62.80/63.24	YES
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	(VAR v_NonEmpty:S x1:S)
62.80/63.24	(RULES
62.80/63.24	a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	)
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	Dependency Pairs Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> A(b(a(x1:S)))
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(x1:S))
62.80/63.24	 A(s(x1:S)) -> A(x1:S)
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(b(s(a(x1:S))))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	 B(a(b(s(x1:S)))) -> B(s(a(x1:S)))
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	SCC Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> A(b(a(x1:S)))
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(x1:S))
62.80/63.24	 A(s(x1:S)) -> A(x1:S)
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(b(s(a(x1:S))))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	 B(a(b(s(x1:S)))) -> B(s(a(x1:S)))
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Strongly Connected Components:
62.80/63.24	->->Cycle:
62.80/63.24	->->-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> A(b(a(x1:S)))
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(x1:S))
62.80/63.24	 A(s(x1:S)) -> A(x1:S)
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	->->-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	Reduction Pair Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> A(b(a(x1:S)))
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(x1:S))
62.80/63.24	 A(s(x1:S)) -> A(x1:S)
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	-> Usable rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Interpretation type:
62.80/63.24	 Linear
62.80/63.24	->Coefficients:
62.80/63.24	 Natural Numbers
62.80/63.24	->Dimension:
62.80/63.24	 1
62.80/63.24	->Bound:
62.80/63.24	 2
62.80/63.24	->Interpretation:
62.80/63.24	 
62.80/63.24	[a](X) = 2.X + 2
62.80/63.24	[b](X) = 2.X + 2
62.80/63.24	[s](X) = 2.X + 2
62.80/63.24	[A](X) = 2.X + 2
62.80/63.24	[B](X) = 2.X + 2
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	SCC Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(x1:S))
62.80/63.24	 A(s(x1:S)) -> A(x1:S)
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Strongly Connected Components:
62.80/63.24	->->Cycle:
62.80/63.24	->->-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(x1:S))
62.80/63.24	 A(s(x1:S)) -> A(x1:S)
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	->->-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	Reduction Pair Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(x1:S))
62.80/63.24	 A(s(x1:S)) -> A(x1:S)
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	-> Usable rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Interpretation type:
62.80/63.24	 Linear
62.80/63.24	->Coefficients:
62.80/63.24	 Natural Numbers
62.80/63.24	->Dimension:
62.80/63.24	 1
62.80/63.24	->Bound:
62.80/63.24	 2
62.80/63.24	->Interpretation:
62.80/63.24	 
62.80/63.24	[a](X) = 2.X + 2
62.80/63.24	[b](X) = 2.X + 2
62.80/63.24	[s](X) = 2.X + 2
62.80/63.24	[A](X) = 2.X + 2
62.80/63.24	[B](X) = 2.X + 2
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	SCC Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 A(s(x1:S)) -> A(x1:S)
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Strongly Connected Components:
62.80/63.24	->->Cycle:
62.80/63.24	->->-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 A(s(x1:S)) -> A(x1:S)
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	->->-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	Reduction Pair Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 A(s(x1:S)) -> A(x1:S)
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	-> Usable rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Interpretation type:
62.80/63.24	 Linear
62.80/63.24	->Coefficients:
62.80/63.24	 Natural Numbers
62.80/63.24	->Dimension:
62.80/63.24	 1
62.80/63.24	->Bound:
62.80/63.24	 2
62.80/63.24	->Interpretation:
62.80/63.24	 
62.80/63.24	[a](X) = 2.X + 2
62.80/63.24	[b](X) = 2.X + 2
62.80/63.24	[s](X) = X + 2
62.80/63.24	[A](X) = X + 2
