0.00/0.18	YES
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	(VAR v_NonEmpty:S x1:S)
0.00/0.18	(RULES
0.00/0.18	a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	)
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Dependency Pairs Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.18	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.18	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.18	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.18	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.18	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	 C(b(x1:S)) -> A(x1:S)
0.00/0.18	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.18	-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.18	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.18	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.18	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.18	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.18	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	 C(b(x1:S)) -> A(x1:S)
0.00/0.18	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.18	-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.18	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.18	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.18	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.18	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.18	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	 C(b(x1:S)) -> A(x1:S)
0.00/0.18	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.18	->->-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Reduction Pair Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.18	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.18	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.18	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.18	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.18	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	 C(b(x1:S)) -> A(x1:S)
0.00/0.18	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.18	-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	-> Usable rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 Natural Numbers
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[a](X) = 2.X + 2
0.00/0.18	[b](X) = X
0.00/0.18	[c](X) = 2.X + 2
0.00/0.18	[A](X) = 2.X + 1
0.00/0.18	[B](X) = X
0.00/0.18	[C](X) = 2.X + 2
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.18	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.18	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.18	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.18	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	 C(b(x1:S)) -> A(x1:S)
0.00/0.18	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.18	-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.18	->->-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.18	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.18	->->-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	
0.00/0.18	
0.00/0.18	The problem is decomposed in 2 subproblems.
0.00/0.18	
0.00/0.18	Problem 1.1: 
0.00/0.18	
0.00/0.18	Reduction Pair Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.18	-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	-> Usable rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 All rationals
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[a](X) = 2.X + 2
0.00/0.18	[b](X) = 1/2.X + 1/2
0.00/0.18	[c](X) = 2.X + 1/2
0.00/0.18	[A](X) = X
0.00/0.18	
0.00/0.18	Problem 1.1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 Empty
0.00/0.18	-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	->Strongly Connected Components:
0.00/0.18	 There is no strongly connected component
0.00/0.18	
0.00/0.18	The problem is finite.
0.00/0.18	
0.00/0.18	Problem 1.2: 
0.00/0.18	
0.00/0.18	Reduction Pair Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.18	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.18	-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	-> Usable rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 Natural Numbers
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[a](X) = X + 2
0.00/0.18	[b](X) = X
0.00/0.18	[c](X) = X + 2
0.00/0.18	[B](X) = X
0.00/0.18	[C](X) = X + 2
0.00/0.18	
0.00/0.18	Problem 1.2: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.18	-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.18	->->-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	
0.00/0.18	Problem 1.2: 
0.00/0.18	
0.00/0.18	Reduction Pair Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.18	-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	-> Usable rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 Natural Numbers
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[a](X) = 2.X + 2
0.00/0.18	[b](X) = X
0.00/0.18	[c](X) = 2.X + 2
0.00/0.18	[B](X) = X
0.00/0.18	[C](X) = 2.X + 2
0.00/0.18	
0.00/0.18	Problem 1.2: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.18	-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	->->-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	
0.00/0.18	Problem 1.2: 
0.00/0.18	
0.00/0.18	Subterm Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 C(a(x1:S)) -> C(x1:S)
0.00/0.18	-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	->Projection:
0.00/0.18	 pi(C) = 1
0.00/0.18	
0.00/0.18	Problem 1.2: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 Empty
0.00/0.18	-> Rules:
0.00/0.18	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.18	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.18	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.18	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.18	->Strongly Connected Components:
0.00/0.18	 There is no strongly connected component
0.00/0.18	
0.00/0.18	The problem is finite.
0.00/0.18	EOF