2.85/2.88	YES
2.85/2.88	
2.85/2.88	Problem 1: 
2.85/2.88	
2.85/2.88	(VAR v_NonEmpty:S x1:S)
2.85/2.88	(RULES
2.85/2.88	A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.88	A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.88	A(C(x1:S)) -> b(x1:S)
2.85/2.88	A(a(x1:S)) -> x1:S
2.85/2.88	A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.88	B(A(x1:S)) -> c(x1:S)
2.85/2.88	B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.88	B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.88	B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.88	B(b(x1:S)) -> x1:S
2.85/2.88	C(B(x1:S)) -> a(x1:S)
2.85/2.88	C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.88	C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.88	C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.88	C(c(x1:S)) -> x1:S
2.85/2.88	a(A(x1:S)) -> x1:S
2.85/2.88	a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.88	a(b(x1:S)) -> C(x1:S)
2.85/2.88	b(B(x1:S)) -> x1:S
2.85/2.88	b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.88	b(c(x1:S)) -> A(x1:S)
2.85/2.88	c(C(x1:S)) -> x1:S
2.85/2.88	c(a(x1:S)) -> B(x1:S)
2.85/2.88	c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.88	)
2.85/2.88	
2.85/2.88	Problem 1: 
2.85/2.88	
2.85/2.88	Dependency Pairs Processor:
2.85/2.88	-> Pairs:
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(a(a(x1:S)))
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(a(x1:S))
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.88	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.88	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.88	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.88	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.88	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.88	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.88	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.88	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.88	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.88	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	-> Rules:
2.85/2.88	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.88	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.88	 A(C(x1:S)) -> b(x1:S)
2.85/2.88	 A(a(x1:S)) -> x1:S
2.85/2.88	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.88	 B(A(x1:S)) -> c(x1:S)
2.85/2.88	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.88	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.88	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.88	 B(b(x1:S)) -> x1:S
2.85/2.88	 C(B(x1:S)) -> a(x1:S)
2.85/2.88	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.88	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.88	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.88	 C(c(x1:S)) -> x1:S
2.85/2.88	 a(A(x1:S)) -> x1:S
2.85/2.88	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.88	 a(b(x1:S)) -> C(x1:S)
2.85/2.88	 b(B(x1:S)) -> x1:S
2.85/2.88	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.88	 b(c(x1:S)) -> A(x1:S)
2.85/2.88	 c(C(x1:S)) -> x1:S
2.85/2.88	 c(a(x1:S)) -> B(x1:S)
2.85/2.88	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.88	
2.85/2.88	Problem 1: 
2.85/2.88	
2.85/2.88	SCC Processor:
2.85/2.88	-> Pairs:
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(a(a(x1:S)))
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(a(x1:S))
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.88	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.88	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.88	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.88	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.88	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.88	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.88	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.88	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.88	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.88	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	-> Rules:
2.85/2.88	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.88	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.88	 A(C(x1:S)) -> b(x1:S)
2.85/2.88	 A(a(x1:S)) -> x1:S
2.85/2.88	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.88	 B(A(x1:S)) -> c(x1:S)
2.85/2.88	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.88	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.88	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.88	 B(b(x1:S)) -> x1:S
2.85/2.88	 C(B(x1:S)) -> a(x1:S)
2.85/2.88	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.88	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.88	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.88	 C(c(x1:S)) -> x1:S
2.85/2.88	 a(A(x1:S)) -> x1:S
2.85/2.88	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.88	 a(b(x1:S)) -> C(x1:S)
2.85/2.88	 b(B(x1:S)) -> x1:S
2.85/2.88	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.88	 b(c(x1:S)) -> A(x1:S)
2.85/2.88	 c(C(x1:S)) -> x1:S
2.85/2.88	 c(a(x1:S)) -> B(x1:S)
2.85/2.88	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.88	->Strongly Connected Components:
2.85/2.88	->->Cycle:
2.85/2.88	->->-> Pairs:
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(a(a(x1:S)))
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(a(x1:S))
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.88	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.88	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.88	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.88	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.88	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.88	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.88	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.88	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.88	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.88	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	->->-> Rules:
2.85/2.88	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.88	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.88	 A(C(x1:S)) -> b(x1:S)
2.85/2.88	 A(a(x1:S)) -> x1:S
2.85/2.88	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.88	 B(A(x1:S)) -> c(x1:S)
2.85/2.88	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.88	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.88	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.88	 B(b(x1:S)) -> x1:S
2.85/2.88	 C(B(x1:S)) -> a(x1:S)
2.85/2.88	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.88	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.88	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.88	 C(c(x1:S)) -> x1:S
2.85/2.88	 a(A(x1:S)) -> x1:S
2.85/2.88	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.88	 a(b(x1:S)) -> C(x1:S)
2.85/2.88	 b(B(x1:S)) -> x1:S
2.85/2.88	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.88	 b(c(x1:S)) -> A(x1:S)
2.85/2.88	 c(C(x1:S)) -> x1:S
2.85/2.88	 c(a(x1:S)) -> B(x1:S)
2.85/2.88	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.88	
2.85/2.88	Problem 1: 
2.85/2.88	
2.85/2.88	Reduction Pair Processor:
2.85/2.88	-> Pairs:
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(a(a(x1:S)))
