0.00/0.43	YES
0.00/0.43	
0.00/0.43	Problem 1: 
0.00/0.43	
0.00/0.43	(VAR v_NonEmpty:S x1:S)
0.00/0.43	(RULES
0.00/0.43	a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	a(x1:S) -> b(x1:S)
0.00/0.43	b(x1:S) -> c(x1:S)
0.00/0.43	c(b(x1:S)) -> a(x1:S)
0.00/0.43	)
0.00/0.43	
0.00/0.43	Problem 1: 
0.00/0.43	
0.00/0.43	Dependency Pairs Processor:
0.00/0.43	-> Pairs:
0.00/0.43	 A(b(x1:S)) -> A(x1:S)
0.00/0.43	 A(b(x1:S)) -> B(c(a(x1:S)))
0.00/0.43	 A(b(x1:S)) -> C(a(x1:S))
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	
0.00/0.43	Problem 1: 
0.00/0.43	
0.00/0.43	SCC Processor:
0.00/0.43	-> Pairs:
0.00/0.43	 A(b(x1:S)) -> A(x1:S)
0.00/0.43	 A(b(x1:S)) -> B(c(a(x1:S)))
0.00/0.43	 A(b(x1:S)) -> C(a(x1:S))
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	->Strongly Connected Components:
0.00/0.43	->->Cycle:
0.00/0.43	->->-> Pairs:
0.00/0.43	 A(b(x1:S)) -> A(x1:S)
0.00/0.43	 A(b(x1:S)) -> B(c(a(x1:S)))
0.00/0.43	 A(b(x1:S)) -> C(a(x1:S))
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	->->-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	
0.00/0.43	Problem 1: 
0.00/0.43	
0.00/0.43	Reduction Pair Processor:
0.00/0.43	-> Pairs:
0.00/0.43	 A(b(x1:S)) -> A(x1:S)
0.00/0.43	 A(b(x1:S)) -> B(c(a(x1:S)))
0.00/0.43	 A(b(x1:S)) -> C(a(x1:S))
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	-> Usable rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	->Interpretation type:
0.00/0.43	 Linear
0.00/0.43	->Coefficients:
0.00/0.43	 Natural Numbers
0.00/0.43	->Dimension:
0.00/0.43	 1
0.00/0.43	->Bound:
0.00/0.43	 2
0.00/0.43	->Interpretation:
0.00/0.43	 
0.00/0.43	[a](X) = 2.X + 1
0.00/0.43	[b](X) = 2.X + 1
0.00/0.43	[c](X) = X
0.00/0.43	[A](X) = 2.X + 1
0.00/0.43	[B](X) = 2.X + 1
0.00/0.43	[C](X) = 2.X + 1
0.00/0.43	
0.00/0.43	Problem 1: 
0.00/0.43	
0.00/0.43	SCC Processor:
0.00/0.43	-> Pairs:
0.00/0.43	 A(b(x1:S)) -> B(c(a(x1:S)))
0.00/0.43	 A(b(x1:S)) -> C(a(x1:S))
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	->Strongly Connected Components:
0.00/0.43	->->Cycle:
0.00/0.43	->->-> Pairs:
0.00/0.43	 A(b(x1:S)) -> B(c(a(x1:S)))
0.00/0.43	 A(b(x1:S)) -> C(a(x1:S))
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	->->-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	
0.00/0.43	Problem 1: 
0.00/0.43	
0.00/0.43	Reduction Pair Processor:
0.00/0.43	-> Pairs:
0.00/0.43	 A(b(x1:S)) -> B(c(a(x1:S)))
0.00/0.43	 A(b(x1:S)) -> C(a(x1:S))
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	-> Usable rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	->Interpretation type:
0.00/0.43	 Linear
0.00/0.43	->Coefficients:
0.00/0.43	 Natural Numbers
0.00/0.43	->Dimension:
0.00/0.43	 1
0.00/0.43	->Bound:
0.00/0.43	 2
0.00/0.43	->Interpretation:
0.00/0.43	 
0.00/0.43	[a](X) = 2.X + 2
0.00/0.43	[b](X) = 2.X + 2
0.00/0.43	[c](X) = X
0.00/0.43	[A](X) = 2.X
0.00/0.43	[B](X) = X
0.00/0.43	[C](X) = X
0.00/0.43	
0.00/0.43	Problem 1: 
0.00/0.43	
0.00/0.43	SCC Processor:
0.00/0.43	-> Pairs:
0.00/0.43	 A(b(x1:S)) -> C(a(x1:S))
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	->Strongly Connected Components:
0.00/0.43	->->Cycle:
0.00/0.43	->->-> Pairs:
0.00/0.43	 A(b(x1:S)) -> C(a(x1:S))
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	->->-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	
0.00/0.43	Problem 1: 
0.00/0.43	
0.00/0.43	Reduction Pair Processor:
0.00/0.43	-> Pairs:
0.00/0.43	 A(b(x1:S)) -> C(a(x1:S))
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	-> Usable rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	->Interpretation type:
0.00/0.43	 Linear
0.00/0.43	->Coefficients:
0.00/0.43	 Natural Numbers
0.00/0.43	->Dimension:
0.00/0.43	 1
0.00/0.43	->Bound:
0.00/0.43	 2
0.00/0.43	->Interpretation:
0.00/0.43	 
0.00/0.43	[a](X) = 2.X + 2
0.00/0.43	[b](X) = 2.X + 2
0.00/0.43	[c](X) = X
0.00/0.43	[A](X) = 2.X + 2
0.00/0.43	[B](X) = 2.X + 1
0.00/0.43	[C](X) = 2.X + 1
0.00/0.43	
0.00/0.43	Problem 1: 
0.00/0.43	
0.00/0.43	SCC Processor:
0.00/0.43	-> Pairs:
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	->Strongly Connected Components:
0.00/0.43	->->Cycle:
0.00/0.43	->->-> Pairs:
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	->->-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	
0.00/0.43	Problem 1: 
0.00/0.43	
0.00/0.43	Subterm Processor:
0.00/0.43	-> Pairs:
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	 C(b(x1:S)) -> A(x1:S)
0.00/0.43	-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	->Projection:
0.00/0.43	 pi(A) = 1
0.00/0.43	 pi(B) = 1
0.00/0.43	 pi(C) = 1
0.00/0.43	
0.00/0.43	Problem 1: 
0.00/0.43	
0.00/0.43	SCC Processor:
0.00/0.43	-> Pairs:
0.00/0.43	 A(x1:S) -> B(x1:S)
0.00/0.43	 B(x1:S) -> C(x1:S)
0.00/0.43	-> Rules:
0.00/0.43	 a(b(x1:S)) -> b(c(a(x1:S)))
0.00/0.43	 a(x1:S) -> b(x1:S)
0.00/0.43	 b(x1:S) -> c(x1:S)
0.00/0.43	 c(b(x1:S)) -> a(x1:S)
0.00/0.43	->Strongly Connected Components:
0.00/0.43	 There is no strongly connected component
0.00/0.43	
0.00/0.43	The problem is finite.
0.00/0.43	EOF