1.82/2.04	YES
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	(VAR v_NonEmpty:S x1:S)
1.82/2.04	(RULES
1.82/2.04	a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	)
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	Dependency Pairs Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 A(a(x1:S)) -> B(b(b(x1:S)))
1.82/2.04	 A(a(x1:S)) -> B(b(x1:S))
1.82/2.04	 A(a(x1:S)) -> B(x1:S)
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> A(b(x1:S))
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	SCC Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 A(a(x1:S)) -> B(b(b(x1:S)))
1.82/2.04	 A(a(x1:S)) -> B(b(x1:S))
1.82/2.04	 A(a(x1:S)) -> B(x1:S)
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> A(b(x1:S))
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Strongly Connected Components:
1.82/2.04	->->Cycle:
1.82/2.04	->->-> Pairs:
1.82/2.04	 A(a(x1:S)) -> B(b(b(x1:S)))
1.82/2.04	 A(a(x1:S)) -> B(b(x1:S))
1.82/2.04	 A(a(x1:S)) -> B(x1:S)
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> A(b(x1:S))
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	->->-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	Reduction Pair Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 A(a(x1:S)) -> B(b(b(x1:S)))
1.82/2.04	 A(a(x1:S)) -> B(b(x1:S))
1.82/2.04	 A(a(x1:S)) -> B(x1:S)
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> A(b(x1:S))
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	-> Usable rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Interpretation type:
1.82/2.04	 Linear
1.82/2.04	->Coefficients:
1.82/2.04	 All rationals
1.82/2.04	->Dimension:
1.82/2.04	 1
1.82/2.04	->Bound:
1.82/2.04	 4
1.82/2.04	->Interpretation:
1.82/2.04	 
1.82/2.04	[a](X) = X + 3
1.82/2.04	[b](X) = X + 2
1.82/2.04	[c](X) = X + 4/3
1.82/2.04	[A](X) = 1/4.X + 1
1.82/2.04	[B](X) = 1/4.X + 2/3
1.82/2.04	[C](X) = 1/4.X + 1/2
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	SCC Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 A(a(x1:S)) -> B(b(x1:S))
1.82/2.04	 A(a(x1:S)) -> B(x1:S)
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> A(b(x1:S))
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Strongly Connected Components:
1.82/2.04	->->Cycle:
1.82/2.04	->->-> Pairs:
1.82/2.04	 A(a(x1:S)) -> B(b(x1:S))
1.82/2.04	 A(a(x1:S)) -> B(x1:S)
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> A(b(x1:S))
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	->->-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	Reduction Pair Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 A(a(x1:S)) -> B(b(x1:S))
1.82/2.04	 A(a(x1:S)) -> B(x1:S)
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> A(b(x1:S))
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	-> Usable rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Interpretation type:
1.82/2.04	 Linear
1.82/2.04	->Coefficients:
1.82/2.04	 All rationals
1.82/2.04	->Dimension:
1.82/2.04	 1
1.82/2.04	->Bound:
1.82/2.04	 4
1.82/2.04	->Interpretation:
1.82/2.04	 
1.82/2.04	[a](X) = X + 3
1.82/2.04	[b](X) = X + 2
1.82/2.04	[c](X) = X + 4/3
1.82/2.04	[A](X) = 3/2.X + 3
1.82/2.04	[B](X) = 3/2.X + 1
1.82/2.04	[C](X) = 3/2.X
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	SCC Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 A(a(x1:S)) -> B(x1:S)
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> A(b(x1:S))
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Strongly Connected Components:
1.82/2.04	->->Cycle:
1.82/2.04	->->-> Pairs:
1.82/2.04	 A(a(x1:S)) -> B(x1:S)
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> A(b(x1:S))
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	->->-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	Reduction Pair Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 A(a(x1:S)) -> B(x1:S)
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> A(b(x1:S))
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	-> Usable rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Interpretation type:
1.82/2.04	 Linear
1.82/2.04	->Coefficients:
1.82/2.04	 All rationals
1.82/2.04	->Dimension:
1.82/2.04	 1
1.82/2.04	->Bound:
1.82/2.04	 4
1.82/2.04	->Interpretation:
1.82/2.04	 
1.82/2.04	[a](X) = X + 3/2
1.82/2.04	[b](X) = X + 1
1.82/2.04	[c](X) = X + 2/3
1.82/2.04	[A](X) = 3.X + 4/3
1.82/2.04	[B](X) = 3.X + 2
1.82/2.04	[C](X) = 3.X + 1/4
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	SCC Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> A(b(x1:S))
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Strongly Connected Components:
1.82/2.04	->->Cycle:
1.82/2.04	->->-> Pairs:
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	->->-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	Reduction Pair Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 B(b(x1:S)) -> C(c(c(x1:S)))
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	-> Usable rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Interpretation type:
1.82/2.04	 Linear
1.82/2.04	->Coefficients:
1.82/2.04	 All rationals
1.82/2.04	->Dimension:
1.82/2.04	 1
1.82/2.04	->Bound:
1.82/2.04	 4
1.82/2.04	->Interpretation:
1.82/2.04	 
1.82/2.04	[a](X) = X + 3
1.82/2.04	[b](X) = X + 2
1.82/2.04	[c](X) = X + 4/3
1.82/2.04	[B](X) = 2.X + 3/2
1.82/2.04	[C](X) = 2.X
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	SCC Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Strongly Connected Components:
1.82/2.04	->->Cycle:
1.82/2.04	->->-> Pairs:
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	->->-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	Reduction Pair Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 B(b(x1:S)) -> C(c(x1:S))
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	-> Usable rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Interpretation type:
1.82/2.04	 Linear
1.82/2.04	->Coefficients:
1.82/2.04	 All rationals
1.82/2.04	->Dimension:
1.82/2.04	 1
1.82/2.04	->Bound:
1.82/2.04	 4
1.82/2.04	->Interpretation:
1.82/2.04	 
1.82/2.04	[a](X) = X + 3/4
1.82/2.04	[b](X) = X + 1/2
1.82/2.04	[c](X) = X + 1/3
1.82/2.04	[B](X) = 4.X + 4
1.82/2.04	[C](X) = 4.X + 4
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	SCC Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Strongly Connected Components:
1.82/2.04	->->Cycle:
1.82/2.04	->->-> Pairs:
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	->->-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	Subterm Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 B(b(x1:S)) -> C(x1:S)
1.82/2.04	 C(c(c(c(x1:S)))) -> B(x1:S)
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Projection:
1.82/2.04	 pi(B) = 1
1.82/2.04	 pi(C) = 1
1.82/2.04	
1.82/2.04	Problem 1: 
1.82/2.04	
1.82/2.04	SCC Processor:
1.82/2.04	-> Pairs:
1.82/2.04	 Empty
1.82/2.04	-> Rules:
1.82/2.04	 a(a(x1:S)) -> b(b(b(x1:S)))
1.82/2.04	 b(b(x1:S)) -> c(c(c(x1:S)))
1.82/2.04	 c(c(c(c(x1:S)))) -> a(b(x1:S))
1.82/2.04	->Strongly Connected Components:
1.82/2.04	 There is no strongly connected component
1.82/2.04	
1.82/2.04	The problem is finite.
1.82/2.04	EOF