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(a(x1:S))
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.88	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.88	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.88	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.88	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.88	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.88	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.88	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.88	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.88	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.88	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	-> Rules:
2.85/2.88	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.88	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.88	 A(C(x1:S)) -> b(x1:S)
2.85/2.88	 A(a(x1:S)) -> x1:S
2.85/2.88	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.88	 B(A(x1:S)) -> c(x1:S)
2.85/2.88	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.88	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.88	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.88	 B(b(x1:S)) -> x1:S
2.85/2.88	 C(B(x1:S)) -> a(x1:S)
2.85/2.88	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.88	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.88	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.88	 C(c(x1:S)) -> x1:S
2.85/2.88	 a(A(x1:S)) -> x1:S
2.85/2.88	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.88	 a(b(x1:S)) -> C(x1:S)
2.85/2.88	 b(B(x1:S)) -> x1:S
2.85/2.88	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.88	 b(c(x1:S)) -> A(x1:S)
2.85/2.88	 c(C(x1:S)) -> x1:S
2.85/2.88	 c(a(x1:S)) -> B(x1:S)
2.85/2.88	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.88	-> Usable rules:
2.85/2.88	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.88	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.88	 A(C(x1:S)) -> b(x1:S)
2.85/2.88	 A(a(x1:S)) -> x1:S
2.85/2.88	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.88	 B(A(x1:S)) -> c(x1:S)
2.85/2.88	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.88	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.88	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.88	 B(b(x1:S)) -> x1:S
2.85/2.88	 C(B(x1:S)) -> a(x1:S)
2.85/2.88	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.88	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.88	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.88	 C(c(x1:S)) -> x1:S
2.85/2.88	 a(A(x1:S)) -> x1:S
2.85/2.88	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.88	 a(b(x1:S)) -> C(x1:S)
2.85/2.88	 b(B(x1:S)) -> x1:S
2.85/2.88	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.88	 b(c(x1:S)) -> A(x1:S)
2.85/2.88	 c(C(x1:S)) -> x1:S
2.85/2.88	 c(a(x1:S)) -> B(x1:S)
2.85/2.88	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.88	->Interpretation type:
2.85/2.88	 Linear
2.85/2.88	->Coefficients:
2.85/2.88	 Natural Numbers
2.85/2.88	->Dimension:
2.85/2.88	 1
2.85/2.88	->Bound:
2.85/2.88	 2
2.85/2.88	->Interpretation:
2.85/2.88	 
2.85/2.88	[A](X) = 2.X + 2
2.85/2.88	[B](X) = 2.X + 2
2.85/2.88	[C](X) = 2.X + 2
2.85/2.88	[a](X) = 2.X + 2
2.85/2.88	[b](X) = 2.X + 2
2.85/2.88	[c](X) = 2.X + 2
2.85/2.88	[A#](X) = 2.X + 2
2.85/2.88	[B#](X) = 2.X + 2
2.85/2.88	[C#](X) = 2.X + 2
2.85/2.88	[a#](X) = 2.X + 1
2.85/2.88	[b#](X) = 2.X + 2
2.85/2.88	[c#](X) = 2.X + 2
2.85/2.88	
2.85/2.88	Problem 1: 
2.85/2.88	
2.85/2.88	SCC Processor:
2.85/2.88	-> Pairs:
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(a(x1:S))
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.88	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.88	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.88	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.88	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.88	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.88	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.88	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.88	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.88	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.88	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	-> Rules:
2.85/2.88	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.88	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.88	 A(C(x1:S)) -> b(x1:S)
2.85/2.88	 A(a(x1:S)) -> x1:S
2.85/2.88	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.88	 B(A(x1:S)) -> c(x1:S)
2.85/2.88	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.88	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.88	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.88	 B(b(x1:S)) -> x1:S
2.85/2.88	 C(B(x1:S)) -> a(x1:S)
2.85/2.88	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.88	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.88	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.88	 C(c(x1:S)) -> x1:S
2.85/2.88	 a(A(x1:S)) -> x1:S
2.85/2.88	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.88	 a(b(x1:S)) -> C(x1:S)
2.85/2.88	 b(B(x1:S)) -> x1:S
2.85/2.88	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.88	 b(c(x1:S)) -> A(x1:S)
2.85/2.88	 c(C(x1:S)) -> x1:S
2.85/2.88	 c(a(x1:S)) -> B(x1:S)
2.85/2.88	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.88	->Strongly Connected Components:
2.85/2.88	->->Cycle:
2.85/2.88	->->-> Pairs:
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(a(x1:S))
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.88	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.88	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.88	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.88	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.88	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.88	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.88	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.88	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.88	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.88	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.88	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.88	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.88	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.88	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.88	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.88	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.88	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	->->-> Rules:
2.85/2.88	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.88	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.88	 A(C(x1:S)) -> b(x1:S)
2.85/2.88	 A(a(x1:S)) -> x1:S
2.85/2.88	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.88	 B(A(x1:S)) -> c(x1:S)
2.85/2.88	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.88	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.88	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.88	 B(b(x1:S)) -> x1:S
2.85/2.88	 C(B(x1:S)) -> a(x1:S)
2.85/2.88	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.88	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.88	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.88	 C(c(x1:S)) -> x1:S
