0.00/0.41	YES
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	(VAR v_NonEmpty:S x1:S)
0.00/0.41	(RULES
0.00/0.41	A(a(x1:S)) -> x1:S
0.00/0.41	A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	B(b(x1:S)) -> x1:S
0.00/0.41	C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	C(c(x1:S)) -> x1:S
0.00/0.41	a(A(x1:S)) -> x1:S
0.00/0.41	a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	b(B(x1:S)) -> x1:S
0.00/0.41	b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	c(C(x1:S)) -> x1:S
0.00/0.41	)
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Dependency Pairs Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A#(c(b(x1:S))) -> A#(x1:S)
0.00/0.41	 A#(c(b(x1:S))) -> b#(c(A(x1:S)))
0.00/0.41	 A#(c(b(x1:S))) -> c#(A(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> A#(B(C(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> A#(c(x1:S))
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A#(c(b(x1:S))) -> A#(x1:S)
0.00/0.41	 A#(c(b(x1:S))) -> b#(c(A(x1:S)))
0.00/0.41	 A#(c(b(x1:S))) -> c#(A(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> A#(B(C(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> A#(c(x1:S))
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 A#(c(b(x1:S))) -> A#(x1:S)
0.00/0.41	 A#(c(b(x1:S))) -> b#(c(A(x1:S)))
0.00/0.41	 A#(c(b(x1:S))) -> c#(A(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> A#(B(C(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> A#(c(x1:S))
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	->->-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A#(c(b(x1:S))) -> A#(x1:S)
0.00/0.41	 A#(c(b(x1:S))) -> b#(c(A(x1:S)))
0.00/0.41	 A#(c(b(x1:S))) -> c#(A(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> A#(B(C(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> A#(c(x1:S))
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	-> Usable rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[A](X) = 2.X + 2
0.00/0.41	[B](X) = 2.X + 1
0.00/0.41	[C](X) = 2.X + 2
0.00/0.41	[a](X) = 2.X + 1
0.00/0.41	[b](X) = 2.X + 2
0.00/0.41	[c](X) = 2.X + 1
0.00/0.41	[A#](X) = 2.X + 2
0.00/0.41	[B#](X) = 2.X + 2
0.00/0.41	[C#](X) = 2.X + 2
0.00/0.41	[a#](X) = 2.X + 2
0.00/0.41	[b#](X) = 2.X + 2
0.00/0.41	[c#](X) = 2.X + 2
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A#(c(b(x1:S))) -> b#(c(A(x1:S)))
0.00/0.41	 A#(c(b(x1:S))) -> c#(A(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> A#(B(C(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> A#(c(x1:S))
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 A#(c(b(x1:S))) -> b#(c(A(x1:S)))
0.00/0.41	 A#(c(b(x1:S))) -> c#(A(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> A#(B(C(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> A#(c(x1:S))
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	->->-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A#(c(b(x1:S))) -> b#(c(A(x1:S)))
0.00/0.41	 A#(c(b(x1:S))) -> c#(A(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> A#(B(C(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> A#(c(x1:S))
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	-> Usable rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[A](X) = X
0.00/0.41	[B](X) = 2.X + 2
0.00/0.41	[C](X) = 2.X + 2
0.00/0.41	[a](X) = X
0.00/0.41	[b](X) = 2.X + 1
0.00/0.41	[c](X) = 2.X + 1
0.00/0.41	[A#](X) = X
0.00/0.41	[B#](X) = 2.X + 2
0.00/0.41	[C#](X) = 2.X + 2
0.00/0.41	[a#](X) = X
0.00/0.41	[b#](X) = 2.X
0.00/0.41	[c#](X) = 2.X
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A#(c(b(x1:S))) -> c#(A(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> A#(B(C(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> A#(c(x1:S))
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 A#(c(b(x1:S))) -> c#(A(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> A#(B(C(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> A#(c(x1:S))
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	->->-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A#(c(b(x1:S))) -> c#(A(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> A#(B(C(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> A#(c(x1:S))
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	-> Usable rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[A](X) = 2.X + 2
0.00/0.41	[B](X) = 2.X + 2
0.00/0.41	[C](X) = 2.X + 2
0.00/0.41	[a](X) = 2.X + 2
0.00/0.41	[b](X) = 2.X + 2
0.00/0.41	[c](X) = 2.X + 2
0.00/0.41	[A#](X) = X + 2
0.00/0.41	[B#](X) = 2.X + 2
0.00/0.41	[C#](X) = 2.X + 2
0.00/0.41	[a#](X) = 2.X + 2
0.00/0.41	[b#](X) = 2.X + 2
0.00/0.41	[c#](X) = 2.X + 2
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> A#(B(C(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> A#(c(x1:S))
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	->->-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 B#(C(a(x1:S))) -> B#(x1:S)
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	-> Usable rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[A](X) = 2.X + 2
0.00/0.41	[B](X) = 2.X + 2
0.00/0.41	[C](X) = 2.X + 2
