1.30/1.40	YES
1.30/1.40	
1.30/1.40	Problem 1: 
1.30/1.40	
1.30/1.40	(VAR v_NonEmpty:S x1:S)
1.30/1.40	(RULES
1.30/1.40	a(b(a(x1:S))) -> a(b(b(a(x1:S))))
1.30/1.40	b(b(b(x1:S))) -> b(b(x1:S))
1.30/1.40	)
1.30/1.40	
1.30/1.40	Problem 1: 
1.30/1.40	
1.30/1.40	Dependency Pairs Processor:
1.30/1.40	-> Pairs:
1.30/1.40	 A(b(a(x1:S))) -> A(b(b(a(x1:S))))
1.30/1.40	 A(b(a(x1:S))) -> B(b(a(x1:S)))
1.30/1.40	-> Rules:
1.30/1.40	 a(b(a(x1:S))) -> a(b(b(a(x1:S))))
1.30/1.40	 b(b(b(x1:S))) -> b(b(x1:S))
1.30/1.40	
1.30/1.40	Problem 1: 
1.30/1.40	
1.30/1.40	SCC Processor:
1.30/1.40	-> Pairs:
1.30/1.40	 A(b(a(x1:S))) -> A(b(b(a(x1:S))))
1.30/1.40	 A(b(a(x1:S))) -> B(b(a(x1:S)))
1.30/1.40	-> Rules:
1.30/1.40	 a(b(a(x1:S))) -> a(b(b(a(x1:S))))
1.30/1.40	 b(b(b(x1:S))) -> b(b(x1:S))
1.30/1.40	->Strongly Connected Components:
1.30/1.40	->->Cycle:
1.30/1.40	->->-> Pairs:
1.30/1.40	 A(b(a(x1:S))) -> A(b(b(a(x1:S))))
1.30/1.40	->->-> Rules:
1.30/1.40	 a(b(a(x1:S))) -> a(b(b(a(x1:S))))
1.30/1.40	 b(b(b(x1:S))) -> b(b(x1:S))
1.30/1.40	
1.30/1.40	Problem 1: 
1.30/1.40	
1.30/1.40	Reduction Pair Processor:
1.30/1.40	-> Pairs:
1.30/1.40	 A(b(a(x1:S))) -> A(b(b(a(x1:S))))
1.30/1.40	-> Rules:
1.30/1.40	 a(b(a(x1:S))) -> a(b(b(a(x1:S))))
1.30/1.40	 b(b(b(x1:S))) -> b(b(x1:S))
1.30/1.40	-> Usable rules:
1.30/1.40	 a(b(a(x1:S))) -> a(b(b(a(x1:S))))
1.30/1.40	 b(b(b(x1:S))) -> b(b(x1:S))
1.30/1.40	->Interpretation type:
1.30/1.40	 Linear
1.30/1.40	->Coefficients:
1.30/1.40	 Natural Numbers
1.30/1.40	->Dimension:
1.30/1.40	 2
1.30/1.40	->Bound:
1.30/1.40	 1
1.30/1.40	->Interpretation:
1.30/1.40	 
1.30/1.40	[a](X) = [1 0;0 0].X + [0;1]
1.30/1.40	[b](X) = [0 1;0 0].X
1.30/1.40	[A](X) = [1 0;1 1].X
1.30/1.40	
1.30/1.40	Problem 1: 
1.30/1.40	
1.30/1.40	SCC Processor:
1.30/1.40	-> Pairs:
1.30/1.40	 Empty
1.30/1.40	-> Rules:
1.30/1.40	 a(b(a(x1:S))) -> a(b(b(a(x1:S))))
1.30/1.40	 b(b(b(x1:S))) -> b(b(x1:S))
1.30/1.40	->Strongly Connected Components:
1.30/1.40	 There is no strongly connected component
1.30/1.40	
1.30/1.40	The problem is finite.
1.30/1.41	EOF