0.00/0.32	YES
0.00/0.32	
0.00/0.32	Problem 1: 
0.00/0.32	
0.00/0.32	(VAR v_NonEmpty:S x1:S)
0.00/0.32	(RULES
0.00/0.32	a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	b(c(a(x1:S))) -> x1:S
0.00/0.32	)
0.00/0.32	
0.00/0.32	Problem 1: 
0.00/0.32	
0.00/0.32	Dependency Pairs Processor:
0.00/0.32	-> Pairs:
0.00/0.32	 A(a(b(x1:S))) -> A(a(a(x1:S)))
0.00/0.32	 A(a(b(x1:S))) -> A(a(x1:S))
0.00/0.32	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.32	 A(a(b(x1:S))) -> B(b(c(a(a(a(x1:S))))))
0.00/0.32	 A(a(b(x1:S))) -> B(c(a(a(a(x1:S)))))
0.00/0.32	-> Rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	
0.00/0.32	Problem 1: 
0.00/0.32	
0.00/0.32	SCC Processor:
0.00/0.32	-> Pairs:
0.00/0.32	 A(a(b(x1:S))) -> A(a(a(x1:S)))
0.00/0.32	 A(a(b(x1:S))) -> A(a(x1:S))
0.00/0.32	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.32	 A(a(b(x1:S))) -> B(b(c(a(a(a(x1:S))))))
0.00/0.32	 A(a(b(x1:S))) -> B(c(a(a(a(x1:S)))))
0.00/0.32	-> Rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	->Strongly Connected Components:
0.00/0.32	->->Cycle:
0.00/0.32	->->-> Pairs:
0.00/0.32	 A(a(b(x1:S))) -> A(a(a(x1:S)))
0.00/0.32	 A(a(b(x1:S))) -> A(a(x1:S))
0.00/0.32	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.32	->->-> Rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	
0.00/0.32	Problem 1: 
0.00/0.32	
0.00/0.32	Reduction Pair Processor:
0.00/0.32	-> Pairs:
0.00/0.32	 A(a(b(x1:S))) -> A(a(a(x1:S)))
0.00/0.32	 A(a(b(x1:S))) -> A(a(x1:S))
0.00/0.32	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.32	-> Rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	-> Usable rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	->Interpretation type:
0.00/0.32	 Linear
0.00/0.32	->Coefficients:
0.00/0.32	 All rationals
0.00/0.32	->Dimension:
0.00/0.32	 1
0.00/0.32	->Bound:
0.00/0.32	 4
0.00/0.32	->Interpretation:
0.00/0.32	 
0.00/0.32	[a](X) = 2.X + 1/4
0.00/0.32	[b](X) = 2.X + 4
0.00/0.32	[c](X) = 1/4.X + 1/4
0.00/0.32	[A](X) = 1/3.X
0.00/0.32	
0.00/0.32	Problem 1: 
0.00/0.32	
0.00/0.32	SCC Processor:
0.00/0.32	-> Pairs:
0.00/0.32	 A(a(b(x1:S))) -> A(a(x1:S))
0.00/0.32	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.32	-> Rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	->Strongly Connected Components:
0.00/0.32	->->Cycle:
0.00/0.32	->->-> Pairs:
0.00/0.32	 A(a(b(x1:S))) -> A(a(x1:S))
0.00/0.32	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.32	->->-> Rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	
0.00/0.32	Problem 1: 
0.00/0.32	
0.00/0.32	Reduction Pair Processor:
0.00/0.32	-> Pairs:
0.00/0.32	 A(a(b(x1:S))) -> A(a(x1:S))
0.00/0.32	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.32	-> Rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	-> Usable rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	->Interpretation type:
0.00/0.32	 Linear
0.00/0.32	->Coefficients:
0.00/0.32	 All rationals
0.00/0.32	->Dimension:
0.00/0.32	 1
0.00/0.32	->Bound:
0.00/0.32	 2
0.00/0.32	->Interpretation:
0.00/0.32	 
0.00/0.32	[a](X) = 2.X + 2
0.00/0.32	[b](X) = X + 2
0.00/0.32	[c](X) = 1/2.X + 1/2
0.00/0.32	[A](X) = 2.X
0.00/0.32	
0.00/0.32	Problem 1: 
0.00/0.32	
0.00/0.32	SCC Processor:
0.00/0.32	-> Pairs:
0.00/0.32	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.32	-> Rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	->Strongly Connected Components:
0.00/0.32	->->Cycle:
0.00/0.32	->->-> Pairs:
0.00/0.32	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.32	->->-> Rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	
0.00/0.32	Problem 1: 
0.00/0.32	
0.00/0.32	Subterm Processor:
0.00/0.32	-> Pairs:
0.00/0.32	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.32	-> Rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	->Projection:
0.00/0.32	 pi(A) = 1
0.00/0.32	
0.00/0.32	Problem 1: 
0.00/0.32	
0.00/0.32	SCC Processor:
0.00/0.32	-> Pairs:
0.00/0.32	 Empty
0.00/0.32	-> Rules:
0.00/0.32	 a(a(b(x1:S))) -> b(b(c(a(a(a(x1:S))))))
0.00/0.32	 b(c(a(x1:S))) -> x1:S
0.00/0.32	->Strongly Connected Components:
0.00/0.32	 There is no strongly connected component
0.00/0.32	
0.00/0.32	The problem is finite.
0.00/0.33	EOF