13.68/14.81	YES
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	(VAR v_NonEmpty:S x1:S)
13.68/14.81	(RULES
13.68/14.81	a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	a(a(x1:S)) -> b(x1:S)
13.68/14.81	a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	)
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Dependency Pairs Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(a(b(a(a(a(x1:S))))))
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(b(a(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(b(a(a(b(x1:S))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(b(a(b(x1:S)))))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(a(b(b(a(x1:S))))) -> A(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 A(a(b(b(a(x1:S))))) -> A(b(b(x1:S)))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(b(b(a(a(x1:S)))))
13.68/14.81	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(b(b(a(b(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(b(b(a(a(x1:S))))) -> A(b(b(b(a(x1:S)))))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(a(b(a(a(a(x1:S))))))
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(b(a(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(b(a(a(b(x1:S))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(b(a(b(x1:S)))))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(a(b(b(a(x1:S))))) -> A(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 A(a(b(b(a(x1:S))))) -> A(b(b(x1:S)))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(b(b(a(a(x1:S)))))
13.68/14.81	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(b(b(a(b(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(b(b(a(a(x1:S))))) -> A(b(b(b(a(x1:S)))))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(a(b(a(a(a(x1:S))))))
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(b(a(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(a(b(a(a(a(x1:S))))))
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(b(a(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 3/2.X + 1
13.68/14.81	[b](X) = 1/2.X
13.68/14.81	[A](X) = 4.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(a(b(a(a(a(x1:S))))))
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(b(a(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(a(b(a(a(a(x1:S))))))
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(b(a(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(a(b(a(a(a(x1:S))))))
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(b(a(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 3.X + 4
13.68/14.81	[b](X) = 1/4.X + 2
13.68/14.81	[A](X) = 3.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(b(a(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(b(a(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(a(a(x1:S))))) -> A(b(a(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 2.X + 4/3
13.68/14.81	[b](X) = 1/3.X
13.68/14.81	[A](X) = 3/2.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(a(x1:S)))) -> A(a(b(a(a(x1:S)))))
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 3.X + 1
13.68/14.81	[b](X) = 1/4.X + 1/3
13.68/14.81	[A](X) = 1/4.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 3/2.X + 3/4
13.68/14.81	[b](X) = 1/2.X
13.68/14.81	[A](X) = 3.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 3/2.X + 4
13.68/14.81	[b](X) = 1/2.X + 1/3
13.68/14.81	[A](X) = 3.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(a(b(x1:S)))
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 3/2.X + 1
13.68/14.81	[b](X) = 1/2.X
13.68/14.81	[A](X) = 2.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 3/2.X + 4
13.68/14.81	[b](X) = 1/2.X + 1/4
13.68/14.81	[A](X) = X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(a(x1:S))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 3/2.X + 1/4
13.68/14.81	[b](X) = 1/2.X
13.68/14.81	[A](X) = 4.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 2.X + 2/3
13.68/14.81	[b](X) = 1/3.X
13.68/14.81	[A](X) = 1/2.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(b(a(x1:S)))))
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 2.X + 1
13.68/14.81	[b](X) = 1/3.X
13.68/14.81	[A](X) = 2.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(b(a(a(x1:S))))) -> A(b(a(x1:S)))
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 3/2.X + 4/3
13.68/14.81	[b](X) = 1/2.X
13.68/14.81	[A](X) = 3/4.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(a(b(a(x1:S)))) -> A(b(x1:S))
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 2.X + 2
13.68/14.81	[b](X) = 1/4.X + 1/2
13.68/14.81	[A](X) = 1/3.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(b(a(a(a(x1:S))))) -> A(a(b(b(a(a(x1:S))))))
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 All rationals
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 4
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 3/2.X + 4
13.68/14.81	[b](X) = 1/2.X + 1/2
13.68/14.81	[A](X) = X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	->->Cycle:
13.68/14.81	->->-> Pairs:
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	->->-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	Reduction Pair Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 A(b(a(b(a(x1:S))))) -> A(b(x1:S))
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	-> Usable rules:
13.68/14.81	 Empty
13.68/14.81	->Interpretation type:
13.68/14.81	 Linear
13.68/14.81	->Coefficients:
13.68/14.81	 Natural Numbers
13.68/14.81	->Dimension:
13.68/14.81	 1
13.68/14.81	->Bound:
13.68/14.81	 2
13.68/14.81	->Interpretation:
13.68/14.81	 
13.68/14.81	[a](X) = 2.X + 2
13.68/14.81	[b](X) = 2.X + 2
13.68/14.81	[A](X) = 2.X
13.68/14.81	
13.68/14.81	Problem 1: 
13.68/14.81	
13.68/14.81	SCC Processor:
13.68/14.81	-> Pairs:
13.68/14.81	 Empty
13.68/14.81	-> Rules:
13.68/14.81	 a(a(a(a(a(x1:S))))) -> a(a(a(b(a(a(a(x1:S)))))))
13.68/14.81	 a(a(a(a(x1:S)))) -> a(a(b(a(a(x1:S)))))
13.68/14.81	 a(a(a(b(a(x1:S))))) -> a(a(b(b(a(a(b(x1:S)))))))
13.68/14.81	 a(a(a(x1:S))) -> a(b(a(x1:S)))
13.68/14.81	 a(a(b(a(a(x1:S))))) -> a(b(a(b(a(b(a(x1:S)))))))
13.68/14.81	 a(a(b(a(x1:S)))) -> a(b(b(a(b(x1:S)))))
13.68/14.81	 a(a(b(b(a(x1:S))))) -> a(b(b(b(a(b(b(x1:S)))))))
13.68/14.81	 a(a(x1:S)) -> b(x1:S)
13.68/14.81	 a(b(a(a(a(x1:S))))) -> b(a(a(b(b(a(a(x1:S)))))))
13.68/14.81	 a(b(a(a(x1:S)))) -> b(a(b(b(a(x1:S)))))
13.68/14.81	 a(b(a(b(a(x1:S))))) -> b(a(b(b(b(a(b(x1:S)))))))
13.68/14.81	 a(b(a(x1:S))) -> b(b(b(x1:S)))
13.68/14.81	 a(b(b(a(a(x1:S))))) -> b(b(a(b(b(b(a(x1:S)))))))
13.68/14.81	 a(b(b(a(x1:S)))) -> b(b(b(b(b(x1:S)))))
13.68/14.81	 a(b(b(b(a(x1:S))))) -> b(b(b(b(b(b(b(x1:S)))))))
13.68/14.81	->Strongly Connected Components:
13.68/14.81	 There is no strongly connected component
13.68/14.81	
13.68/14.81	The problem is finite.
13.68/14.81	EOF