0.51/0.58	YES
0.51/0.58	
0.51/0.58	Problem 1: 
0.51/0.58	
0.51/0.58	(VAR v_NonEmpty:S x1:S)
0.51/0.58	(RULES
0.51/0.58	a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	)
0.51/0.58	
0.51/0.58	Problem 1: 
0.51/0.58	
0.51/0.58	Dependency Pairs Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 A(b(x1:S)) -> A(x1:S)
0.51/0.58	 A(b(x1:S)) -> B(c(a(x1:S)))
0.51/0.58	 A(b(x1:S)) -> C(a(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(b(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	 B(c(x1:S)) -> C(b(b(x1:S)))
0.51/0.58	 C(a(x1:S)) -> A(c(x1:S))
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	
0.51/0.58	Problem 1: 
0.51/0.58	
0.51/0.58	SCC Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 A(b(x1:S)) -> A(x1:S)
0.51/0.58	 A(b(x1:S)) -> B(c(a(x1:S)))
0.51/0.58	 A(b(x1:S)) -> C(a(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(b(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	 B(c(x1:S)) -> C(b(b(x1:S)))
0.51/0.58	 C(a(x1:S)) -> A(c(x1:S))
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Strongly Connected Components:
0.51/0.58	->->Cycle:
0.51/0.58	->->-> Pairs:
0.51/0.58	 A(b(x1:S)) -> A(x1:S)
0.51/0.58	 A(b(x1:S)) -> B(c(a(x1:S)))
0.51/0.58	 A(b(x1:S)) -> C(a(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(b(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	 B(c(x1:S)) -> C(b(b(x1:S)))
0.51/0.58	 C(a(x1:S)) -> A(c(x1:S))
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	->->-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	
0.51/0.58	Problem 1: 
0.51/0.58	
0.51/0.58	Reduction Pair Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 A(b(x1:S)) -> A(x1:S)
0.51/0.58	 A(b(x1:S)) -> B(c(a(x1:S)))
0.51/0.58	 A(b(x1:S)) -> C(a(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(b(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	 B(c(x1:S)) -> C(b(b(x1:S)))
0.51/0.58	 C(a(x1:S)) -> A(c(x1:S))
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	-> Usable rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Interpretation type:
0.51/0.58	 Linear
0.51/0.58	->Coefficients:
0.51/0.58	 Natural Numbers
0.51/0.58	->Dimension:
0.51/0.58	 1
0.51/0.58	->Bound:
0.51/0.58	 2
0.51/0.58	->Interpretation:
0.51/0.58	 
0.51/0.58	[a](X) = 2.X
0.51/0.58	[b](X) = 2.X + 2
0.51/0.58	[c](X) = 0
0.51/0.58	[A](X) = 2.X
0.51/0.58	[B](X) = 0
0.51/0.58	[C](X) = 0
0.51/0.58	
0.51/0.58	Problem 1: 
0.51/0.58	
0.51/0.58	SCC Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 A(b(x1:S)) -> B(c(a(x1:S)))
0.51/0.58	 A(b(x1:S)) -> C(a(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(b(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	 B(c(x1:S)) -> C(b(b(x1:S)))
0.51/0.58	 C(a(x1:S)) -> A(c(x1:S))
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Strongly Connected Components:
0.51/0.58	->->Cycle:
0.51/0.58	->->-> Pairs:
0.51/0.58	 A(b(x1:S)) -> B(c(a(x1:S)))
0.51/0.58	 A(b(x1:S)) -> C(a(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(b(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	 B(c(x1:S)) -> C(b(b(x1:S)))
0.51/0.58	 C(a(x1:S)) -> A(c(x1:S))
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	->->-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	
0.51/0.58	Problem 1: 
0.51/0.58	
0.51/0.58	Reduction Pair Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 A(b(x1:S)) -> B(c(a(x1:S)))
0.51/0.58	 A(b(x1:S)) -> C(a(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(b(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	 B(c(x1:S)) -> C(b(b(x1:S)))
0.51/0.58	 C(a(x1:S)) -> A(c(x1:S))
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	-> Usable rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Interpretation type:
0.51/0.58	 Linear
0.51/0.58	->Coefficients:
0.51/0.58	 Natural Numbers
0.51/0.58	->Dimension:
0.51/0.58	 1
0.51/0.58	->Bound:
0.51/0.58	 2
0.51/0.58	->Interpretation:
0.51/0.58	 
0.51/0.58	[a](X) = 2.X
0.51/0.58	[b](X) = 2.X + 2
0.51/0.58	[c](X) = 0
0.51/0.58	[A](X) = X + 2
0.51/0.58	[B](X) = 2
0.51/0.58	[C](X) = 2
0.51/0.58	
0.51/0.58	Problem 1: 
0.51/0.58	
0.51/0.58	SCC Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 A(b(x1:S)) -> C(a(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(b(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	 B(c(x1:S)) -> C(b(b(x1:S)))
0.51/0.58	 C(a(x1:S)) -> A(c(x1:S))
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Strongly Connected Components:
0.51/0.58	->->Cycle:
0.51/0.58	->->-> Pairs:
0.51/0.58	 A(b(x1:S)) -> C(a(x1:S))
0.51/0.58	 C(a(x1:S)) -> A(c(x1:S))
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	->->-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->->Cycle:
0.51/0.58	->->-> Pairs:
0.51/0.58	 B(c(x1:S)) -> B(b(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	->->-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	
0.51/0.58	
0.51/0.58	The problem is decomposed in 2 subproblems.
