0.71/0.91	YES
0.71/0.91	
0.71/0.91	Problem 1: 
0.71/0.91	
0.71/0.91	(VAR v_NonEmpty:S x1:S)
0.71/0.91	(RULES
0.71/0.91	a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.91	b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.91	)
0.71/0.91	
0.71/0.91	Problem 1: 
0.71/0.91	
0.71/0.91	Dependency Pairs Processor:
0.71/0.91	-> Pairs:
0.71/0.91	 A(a(x1:S)) -> B(b(b(x1:S)))
0.71/0.91	 A(a(x1:S)) -> B(b(x1:S))
0.71/0.91	 A(a(x1:S)) -> B(x1:S)
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(a(a(x1:S)))
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(a(x1:S))
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(x1:S)
0.71/0.91	-> Rules:
0.71/0.91	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.91	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.91	
0.71/0.91	Problem 1: 
0.71/0.91	
0.71/0.91	SCC Processor:
0.71/0.91	-> Pairs:
0.71/0.91	 A(a(x1:S)) -> B(b(b(x1:S)))
0.71/0.91	 A(a(x1:S)) -> B(b(x1:S))
0.71/0.91	 A(a(x1:S)) -> B(x1:S)
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(a(a(x1:S)))
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(a(x1:S))
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(x1:S)
0.71/0.91	-> Rules:
0.71/0.91	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.91	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.91	->Strongly Connected Components:
0.71/0.91	->->Cycle:
0.71/0.91	->->-> Pairs:
0.71/0.91	 A(a(x1:S)) -> B(b(b(x1:S)))
0.71/0.91	 A(a(x1:S)) -> B(b(x1:S))
0.71/0.91	 A(a(x1:S)) -> B(x1:S)
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(a(a(x1:S)))
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(a(x1:S))
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(x1:S)
0.71/0.91	->->-> Rules:
0.71/0.91	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.91	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.91	
0.71/0.91	Problem 1: 
0.71/0.91	
0.71/0.91	Reduction Pair Processor:
0.71/0.91	-> Pairs:
0.71/0.91	 A(a(x1:S)) -> B(b(b(x1:S)))
0.71/0.91	 A(a(x1:S)) -> B(b(x1:S))
0.71/0.91	 A(a(x1:S)) -> B(x1:S)
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(a(a(x1:S)))
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(a(x1:S))
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(x1:S)
0.71/0.91	-> Rules:
0.71/0.91	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.91	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.91	-> Usable rules:
0.71/0.91	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.91	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.91	->Interpretation type:
0.71/0.91	 Linear
0.71/0.91	->Coefficients:
0.71/0.91	 All rationals
0.71/0.91	->Dimension:
0.71/0.91	 1
0.71/0.91	->Bound:
0.71/0.91	 4
0.71/0.91	->Interpretation:
0.71/0.91	 
0.71/0.91	[a](X) = 3.X + 1/2
0.71/0.91	[b](X) = 2.X + 1/4
0.71/0.91	[A](X) = 3.X + 2
0.71/0.91	[B](X) = 2.X + 4/3
0.71/0.91	
0.71/0.91	Problem 1: 
0.71/0.91	
0.71/0.91	SCC Processor:
0.71/0.91	-> Pairs:
0.71/0.91	 A(a(x1:S)) -> B(b(x1:S))
0.71/0.91	 A(a(x1:S)) -> B(x1:S)
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(a(a(x1:S)))
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(a(x1:S))
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(x1:S)
0.71/0.91	-> Rules:
0.71/0.91	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.91	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.91	->Strongly Connected Components:
0.71/0.91	->->Cycle:
0.71/0.91	->->-> Pairs:
0.71/0.91	 A(a(x1:S)) -> B(b(x1:S))
0.71/0.91	 A(a(x1:S)) -> B(x1:S)
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(a(a(x1:S)))
0.71/0.91	 B(b(b(b(b(x1:S))))) -> A(a(x1:S))
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(x1:S)
0.71/0.92	->->-> Rules:
0.71/0.92	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.92	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.92	
0.71/0.92	Problem 1: 
0.71/0.92	
0.71/0.92	Reduction Pair Processor:
0.71/0.92	-> Pairs:
0.71/0.92	 A(a(x1:S)) -> B(b(x1:S))
0.71/0.92	 A(a(x1:S)) -> B(x1:S)
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(a(a(x1:S)))
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(a(x1:S))
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(x1:S)
0.71/0.92	-> Rules:
0.71/0.92	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.92	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.92	-> Usable rules:
0.71/0.92	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.92	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.92	->Interpretation type:
0.71/0.92	 Linear
0.71/0.92	->Coefficients:
0.71/0.92	 All rationals
0.71/0.92	->Dimension:
0.71/0.92	 1
0.71/0.92	->Bound:
0.71/0.92	 4
0.71/0.92	->Interpretation:
0.71/0.92	 
0.71/0.92	[a](X) = 3.X + 4/3
0.71/0.92	[b](X) = 2.X + 2/3
0.71/0.92	[A](X) = 2/3.X + 3/4
0.71/0.92	[B](X) = 3/4.X + 1/3
0.71/0.92	
0.71/0.92	Problem 1: 
0.71/0.92	
0.71/0.92	SCC Processor:
0.71/0.92	-> Pairs:
0.71/0.92	 A(a(x1:S)) -> B(x1:S)
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(a(a(x1:S)))
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(a(x1:S))
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(x1:S)
0.71/0.92	-> Rules:
0.71/0.92	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.92	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.92	->Strongly Connected Components:
0.71/0.92	->->Cycle:
0.71/0.92	->->-> Pairs:
0.71/0.92	 A(a(x1:S)) -> B(x1:S)
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(a(a(x1:S)))
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(a(x1:S))
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(x1:S)
0.71/0.92	->->-> Rules:
0.71/0.92	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.92	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.92	
0.71/0.92	Problem 1: 
0.71/0.92	
0.71/0.92	Reduction Pair Processor:
0.71/0.92	-> Pairs:
0.71/0.92	 A(a(x1:S)) -> B(x1:S)
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(a(a(x1:S)))
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(a(x1:S))
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(x1:S)
0.71/0.92	-> Rules:
0.71/0.92	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.92	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.92	-> Usable rules:
0.71/0.92	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.92	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.92	->Interpretation type:
0.71/0.92	 Linear
0.71/0.92	->Coefficients:
0.71/0.92	 All rationals
0.71/0.92	->Dimension:
0.71/0.92	 1
0.71/0.92	->Bound:
0.71/0.92	 4
0.71/0.92	->Interpretation:
0.71/0.92	 
0.71/0.92	[a](X) = X + 1/2
0.71/0.92	[b](X) = X + 1/3
0.71/0.92	[A](X) = 4.X + 1/2
0.71/0.92	[B](X) = 4.X + 3/2
0.71/0.92	
0.71/0.92	Problem 1: 
0.71/0.92	
0.71/0.92	SCC Processor:
0.71/0.92	-> Pairs:
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(a(a(x1:S)))
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(a(x1:S))
0.71/0.92	 B(b(b(b(b(x1:S))))) -> A(x1:S)
0.71/0.92	-> Rules:
0.71/0.92	 a(a(x1:S)) -> b(b(b(x1:S)))
0.71/0.92	 b(b(b(b(b(x1:S))))) -> a(a(a(x1:S)))
0.71/0.92	->Strongly Connected Components:
0.71/0.92	 There is no strongly connected component
0.71/0.92	
0.71/0.92	The problem is finite.
0.71/0.92	EOF