62.80/63.24	[B](X) = X + 2
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	SCC Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Strongly Connected Components:
62.80/63.24	->->Cycle:
62.80/63.24	->->-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	->->-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	Reduction Pair Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(x1:S))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	-> Usable rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Interpretation type:
62.80/63.24	 Linear
62.80/63.24	->Coefficients:
62.80/63.24	 Natural Numbers
62.80/63.24	->Dimension:
62.80/63.24	 1
62.80/63.24	->Bound:
62.80/63.24	 2
62.80/63.24	->Interpretation:
62.80/63.24	 
62.80/63.24	[a](X) = 2.X + 1
62.80/63.24	[b](X) = 2.X + 1
62.80/63.24	[s](X) = 2.X + 2
62.80/63.24	[A](X) = 2.X + 2
62.80/63.24	[B](X) = 2.X + 2
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	SCC Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Strongly Connected Components:
62.80/63.24	->->Cycle:
62.80/63.24	->->-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	->->-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	Reduction Pair Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> B(a(b(x1:S)))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	-> Usable rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Interpretation type:
62.80/63.24	 Linear
62.80/63.24	->Coefficients:
62.80/63.24	 Natural Numbers
62.80/63.24	->Dimension:
62.80/63.24	 1
62.80/63.24	->Bound:
62.80/63.24	 2
62.80/63.24	->Interpretation:
62.80/63.24	 
62.80/63.24	[a](X) = 2.X + 2
62.80/63.24	[b](X) = 2.X + 2
62.80/63.24	[s](X) = 2.X + 2
62.80/63.24	[A](X) = 2.X + 1
62.80/63.24	[B](X) = 2.X + 1
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	SCC Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Strongly Connected Components:
62.80/63.24	->->Cycle:
62.80/63.24	->->-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	->->-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	Reduction Pair Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	 B(a(b(s(x1:S)))) -> A(x1:S)
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	-> Usable rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Interpretation type:
62.80/63.24	 Linear
62.80/63.24	->Coefficients:
62.80/63.24	 Natural Numbers
62.80/63.24	->Dimension:
62.80/63.24	 1
62.80/63.24	->Bound:
62.80/63.24	 2
62.80/63.24	->Interpretation:
62.80/63.24	 
62.80/63.24	[a](X) = 2.X + 2
62.80/63.24	[b](X) = 2.X + 2
62.80/63.24	[s](X) = 2.X + 2
62.80/63.24	[A](X) = 2.X + 1
62.80/63.24	[B](X) = 2.X + 1
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	SCC Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Strongly Connected Components:
62.80/63.24	->->Cycle:
62.80/63.24	->->-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	->->-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	Reduction Pair Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 A(b(a(a(x1:S)))) -> B(a(b(a(x1:S))))
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	-> Usable rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Interpretation type:
62.80/63.24	 Linear
62.80/63.24	->Coefficients:
62.80/63.24	 Natural Numbers
62.80/63.24	->Dimension:
62.80/63.24	 2
62.80/63.24	->Bound:
62.80/63.24	 1
62.80/63.24	->Interpretation:
62.80/63.24	 
62.80/63.24	[a](X) = [1 0;1 0].X + [1;0]
62.80/63.24	[b](X) = [0 1;0 1].X + [1;1]
62.80/63.24	[s](X) = [1 0;0 0].X + [1;1]
62.80/63.24	[A](X) = [1 1;1 1].X + [0;1]
62.80/63.24	[B](X) = [1 1;1 1].X + [0;1]
62.80/63.24	
62.80/63.24	Problem 1: 
62.80/63.24	
62.80/63.24	SCC Processor:
62.80/63.24	-> Pairs:
62.80/63.24	 B(a(b(b(x1:S)))) -> A(b(a(b(x1:S))))
62.80/63.24	-> Rules:
62.80/63.24	 a(b(a(a(x1:S)))) -> b(a(b(a(x1:S))))
62.80/63.24	 a(s(x1:S)) -> s(a(x1:S))
62.80/63.24	 b(a(b(b(x1:S)))) -> a(b(a(b(x1:S))))
62.80/63.24	 b(a(b(s(x1:S)))) -> a(b(s(a(x1:S))))
62.80/63.24	->Strongly Connected Components:
62.80/63.24	 There is no strongly connected component
62.80/63.24	
62.80/63.24	The problem is finite.
62.82/110.41	EOF