0.51/0.58	
0.51/0.58	Problem 1.1: 
0.51/0.58	
0.51/0.58	Reduction Pair Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 A(b(x1:S)) -> C(a(x1:S))
0.51/0.58	 C(a(x1:S)) -> A(c(x1:S))
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	-> Usable rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Interpretation type:
0.51/0.58	 Linear
0.51/0.58	->Coefficients:
0.51/0.58	 Natural Numbers
0.51/0.58	->Dimension:
0.51/0.58	 1
0.51/0.58	->Bound:
0.51/0.58	 2
0.51/0.58	->Interpretation:
0.51/0.58	 
0.51/0.58	[a](X) = 2.X
0.51/0.58	[b](X) = 2.X + 2
0.51/0.58	[c](X) = 0
0.51/0.58	[A](X) = 2.X + 2
0.51/0.58	[C](X) = 2.X + 2
0.51/0.58	
0.51/0.58	Problem 1.1: 
0.51/0.58	
0.51/0.58	SCC Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 C(a(x1:S)) -> A(c(x1:S))
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Strongly Connected Components:
0.51/0.58	->->Cycle:
0.51/0.58	->->-> Pairs:
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	->->-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	
0.51/0.58	Problem 1.1: 
0.51/0.58	
0.51/0.58	Subterm Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 C(a(x1:S)) -> C(x1:S)
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Projection:
0.51/0.58	 pi(C) = 1
0.51/0.58	
0.51/0.58	Problem 1.1: 
0.51/0.58	
0.51/0.58	SCC Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 Empty
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Strongly Connected Components:
0.51/0.58	 There is no strongly connected component
0.51/0.58	
0.51/0.58	The problem is finite.
0.51/0.58	
0.51/0.58	Problem 1.2: 
0.51/0.58	
0.51/0.58	Reduction Pair Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 B(c(x1:S)) -> B(b(x1:S))
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	-> Usable rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Interpretation type:
0.51/0.58	 Linear
0.51/0.58	->Coefficients:
0.51/0.58	 Natural Numbers
0.51/0.58	->Dimension:
0.51/0.58	 2
0.51/0.58	->Bound:
0.51/0.58	 1
0.51/0.58	->Interpretation:
0.51/0.58	 
0.51/0.58	[a](X) = [1 0;1 1].X
0.51/0.58	[b](X) = [1 0;0 1].X + [1;0]
0.51/0.58	[c](X) = [0 0;0 1].X + [0;1]
0.51/0.58	[B](X) = [0 1;0 0].X
0.51/0.58	
0.51/0.58	Problem 1.2: 
0.51/0.58	
0.51/0.58	SCC Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Strongly Connected Components:
0.51/0.58	->->Cycle:
0.51/0.58	->->-> Pairs:
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	->->-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	
0.51/0.58	Problem 1.2: 
0.51/0.58	
0.51/0.58	Subterm Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 B(c(x1:S)) -> B(x1:S)
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Projection:
0.51/0.58	 pi(B) = 1
0.51/0.58	
0.51/0.58	Problem 1.2: 
0.51/0.58	
0.51/0.58	SCC Processor:
0.51/0.58	-> Pairs:
0.51/0.58	 Empty
0.51/0.58	-> Rules:
0.51/0.58	 a(b(x1:S)) -> b(c(a(x1:S)))
0.51/0.58	 b(c(x1:S)) -> c(b(b(x1:S)))
0.51/0.58	 c(a(x1:S)) -> a(c(x1:S))
0.51/0.58	->Strongly Connected Components:
0.51/0.58	 There is no strongly connected component
0.51/0.58	
0.51/0.58	The problem is finite.
0.56/0.59	EOF