0.00/0.51	YES
0.00/0.51	
0.00/0.51	Problem 1: 
0.00/0.51	
0.00/0.51	(VAR v_NonEmpty:S x1:S)
0.00/0.51	(RULES
0.00/0.51	a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	)
0.00/0.51	
0.00/0.51	Problem 1: 
0.00/0.51	
0.00/0.51	Dependency Pairs Processor:
0.00/0.51	-> Pairs:
0.00/0.51	 A(c(x1:S)) -> B(x1:S)
0.00/0.51	 A(x1:S) -> B(b(b(x1:S)))
0.00/0.51	 A(x1:S) -> B(b(x1:S))
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	
0.00/0.51	Problem 1: 
0.00/0.51	
0.00/0.51	SCC Processor:
0.00/0.51	-> Pairs:
0.00/0.51	 A(c(x1:S)) -> B(x1:S)
0.00/0.51	 A(x1:S) -> B(b(b(x1:S)))
0.00/0.51	 A(x1:S) -> B(b(x1:S))
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	->Strongly Connected Components:
0.00/0.51	->->Cycle:
0.00/0.51	->->-> Pairs:
0.00/0.51	 A(c(x1:S)) -> B(x1:S)
0.00/0.51	 A(x1:S) -> B(b(b(x1:S)))
0.00/0.51	 A(x1:S) -> B(b(x1:S))
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	->->-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	
0.00/0.51	Problem 1: 
0.00/0.51	
0.00/0.51	Reduction Pair Processor:
0.00/0.51	-> Pairs:
0.00/0.51	 A(c(x1:S)) -> B(x1:S)
0.00/0.51	 A(x1:S) -> B(b(b(x1:S)))
0.00/0.51	 A(x1:S) -> B(b(x1:S))
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	-> Usable rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	->Interpretation type:
0.00/0.51	 Linear
0.00/0.51	->Coefficients:
0.00/0.51	 Natural Numbers
0.00/0.51	->Dimension:
0.00/0.51	 1
0.00/0.51	->Bound:
0.00/0.51	 2
0.00/0.51	->Interpretation:
0.00/0.51	 
0.00/0.51	[a](X) = X
0.00/0.51	[b](X) = X
0.00/0.51	[c](X) = 2.X + 2
0.00/0.51	[A](X) = 2.X + 2
0.00/0.51	[B](X) = 2.X + 2
0.00/0.51	
0.00/0.51	Problem 1: 
0.00/0.51	
0.00/0.51	SCC Processor:
0.00/0.51	-> Pairs:
0.00/0.51	 A(x1:S) -> B(b(b(x1:S)))
0.00/0.51	 A(x1:S) -> B(b(x1:S))
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	->Strongly Connected Components:
0.00/0.51	->->Cycle:
0.00/0.51	->->-> Pairs:
0.00/0.51	 A(x1:S) -> B(b(b(x1:S)))
0.00/0.51	 A(x1:S) -> B(b(x1:S))
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	->->-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	
0.00/0.51	Problem 1: 
0.00/0.51	
0.00/0.51	Reduction Pair Processor:
0.00/0.51	-> Pairs:
0.00/0.51	 A(x1:S) -> B(b(b(x1:S)))
0.00/0.51	 A(x1:S) -> B(b(x1:S))
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	-> Usable rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	->Interpretation type:
0.00/0.51	 Linear
0.00/0.51	->Coefficients:
0.00/0.51	 All rationals
0.00/0.51	->Dimension:
0.00/0.51	 1
0.00/0.51	->Bound:
0.00/0.51	 4
0.00/0.51	->Interpretation:
0.00/0.51	 
0.00/0.51	[a](X) = X + 3/4
0.00/0.51	[b](X) = X + 1/4
0.00/0.51	[c](X) = 3.X + 1
0.00/0.51	[A](X) = 4.X + 3
0.00/0.51	[B](X) = 4.X + 2/3
0.00/0.51	
0.00/0.51	Problem 1: 
0.00/0.51	
0.00/0.51	SCC Processor:
0.00/0.51	-> Pairs:
0.00/0.51	 A(x1:S) -> B(b(x1:S))
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	->Strongly Connected Components:
0.00/0.51	->->Cycle:
0.00/0.51	->->-> Pairs:
0.00/0.51	 A(x1:S) -> B(b(x1:S))
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	->->-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	
0.00/0.51	Problem 1: 
0.00/0.51	
0.00/0.51	Reduction Pair Processor:
0.00/0.51	-> Pairs:
0.00/0.51	 A(x1:S) -> B(b(x1:S))
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	-> Usable rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	->Interpretation type:
0.00/0.51	 Linear
0.00/0.51	->Coefficients:
0.00/0.51	 All rationals
0.00/0.51	->Dimension:
0.00/0.51	 1
0.00/0.51	->Bound:
0.00/0.51	 4
0.00/0.51	->Interpretation:
0.00/0.51	 
0.00/0.51	[a](X) = X + 3/4
0.00/0.51	[b](X) = X + 1/4
0.00/0.51	[c](X) = 2.X + 3/2
0.00/0.51	[A](X) = 1/2.X + 2/3
0.00/0.51	[B](X) = 1/2.X + 1/2
0.00/0.51	
0.00/0.51	Problem 1: 
0.00/0.51	
0.00/0.51	SCC Processor:
0.00/0.51	-> Pairs:
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	->Strongly Connected Components:
0.00/0.51	->->Cycle:
0.00/0.51	->->-> Pairs:
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	->->-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	
0.00/0.51	Problem 1: 
0.00/0.51	
0.00/0.51	Reduction Pair Processor:
0.00/0.51	-> Pairs:
0.00/0.51	 A(x1:S) -> B(x1:S)
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	-> Usable rules:
0.00/0.51	 Empty
0.00/0.51	->Interpretation type:
0.00/0.51	 Linear
0.00/0.51	->Coefficients:
0.00/0.51	 Natural Numbers
0.00/0.51	->Dimension:
0.00/0.51	 1
0.00/0.51	->Bound:
0.00/0.51	 2
0.00/0.51	->Interpretation:
0.00/0.51	 
0.00/0.51	[b](X) = 2.X + 2
0.00/0.51	[c](X) = 2.X + 2
0.00/0.51	[A](X) = 2.X + 2
0.00/0.51	[B](X) = 2.X + 1
0.00/0.51	
0.00/0.51	Problem 1: 
0.00/0.51	
0.00/0.51	SCC Processor:
0.00/0.51	-> Pairs:
0.00/0.51	 B(c(b(x1:S))) -> A(c(x1:S))
0.00/0.51	-> Rules:
0.00/0.51	 a(c(x1:S)) -> c(b(x1:S))
0.00/0.51	 a(x1:S) -> b(b(b(x1:S)))
0.00/0.51	 b(c(b(x1:S))) -> a(c(x1:S))
0.00/0.51	->Strongly Connected Components:
0.00/0.51	 There is no strongly connected component
0.00/0.51	
0.00/0.51	The problem is finite.
0.00/0.51	EOF