1.17/1.34	YES
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	(VAR v_NonEmpty:S x1:S)
1.17/1.34	(RULES
1.17/1.34	a(a(x1:S)) -> b(x1:S)
1.17/1.34	b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	)
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	Dependency Pairs Processor:
1.17/1.34	-> Pairs:
1.17/1.34	 A(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(a(x1:S)) -> A(b(x1:S))
1.17/1.34	 B(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> A(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(a(a(x1:S)))
1.17/1.34	 B(b(x1:S)) -> A(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(x1:S)
1.17/1.34	 C(a(x1:S)) -> A(c(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	SCC Processor:
1.17/1.34	-> Pairs:
1.17/1.34	 A(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(a(x1:S)) -> A(b(x1:S))
1.17/1.34	 B(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> A(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(a(a(x1:S)))
1.17/1.34	 B(b(x1:S)) -> A(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(x1:S)
1.17/1.34	 C(a(x1:S)) -> A(c(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	->Strongly Connected Components:
1.17/1.34	->->Cycle:
1.17/1.34	->->-> Pairs:
1.17/1.34	 A(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(a(x1:S)) -> A(b(x1:S))
1.17/1.34	 B(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> A(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(a(a(x1:S)))
1.17/1.34	 B(b(x1:S)) -> A(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(x1:S)
1.17/1.34	 C(a(x1:S)) -> A(c(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	->->-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	Reduction Pair Processor:
1.17/1.34	-> Pairs:
1.17/1.34	 A(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(a(x1:S)) -> A(b(x1:S))
1.17/1.34	 B(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> A(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(a(a(x1:S)))
1.17/1.34	 B(b(x1:S)) -> A(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(x1:S)
1.17/1.34	 C(a(x1:S)) -> A(c(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	-> Usable rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	->Interpretation type:
1.17/1.34	 Linear
1.17/1.34	->Coefficients:
1.17/1.34	 Natural Numbers
1.17/1.34	->Dimension:
1.17/1.34	 1
1.17/1.34	->Bound:
1.17/1.34	 2
1.17/1.34	->Interpretation:
1.17/1.34	 
1.17/1.34	[a](X) = X
1.17/1.34	[b](X) = X
1.17/1.34	[c](X) = X + 1
1.17/1.34	[A](X) = 2.X
1.17/1.34	[B](X) = 2.X
1.17/1.34	[C](X) = 2.X + 2
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	SCC Processor:
1.17/1.34	-> Pairs:
1.17/1.34	 A(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(a(x1:S)) -> A(b(x1:S))
1.17/1.34	 B(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(a(a(x1:S)))
1.17/1.34	 B(b(x1:S)) -> A(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(x1:S)
1.17/1.34	 C(a(x1:S)) -> A(c(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	->Strongly Connected Components:
1.17/1.34	->->Cycle:
1.17/1.34	->->-> Pairs:
1.17/1.34	 A(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(a(x1:S)) -> A(b(x1:S))
1.17/1.34	 B(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(a(a(x1:S)))
1.17/1.34	 B(b(x1:S)) -> A(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(x1:S)
1.17/1.34	 C(a(x1:S)) -> A(c(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	->->-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	Reduction Pair Processor:
1.17/1.34	-> Pairs:
1.17/1.34	 A(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(a(x1:S)) -> A(b(x1:S))
1.17/1.34	 B(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(a(a(x1:S)))