2.85/2.88	 a(A(x1:S)) -> x1:S
2.85/2.88	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.88	 a(b(x1:S)) -> C(x1:S)
2.85/2.88	 b(B(x1:S)) -> x1:S
2.85/2.88	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.88	 b(c(x1:S)) -> A(x1:S)
2.85/2.88	 c(C(x1:S)) -> x1:S
2.85/2.88	 c(a(x1:S)) -> B(x1:S)
2.85/2.88	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.88	
2.85/2.88	Problem 1: 
2.85/2.88	
2.85/2.88	Reduction Pair Processor:
2.85/2.88	-> Pairs:
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(a(x1:S))
2.85/2.88	 A#(A(A(A(x1:S)))) -> a#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.88	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.88	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.88	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.88	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.88	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.88	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	-> Usable rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	->Interpretation type:
2.85/2.89	 Linear
2.85/2.89	->Coefficients:
2.85/2.89	 Natural Numbers
2.85/2.89	->Dimension:
2.85/2.89	 1
2.85/2.89	->Bound:
2.85/2.89	 2
2.85/2.89	->Interpretation:
2.85/2.89	 
2.85/2.89	[A](X) = 2.X + 2
2.85/2.89	[B](X) = 2.X + 2
2.85/2.89	[C](X) = 2.X + 2
2.85/2.89	[a](X) = 2.X + 2
2.85/2.89	[b](X) = 2.X + 2
2.85/2.89	[c](X) = 2.X + 2
2.85/2.89	[A#](X) = 2.X + 2
2.85/2.89	[B#](X) = 2.X + 2
2.85/2.89	[C#](X) = X + 2
2.85/2.89	[a#](X) = X + 2
2.85/2.89	[b#](X) = 2.X + 2
2.85/2.89	[c#](X) = X + 2
2.85/2.89	
2.85/2.89	Problem 1: 
2.85/2.89	
2.85/2.89	SCC Processor:
2.85/2.89	-> Pairs:
2.85/2.89	 A#(A(A(A(x1:S)))) -> a#(x1:S)
2.85/2.89	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	->Strongly Connected Components:
2.85/2.89	->->Cycle:
2.85/2.89	->->-> Pairs:
2.85/2.89	 A#(A(A(A(x1:S)))) -> a#(x1:S)
2.85/2.89	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	->->-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	
2.85/2.89	Problem 1: 
2.85/2.89	
2.85/2.89	Reduction Pair Processor:
2.85/2.89	-> Pairs:
2.85/2.89	 A#(A(A(A(x1:S)))) -> a#(x1:S)
2.85/2.89	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	-> Usable rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	->Interpretation type:
2.85/2.89	 Linear
2.85/2.89	->Coefficients:
2.85/2.89	 Natural Numbers
2.85/2.89	->Dimension:
2.85/2.89	 1
2.85/2.89	->Bound:
2.85/2.89	 2
2.85/2.89	->Interpretation:
2.85/2.89	 
2.85/2.89	[A](X) = 2.X + 2
2.85/2.89	[B](X) = 2.X + 2
2.85/2.89	[C](X) = 2.X + 2
2.85/2.89	[a](X) = 2.X + 2
2.85/2.89	[b](X) = 2.X + 2
2.85/2.89	[c](X) = 2.X + 2
2.85/2.89	[A#](X) = 2.X
2.85/2.89	[B#](X) = 2.X + 2
2.85/2.89	[C#](X) = 2.X
2.85/2.89	[a#](X) = X + 1
2.85/2.89	[b#](X) = 2.X
2.85/2.89	[c#](X) = 2.X
2.85/2.89	
2.85/2.89	Problem 1: 
2.85/2.89	
2.85/2.89	SCC Processor:
2.85/2.89	-> Pairs:
2.85/2.89	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	->Strongly Connected Components:
2.85/2.89	->->Cycle:
2.85/2.89	->->-> Pairs:
2.85/2.89	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	->->-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	
2.85/2.89	Problem 1: 
2.85/2.89	
2.85/2.89	Reduction Pair Processor:
2.85/2.89	-> Pairs:
2.85/2.89	 A#(A(A(b(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	-> Usable rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	->Interpretation type:
2.85/2.89	 Linear
2.85/2.89	->Coefficients:
2.85/2.89	 Natural Numbers
2.85/2.89	->Dimension:
2.85/2.89	 1
2.85/2.89	->Bound:
2.85/2.89	 2
2.85/2.89	->Interpretation:
2.85/2.89	 
2.85/2.89	[A](X) = 2.X + 2
2.85/2.89	[B](X) = 2.X + 2
2.85/2.89	[C](X) = 2.X + 2
2.85/2.89	[a](X) = 2.X + 2
2.85/2.89	[b](X) = 2.X + 2
2.85/2.89	[c](X) = 2.X + 2
2.85/2.89	[A#](X) = 2.X + 2
2.85/2.89	[B#](X) = 2.X + 2
2.85/2.89	[C#](X) = 2.X + 2
2.85/2.89	[a#](X) = 2.X + 2
2.85/2.89	[b#](X) = X + 1
2.85/2.89	[c#](X) = 2.X + 2
2.85/2.89	
2.85/2.89	Problem 1: 
2.85/2.89	
2.85/2.89	SCC Processor:
2.85/2.89	-> Pairs:
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	->Strongly Connected Components:
2.85/2.89	->->Cycle:
2.85/2.89	->->-> Pairs:
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	->->-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	
2.85/2.89	Problem 1: 
2.85/2.89	
2.85/2.89	Reduction Pair Processor:
2.85/2.89	-> Pairs:
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(C(x1:S))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	-> Usable rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	->Interpretation type:
2.85/2.89	 Linear
2.85/2.89	->Coefficients:
2.85/2.89	 Natural Numbers
2.85/2.89	->Dimension:
2.85/2.89	 1
2.85/2.89	->Bound:
2.85/2.89	 2
2.85/2.89	->Interpretation:
2.85/2.89	 
2.85/2.89	[A](X) = 2.X + 2
2.85/2.89	[B](X) = 2.X + 2
2.85/2.89	[C](X) = 2.X + 2
2.85/2.89	[a](X) = 2.X + 2
2.85/2.89	[b](X) = 2.X + 2
2.85/2.89	[c](X) = 2.X + 2
2.85/2.89	[A#](X) = 2.X + 2
2.85/2.89	[B#](X) = 2.X + 2
2.85/2.89	[C#](X) = 2.X
2.85/2.89	[a#](X) = X
2.85/2.89	[b#](X) = 2.X + 2
2.85/2.89	[c#](X) = 2.X
2.85/2.89	
2.85/2.89	Problem 1: 
2.85/2.89	
2.85/2.89	SCC Processor:
2.85/2.89	-> Pairs:
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	->Strongly Connected Components:
2.85/2.89	->->Cycle:
2.85/2.89	->->-> Pairs:
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	->->-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	
2.85/2.89	Problem 1: 
2.85/2.89	
2.85/2.89	Reduction Pair Processor:
2.85/2.89	-> Pairs:
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(C(x1:S)))
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	-> Usable rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	->Interpretation type:
2.85/2.89	 Linear
2.85/2.89	->Coefficients:
2.85/2.89	 Natural Numbers
2.85/2.89	->Dimension:
2.85/2.89	 1
2.85/2.89	->Bound:
2.85/2.89	 2
2.85/2.89	->Interpretation:
2.85/2.89	 
2.85/2.89	[A](X) = 2.X + 2
2.85/2.89	[B](X) = 2.X + 2
2.85/2.89	[C](X) = 2.X + 2
2.85/2.89	[a](X) = 2.X + 2
2.85/2.89	[b](X) = 2.X + 2
2.85/2.89	[c](X) = 2.X + 2
2.85/2.89	[A#](X) = 2.X
2.85/2.89	[B#](X) = 2.X + 2
2.85/2.89	[C#](X) = 2.X + 2
2.85/2.89	[a#](X) = 2.X
2.85/2.89	[b#](X) = 2.X
2.85/2.89	[c#](X) = 2.X + 2
2.85/2.89	
2.85/2.89	Problem 1: 
2.85/2.89	
2.85/2.89	SCC Processor:
2.85/2.89	-> Pairs:
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	->Strongly Connected Components:
2.85/2.89	->->Cycle:
2.85/2.89	->->-> Pairs:
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	->->-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	
2.85/2.89	Problem 1: 
2.85/2.89	
2.85/2.89	Reduction Pair Processor:
2.85/2.89	-> Pairs:
2.85/2.89	 A#(A(A(b(x1:S)))) -> a#(a(a(C(x1:S))))
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.85/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.85/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.85/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.85/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.85/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.85/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.85/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.85/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	-> Rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	-> Usable rules:
