1.06/1.18	YES
1.06/1.18	
1.06/1.18	Problem 1: 
1.06/1.18	
1.06/1.18	(VAR v_NonEmpty:S x1:S)
1.06/1.18	(RULES
1.06/1.18	a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	)
1.06/1.18	
1.06/1.18	Problem 1: 
1.06/1.18	
1.06/1.18	Dependency Pairs Processor:
1.06/1.18	-> Pairs:
1.06/1.18	 A(a(a(b(x1:S)))) -> A(b(a(x1:S)))
1.06/1.18	 A(a(a(b(x1:S)))) -> A(x1:S)
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(x1:S))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.18	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.18	-> Rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	
1.06/1.18	Problem 1: 
1.06/1.18	
1.06/1.18	SCC Processor:
1.06/1.18	-> Pairs:
1.06/1.18	 A(a(a(b(x1:S)))) -> A(b(a(x1:S)))
1.06/1.18	 A(a(a(b(x1:S)))) -> A(x1:S)
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(x1:S))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.18	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.18	-> Rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	->Strongly Connected Components:
1.06/1.18	->->Cycle:
1.06/1.18	->->-> Pairs:
1.06/1.18	 A(a(a(b(x1:S)))) -> A(b(a(x1:S)))
1.06/1.18	 A(a(a(b(x1:S)))) -> A(x1:S)
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(x1:S))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.18	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.18	->->-> Rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	
1.06/1.18	Problem 1: 
1.06/1.18	
1.06/1.18	Reduction Pair Processor:
1.06/1.18	-> Pairs:
1.06/1.18	 A(a(a(b(x1:S)))) -> A(b(a(x1:S)))
1.06/1.18	 A(a(a(b(x1:S)))) -> A(x1:S)
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(x1:S))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.18	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.18	-> Rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	-> Usable rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	->Interpretation type:
1.06/1.18	 Linear
1.06/1.18	->Coefficients:
1.06/1.18	 Natural Numbers
1.06/1.18	->Dimension:
1.06/1.18	 1
1.06/1.18	->Bound:
1.06/1.18	 2
1.06/1.18	->Interpretation:
1.06/1.18	 
1.06/1.18	[a](X) = 2.X + 1
1.06/1.18	[b](X) = 2.X + 1
1.06/1.18	[A](X) = 2.X + 2
1.06/1.18	[B](X) = 2.X + 2
1.06/1.18	
1.06/1.18	Problem 1: 
1.06/1.18	
1.06/1.18	SCC Processor:
1.06/1.18	-> Pairs:
1.06/1.18	 A(a(a(b(x1:S)))) -> A(x1:S)
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(x1:S))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.18	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.18	-> Rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	->Strongly Connected Components:
1.06/1.18	->->Cycle:
1.06/1.18	->->-> Pairs:
1.06/1.18	 A(a(a(b(x1:S)))) -> A(x1:S)
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(x1:S))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.18	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.18	->->-> Rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	
1.06/1.18	Problem 1: 
1.06/1.18	
1.06/1.18	Reduction Pair Processor:
1.06/1.18	-> Pairs:
1.06/1.18	 A(a(a(b(x1:S)))) -> A(x1:S)
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(x1:S))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.18	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.18	-> Rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	-> Usable rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	->Interpretation type:
1.06/1.18	 Linear
1.06/1.18	->Coefficients:
1.06/1.18	 Natural Numbers
1.06/1.18	->Dimension:
1.06/1.18	 1
1.06/1.18	->Bound:
1.06/1.18	 2
1.06/1.18	->Interpretation:
1.06/1.18	 
1.06/1.18	[a](X) = 2.X + 2
1.06/1.18	[b](X) = 2.X + 2
1.06/1.18	[A](X) = 2.X + 2
1.06/1.18	[B](X) = 2.X + 2
1.06/1.18	
1.06/1.18	Problem 1: 
1.06/1.18	
1.06/1.18	SCC Processor:
1.06/1.18	-> Pairs:
