47	->Dimension:
30.38/30.47	 1
30.38/30.47	->Bound:
30.38/30.47	 2
30.38/30.47	->Interpretation:
30.38/30.47	 
30.38/30.47	[max](X) = X
30.38/30.47	[union](X1,X2) = X1 + X2 + 1
30.38/30.47	[0] = 0
30.38/30.47	[empty] = 0
30.38/30.47	[s](X) = X + 1
30.38/30.47	[singl](X) = X
30.38/30.47	
30.38/30.47	Problem 1: 
30.38/30.47	
30.38/30.47	Reduction Order Processor:
30.38/30.47	-> Rules:
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(union(singl(x),singl(0))) -> x
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	 union(empty,X) -> X
30.38/30.47	->Interpretation type:
30.38/30.47	 Linear
30.38/30.47	->Coefficients:
30.38/30.47	 Natural Numbers
30.38/30.47	->Dimension:
30.38/30.47	 1
30.38/30.47	->Bound:
30.38/30.47	 2
30.38/30.47	->Interpretation:
30.38/30.47	 
30.38/30.47	[max](X) = X
30.38/30.47	[union](X1,X2) = X1 + X2
30.38/30.47	[0] = 2
30.38/30.47	[empty] = 0
30.38/30.47	[s](X) = 2.X
30.38/30.47	[singl](X) = X
30.38/30.47	
30.38/30.47	Problem 1: 
30.38/30.47	
30.38/30.47	Reduction Order Processor:
30.38/30.47	-> Rules:
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	 union(empty,X) -> X
30.38/30.47	->Interpretation type:
30.38/30.47	 Linear
30.38/30.47	->Coefficients:
30.38/30.47	 Natural Numbers
30.38/30.47	->Dimension:
30.38/30.47	 1
30.38/30.47	->Bound:
30.38/30.47	 2
30.38/30.47	->Interpretation:
30.38/30.47	 
30.38/30.47	[max](X) = X
30.38/30.47	[union](X1,X2) = X1 + X2 + 1
30.38/30.47	[0] = 0
30.38/30.47	[empty] = 2
30.38/30.47	[s](X) = 2.X
30.38/30.47	[singl](X) = X
30.38/30.47	
30.38/30.47	Problem 1: 
30.38/30.47	
30.38/30.47	Dependency Pairs Processor:
30.38/30.47	-> FAxioms:
30.38/30.47	 UNION(union(x5,x6),x7) = UNION(x5,union(x6,x7))
30.38/30.47	 UNION(x5,x6) = UNION(x6,x5)
30.38/30.47	-> Pairs:
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> MAX(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> MAX(union(Y,Z))
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> UNION(singl(x),singl(max(union(Y,Z))))
30.38/30.47	-> EAxioms:
30.38/30.47	 union(union(x5,x6),x7) = union(x5,union(x6,x7))
30.38/30.47	 union(x5,x6) = union(x6,x5)
30.38/30.47	-> Rules:
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	-> SRules:
30.38/30.47	 UNION(union(x5,x6),x7) -> UNION(x5,x6)
30.38/30.47	 UNION(x5,union(x6,x7)) -> UNION(x6,x7)
30.38/30.47	
30.38/30.47	Problem 1: 
30.38/30.47	
30.38/30.47	SCC Processor:
30.38/30.47	-> FAxioms:
30.38/30.47	 UNION(union(x5,x6),x7) = UNION(x5,union(x6,x7))
30.38/30.47	 UNION(x5,x6) = UNION(x6,x5)
30.38/30.47	-> Pairs:
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> MAX(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> MAX(union(Y,Z))
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> UNION(singl(x),singl(max(union(Y,Z))))
30.38/30.47	-> EAxioms:
30.38/30.47	 union(union(x5,x6),x7) = union(x5,union(x6,x7))
30.38/30.47	 union(x5,x6) = union(x6,x5)
30.38/30.47	-> Rules:
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	-> SRules:
30.38/30.47	 UNION(union(x5,x6),x7) -> UNION(x5,x6)
30.38/30.47	 UNION(x5,union(x6,x7)) -> UNION(x6,x7)
30.38/30.47	->Strongly Connected Components:
30.38/30.47	->->Cycle:
30.38/30.47	->->-> Pairs:
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> MAX(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> MAX(union(Y,Z))
30.38/30.47	-> FAxioms:
30.38/30.47	 union(union(x5,x6),x7) -> union(x5,union(x6,x7))
30.38/30.47	 union(x5,x6) -> union(x6,x5)
30.38/30.47	-> EAxioms:
30.38/30.47	 union(union(x5,x6),x7) = union(x5,union(x6,x7))
30.38/30.47	 union(x5,x6) = union(x6,x5)
30.38/30.47	->->-> Rules:
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	-> SRules:
30.38/30.47	 Empty
30.38/30.47	
30.38/30.47	Problem 1: 
30.38/30.47	
30.38/30.47	Reduction Pairs Processor:
30.38/30.47	-> FAxioms:
30.38/30.47	 Empty
30.38/30.47	-> Pairs:
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> MAX(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> MAX(union(Y,Z))
30.38/30.47	-> EAxioms:
30.38/30.47	 union(union(x5,x6),x7) = union(x5,union(x6,x7))
30.38/30.47	 union(x5,x6) = union(x6,x5)
30.38/30.47	-> Usable Equations:
30.38/30.47	 union(union(x5,x6),x7) = union(x5,union(x6,x7))
30.38/30.47	 union(x5,x6) = union(x6,x5)
30.38/30.47	-> Rules:
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	-> Usable Rules:
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	-> SRules:
30.38/30.47	 Empty
30.38/30.47	->Interpretation type:
30.38/30.47	 Linear
30.38/30.47	->Coefficients:
30.38/30.47	 Natural Numbers
30.38/30.47	->Dimension:
30.38/30.47	 1
30.38/30.47	->Bound:
30.38/30.47	 2
30.38/30.47	->Interpretation:
30.38/30.47	 
30.38/30.47	[max](X) = X
30.38/30.47	[union](X1,X2) = X1 + X2 + 2
30.38/30.47	[0] = 0
30.38/30.47	[empty] = 0
30.38/30.47	[s](X) = 0
30.38/30.47	[singl](X) = X
30.38/30.47	[MAX](X) = 2.X
30.38/30.47	[UNION](X1,X2) = 0
30.38/30.47	
30.38/30.47	Problem 1: 
30.38/30.47	
30.38/30.47	SCC Processor:
30.38/30.47	-> FAxioms:
30.38/30.47	 Empty
30.38/30.47	-> Pairs:
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> MAX(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	-> EAxioms:
30.38/30.47	 union(union(x5,x6),x7) = union(x5,union(x6,x7))
30.38/30.47	 union(x5,x6) = union(x6,x5)
30.38/30.47	-> Rules:
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	-> SRules:
30.38/30.47	 Empty
30.38/30.47	->Strongly Connected Components:
30.38/30.47	->->Cycle:
30.38/30.47	->->-> Pairs:
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> MAX(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	-> FAxioms:
30.38/30.47	 union(union(x5,x6),x7) -> union(x5,union(x6,x7))
30.38/30.47	 union(x5,x6) -> union(x6,x5)
30.38/30.47	-> EAxioms:
30.38/30.47	 union(union(x5,x6),x7) = union(x5,union(x6,x7))
30.38/30.47	 union(x5,x6) = union(x6,x5)
30.38/30.47	->->-> Rules:
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	-> SRules:
30.38/30.47	 Empty
30.38/30.47	
30.38/30.47	Problem 1: 
30.38/30.47	
30.38/30.47	Reduction Pairs Processor:
30.38/30.47	-> FAxioms:
30.38/30.47	 Empty
30.38/30.47	-> Pairs:
30.38/30.47	 MAX(union(singl(x),union(Y,Z))) -> MAX(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	-> EAxioms:
30.38/30.47	 union(union(x5,x6),x7) = union(x5,union(x6,x7))
30.38/30.47	 union(x5,x6) = union(x6,x5)
30.38/30.47	-> Usable Equations:
30.38/30.47	 union(union(x5,x6),x7) = union(x5,union(x6,x7))
30.38/30.47	 union(x5,x6) = union(x6,x5)
30.38/30.47	-> Rules:
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	-> Usable Rules:
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	-> SRules:
30.38/30.47	 Empty
30.38/30.47	->Interpretation type:
30.38/30.47	 Linear
30.38/30.47	->Coefficients:
30.38/30.47	 Natural Numbers
30.38/30.47	->Dimension:
30.38/30.47	 2
30.38/30.47	->Bound:
30.38/30.47	 1
30.38/30.47	->Interpretation:
30.38/30.47	 
30.38/30.47	[max](X) = [0 1;1 1].X
30.38/30.47	[union](X1,X2) = [1 0;1 0].X1 + [1 0;1 0].X2 + [1;0]
30.38/30.47	[0] = 0
30.38/30.47	[empty] = 0
30.38/30.47	[s](X) = 0
30.38/30.47	[singl](X) = [0 0;1 1].X
30.38/30.47	[MAX](X) = [1 1;1 1].X
30.38/30.47	[UNION](X1,X2) = 0
30.38/30.47	
30.38/30.47	Problem 1: 
30.38/30.47	
30.38/30.47	SCC Processor:
30.38/30.47	-> FAxioms:
30.38/30.47	 Empty
30.38/30.47	-> Pairs:
30.38/30.47	 Empty
30.38/30.47	-> EAxioms:
30.38/30.47	 union(union(x5,x6),x7) = union(x5,union(x6,x7))
30.38/30.47	 union(x5,x6) = union(x6,x5)
30.38/30.47	-> Rules:
30.38/30.47	 max(union(singl(x),union(Y,Z))) -> max(union(singl(x),singl(max(union(Y,Z)))))
30.38/30.47	 max(singl(x)) -> x
30.38/30.47	-> SRules:
30.38/30.47	 Empty
30.38/30.47	->Strongly Connected Components:
30.38/30.47	 There is no strongly connected component
30.38/30.47	
30.38/30.47	The problem is finite.
30.38/30.48	EOF