0.00/0.22	YES
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	(VAR v_NonEmpty:S x1:S)
0.00/0.22	(RULES
0.00/0.22	a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	)
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	Dependency Pairs Processor:
0.00/0.22	-> Pairs:
0.00/0.22	 A(a(x1:S)) -> A(c(b(x1:S)))
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> A(a(a(x1:S)))
0.00/0.22	 A(b(x1:S)) -> A(a(x1:S))
0.00/0.22	 A(b(x1:S)) -> A(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	SCC Processor:
0.00/0.22	-> Pairs:
0.00/0.22	 A(a(x1:S)) -> A(c(b(x1:S)))
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> A(a(a(x1:S)))
0.00/0.22	 A(b(x1:S)) -> A(a(x1:S))
0.00/0.22	 A(b(x1:S)) -> A(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	->Strongly Connected Components:
0.00/0.22	->->Cycle:
0.00/0.22	->->-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> A(a(a(x1:S)))
0.00/0.22	 A(b(x1:S)) -> A(a(x1:S))
0.00/0.22	 A(b(x1:S)) -> A(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	->->-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	Reduction Pair Processor:
0.00/0.22	-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> A(a(a(x1:S)))
0.00/0.22	 A(b(x1:S)) -> A(a(x1:S))
0.00/0.22	 A(b(x1:S)) -> A(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	-> Usable rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	->Interpretation type:
0.00/0.22	 Linear
0.00/0.22	->Coefficients:
0.00/0.22	 Natural Numbers
0.00/0.22	->Dimension:
0.00/0.22	 1
0.00/0.22	->Bound:
0.00/0.22	 2
0.00/0.22	->Interpretation:
0.00/0.22	 
0.00/0.22	[a](X) = X
0.00/0.22	[b](X) = 2.X + 1
0.00/0.22	[c](X) = 0
0.00/0.22	[A](X) = 2.X
0.00/0.22	[B](X) = 2.X
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	SCC Processor:
0.00/0.22	-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> A(a(x1:S))
0.00/0.22	 A(b(x1:S)) -> A(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	->Strongly Connected Components:
0.00/0.22	->->Cycle:
0.00/0.22	->->-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> A(a(x1:S))
0.00/0.22	 A(b(x1:S)) -> A(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	->->-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	Reduction Pair Processor:
0.00/0.22	-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> A(a(x1:S))
0.00/0.22	 A(b(x1:S)) -> A(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	-> Usable rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	->Interpretation type:
0.00/0.22	 Linear
0.00/0.22	->Coefficients:
0.00/0.22	 Natural Numbers
0.00/0.22	->Dimension:
0.00/0.22	 1
0.00/0.22	->Bound:
0.00/0.22	 2
0.00/0.22	->Interpretation:
0.00/0.22	 
0.00/0.22	[a](X) = X
0.00/0.22	[b](X) = X + 2
0.00/0.22	[c](X) = 0
0.00/0.22	[A](X) = X
0.00/0.22	[B](X) = X
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	SCC Processor:
0.00/0.22	-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> A(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	->Strongly Connected Components:
0.00/0.22	->->Cycle:
0.00/0.22	->->-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> A(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	->->-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	Reduction Pair Processor:
0.00/0.22	-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> A(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	-> Usable rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	->Interpretation type:
0.00/0.22	 Linear
0.00/0.22	->Coefficients:
0.00/0.22	 Natural Numbers
0.00/0.22	->Dimension:
0.00/0.22	 1
0.00/0.22	->Bound:
0.00/0.22	 2
0.00/0.22	->Interpretation:
0.00/0.22	 
0.00/0.22	[a](X) = X
0.00/0.22	[b](X) = 2.X + 2
0.00/0.22	[c](X) = 0
0.00/0.22	[A](X) = 2.X
0.00/0.22	[B](X) = 2.X
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	SCC Processor:
0.00/0.22	-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	->Strongly Connected Components:
0.00/0.22	->->Cycle:
0.00/0.22	->->-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	->->-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	Reduction Pair Processor:
0.00/0.22	-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 A(b(x1:S)) -> B(a(a(a(x1:S))))
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	-> Usable rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	->Interpretation type:
0.00/0.22	 Linear
0.00/0.22	->Coefficients:
0.00/0.22	 Natural Numbers
0.00/0.22	->Dimension:
0.00/0.22	 1
0.00/0.22	->Bound:
0.00/0.22	 2
0.00/0.22	->Interpretation:
0.00/0.22	 
0.00/0.22	[a](X) = X
0.00/0.22	[b](X) = X + 2
0.00/0.22	[c](X) = 0
0.00/0.22	[A](X) = 2.X
0.00/0.22	[B](X) = 2.X
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	SCC Processor:
0.00/0.22	-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	->Strongly Connected Components:
0.00/0.22	->->Cycle:
0.00/0.22	->->-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	->->-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	Subterm Processor:
0.00/0.22	-> Pairs:
0.00/0.22	 A(a(x1:S)) -> B(x1:S)
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	->Projection:
0.00/0.22	 pi(A) = 1
0.00/0.22	 pi(B) = 1
0.00/0.22	
0.00/0.22	Problem 1: 
0.00/0.22	
0.00/0.22	SCC Processor:
0.00/0.22	-> Pairs:
0.00/0.22	 B(a(x1:S)) -> A(a(x1:S))
0.00/0.22	-> Rules:
0.00/0.22	 a(a(x1:S)) -> a(c(b(x1:S)))
0.00/0.22	 a(b(x1:S)) -> b(a(a(a(x1:S))))
0.00/0.22	 b(a(x1:S)) -> a(a(x1:S))
0.00/0.22	->Strongly Connected Components:
0.00/0.22	 There is no strongly connected component
0.00/0.22	
0.00/0.22	The problem is finite.
0.00/0.22	EOF