8.81/9.06	YES
8.81/9.06	
8.81/9.06	Problem 1: 
8.81/9.06	
8.81/9.06	(VAR v_NonEmpty:S x1:S)
8.81/9.06	(RULES
8.81/9.06	a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	)
8.81/9.06	
8.81/9.06	Problem 1: 
8.81/9.06	
8.81/9.06	Dependency Pairs Processor:
8.81/9.06	-> Pairs:
8.81/9.06	 A(c(x1:S)) -> A(x1:S)
8.81/9.06	 A(c(x1:S)) -> C(a(x1:S))
8.81/9.06	 A(c(x1:S)) -> C(c(a(x1:S)))
8.81/9.06	 A(b(b(a(x1:S)))) -> A(c(a(b(x1:S))))
8.81/9.06	 A(b(b(a(x1:S)))) -> A(b(x1:S))
8.81/9.06	 A(b(b(a(x1:S)))) -> C(a(b(x1:S)))
8.81/9.06	-> Rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	
8.81/9.06	Problem 1: 
8.81/9.06	
8.81/9.06	SCC Processor:
8.81/9.06	-> Pairs:
8.81/9.06	 A(c(x1:S)) -> A(x1:S)
8.81/9.06	 A(c(x1:S)) -> C(a(x1:S))
8.81/9.06	 A(c(x1:S)) -> C(c(a(x1:S)))
8.81/9.06	 A(b(b(a(x1:S)))) -> A(c(a(b(x1:S))))
8.81/9.06	 A(b(b(a(x1:S)))) -> A(b(x1:S))
8.81/9.06	 A(b(b(a(x1:S)))) -> C(a(b(x1:S)))
8.81/9.06	-> Rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	->Strongly Connected Components:
8.81/9.06	->->Cycle:
8.81/9.06	->->-> Pairs:
8.81/9.06	 A(c(x1:S)) -> A(x1:S)
8.81/9.06	 A(b(b(a(x1:S)))) -> A(c(a(b(x1:S))))
8.81/9.06	 A(b(b(a(x1:S)))) -> A(b(x1:S))
8.81/9.06	->->-> Rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	
8.81/9.06	Problem 1: 
8.81/9.06	
8.81/9.06	Reduction Pair Processor:
8.81/9.06	-> Pairs:
8.81/9.06	 A(c(x1:S)) -> A(x1:S)
8.81/9.06	 A(b(b(a(x1:S)))) -> A(c(a(b(x1:S))))
8.81/9.06	 A(b(b(a(x1:S)))) -> A(b(x1:S))
8.81/9.06	-> Rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	-> Usable rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	->Interpretation type:
8.81/9.06	 Linear
8.81/9.06	->Coefficients:
8.81/9.06	 Natural Numbers
8.81/9.06	->Dimension:
8.81/9.06	 1
8.81/9.06	->Bound:
8.81/9.06	 2
8.81/9.06	->Interpretation:
8.81/9.06	 
8.81/9.06	[a](X) = 2.X + 1
8.81/9.06	[c](X) = X
8.81/9.06	[b](X) = X
8.81/9.06	[A](X) = 2.X
8.81/9.06	
8.81/9.06	Problem 1: 
8.81/9.06	
8.81/9.06	SCC Processor:
8.81/9.06	-> Pairs:
8.81/9.06	 A(c(x1:S)) -> A(x1:S)
8.81/9.06	 A(b(b(a(x1:S)))) -> A(c(a(b(x1:S))))
8.81/9.06	-> Rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	->Strongly Connected Components:
8.81/9.06	->->Cycle:
8.81/9.06	->->-> Pairs:
8.81/9.06	 A(c(x1:S)) -> A(x1:S)
8.81/9.06	 A(b(b(a(x1:S)))) -> A(c(a(b(x1:S))))
8.81/9.06	->->-> Rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	
8.81/9.06	Problem 1: 
8.81/9.06	
8.81/9.06	Reduction Pair Processor:
8.81/9.06	-> Pairs:
8.81/9.06	 A(c(x1:S)) -> A(x1:S)
8.81/9.06	 A(b(b(a(x1:S)))) -> A(c(a(b(x1:S))))
8.81/9.06	-> Rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	-> Usable rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	->Interpretation type:
8.81/9.06	 Linear
8.81/9.06	->Coefficients:
8.81/9.06	 Natural Numbers
8.81/9.06	->Dimension:
8.81/9.06	 2
8.81/9.06	->Bound:
8.81/9.06	 1
8.81/9.06	->Interpretation:
8.81/9.06	 
8.81/9.06	[a](X) = [0;1]
8.81/9.06	[c](X) = [1 0;0 0].X
8.81/9.06	[b](X) = [0 1;0 1].X
8.81/9.06	[A](X) = [1 0;0 0].X
8.81/9.06	
8.81/9.06	Problem 1: 
8.81/9.06	
8.81/9.06	SCC Processor:
8.81/9.06	-> Pairs:
8.81/9.06	 A(c(x1:S)) -> A(x1:S)
8.81/9.06	-> Rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	->Strongly Connected Components:
8.81/9.06	->->Cycle:
8.81/9.06	->->-> Pairs:
8.81/9.06	 A(c(x1:S)) -> A(x1:S)
8.81/9.06	->->-> Rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	
8.81/9.06	Problem 1: 
8.81/9.06	
8.81/9.06	Subterm Processor:
8.81/9.06	-> Pairs:
8.81/9.06	 A(c(x1:S)) -> A(x1:S)
8.81/9.06	-> Rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	->Projection:
8.81/9.06	 pi(A) = 1
8.81/9.06	
8.81/9.06	Problem 1: 
8.81/9.06	
8.81/9.06	SCC Processor:
8.81/9.06	-> Pairs:
8.81/9.06	 Empty
8.81/9.06	-> Rules:
8.81/9.06	 a(c(x1:S)) -> c(c(a(x1:S)))
8.81/9.06	 a(b(b(a(x1:S)))) -> a(c(a(b(x1:S))))
8.81/9.06	 c(c(c(x1:S))) -> b(c(b(x1:S)))
8.81/9.06	->Strongly Connected Components:
8.81/9.06	 There is no strongly connected component
8.81/9.06	
8.81/9.06	The problem is finite.
8.81/9.06	EOF