2.85/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.85/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.85/2.89	 A(C(x1:S)) -> b(x1:S)
2.85/2.89	 A(a(x1:S)) -> x1:S
2.85/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.85/2.89	 B(A(x1:S)) -> c(x1:S)
2.85/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.85/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.85/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.85/2.89	 B(b(x1:S)) -> x1:S
2.85/2.89	 C(B(x1:S)) -> a(x1:S)
2.85/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.85/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.85/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.85/2.89	 C(c(x1:S)) -> x1:S
2.85/2.89	 a(A(x1:S)) -> x1:S
2.85/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.85/2.89	 a(b(x1:S)) -> C(x1:S)
2.85/2.89	 b(B(x1:S)) -> x1:S
2.85/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.85/2.89	 b(c(x1:S)) -> A(x1:S)
2.85/2.89	 c(C(x1:S)) -> x1:S
2.85/2.89	 c(a(x1:S)) -> B(x1:S)
2.85/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.85/2.89	->Interpretation type:
2.85/2.89	 Linear
2.85/2.89	->Coefficients:
2.85/2.89	 Natural Numbers
2.85/2.89	->Dimension:
2.85/2.89	 1
2.85/2.89	->Bound:
2.85/2.89	 2
2.85/2.89	->Interpretation:
2.85/2.89	 
2.85/2.89	[A](X) = 2.X + 2
2.85/2.89	[B](X) = 2.X + 2
2.85/2.89	[C](X) = 2.X + 2
2.85/2.89	[a](X) = 2.X + 2
2.85/2.89	[b](X) = 2.X + 2
2.85/2.89	[c](X) = 2.X + 2
2.85/2.89	[A#](X) = 2.X + 2
2.85/2.89	[B#](X) = 2.X + 2
2.85/2.89	[C#](X) = 2.X + 2
2.85/2.89	[a#](X) = 2.X + 1
2.85/2.89	[b#](X) = 2.X + 2
2.85/2.89	[c#](X) = 2.X + 2
2.85/2.89	
2.85/2.89	Problem 1: 
2.85/2.89	
2.85/2.89	SCC Processor:
2.85/2.89	-> Pairs:
2.85/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.85/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.85/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.85/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.85/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.85/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	-> Rules:
2.87/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.89	 A(C(x1:S)) -> b(x1:S)
2.87/2.89	 A(a(x1:S)) -> x1:S
2.87/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.89	 B(A(x1:S)) -> c(x1:S)
2.87/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.89	 B(b(x1:S)) -> x1:S
2.87/2.89	 C(B(x1:S)) -> a(x1:S)
2.87/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.89	 C(c(x1:S)) -> x1:S
2.87/2.89	 a(A(x1:S)) -> x1:S
2.87/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.89	 a(b(x1:S)) -> C(x1:S)
2.87/2.89	 b(B(x1:S)) -> x1:S
2.87/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.89	 b(c(x1:S)) -> A(x1:S)
2.87/2.89	 c(C(x1:S)) -> x1:S
2.87/2.89	 c(a(x1:S)) -> B(x1:S)
2.87/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.89	->Strongly Connected Components:
2.87/2.89	->->Cycle:
2.87/2.89	->->-> Pairs:
2.87/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	->->-> Rules:
2.87/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.89	 A(C(x1:S)) -> b(x1:S)
2.87/2.89	 A(a(x1:S)) -> x1:S
2.87/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.89	 B(A(x1:S)) -> c(x1:S)
2.87/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.89	 B(b(x1:S)) -> x1:S
2.87/2.89	 C(B(x1:S)) -> a(x1:S)
2.87/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.89	 C(c(x1:S)) -> x1:S
2.87/2.89	 a(A(x1:S)) -> x1:S
2.87/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.89	 a(b(x1:S)) -> C(x1:S)
2.87/2.89	 b(B(x1:S)) -> x1:S
2.87/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.89	 b(c(x1:S)) -> A(x1:S)
2.87/2.89	 c(C(x1:S)) -> x1:S
2.87/2.89	 c(a(x1:S)) -> B(x1:S)
2.87/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.89	
2.87/2.89	Problem 1: 
2.87/2.89	
2.87/2.89	Reduction Pair Processor:
2.87/2.89	-> Pairs:
2.87/2.89	 A#(C(x1:S)) -> b#(x1:S)
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	-> Rules:
2.87/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.89	 A(C(x1:S)) -> b(x1:S)
2.87/2.89	 A(a(x1:S)) -> x1:S
2.87/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.89	 B(A(x1:S)) -> c(x1:S)
2.87/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.89	 B(b(x1:S)) -> x1:S
2.87/2.89	 C(B(x1:S)) -> a(x1:S)
2.87/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.89	 C(c(x1:S)) -> x1:S
2.87/2.89	 a(A(x1:S)) -> x1:S
2.87/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.89	 a(b(x1:S)) -> C(x1:S)
2.87/2.89	 b(B(x1:S)) -> x1:S
2.87/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.89	 b(c(x1:S)) -> A(x1:S)
2.87/2.89	 c(C(x1:S)) -> x1:S
2.87/2.89	 c(a(x1:S)) -> B(x1:S)
2.87/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.89	-> Usable rules:
2.87/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.89	 A(C(x1:S)) -> b(x1:S)
2.87/2.89	 A(a(x1:S)) -> x1:S
2.87/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.89	 B(A(x1:S)) -> c(x1:S)
2.87/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.89	 B(b(x1:S)) -> x1:S
2.87/2.89	 C(B(x1:S)) -> a(x1:S)
2.87/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.89	 C(c(x1:S)) -> x1:S
2.87/2.89	 a(A(x1:S)) -> x1:S
2.87/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.89	 a(b(x1:S)) -> C(x1:S)
2.87/2.89	 b(B(x1:S)) -> x1:S
2.87/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.89	 b(c(x1:S)) -> A(x1:S)
2.87/2.89	 c(C(x1:S)) -> x1:S
2.87/2.89	 c(a(x1:S)) -> B(x1:S)
2.87/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.89	->Interpretation type:
2.87/2.89	 Linear
2.87/2.89	->Coefficients:
2.87/2.89	 Natural Numbers
2.87/2.89	->Dimension:
2.87/2.89	 1
2.87/2.89	->Bound:
2.87/2.89	 2
2.87/2.89	->Interpretation:
2.87/2.89	 
2.87/2.89	[A](X) = 2.X + 2
2.87/2.89	[B](X) = 2.X + 2
2.87/2.89	[C](X) = 2.X + 2
2.87/2.89	[a](X) = 2.X + 2
2.87/2.89	[b](X) = 2.X + 2
2.87/2.89	[c](X) = 2.X + 2
2.87/2.89	[A#](X) = 2.X + 2
2.87/2.89	[B#](X) = 2.X + 2
2.87/2.89	[C#](X) = 2.X + 2
2.87/2.89	[a#](X) = 2.X + 2
2.87/2.89	[b#](X) = 2.X + 2
2.87/2.89	[c#](X) = 2.X + 2
2.87/2.89	
2.87/2.89	Problem 1: 
2.87/2.89	
2.87/2.89	SCC Processor:
2.87/2.89	-> Pairs:
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	-> Rules:
2.87/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.89	 A(C(x1:S)) -> b(x1:S)
2.87/2.89	 A(a(x1:S)) -> x1:S
2.87/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.89	 B(A(x1:S)) -> c(x1:S)
2.87/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.89	 B(b(x1:S)) -> x1:S
2.87/2.89	 C(B(x1:S)) -> a(x1:S)
2.87/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.89	 C(c(x1:S)) -> x1:S
2.87/2.89	 a(A(x1:S)) -> x1:S
2.87/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.89	 a(b(x1:S)) -> C(x1:S)
2.87/2.89	 b(B(x1:S)) -> x1:S
2.87/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.89	 b(c(x1:S)) -> A(x1:S)
2.87/2.89	 c(C(x1:S)) -> x1:S
2.87/2.89	 c(a(x1:S)) -> B(x1:S)
2.87/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.89	->Strongly Connected Components:
2.87/2.89	->->Cycle:
2.87/2.89	->->-> Pairs:
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	->->-> Rules:
2.87/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.89	 A(C(x1:S)) -> b(x1:S)