1.17/1.34	 B(b(x1:S)) -> A(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(x1:S)
1.17/1.34	 C(a(x1:S)) -> A(c(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	-> Usable rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	->Interpretation type:
1.17/1.34	 Linear
1.17/1.34	->Coefficients:
1.17/1.34	 All rationals
1.17/1.34	->Dimension:
1.17/1.34	 1
1.17/1.34	->Bound:
1.17/1.34	 4
1.17/1.34	->Interpretation:
1.17/1.34	 
1.17/1.34	[a](X) = X + 2
1.17/1.34	[b](X) = X + 3
1.17/1.34	[c](X) = 3.X
1.17/1.34	[A](X) = 4/3.X + 3/2
1.17/1.34	[B](X) = 4/3.X + 4
1.17/1.34	[C](X) = 4.X
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	SCC Processor:
1.17/1.34	-> Pairs:
1.17/1.34	 B(a(x1:S)) -> A(b(x1:S))
1.17/1.34	 B(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(a(a(x1:S)))
1.17/1.34	 B(b(x1:S)) -> A(a(x1:S))
1.17/1.34	 B(b(x1:S)) -> A(x1:S)
1.17/1.34	 C(a(x1:S)) -> A(c(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	->Strongly Connected Components:
1.17/1.34	->->Cycle:
1.17/1.34	->->-> Pairs:
1.17/1.34	 B(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	->->-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	Reduction Pair Processor:
1.17/1.34	-> Pairs:
1.17/1.34	 B(a(x1:S)) -> B(x1:S)
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	-> Usable rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	->Interpretation type:
1.17/1.34	 Linear
1.17/1.34	->Coefficients:
1.17/1.34	 All rationals
1.17/1.34	->Dimension:
1.17/1.34	 1
1.17/1.34	->Bound:
1.17/1.34	 4
1.17/1.34	->Interpretation:
1.17/1.34	 
1.17/1.34	[a](X) = X + 1/4
1.17/1.34	[b](X) = X + 1/2
1.17/1.34	[c](X) = 4.X + 2
1.17/1.34	[B](X) = X + 1/2
1.17/1.34	[C](X) = 4.X + 2
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	SCC Processor:
1.17/1.34	-> Pairs:
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	->Strongly Connected Components:
1.17/1.34	->->Cycle:
1.17/1.34	->->-> Pairs:
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	->->-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	Reduction Pair Processor:
1.17/1.34	-> Pairs:
1.17/1.34	 B(b(c(x1:S))) -> C(a(x1:S))
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	-> Usable rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	->Interpretation type:
1.17/1.34	 Linear
1.17/1.34	->Coefficients:
1.17/1.34	 All rationals
1.17/1.34	->Dimension:
1.17/1.34	 1
1.17/1.34	->Bound:
1.17/1.34	 4
1.17/1.34	->Interpretation:
1.17/1.34	 
1.17/1.34	[a](X) = X + 2
1.17/1.34	[b](X) = X + 4
1.17/1.34	[c](X) = 4.X + 2/3
1.17/1.34	[B](X) = 1/3.X + 2
1.17/1.34	[C](X) = 4/3.X + 1/3
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	SCC Processor:
1.17/1.34	-> Pairs:
1.17/1.34	 C(a(x1:S)) -> B(a(c(x1:S)))
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	->Strongly Connected Components:
1.17/1.34	->->Cycle:
1.17/1.34	->->-> Pairs:
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	->->-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	Subterm Processor:
1.17/1.34	-> Pairs:
1.17/1.34	 C(a(x1:S)) -> C(x1:S)
1.17/1.34	-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	->Projection:
1.17/1.34	 pi(C) = 1
1.17/1.34	
1.17/1.34	Problem 1: 
1.17/1.34	
1.17/1.34	SCC Processor:
1.17/1.34	-> Pairs:
1.17/1.34	 Empty
1.17/1.34	-> Rules:
1.17/1.34	 a(a(x1:S)) -> b(x1:S)
1.17/1.34	 b(a(x1:S)) -> a(b(x1:S))
1.17/1.34	 b(b(c(x1:S))) -> c(a(x1:S))
1.17/1.34	 b(b(x1:S)) -> a(a(a(x1:S)))
1.17/1.34	 c(a(x1:S)) -> b(a(c(x1:S)))
1.17/1.34	->Strongly Connected Components:
1.17/1.34	 There is no strongly connected component
1.17/1.34	
1.17/1.34	The problem is finite.
1.17/1.34	EOF