93.82/94.84	YES
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	(VAR v_NonEmpty:S x1:S)
93.82/94.84	(RULES
93.82/94.84	a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	)
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Dependency Pairs Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> A(x1:S)
93.82/94.84	 A(b(c(x1:S))) -> B(a(x1:S))
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> A(x1:S)
93.82/94.84	 A(b(c(x1:S))) -> B(a(x1:S))
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> A(x1:S)
93.82/94.84	 A(b(c(x1:S))) -> B(a(x1:S))
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> A(x1:S)
93.82/94.84	 A(b(c(x1:S))) -> B(a(x1:S))
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 Natural Numbers
93.82/94.84	->Dimension:
93.82/94.84	 1
93.82/94.84	->Bound:
93.82/94.84	 2
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = X
93.82/94.84	[b](X) = 2.X + 2
93.82/94.84	[c](X) = 2.X + 2
93.82/94.84	[A](X) = X
93.82/94.84	[B](X) = 2.X + 2
93.82/94.84	[C](X) = 2.X + 2
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> B(a(x1:S))
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> B(a(x1:S))
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> B(a(x1:S))
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 Natural Numbers
93.82/94.84	->Dimension:
93.82/94.84	 1
93.82/94.84	->Bound:
93.82/94.84	 2
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = 2.X + 2
93.82/94.84	[b](X) = 2.X + 2
93.82/94.84	[c](X) = 2.X + 2
93.82/94.84	[A](X) = 2.X
93.82/94.84	[B](X) = 2.X
93.82/94.84	[C](X) = 2.X
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 Natural Numbers
93.82/94.84	->Dimension:
93.82/94.84	 1
93.82/94.84	->Bound:
93.82/94.84	 2
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = 2.X + 2
93.82/94.84	[b](X) = 2.X + 2
93.82/94.84	[c](X) = 2.X + 2
93.82/94.84	[A](X) = X
93.82/94.84	[B](X) = X
93.82/94.84	[C](X) = X
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(b(x1:S))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 Natural Numbers
93.82/94.84	->Dimension:
93.82/94.84	 1
93.82/94.84	->Bound:
93.82/94.84	 2
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = 2.X + 2
93.82/94.84	[b](X) = 2.X + 2
93.82/94.84	[c](X) = X
93.82/94.84	[A](X) = 2.X + 2
93.82/94.84	[B](X) = 2.X + 2
93.82/94.84	[C](X) = X
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 B(a(a(a(x1:S)))) -> B(x1:S)
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 Natural Numbers
93.82/94.84	->Dimension:
93.82/94.84	 1
93.82/94.84	->Bound:
93.82/94.84	 2
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = X + 1
93.82/94.84	[b](X) = X + 2
93.82/94.84	[c](X) = X + 2
93.82/94.84	[A](X) = 2.X
93.82/94.84	[B](X) = 2.X + 2
93.82/94.84	[C](X) = 2.X + 2
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 Natural Numbers
93.82/94.84	->Dimension:
93.82/94.84	 1
93.82/94.84	->Bound:
93.82/94.84	 2
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = X + 2
93.82/94.84	[b](X) = X + 2
93.82/94.84	[c](X) = X + 2
93.82/94.84	[A](X) = 2.X + 2
93.82/94.84	[B](X) = 2.X + 2
93.82/94.84	[C](X) = 2.X + 2
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> B(c(x1:S))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 Natural Numbers
93.82/94.84	->Dimension:
93.82/94.84	 1
93.82/94.84	->Bound:
93.82/94.84	 2
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = 2.X + 2
93.82/94.84	[b](X) = 2.X + 2
93.82/94.84	[c](X) = 2.X + 2
93.82/94.84	[A](X) = 2.X + 2
93.82/94.84	[B](X) = 2.X + 2
93.82/94.84	[C](X) = 2.X + 2
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> C(x1:S)
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 Natural Numbers
93.82/94.84	->Dimension:
93.82/94.84	 1
93.82/94.84	->Bound:
93.82/94.84	 2
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = 2.X + 2
93.82/94.84	[b](X) = 2.X + 2
93.82/94.84	[c](X) = 2.X + 2
93.82/94.84	[A](X) = 2.X + 2
93.82/94.84	[B](X) = 2.X + 2
93.82/94.84	[C](X) = 2.X + 2
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 Natural Numbers
93.82/94.84	->Dimension:
93.82/94.84	 1
93.82/94.84	->Bound:
93.82/94.84	 2
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = X + 2
93.82/94.84	[b](X) = X + 2
93.82/94.84	[c](X) = X + 2
93.82/94.84	[A](X) = 2.X + 2
93.82/94.84	[B](X) = 2.X + 2
93.82/94.84	[C](X) = 2.X + 2
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(c(x1:S))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 Natural Numbers
93.82/94.84	->Dimension:
93.82/94.84	 1
93.82/94.84	->Bound:
93.82/94.84	 2
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = 2.X + 2
93.82/94.84	[b](X) = 2.X + 2
93.82/94.84	[c](X) = 2.X + 2
93.82/94.84	[A](X) = 2.X + 2
93.82/94.84	[B](X) = 2.X + 2
93.82/94.84	[C](X) = 2.X + 2
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> C(x1:S)
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 Natural Numbers
93.82/94.84	->Dimension:
93.82/94.84	 1
93.82/94.84	->Bound:
93.82/94.84	 2
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = 2.X + 2
93.82/94.84	[b](X) = 2.X + 2
93.82/94.84	[c](X) = 2.X + 2
93.82/94.84	[A](X) = 2.X + 2
93.82/94.84	[B](X) = 2.X + 2
93.82/94.84	[C](X) = 2.X + 2
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 All rationals
93.82/94.84	->Dimension:
93.82/94.84	 1
93.82/94.84	->Bound:
93.82/94.84	 2
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = 1/2.X + 1
93.82/94.84	[b](X) = 2.X
93.82/94.84	[c](X) = 1/2.X
93.82/94.84	[A](X) = 1/2.X + 2
93.82/94.84	[B](X) = 2.X + 1
93.82/94.84	[C](X) = 1/2.X + 1
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	->->Cycle:
93.82/94.84	->->-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	->->-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	Reduction Pair Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 A(b(c(x1:S))) -> C(b(a(x1:S)))
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	-> Usable rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Interpretation type:
93.82/94.84	 Linear
93.82/94.84	->Coefficients:
93.82/94.84	 Natural Numbers
93.82/94.84	->Dimension:
93.82/94.84	 2
93.82/94.84	->Bound:
93.82/94.84	 1
93.82/94.84	->Interpretation:
93.82/94.84	 
93.82/94.84	[a](X) = [0 1;0 0].X + [0;1]
93.82/94.84	[b](X) = [0 0;1 0].X + [1;0]
93.82/94.84	[c](X) = [0 1;1 0].X + [1;0]
93.82/94.84	[A](X) = [0 1;0 1].X + [1;1]
93.82/94.84	[C](X) = [0 1;1 0].X + [1;1]
93.82/94.84	
93.82/94.84	Problem 1: 
93.82/94.84	
93.82/94.84	SCC Processor:
93.82/94.84	-> Pairs:
93.82/94.84	 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
93.82/94.84	-> Rules:
93.82/94.84	 a(b(c(x1:S))) -> c(b(a(x1:S)))
93.82/94.84	 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
93.82/94.84	 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
93.82/94.84	 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
93.82/94.84	->Strongly Connected Components:
93.82/94.84	 There is no strongly connected component
93.82/94.84	
93.82/94.84	The problem is finite.
93.82/141.00	EOF