2.87/2.89	 A(a(x1:S)) -> x1:S
2.87/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.89	 B(A(x1:S)) -> c(x1:S)
2.87/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.89	 B(b(x1:S)) -> x1:S
2.87/2.89	 C(B(x1:S)) -> a(x1:S)
2.87/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.89	 C(c(x1:S)) -> x1:S
2.87/2.89	 a(A(x1:S)) -> x1:S
2.87/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.89	 a(b(x1:S)) -> C(x1:S)
2.87/2.89	 b(B(x1:S)) -> x1:S
2.87/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.89	 b(c(x1:S)) -> A(x1:S)
2.87/2.89	 c(C(x1:S)) -> x1:S
2.87/2.89	 c(a(x1:S)) -> B(x1:S)
2.87/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.89	
2.87/2.89	Problem 1: 
2.87/2.89	
2.87/2.89	Reduction Pair Processor:
2.87/2.89	-> Pairs:
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	-> Rules:
2.87/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.89	 A(C(x1:S)) -> b(x1:S)
2.87/2.89	 A(a(x1:S)) -> x1:S
2.87/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.89	 B(A(x1:S)) -> c(x1:S)
2.87/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.89	 B(b(x1:S)) -> x1:S
2.87/2.89	 C(B(x1:S)) -> a(x1:S)
2.87/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.89	 C(c(x1:S)) -> x1:S
2.87/2.89	 a(A(x1:S)) -> x1:S
2.87/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.89	 a(b(x1:S)) -> C(x1:S)
2.87/2.89	 b(B(x1:S)) -> x1:S
2.87/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.89	 b(c(x1:S)) -> A(x1:S)
2.87/2.89	 c(C(x1:S)) -> x1:S
2.87/2.89	 c(a(x1:S)) -> B(x1:S)
2.87/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.89	-> Usable rules:
2.87/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.89	 A(C(x1:S)) -> b(x1:S)
2.87/2.89	 A(a(x1:S)) -> x1:S
2.87/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.89	 B(A(x1:S)) -> c(x1:S)
2.87/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.89	 B(b(x1:S)) -> x1:S
2.87/2.89	 C(B(x1:S)) -> a(x1:S)
2.87/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.89	 C(c(x1:S)) -> x1:S
2.87/2.89	 a(A(x1:S)) -> x1:S
2.87/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.89	 a(b(x1:S)) -> C(x1:S)
2.87/2.89	 b(B(x1:S)) -> x1:S
2.87/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.89	 b(c(x1:S)) -> A(x1:S)
2.87/2.89	 c(C(x1:S)) -> x1:S
2.87/2.89	 c(a(x1:S)) -> B(x1:S)
2.87/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.89	->Interpretation type:
2.87/2.89	 Linear
2.87/2.89	->Coefficients:
2.87/2.89	 Natural Numbers
2.87/2.89	->Dimension:
2.87/2.89	 1
2.87/2.89	->Bound:
2.87/2.89	 2
2.87/2.89	->Interpretation:
2.87/2.89	 
2.87/2.89	[A](X) = 2.X + 2
2.87/2.89	[B](X) = 2.X + 2
2.87/2.89	[C](X) = 2.X + 2
2.87/2.89	[a](X) = 2.X + 2
2.87/2.89	[b](X) = 2.X + 2
2.87/2.89	[c](X) = 2.X + 2
2.87/2.89	[A#](X) = 2.X + 2
2.87/2.89	[B#](X) = 2.X + 2
2.87/2.89	[C#](X) = 2.X + 2
2.87/2.89	[a#](X) = 2.X + 1
2.87/2.89	[b#](X) = 2.X + 2
2.87/2.89	[c#](X) = 2.X + 2
2.87/2.89	
2.87/2.89	Problem 1: 
2.87/2.89	
2.87/2.89	SCC Processor:
2.87/2.89	-> Pairs:
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	-> Rules:
2.87/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.89	 A(C(x1:S)) -> b(x1:S)
2.87/2.89	 A(a(x1:S)) -> x1:S
2.87/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.89	 B(A(x1:S)) -> c(x1:S)
2.87/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.89	 B(b(x1:S)) -> x1:S
2.87/2.89	 C(B(x1:S)) -> a(x1:S)
2.87/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.89	 C(c(x1:S)) -> x1:S
2.87/2.89	 a(A(x1:S)) -> x1:S
2.87/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.89	 a(b(x1:S)) -> C(x1:S)
2.87/2.89	 b(B(x1:S)) -> x1:S
2.87/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.89	 b(c(x1:S)) -> A(x1:S)
2.87/2.89	 c(C(x1:S)) -> x1:S
2.87/2.89	 c(a(x1:S)) -> B(x1:S)
2.87/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.89	->Strongly Connected Components:
2.87/2.89	->->Cycle:
2.87/2.89	->->-> Pairs:
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.89	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.89	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.89	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.89	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.89	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.89	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.89	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.89	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.89	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.89	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.89	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.89	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.89	->->-> Rules:
2.87/2.89	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.89	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.89	 A(C(x1:S)) -> b(x1:S)
2.87/2.89	 A(a(x1:S)) -> x1:S
2.87/2.89	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.89	 B(A(x1:S)) -> c(x1:S)
2.87/2.89	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.89	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.89	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.89	 B(b(x1:S)) -> x1:S
2.87/2.89	 C(B(x1:S)) -> a(x1:S)
2.87/2.89	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.89	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.89	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.89	 C(c(x1:S)) -> x1:S
2.87/2.89	 a(A(x1:S)) -> x1:S
2.87/2.89	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.89	 a(b(x1:S)) -> C(x1:S)
2.87/2.89	 b(B(x1:S)) -> x1:S
2.87/2.89	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.89	 b(c(x1:S)) -> A(x1:S)
2.87/2.89	 c(C(x1:S)) -> x1:S
2.87/2.89	 c(a(x1:S)) -> B(x1:S)
2.87/2.89	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	Reduction Pair Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 A#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.90	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	-> Usable rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Interpretation type:
2.87/2.90	 Linear
2.87/2.90	->Coefficients:
2.87/2.90	 Natural Numbers
2.87/2.90	->Dimension:
2.87/2.90	 1
2.87/2.90	->Bound:
2.87/2.90	 2
2.87/2.90	->Interpretation:
2.87/2.90	 
2.87/2.90	[A](X) = X + 2
2.87/2.90	[B](X) = X + 2
2.87/2.90	[C](X) = X + 2
2.87/2.90	[a](X) = X + 2
2.87/2.90	[b](X) = X + 2
2.87/2.90	[c](X) = X + 2
2.87/2.90	[A#](X) = 2.X + 2
2.87/2.90	[B#](X) = 2.X + 2
2.87/2.90	[C#](X) = 2.X + 2
2.87/2.90	[a#](X) = 2.X + 2
2.87/2.90	[b#](X) = 2.X + 1
2.87/2.90	[c#](X) = 2.X + 2
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	SCC Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.90	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Strongly Connected Components:
2.87/2.90	->->Cycle:
2.87/2.90	->->-> Pairs:
2.87/2.90	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.90	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	->->-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	Reduction Pair Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 A#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.90	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	-> Usable rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Interpretation type:
2.87/2.90	 Linear
2.87/2.90	->Coefficients:
2.87/2.90	 Natural Numbers
2.87/2.90	->Dimension:
2.87/2.90	 1
2.87/2.90	->Bound:
2.87/2.90	 2
2.87/2.90	->Interpretation:
2.87/2.90	 
2.87/2.90	[A](X) = 2.X + 2
2.87/2.90	[B](X) = 2.X + 2
2.87/2.90	[C](X) = 2.X + 2
2.87/2.90	[a](X) = 2.X + 2
2.87/2.90	[b](X) = 2.X + 2
2.87/2.90	[c](X) = 2.X + 2
2.87/2.90	[A#](X) = 2.X + 2
2.87/2.90	[B#](X) = 2.X + 2
2.87/2.90	[C#](X) = 2.X + 2
2.87/2.90	[a#](X) = X + 2
2.87/2.90	[b#](X) = 2.X + 2
2.87/2.90	[c#](X) = 2.X + 1
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	SCC Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.90	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Strongly Connected Components:
2.87/2.90	->->Cycle:
2.87/2.90	->->-> Pairs:
2.87/2.90	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.90	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	->->-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	Reduction Pair Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 A#(c(c(c(x1:S)))) -> b#(C(C(C(x1:S))))
2.87/2.90	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	-> Usable rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Interpretation type:
2.87/2.90	 Linear
2.87/2.90	->Coefficients:
2.87/2.90	 Natural Numbers
2.87/2.90	->Dimension:
2.87/2.90	 1
2.87/2.90	->Bound:
2.87/2.90	 2
2.87/2.90	->Interpretation:
2.87/2.90	 
2.87/2.90	[A](X) = 2.X + 2
2.87/2.90	[B](X) = 2.X + 2
2.87/2.90	[C](X) = 2.X + 2
2.87/2.90	[a](X) = 2.X + 2
2.87/2.90	[b](X) = 2.X + 2
2.87/2.90	[c](X) = 2.X + 2
2.87/2.90	[A#](X) = 2.X + 1
2.87/2.90	[B#](X) = 2.X
2.87/2.90	[C#](X) = 2.X + 2
2.87/2.90	[a#](X) = X
2.87/2.90	[b#](X) = 2.X
2.87/2.90	[c#](X) = 2.X
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	SCC Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 B#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(A(x1:S)))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(A(x1:S))
2.87/2.90	 a#(a(a(a(x1:S)))) -> A#(x1:S)
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 b#(c(x1:S)) -> A#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Strongly Connected Components:
2.87/2.90	->->Cycle:
2.87/2.90	->->-> Pairs:
2.87/2.90	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	->->-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	Reduction Pair Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(A(x1:S)) -> c#(x1:S)
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	-> Usable rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Interpretation type:
2.87/2.90	 Linear
2.87/2.90	->Coefficients:
2.87/2.90	 Natural Numbers
2.87/2.90	->Dimension:
2.87/2.90	 1
2.87/2.90	->Bound:
2.87/2.90	 2
2.87/2.90	->Interpretation:
2.87/2.90	 
2.87/2.90	[A](X) = X + 2
2.87/2.90	[B](X) = X + 2
2.87/2.90	[C](X) = X + 2
2.87/2.90	[a](X) = X + 2
2.87/2.90	[b](X) = X + 2
2.87/2.90	[c](X) = X + 2
2.87/2.90	[B#](X) = X + 1
2.87/2.90	[C#](X) = X + 2
2.87/2.90	[a#](X) = X + 2
2.87/2.90	[b#](X) = X
2.87/2.90	[c#](X) = X + 1
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	SCC Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Strongly Connected Components:
2.87/2.90	->->Cycle:
2.87/2.90	->->-> Pairs:
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	->->-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	Reduction Pair Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(b(x1:S)))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	-> Usable rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Interpretation type:
2.87/2.90	 Linear
2.87/2.90	->Coefficients:
2.87/2.90	 Natural Numbers
2.87/2.90	->Dimension:
2.87/2.90	 1
2.87/2.90	->Bound:
2.87/2.90	 2
2.87/2.90	->Interpretation:
2.87/2.90	 
2.87/2.90	[A](X) = 2.X + 2
2.87/2.90	[B](X) = 2.X + 2
2.87/2.90	[C](X) = 2.X + 2
2.87/2.90	[a](X) = 2.X + 2
2.87/2.90	[b](X) = 2.X + 2
2.87/2.90	[c](X) = 2.X + 2
2.87/2.90	[B#](X) = 2.X + 2
2.87/2.90	[C#](X) = 2.X + 2
2.87/2.90	[a#](X) = 2.X + 2
2.87/2.90	[b#](X) = X
2.87/2.90	[c#](X) = 2.X + 2
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	SCC Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Strongly Connected Components:
2.87/2.90	->->Cycle:
2.87/2.90	->->-> Pairs:
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	->->-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	Reduction Pair Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(b(x1:S))
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	-> Usable rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Interpretation type:
2.87/2.90	 Linear
2.87/2.90	->Coefficients:
2.87/2.90	 Natural Numbers
2.87/2.90	->Dimension:
2.87/2.90	 1
2.87/2.90	->Bound:
2.87/2.90	 2
2.87/2.90	->Interpretation:
2.87/2.90	 
2.87/2.90	[A](X) = 2.X + 2
2.87/2.90	[B](X) = 2.X + 2
2.87/2.90	[C](X) = 2.X + 2
2.87/2.90	[a](X) = 2.X + 2
2.87/2.90	[b](X) = 2.X + 2
2.87/2.90	[c](X) = 2.X + 2
2.87/2.90	[B#](X) = 2.X + 2
2.87/2.90	[C#](X) = 2.X + 2
2.87/2.90	[a#](X) = 2.X + 2
2.87/2.90	[b#](X) = X
2.87/2.90	[c#](X) = 2.X + 2
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	SCC Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Strongly Connected Components:
2.87/2.90	->->Cycle:
2.87/2.90	->->-> Pairs:
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	->->-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	Reduction Pair Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(B(B(B(x1:S)))) -> b#(x1:S)
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	-> Usable rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Interpretation type:
2.87/2.90	 Linear
2.87/2.90	->Coefficients:
2.87/2.90	 Natural Numbers
2.87/2.90	->Dimension:
2.87/2.90	 1
2.87/2.90	->Bound:
2.87/2.90	 2
2.87/2.90	->Interpretation:
2.87/2.90	 
2.87/2.90	[A](X) = 2.X + 2
2.87/2.90	[B](X) = 2.X + 2
2.87/2.90	[C](X) = 2.X + 2
2.87/2.90	[a](X) = 2.X + 2
2.87/2.90	[b](X) = 2.X + 2
2.87/2.90	[c](X) = 2.X + 2
2.87/2.90	[B#](X) = 2.X + 1
2.87/2.90	[C#](X) = 2.X + 2
2.87/2.90	[a#](X) = 2.X + 2
2.87/2.90	[b#](X) = 2.X + 1
2.87/2.90	[c#](X) = 2.X + 1
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	SCC Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Strongly Connected Components:
2.87/2.90	->->Cycle:
2.87/2.90	->->-> Pairs:
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	->->-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	Reduction Pair Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(A(x1:S))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	-> Usable rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Interpretation type:
2.87/2.90	 Linear
2.87/2.90	->Coefficients:
2.87/2.90	 Natural Numbers
2.87/2.90	->Dimension:
2.87/2.90	 1
2.87/2.90	->Bound:
2.87/2.90	 2
2.87/2.90	->Interpretation:
2.87/2.90	 
2.87/2.90	[A](X) = 2.X + 2
2.87/2.90	[B](X) = 2.X + 2
2.87/2.90	[C](X) = 2.X + 2
2.87/2.90	[a](X) = 2.X + 2
2.87/2.90	[b](X) = 2.X + 2
2.87/2.90	[c](X) = 2.X + 2
2.87/2.90	[B#](X) = 2.X + 2
2.87/2.90	[C#](X) = 2.X + 2
2.87/2.90	[a#](X) = 2.X + 2
2.87/2.90	[b#](X) = 2.X
2.87/2.90	[c#](X) = 2.X + 2
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	SCC Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Strongly Connected Components:
2.87/2.90	->->Cycle:
2.87/2.90	->->-> Pairs:
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	->->-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	Reduction Pair Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(A(x1:S)))
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	-> Usable rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Interpretation type:
2.87/2.90	 Linear
2.87/2.90	->Coefficients:
2.87/2.90	 Natural Numbers
2.87/2.90	->Dimension:
2.87/2.90	 1
2.87/2.90	->Bound:
2.87/2.90	 2
2.87/2.90	->Interpretation:
2.87/2.90	 
2.87/2.90	[A](X) = 2.X + 2
2.87/2.90	[B](X) = 2.X + 2
2.87/2.90	[C](X) = 2.X + 2
2.87/2.90	[a](X) = 2.X + 2
2.87/2.90	[b](X) = 2.X + 2
2.87/2.90	[c](X) = 2.X + 2
2.87/2.90	[B#](X) = X + 2
2.87/2.90	[C#](X) = 2.X + 2
2.87/2.90	[a#](X) = 2.X + 2
2.87/2.90	[b#](X) = X + 1
2.87/2.90	[c#](X) = X + 1
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	SCC Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Strongly Connected Components:
2.87/2.90	->->Cycle:
2.87/2.90	->->-> Pairs:
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	->->-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	Reduction Pair Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(B(B(c(x1:S)))) -> b#(b(b(A(x1:S))))
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.90	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.90	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.90	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.90	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.90	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.90	-> Rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	-> Usable rules:
2.87/2.90	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.90	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.90	 A(C(x1:S)) -> b(x1:S)
2.87/2.90	 A(a(x1:S)) -> x1:S
2.87/2.90	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.90	 B(A(x1:S)) -> c(x1:S)
2.87/2.90	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.90	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.90	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.90	 B(b(x1:S)) -> x1:S
2.87/2.90	 C(B(x1:S)) -> a(x1:S)
2.87/2.90	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.90	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.90	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.90	 C(c(x1:S)) -> x1:S
2.87/2.90	 a(A(x1:S)) -> x1:S
2.87/2.90	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.90	 a(b(x1:S)) -> C(x1:S)
2.87/2.90	 b(B(x1:S)) -> x1:S
2.87/2.90	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.90	 b(c(x1:S)) -> A(x1:S)
2.87/2.90	 c(C(x1:S)) -> x1:S
2.87/2.90	 c(a(x1:S)) -> B(x1:S)
2.87/2.90	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.90	->Interpretation type:
2.87/2.90	 Linear
2.87/2.90	->Coefficients:
2.87/2.90	 Natural Numbers
2.87/2.90	->Dimension:
2.87/2.90	 1
2.87/2.90	->Bound:
2.87/2.90	 2
2.87/2.90	->Interpretation:
2.87/2.90	 
2.87/2.90	[A](X) = 2.X + 2
2.87/2.90	[B](X) = 2.X + 2
2.87/2.90	[C](X) = 2.X + 2
2.87/2.90	[a](X) = 2.X + 2
2.87/2.90	[b](X) = 2.X + 2
2.87/2.90	[c](X) = 2.X + 2
2.87/2.90	[B#](X) = 2.X
2.87/2.90	[C#](X) = 2.X + 1
2.87/2.90	[a#](X) = 2.X + 1
2.87/2.90	[b#](X) = X + 2
2.87/2.90	[c#](X) = X + 2
2.87/2.90	
2.87/2.90	Problem 1: 
2.87/2.90	
2.87/2.90	SCC Processor:
2.87/2.90	-> Pairs:
2.87/2.90	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.90	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.90	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.91	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.91	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 b#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.91	 b#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.91	 b#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.91	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Strongly Connected Components:
2.87/2.91	->->Cycle:
2.87/2.91	->->-> Pairs:
2.87/2.91	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.91	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.91	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.91	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	->->-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	Reduction Pair Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 B#(a(a(a(x1:S)))) -> c#(A(A(A(x1:S))))
2.87/2.91	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.91	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.91	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	-> Usable rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Interpretation type:
2.87/2.91	 Linear
2.87/2.91	->Coefficients:
2.87/2.91	 Natural Numbers
2.87/2.91	->Dimension:
2.87/2.91	 1
2.87/2.91	->Bound:
2.87/2.91	 2
2.87/2.91	->Interpretation:
2.87/2.91	 
2.87/2.91	[A](X) = 2.X + 2
2.87/2.91	[B](X) = 2.X + 2
2.87/2.91	[C](X) = 2.X + 2
2.87/2.91	[a](X) = 2.X + 2
2.87/2.91	[b](X) = 2.X + 2
2.87/2.91	[c](X) = 2.X + 2
2.87/2.91	[B#](X) = 2.X
2.87/2.91	[C#](X) = 2.X + 2
2.87/2.91	[a#](X) = 2.X + 1
2.87/2.91	[c#](X) = X + 2
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	SCC Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> B#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> B#(B(B(x1:S)))
2.87/2.91	 C#(b(b(b(x1:S)))) -> B#(B(x1:S))
2.87/2.91	 C#(b(b(b(x1:S)))) -> B#(x1:S)
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(a(x1:S)) -> B#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Strongly Connected Components:
2.87/2.91	->->Cycle:
2.87/2.91	->->-> Pairs:
2.87/2.91	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	->->-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	Reduction Pair Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(B(x1:S)) -> a#(x1:S)
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	-> Usable rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Interpretation type:
2.87/2.91	 Linear
2.87/2.91	->Coefficients:
2.87/2.91	 Natural Numbers
2.87/2.91	->Dimension:
2.87/2.91	 1
2.87/2.91	->Bound:
2.87/2.91	 2
2.87/2.91	->Interpretation:
2.87/2.91	 
2.87/2.91	[A](X) = X + 1
2.87/2.91	[B](X) = X + 1
2.87/2.91	[C](X) = X + 1
2.87/2.91	[a](X) = X + 1
2.87/2.91	[b](X) = X + 1
2.87/2.91	[c](X) = X + 1
2.87/2.91	[C#](X) = 2.X + 2
2.87/2.91	[a#](X) = 2.X + 2
2.87/2.91	[c#](X) = 2.X + 1
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	SCC Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Strongly Connected Components:
2.87/2.91	->->Cycle:
2.87/2.91	->->-> Pairs:
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	->->-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	Reduction Pair Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(c(x1:S)))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	-> Usable rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Interpretation type:
2.87/2.91	 Linear
2.87/2.91	->Coefficients:
2.87/2.91	 Natural Numbers
2.87/2.91	->Dimension:
2.87/2.91	 1
2.87/2.91	->Bound:
2.87/2.91	 2
2.87/2.91	->Interpretation:
2.87/2.91	 
2.87/2.91	[A](X) = 2.X + 2
2.87/2.91	[B](X) = 2.X + 2
2.87/2.91	[C](X) = 2.X + 2
2.87/2.91	[a](X) = 2.X + 2
2.87/2.91	[b](X) = 2.X + 2
2.87/2.91	[c](X) = 2.X + 2