0.00/0.41	[a](X) = 2.X + 2
0.00/0.41	[b](X) = X
0.00/0.41	[c](X) = X
0.00/0.41	[B#](X) = 2.X + 2
0.00/0.41	[C#](X) = 2.X + 2
0.00/0.41	[a#](X) = 2.X + 2
0.00/0.41	[b#](X) = X
0.00/0.41	[c#](X) = X
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	->->-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 B#(C(a(x1:S))) -> C#(B(x1:S))
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	-> Usable rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[A](X) = 2.X + 2
0.00/0.41	[B](X) = X
0.00/0.41	[C](X) = 2.X + 2
0.00/0.41	[a](X) = 2.X + 2
0.00/0.41	[b](X) = 2.X + 2
0.00/0.41	[c](X) = X
0.00/0.41	[B#](X) = X
0.00/0.41	[C#](X) = 2.X
0.00/0.41	[a#](X) = 2.X + 2
0.00/0.41	[b#](X) = 2.X
0.00/0.41	[c#](X) = X
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	->->-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 B#(C(a(x1:S))) -> a#(C(B(x1:S)))
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	-> Usable rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[A](X) = 2.X + 2
0.00/0.41	[B](X) = 2.X + 2
0.00/0.41	[C](X) = X
0.00/0.41	[a](X) = X + 2
0.00/0.41	[b](X) = X + 2
0.00/0.41	[c](X) = X
0.00/0.41	[B#](X) = 2.X + 2
0.00/0.41	[C#](X) = X
0.00/0.41	[a#](X) = X + 2
0.00/0.41	[b#](X) = X + 2
0.00/0.41	[c#](X) = X
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 C#(B(A(x1:S))) -> B#(C(x1:S))
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 a#(b(c(x1:S))) -> c#(b(a(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> C#(a(b(x1:S)))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	 c#(A(B(x1:S))) -> B#(A(c(x1:S)))
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	->->-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	->->-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	->->-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	
0.00/0.41	
0.00/0.41	The problem is decomposed in 3 subproblems.
0.00/0.41	
0.00/0.41	Problem 1.1: 
0.00/0.41	
0.00/0.41	Subterm Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 c#(A(B(x1:S))) -> c#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Projection:
0.00/0.41	 pi(c#) = 1
0.00/0.41	
0.00/0.41	Problem 1.1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 Empty
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Strongly Connected Components:
0.00/0.41	 There is no strongly connected component
0.00/0.41	
0.00/0.41	The problem is finite.
0.00/0.41	
0.00/0.41	Problem 1.2: 
0.00/0.41	
0.00/0.41	Subterm Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 C#(B(A(x1:S))) -> C#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Projection:
0.00/0.41	 pi(C#) = 1
0.00/0.41	
0.00/0.41	Problem 1.2: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 Empty
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Strongly Connected Components:
0.00/0.41	 There is no strongly connected component
0.00/0.41	
0.00/0.41	The problem is finite.
0.00/0.41	
0.00/0.41	Problem 1.3: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 a#(b(c(x1:S))) -> a#(x1:S)
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	-> Usable rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[A](X) = X + 2
0.00/0.41	[B](X) = X + 2
0.00/0.41	[C](X) = X + 1
0.00/0.41	[a](X) = X + 2
0.00/0.41	[b](X) = X + 2
0.00/0.41	[c](X) = X
0.00/0.41	[a#](X) = 2.X + 2
0.00/0.41	[b#](X) = 2.X + 2
0.00/0.41	
0.00/0.41	Problem 1.3: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	->->-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	
0.00/0.41	Problem 1.3: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 a#(b(c(x1:S))) -> b#(a(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	-> Usable rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[A](X) = 2.X + 2
0.00/0.41	[B](X) = 2.X + 2
0.00/0.41	[C](X) = 2.X + 2
0.00/0.41	[a](X) = 2.X + 2
0.00/0.41	[b](X) = 2.X + 2
0.00/0.41	[c](X) = 2.X + 2
0.00/0.41	[a#](X) = 2.X + 1
0.00/0.41	[b#](X) = 2.X + 2
0.00/0.41	
0.00/0.41	Problem 1.3: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 b#(a(C(x1:S))) -> a#(b(x1:S))
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	->->-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	
0.00/0.41	Problem 1.3: 
0.00/0.41	
0.00/0.41	Subterm Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 b#(a(C(x1:S))) -> b#(x1:S)
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Projection:
0.00/0.41	 pi(b#) = 1
0.00/0.41	
0.00/0.41	Problem 1.3: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 Empty
0.00/0.41	-> Rules:
0.00/0.41	 A(a(x1:S)) -> x1:S
0.00/0.41	 A(c(b(x1:S))) -> b(c(A(x1:S)))
0.00/0.41	 B(C(a(x1:S))) -> a(C(B(x1:S)))
0.00/0.41	 B(b(x1:S)) -> x1:S
0.00/0.41	 C(B(A(x1:S))) -> A(B(C(x1:S)))
0.00/0.41	 C(c(x1:S)) -> x1:S
0.00/0.41	 a(A(x1:S)) -> x1:S
0.00/0.41	 a(b(c(x1:S))) -> c(b(a(x1:S)))
0.00/0.41	 b(B(x1:S)) -> x1:S
0.00/0.41	 b(a(C(x1:S))) -> C(a(b(x1:S)))
0.00/0.41	 c(A(B(x1:S))) -> B(A(c(x1:S)))
0.00/0.41	 c(C(x1:S)) -> x1:S
0.00/0.41	->Strongly Connected Components:
0.00/0.41	 There is no strongly connected component
0.00/0.41	
0.00/0.41	The problem is finite.
0.00/0.41	EOF