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(x1:S))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.18	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.18	-> Rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	->Strongly Connected Components:
1.06/1.18	->->Cycle:
1.06/1.18	->->-> Pairs:
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(x1:S))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.18	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.18	->->-> Rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	
1.06/1.18	Problem 1: 
1.06/1.18	
1.06/1.18	Reduction Pair Processor:
1.06/1.18	-> Pairs:
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(x1:S))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.18	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.18	-> Rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	-> Usable rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	->Interpretation type:
1.06/1.18	 Linear
1.06/1.18	->Coefficients:
1.06/1.18	 Natural Numbers
1.06/1.18	->Dimension:
1.06/1.18	 1
1.06/1.18	->Bound:
1.06/1.18	 2
1.06/1.18	->Interpretation:
1.06/1.18	 
1.06/1.18	[a](X) = 2.X + 2
1.06/1.18	[b](X) = 2.X + 2
1.06/1.18	[A](X) = 2.X
1.06/1.18	[B](X) = 2.X
1.06/1.18	
1.06/1.18	Problem 1: 
1.06/1.18	
1.06/1.18	SCC Processor:
1.06/1.18	-> Pairs:
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.18	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.18	-> Rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.18	->Strongly Connected Components:
1.06/1.18	->->Cycle:
1.06/1.18	->->-> Pairs:
1.06/1.18	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.18	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.18	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.18	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.18	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.18	->->-> Rules:
1.06/1.18	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.18	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.18	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.19	
1.06/1.19	Problem 1: 
1.06/1.19	
1.06/1.19	Reduction Pair Processor:
1.06/1.19	-> Pairs:
1.06/1.19	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.19	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.19	 A(b(a(b(x1:S)))) -> A(b(b(x1:S)))
1.06/1.19	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.19	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.06/1.19	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.06/1.19	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.06/1.19	 B(b(a(a(x1:S)))) -> B(x1:S)
1.06/1.19	-> Rules:
1.06/1.19	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.19	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.19	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.19	-> Usable rules:
1.06/1.19	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.06/1.19	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.06/1.19	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.06/1.19	->Interpretation type:
1.06/1.19	 Linear
1.06/1.19	->Coefficients:
1.06/1.19	 Natural Numbers
1.06/1.19	->Dimension:
1.06/1.19	 1
1.06/1.19	->Bound:
1.06/1.19	 2
1.06/1.19	->Interpretation:
1.06/1.19	 
1.06/1.19	[a](X) = 2.X + 2
1.06/1.19	[b](X) = 2.X + 2
1.06/1.19	[A](X) = 2.X
1.06/1.19	[B](X) = 2.X
1.06/1.19	
1.06/1.19	Problem 1: 
1.06/1.19	
1.06/1.19	SCC Processor:
1.06/1.19	-> Pairs:
1.06/1.19	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.06/1.19	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.06/1.19	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.06/1.19	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.19	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.10/1.19	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.10/1.19	 B(b(a(a(x1:S)))) -> B(x1:S)
1.10/1.19	-> Rules:
1.10/1.19	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.19	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.19	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.19	->Strongly Connected Components:
1.10/1.19	->->Cycle:
1.10/1.19	->->-> Pairs:
1.10/1.19	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.19	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.19	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.10/1.19	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.19	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.10/1.19	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.10/1.19	 B(b(a(a(x1:S)))) -> B(x1:S)
1.10/1.19	->->-> Rules:
1.10/1.19	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.19	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.19	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.19	
1.10/1.19	Problem 1: 
1.10/1.19	
1.10/1.19	Reduction Pair Processor:
1.10/1.19	-> Pairs:
1.10/1.19	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.19	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.19	 A(b(a(b(x1:S)))) -> B(b(x1:S))
1.10/1.19	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.19	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.10/1.19	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.10/1.19	 B(b(a(a(x1:S)))) -> B(x1:S)
1.10/1.19	-> Rules:
1.10/1.19	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.19	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	-> Usable rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	->Interpretation type:
1.10/1.20	 Linear
1.10/1.20	->Coefficients:
1.10/1.20	 Natural Numbers
1.10/1.20	->Dimension:
1.10/1.20	 1
1.10/1.20	->Bound:
1.10/1.20	 2
1.10/1.20	->Interpretation:
1.10/1.20	 
1.10/1.20	[a](X) = 2.X + 2
1.10/1.20	[b](X) = 2.X + 2
1.10/1.20	[A](X) = 2.X + 2
1.10/1.20	[B](X) = 2.X + 2
1.10/1.20	
1.10/1.20	Problem 1: 
1.10/1.20	
1.10/1.20	SCC Processor:
1.10/1.20	-> Pairs:
1.10/1.20	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.10/1.20	 B(b(a(a(x1:S)))) -> B(x1:S)
1.10/1.20	-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	->Strongly Connected Components:
1.10/1.20	->->Cycle:
1.10/1.20	->->-> Pairs:
1.10/1.20	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.10/1.20	 B(b(a(a(x1:S)))) -> B(x1:S)
1.10/1.20	->->-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	
1.10/1.20	Problem 1: 
1.10/1.20	
1.10/1.20	Reduction Pair Processor:
1.10/1.20	-> Pairs:
1.10/1.20	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(b(x1:S)))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.10/1.20	 B(b(a(a(x1:S)))) -> B(x1:S)
1.10/1.20	-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	-> Usable rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	->Interpretation type:
1.10/1.20	 Linear
1.10/1.20	->Coefficients:
1.10/1.20	 Natural Numbers
1.10/1.20	->Dimension:
1.10/1.20	 1
1.10/1.20	->Bound:
1.10/1.20	 2
1.10/1.20	->Interpretation:
1.10/1.20	 
1.10/1.20	[a](X) = 2.X + 2
1.10/1.20	[b](X) = 2.X + 2
1.10/1.20	[A](X) = 2.X + 2
1.10/1.20	[B](X) = 2.X + 2
1.10/1.20	
1.10/1.20	Problem 1: 
1.10/1.20	
1.10/1.20	SCC Processor:
1.10/1.20	-> Pairs:
1.10/1.20	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.10/1.20	 B(b(a(a(x1:S)))) -> B(x1:S)
1.10/1.20	-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	->Strongly Connected Components:
1.10/1.20	->->Cycle:
1.10/1.20	->->-> Pairs:
1.10/1.20	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.10/1.20	 B(b(a(a(x1:S)))) -> B(x1:S)
1.10/1.20	->->-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	
1.10/1.20	Problem 1: 
1.10/1.20	
1.10/1.20	Reduction Pair Processor:
1.10/1.20	-> Pairs:
1.10/1.20	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(b(x1:S))
1.10/1.20	 B(b(a(a(x1:S)))) -> B(x1:S)
1.10/1.20	-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	-> Usable rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	->Interpretation type:
1.10/1.20	 Linear
1.10/1.20	->Coefficients:
1.10/1.20	 Natural Numbers
1.10/1.20	->Dimension:
1.10/1.20	 1
1.10/1.20	->Bound:
1.10/1.20	 2
1.10/1.20	->Interpretation:
1.10/1.20	 
1.10/1.20	[a](X) = 2.X + 2
1.10/1.20	[b](X) = 2.X + 2
1.10/1.20	[A](X) = 2.X + 2
1.10/1.20	[B](X) = 2.X + 2
1.10/1.20	
1.10/1.20	Problem 1: 
1.10/1.20	
1.10/1.20	SCC Processor:
1.10/1.20	-> Pairs:
1.10/1.20	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> B(x1:S)
1.10/1.20	-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	->Strongly Connected Components:
1.10/1.20	->->Cycle:
1.10/1.20	->->-> Pairs:
1.10/1.20	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> B(x1:S)
1.10/1.20	->->-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	
1.10/1.20	Problem 1: 
1.10/1.20	
1.10/1.20	Reduction Pair Processor:
1.10/1.20	-> Pairs:
1.10/1.20	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> B(x1:S)
1.10/1.20	-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	-> Usable rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	->Interpretation type:
1.10/1.20	 Linear
1.10/1.20	->Coefficients:
1.10/1.20	 Natural Numbers
1.10/1.20	->Dimension:
1.10/1.20	 1
1.10/1.20	->Bound:
1.10/1.20	 2
1.10/1.20	->Interpretation:
1.10/1.20	 
1.10/1.20	[a](X) = 2.X + 2
1.10/1.20	[b](X) = 2.X + 2
1.10/1.20	[A](X) = 2.X + 2
1.10/1.20	[B](X) = 2.X + 2
1.10/1.20	
1.10/1.20	Problem 1: 
1.10/1.20	
1.10/1.20	SCC Processor:
1.10/1.20	-> Pairs:
1.10/1.20	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	->Strongly Connected Components:
1.10/1.20	->->Cycle:
1.10/1.20	->->-> Pairs:
1.10/1.20	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	->->-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	
1.10/1.20	Problem 1: 
1.10/1.20	
1.10/1.20	Reduction Pair Processor:
1.10/1.20	-> Pairs:
1.10/1.20	 A(a(a(b(x1:S)))) -> B(a(b(a(x1:S))))
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	-> Usable rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	->Interpretation type:
1.10/1.20	 Linear
1.10/1.20	->Coefficients:
1.10/1.20	 All rationals
1.10/1.20	->Dimension:
1.10/1.20	 1
1.10/1.20	->Bound:
1.10/1.20	 4
1.10/1.20	->Interpretation:
1.10/1.20	 
1.10/1.20	[a](X) = 4/3.X + 1/2
1.10/1.20	[b](X) = 4/3.X + 1/3
1.10/1.20	[A](X) = 4.X + 1/3
1.10/1.20	[B](X) = 4.X
1.10/1.20	
1.10/1.20	Problem 1: 
1.10/1.20	
1.10/1.20	SCC Processor:
1.10/1.20	-> Pairs:
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	 B(b(a(a(x1:S)))) -> A(a(a(b(x1:S))))
1.10/1.20	-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	->Strongly Connected Components:
1.10/1.20	->->Cycle:
1.10/1.20	->->-> Pairs:
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	->->-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	
1.10/1.20	Problem 1: 
1.10/1.20	
1.10/1.20	Reduction Pair Processor:
1.10/1.20	-> Pairs:
1.10/1.20	 A(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
1.10/1.20	-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	-> Usable rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	->Interpretation type:
1.10/1.20	 Linear
1.10/1.20	->Coefficients:
1.10/1.20	 All rationals
1.10/1.20	->Dimension:
1.10/1.20	 1
1.10/1.20	->Bound:
1.10/1.20	 4
1.10/1.20	->Interpretation:
1.10/1.20	 
1.10/1.20	[a](X) = 4/3.X + 1
1.10/1.20	[b](X) = 4/3.X + 1/2
1.10/1.20	[A](X) = 3.X
1.10/1.20	
1.10/1.20	Problem 1: 
1.10/1.20	
1.10/1.20	SCC Processor:
1.10/1.20	-> Pairs:
1.10/1.20	 Empty
1.10/1.20	-> Rules:
1.10/1.20	 a(a(a(b(x1:S)))) -> b(a(b(a(x1:S))))
1.10/1.20	 a(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
1.10/1.20	 b(b(a(a(x1:S)))) -> a(a(a(b(x1:S))))
1.10/1.20	->Strongly Connected Components:
1.10/1.20	 There is no strongly connected component
1.10/1.20	
1.10/1.20	The problem is finite.
1.10/1.20	EOF