15.29/16.04	YES
15.29/16.04	
15.29/16.04	Problem 1: 
15.29/16.04	
15.29/16.04	(VAR v_NonEmpty:S x1:S)
15.29/16.04	(RULES
15.29/16.04	a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	b(x1:S) -> c(c(x1:S))
15.29/16.04	)
15.29/16.04	
15.29/16.04	Problem 1: 
15.29/16.04	
15.29/16.04	Dependency Pairs Processor:
15.29/16.04	-> Pairs:
15.29/16.04	 A(a(x1:S)) -> A(c(b(a(x1:S))))
15.29/16.04	 A(a(x1:S)) -> B(a(x1:S))
15.29/16.04	 B(c(a(x1:S))) -> A(b(a(b(x1:S))))
15.29/16.04	 B(c(a(x1:S))) -> A(b(x1:S))
15.29/16.04	 B(c(a(x1:S))) -> B(a(b(x1:S)))
15.29/16.04	 B(c(a(x1:S))) -> B(x1:S)
15.29/16.04	-> Rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	
15.29/16.04	Problem 1: 
15.29/16.04	
15.29/16.04	SCC Processor:
15.29/16.04	-> Pairs:
15.29/16.04	 A(a(x1:S)) -> A(c(b(a(x1:S))))
15.29/16.04	 A(a(x1:S)) -> B(a(x1:S))
15.29/16.04	 B(c(a(x1:S))) -> A(b(a(b(x1:S))))
15.29/16.04	 B(c(a(x1:S))) -> A(b(x1:S))
15.29/16.04	 B(c(a(x1:S))) -> B(a(b(x1:S)))
15.29/16.04	 B(c(a(x1:S))) -> B(x1:S)
15.29/16.04	-> Rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	->Strongly Connected Components:
15.29/16.04	->->Cycle:
15.29/16.04	->->-> Pairs:
15.29/16.04	 A(a(x1:S)) -> B(a(x1:S))
15.29/16.04	 B(c(a(x1:S))) -> A(b(a(b(x1:S))))
15.29/16.04	 B(c(a(x1:S))) -> A(b(x1:S))
15.29/16.04	 B(c(a(x1:S))) -> B(a(b(x1:S)))
15.29/16.04	 B(c(a(x1:S))) -> B(x1:S)
15.29/16.04	->->-> Rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	
15.29/16.04	Problem 1: 
15.29/16.04	
15.29/16.04	Reduction Pair Processor:
15.29/16.04	-> Pairs:
15.29/16.04	 A(a(x1:S)) -> B(a(x1:S))
15.29/16.04	 B(c(a(x1:S))) -> A(b(a(b(x1:S))))
15.29/16.04	 B(c(a(x1:S))) -> A(b(x1:S))
15.29/16.04	 B(c(a(x1:S))) -> B(a(b(x1:S)))
15.29/16.04	 B(c(a(x1:S))) -> B(x1:S)
15.29/16.04	-> Rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	-> Usable rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	->Interpretation type:
15.29/16.04	 Linear
15.29/16.04	->Coefficients:
15.29/16.04	 Natural Numbers
15.29/16.04	->Dimension:
15.29/16.04	 2
15.29/16.04	->Bound:
15.29/16.04	 1
15.29/16.04	->Interpretation:
15.29/16.04	 
15.29/16.04	[a](X) = [0 0;1 0].X + [0;1]
15.29/16.04	[b](X) = [1 0;1 0].X
15.29/16.04	[c](X) = [0 1;0 0].X
15.29/16.04	[A](X) = [0 0;0 1].X + [1;1]
15.29/16.04	[B](X) = [1 0;1 0].X + [0;1]
15.29/16.04	
15.29/16.04	Problem 1: 
15.29/16.04	
15.29/16.04	SCC Processor:
15.29/16.04	-> Pairs:
15.29/16.04	 B(c(a(x1:S))) -> A(b(a(b(x1:S))))
15.29/16.04	 B(c(a(x1:S))) -> A(b(x1:S))
15.29/16.04	 B(c(a(x1:S))) -> B(a(b(x1:S)))
15.29/16.04	 B(c(a(x1:S))) -> B(x1:S)
15.29/16.04	-> Rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	->Strongly Connected Components:
15.29/16.04	->->Cycle:
15.29/16.04	->->-> Pairs:
15.29/16.04	 B(c(a(x1:S))) -> B(a(b(x1:S)))
15.29/16.04	 B(c(a(x1:S))) -> B(x1:S)
15.29/16.04	->->-> Rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	
15.29/16.04	Problem 1: 
15.29/16.04	
15.29/16.04	Reduction Pair Processor:
15.29/16.04	-> Pairs:
15.29/16.04	 B(c(a(x1:S))) -> B(a(b(x1:S)))
15.29/16.04	 B(c(a(x1:S))) -> B(x1:S)
15.29/16.04	-> Rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	-> Usable rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	->Interpretation type:
15.29/16.04	 Linear
15.29/16.04	->Coefficients:
15.29/16.04	 Natural Numbers
15.29/16.04	->Dimension:
15.29/16.04	 2
15.29/16.04	->Bound:
15.29/16.04	 1
15.29/16.04	->Interpretation:
15.29/16.04	 
15.29/16.04	[a](X) = [1 1;0 0].X + [1;0]
15.29/16.04	[b](X) = [0 1;0 1].X + [0;1]
15.29/16.04	[c](X) = [0 0;1 0].X + [0;1]
15.29/16.04	[B](X) = [0 1;0 1].X
15.29/16.04	
15.29/16.04	Problem 1: 
15.29/16.04	
15.29/16.04	SCC Processor:
15.29/16.04	-> Pairs:
15.29/16.04	 B(c(a(x1:S))) -> B(x1:S)
15.29/16.04	-> Rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	->Strongly Connected Components:
15.29/16.04	->->Cycle:
15.29/16.04	->->-> Pairs:
15.29/16.04	 B(c(a(x1:S))) -> B(x1:S)
15.29/16.04	->->-> Rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	
15.29/16.04	Problem 1: 
15.29/16.04	
15.29/16.04	Subterm Processor:
15.29/16.04	-> Pairs:
15.29/16.04	 B(c(a(x1:S))) -> B(x1:S)
15.29/16.04	-> Rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	->Projection:
15.29/16.04	 pi(B) = 1
15.29/16.04	
15.29/16.04	Problem 1: 
15.29/16.04	
15.29/16.04	SCC Processor:
15.29/16.04	-> Pairs:
15.29/16.04	 Empty
15.29/16.04	-> Rules:
15.29/16.04	 a(a(x1:S)) -> a(c(b(a(x1:S))))
15.29/16.04	 b(c(a(x1:S))) -> a(b(a(b(x1:S))))
15.29/16.04	 b(x1:S) -> c(c(x1:S))
15.29/16.04	->Strongly Connected Components:
15.29/16.04	 There is no strongly connected component
15.29/16.04	
15.29/16.04	The problem is finite.
15.29/16.04	EOF