0.00/0.08	YES
0.00/0.08	
0.00/0.08	Problem 1: 
0.00/0.08	
0.00/0.08	(VAR v_NonEmpty:S x1:S)
0.00/0.08	(RULES
0.00/0.08	a(a(b(x1:S))) -> c(x1:S)
0.00/0.08	a(c(x1:S)) -> b(c(a(a(x1:S))))
0.00/0.08	b(c(x1:S)) -> x1:S
0.00/0.08	)
0.00/0.08	
0.00/0.08	Problem 1: 
0.00/0.08	
0.00/0.08	Dependency Pairs Processor:
0.00/0.08	-> Pairs:
0.00/0.08	 A(c(x1:S)) -> A(a(x1:S))
0.00/0.08	 A(c(x1:S)) -> A(x1:S)
0.00/0.08	 A(c(x1:S)) -> B(c(a(a(x1:S))))
0.00/0.08	-> Rules:
0.00/0.08	 a(a(b(x1:S))) -> c(x1:S)
0.00/0.08	 a(c(x1:S)) -> b(c(a(a(x1:S))))
0.00/0.08	 b(c(x1:S)) -> x1:S
0.00/0.08	
0.00/0.08	Problem 1: 
0.00/0.08	
0.00/0.08	SCC Processor:
0.00/0.08	-> Pairs:
0.00/0.08	 A(c(x1:S)) -> A(a(x1:S))
0.00/0.08	 A(c(x1:S)) -> A(x1:S)
0.00/0.08	 A(c(x1:S)) -> B(c(a(a(x1:S))))
0.00/0.08	-> Rules:
0.00/0.08	 a(a(b(x1:S))) -> c(x1:S)
0.00/0.08	 a(c(x1:S)) -> b(c(a(a(x1:S))))
0.00/0.08	 b(c(x1:S)) -> x1:S
0.00/0.08	->Strongly Connected Components:
0.00/0.08	->->Cycle:
0.00/0.08	->->-> Pairs:
0.00/0.08	 A(c(x1:S)) -> A(a(x1:S))
0.00/0.08	 A(c(x1:S)) -> A(x1:S)
0.00/0.08	->->-> Rules:
0.00/0.08	 a(a(b(x1:S))) -> c(x1:S)
0.00/0.08	 a(c(x1:S)) -> b(c(a(a(x1:S))))
0.00/0.08	 b(c(x1:S)) -> x1:S
0.00/0.08	
0.00/0.08	Problem 1: 
0.00/0.08	
0.00/0.08	Reduction Pair Processor:
0.00/0.08	-> Pairs:
0.00/0.08	 A(c(x1:S)) -> A(a(x1:S))
0.00/0.08	 A(c(x1:S)) -> A(x1:S)
0.00/0.08	-> Rules:
0.00/0.08	 a(a(b(x1:S))) -> c(x1:S)
0.00/0.08	 a(c(x1:S)) -> b(c(a(a(x1:S))))
0.00/0.08	 b(c(x1:S)) -> x1:S
0.00/0.08	-> Usable rules:
0.00/0.08	 a(a(b(x1:S))) -> c(x1:S)
0.00/0.08	 a(c(x1:S)) -> b(c(a(a(x1:S))))
0.00/0.08	 b(c(x1:S)) -> x1:S
0.00/0.08	->Interpretation type:
0.00/0.08	 Linear
0.00/0.08	->Coefficients:
0.00/0.08	 All rationals
0.00/0.08	->Dimension:
0.00/0.08	 1
0.00/0.08	->Bound:
0.00/0.08	 2
0.00/0.08	->Interpretation:
0.00/0.08	 
0.00/0.08	[a](X) = 2.X
0.00/0.08	[b](X) = 1/2.X + 1/2
0.00/0.08	[c](X) = 2.X + 1
0.00/0.08	[A](X) = X
0.00/0.08	
0.00/0.08	Problem 1: 
0.00/0.08	
0.00/0.08	SCC Processor:
0.00/0.08	-> Pairs:
0.00/0.08	 A(c(x1:S)) -> A(x1:S)
0.00/0.08	-> Rules:
0.00/0.08	 a(a(b(x1:S))) -> c(x1:S)
0.00/0.08	 a(c(x1:S)) -> b(c(a(a(x1:S))))
0.00/0.08	 b(c(x1:S)) -> x1:S
0.00/0.08	->Strongly Connected Components:
0.00/0.08	->->Cycle:
0.00/0.08	->->-> Pairs:
0.00/0.08	 A(c(x1:S)) -> A(x1:S)
0.00/0.08	->->-> Rules:
0.00/0.08	 a(a(b(x1:S))) -> c(x1:S)
0.00/0.08	 a(c(x1:S)) -> b(c(a(a(x1:S))))
0.00/0.08	 b(c(x1:S)) -> x1:S
0.00/0.08	
0.00/0.08	Problem 1: 
0.00/0.08	
0.00/0.08	Subterm Processor:
0.00/0.08	-> Pairs:
0.00/0.08	 A(c(x1:S)) -> A(x1:S)
0.00/0.08	-> Rules:
0.00/0.08	 a(a(b(x1:S))) -> c(x1:S)
0.00/0.08	 a(c(x1:S)) -> b(c(a(a(x1:S))))
0.00/0.08	 b(c(x1:S)) -> x1:S
0.00/0.08	->Projection:
0.00/0.08	 pi(A) = 1
0.00/0.08	
0.00/0.08	Problem 1: 
0.00/0.08	
0.00/0.08	SCC Processor:
0.00/0.08	-> Pairs:
0.00/0.08	 Empty
0.00/0.08	-> Rules:
0.00/0.08	 a(a(b(x1:S))) -> c(x1:S)
0.00/0.08	 a(c(x1:S)) -> b(c(a(a(x1:S))))
0.00/0.08	 b(c(x1:S)) -> x1:S
0.00/0.08	->Strongly Connected Components:
0.00/0.08	 There is no strongly connected component
0.00/0.08	
0.00/0.08	The problem is finite.
0.00/0.09	EOF