0.00/0.15	YES
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	(VAR v_NonEmpty:S x1:S)
0.00/0.15	(RULES
0.00/0.15	a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	)
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	Dependency Pairs Processor:
0.00/0.15	-> Pairs:
0.00/0.15	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.15	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.15	 A(c(x1:S)) -> B(x1:S)
0.00/0.15	 B(a(a(x1:S))) -> A(a(a(b(x1:S))))
0.00/0.15	 B(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.15	 B(a(a(x1:S))) -> A(b(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	SCC Processor:
0.00/0.15	-> Pairs:
0.00/0.15	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.15	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.15	 A(c(x1:S)) -> B(x1:S)
0.00/0.15	 B(a(a(x1:S))) -> A(a(a(b(x1:S))))
0.00/0.15	 B(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.15	 B(a(a(x1:S))) -> A(b(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	->Strongly Connected Components:
0.00/0.15	->->Cycle:
0.00/0.15	->->-> Pairs:
0.00/0.15	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.15	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.15	 A(c(x1:S)) -> B(x1:S)
0.00/0.15	 B(a(a(x1:S))) -> A(a(a(b(x1:S))))
0.00/0.15	 B(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.15	 B(a(a(x1:S))) -> A(b(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	->->-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	Reduction Pair Processor:
0.00/0.15	-> Pairs:
0.00/0.15	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.15	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.15	 A(c(x1:S)) -> B(x1:S)
0.00/0.15	 B(a(a(x1:S))) -> A(a(a(b(x1:S))))
0.00/0.15	 B(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.15	 B(a(a(x1:S))) -> A(b(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	-> Usable rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	->Interpretation type:
0.00/0.15	 Linear
0.00/0.15	->Coefficients:
0.00/0.15	 Natural Numbers
0.00/0.15	->Dimension:
0.00/0.15	 1
0.00/0.15	->Bound:
0.00/0.15	 2
0.00/0.15	->Interpretation:
0.00/0.15	 
0.00/0.15	[a](X) = X
0.00/0.15	[b](X) = X
0.00/0.15	[c](X) = X + 1
0.00/0.15	[A](X) = 2.X + 2
0.00/0.15	[B](X) = 2.X + 2
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	SCC Processor:
0.00/0.15	-> Pairs:
0.00/0.15	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.15	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> A(a(a(b(x1:S))))
0.00/0.15	 B(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.15	 B(a(a(x1:S))) -> A(b(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	->Strongly Connected Components:
0.00/0.15	->->Cycle:
0.00/0.15	->->-> Pairs:
0.00/0.15	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.15	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> A(a(a(b(x1:S))))
0.00/0.15	 B(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.15	 B(a(a(x1:S))) -> A(b(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	->->-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	Reduction Pair Processor:
0.00/0.15	-> Pairs:
0.00/0.15	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.15	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> A(a(a(b(x1:S))))
0.00/0.15	 B(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.15	 B(a(a(x1:S))) -> A(b(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	-> Usable rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	->Interpretation type:
0.00/0.15	 Linear
0.00/0.15	->Coefficients:
0.00/0.15	 Natural Numbers
0.00/0.15	->Dimension:
0.00/0.15	 1
0.00/0.15	->Bound:
0.00/0.15	 2
0.00/0.15	->Interpretation:
0.00/0.15	 
0.00/0.15	[a](X) = X + 1
0.00/0.15	[b](X) = 2.X + 2
0.00/0.15	[c](X) = 2
0.00/0.15	[A](X) = X + 2
0.00/0.15	[B](X) = 2.X + 2
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	SCC Processor:
0.00/0.15	-> Pairs:
0.00/0.15	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> A(a(a(b(x1:S))))
0.00/0.15	 B(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.15	 B(a(a(x1:S))) -> A(b(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	->Strongly Connected Components:
0.00/0.15	->->Cycle:
0.00/0.15	->->-> Pairs:
0.00/0.15	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> A(a(a(b(x1:S))))
0.00/0.15	 B(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.15	 B(a(a(x1:S))) -> A(b(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	->->-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	Reduction Pair Processor:
0.00/0.15	-> Pairs:
0.00/0.15	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> A(a(a(b(x1:S))))
0.00/0.15	 B(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.15	 B(a(a(x1:S))) -> A(b(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	-> Usable rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	->Interpretation type:
0.00/0.15	 Linear
0.00/0.15	->Coefficients:
0.00/0.15	 Natural Numbers
0.00/0.15	->Dimension:
0.00/0.15	 1
0.00/0.15	->Bound:
0.00/0.15	 2
0.00/0.15	->Interpretation:
0.00/0.15	 
0.00/0.15	[a](X) = X + 1
0.00/0.15	[b](X) = 2.X
0.00/0.15	[c](X) = 1
0.00/0.15	[A](X) = X + 2
0.00/0.15	[B](X) = 2.X
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	SCC Processor:
0.00/0.15	-> Pairs:
0.00/0.15	 B(a(a(x1:S))) -> A(a(a(b(x1:S))))
0.00/0.15	 B(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.15	 B(a(a(x1:S))) -> A(b(x1:S))
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	->Strongly Connected Components:
0.00/0.15	->->Cycle:
0.00/0.15	->->-> Pairs:
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	->->-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	Subterm Processor:
0.00/0.15	-> Pairs:
0.00/0.15	 B(a(a(x1:S))) -> B(x1:S)
0.00/0.15	-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	->Projection:
0.00/0.15	 pi(B) = 1
0.00/0.15	
0.00/0.15	Problem 1: 
0.00/0.15	
0.00/0.15	SCC Processor:
0.00/0.15	-> Pairs:
0.00/0.15	 Empty
0.00/0.15	-> Rules:
0.00/0.15	 a(a(b(x1:S))) -> b(a(x1:S))
0.00/0.15	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.15	 b(a(a(x1:S))) -> a(a(a(b(x1:S))))
0.00/0.15	->Strongly Connected Components:
0.00/0.15	 There is no strongly connected component
0.00/0.15	
0.00/0.15	The problem is finite.
0.00/0.15	EOF