2.87/2.91	[C#](X) = 2.X + 2
2.87/2.91	[a#](X) = 2.X + 2
2.87/2.91	[c#](X) = 2.X + 2
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	SCC Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Strongly Connected Components:
2.87/2.91	->->Cycle:
2.87/2.91	->->-> Pairs:
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	->->-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	Reduction Pair Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(c(x1:S))
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	-> Usable rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Interpretation type:
2.87/2.91	 Linear
2.87/2.91	->Coefficients:
2.87/2.91	 Natural Numbers
2.87/2.91	->Dimension:
2.87/2.91	 1
2.87/2.91	->Bound:
2.87/2.91	 2
2.87/2.91	->Interpretation:
2.87/2.91	 
2.87/2.91	[A](X) = 2.X + 2
2.87/2.91	[B](X) = 2.X + 2
2.87/2.91	[C](X) = 2.X + 2
2.87/2.91	[a](X) = 2.X + 2
2.87/2.91	[b](X) = 2.X + 2
2.87/2.91	[c](X) = 2.X + 2
2.87/2.91	[C#](X) = 2.X + 2
2.87/2.91	[a#](X) = X + 1
2.87/2.91	[c#](X) = 2.X + 2
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	SCC Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Strongly Connected Components:
2.87/2.91	->->Cycle:
2.87/2.91	->->-> Pairs:
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	->->-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	Reduction Pair Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(C(C(C(x1:S)))) -> c#(x1:S)
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	-> Usable rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Interpretation type:
2.87/2.91	 Linear
2.87/2.91	->Coefficients:
2.87/2.91	 Natural Numbers
2.87/2.91	->Dimension:
2.87/2.91	 1
2.87/2.91	->Bound:
2.87/2.91	 2
2.87/2.91	->Interpretation:
2.87/2.91	 
2.87/2.91	[A](X) = 2.X + 2
2.87/2.91	[B](X) = 2.X + 2
2.87/2.91	[C](X) = 2.X + 2
2.87/2.91	[a](X) = 2.X + 2
2.87/2.91	[b](X) = 2.X + 2
2.87/2.91	[c](X) = 2.X + 2
2.87/2.91	[C#](X) = X + 2
2.87/2.91	[a#](X) = X + 2
2.87/2.91	[c#](X) = X + 2
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	SCC Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Strongly Connected Components:
2.87/2.91	->->Cycle:
2.87/2.91	->->-> Pairs:
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	->->-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	Reduction Pair Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(B(x1:S))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	-> Usable rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Interpretation type:
2.87/2.91	 Linear
2.87/2.91	->Coefficients:
2.87/2.91	 Natural Numbers
2.87/2.91	->Dimension:
2.87/2.91	 1
2.87/2.91	->Bound:
2.87/2.91	 2
2.87/2.91	->Interpretation:
2.87/2.91	 
2.87/2.91	[A](X) = X + 2
2.87/2.91	[B](X) = X + 2
2.87/2.91	[C](X) = X + 2
2.87/2.91	[a](X) = X + 2
2.87/2.91	[b](X) = X + 2
2.87/2.91	[c](X) = X + 2
2.87/2.91	[C#](X) = 2.X + 2
2.87/2.91	[a#](X) = 2.X + 2
2.87/2.91	[c#](X) = 2.X + 1
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	SCC Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Strongly Connected Components:
2.87/2.91	->->Cycle:
2.87/2.91	->->-> Pairs:
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	->->-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	Reduction Pair Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(B(x1:S)))
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	-> Usable rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Interpretation type:
2.87/2.91	 Linear
2.87/2.91	->Coefficients:
2.87/2.91	 Natural Numbers
2.87/2.91	->Dimension:
2.87/2.91	 1
2.87/2.91	->Bound:
2.87/2.91	 2
2.87/2.91	->Interpretation:
2.87/2.91	 
2.87/2.91	[A](X) = 2.X + 2
2.87/2.91	[B](X) = 2.X + 2
2.87/2.91	[C](X) = 2.X + 2
2.87/2.91	[a](X) = 2.X + 2
2.87/2.91	[b](X) = 2.X + 2
2.87/2.91	[c](X) = 2.X + 2
2.87/2.91	[C#](X) = 2.X + 2
2.87/2.91	[a#](X) = 2.X
2.87/2.91	[c#](X) = 2.X + 2
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	SCC Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Strongly Connected Components:
2.87/2.91	->->Cycle:
2.87/2.91	->->-> Pairs:
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	->->-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	Reduction Pair Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(C(C(a(x1:S)))) -> c#(c(c(B(x1:S))))
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	-> Usable rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Interpretation type:
2.87/2.91	 Linear
2.87/2.91	->Coefficients:
2.87/2.91	 Natural Numbers
2.87/2.91	->Dimension:
2.87/2.91	 1
2.87/2.91	->Bound:
2.87/2.91	 2
2.87/2.91	->Interpretation:
2.87/2.91	 
2.87/2.91	[A](X) = 2.X + 2
2.87/2.91	[B](X) = 2.X + 2
2.87/2.91	[C](X) = 2.X + 2
2.87/2.91	[a](X) = 2.X + 2
2.87/2.91	[b](X) = 2.X + 2
2.87/2.91	[c](X) = 2.X + 2
2.87/2.91	[C#](X) = 2.X + 2
2.87/2.91	[a#](X) = X
2.87/2.91	[c#](X) = X
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	SCC Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(C(x1:S)))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(C(x1:S))
2.87/2.91	 c#(c(c(c(x1:S)))) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Strongly Connected Components:
2.87/2.91	->->Cycle:
2.87/2.91	->->-> Pairs:
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	->->-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	Reduction Pair Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 C#(b(b(b(x1:S)))) -> a#(B(B(B(x1:S))))
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	-> Usable rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Interpretation type:
2.87/2.91	 Linear
2.87/2.91	->Coefficients:
2.87/2.91	 Natural Numbers
2.87/2.91	->Dimension:
2.87/2.91	 1
2.87/2.91	->Bound:
2.87/2.91	 2
2.87/2.91	->Interpretation:
2.87/2.91	 
2.87/2.91	[A](X) = 2.X + 1
2.87/2.91	[B](X) = 2.X + 1
2.87/2.91	[C](X) = 2.X + 1
2.87/2.91	[a](X) = 2.X + 1
2.87/2.91	[b](X) = 2.X + 1
2.87/2.91	[c](X) = 2.X + 1
2.87/2.91	[C#](X) = 2.X + 1
2.87/2.91	[a#](X) = 2.X
2.87/2.91	
2.87/2.91	Problem 1: 
2.87/2.91	
2.87/2.91	SCC Processor:
2.87/2.91	-> Pairs:
2.87/2.91	 a#(b(x1:S)) -> C#(x1:S)
2.87/2.91	-> Rules:
2.87/2.91	 A(A(A(A(x1:S)))) -> a(a(a(x1:S)))
2.87/2.91	 A(A(A(b(x1:S)))) -> a(a(a(C(x1:S))))
2.87/2.91	 A(C(x1:S)) -> b(x1:S)
2.87/2.91	 A(a(x1:S)) -> x1:S
2.87/2.91	 A(c(c(c(x1:S)))) -> b(C(C(C(x1:S))))
2.87/2.91	 B(A(x1:S)) -> c(x1:S)
2.87/2.91	 B(B(B(B(x1:S)))) -> b(b(b(x1:S)))
2.87/2.91	 B(B(B(c(x1:S)))) -> b(b(b(A(x1:S))))
2.87/2.91	 B(a(a(a(x1:S)))) -> c(A(A(A(x1:S))))
2.87/2.91	 B(b(x1:S)) -> x1:S
2.87/2.91	 C(B(x1:S)) -> a(x1:S)
2.87/2.91	 C(C(C(C(x1:S)))) -> c(c(c(x1:S)))
2.87/2.91	 C(C(C(a(x1:S)))) -> c(c(c(B(x1:S))))
2.87/2.91	 C(b(b(b(x1:S)))) -> a(B(B(B(x1:S))))
2.87/2.91	 C(c(x1:S)) -> x1:S
2.87/2.91	 a(A(x1:S)) -> x1:S
2.87/2.91	 a(a(a(a(x1:S)))) -> A(A(A(x1:S)))
2.87/2.91	 a(b(x1:S)) -> C(x1:S)
2.87/2.91	 b(B(x1:S)) -> x1:S
2.87/2.91	 b(b(b(b(x1:S)))) -> B(B(B(x1:S)))
2.87/2.91	 b(c(x1:S)) -> A(x1:S)
2.87/2.91	 c(C(x1:S)) -> x1:S
2.87/2.91	 c(a(x1:S)) -> B(x1:S)
2.87/2.91	 c(c(c(c(x1:S)))) -> C(C(C(x1:S)))
2.87/2.91	->Strongly Connected Components:
2.87/2.91	 There is no strongly connected component
2.87/2.91	
2.87/2.91	The problem is finite.
2.87/2.91	EOF