0.55/0.85	YES
0.55/0.85	
0.55/0.85	Problem 1: 
0.55/0.85	
0.55/0.85	(VAR v_NonEmpty:S x1:S)
0.55/0.85	(RULES
0.55/0.85	a(x1:S) -> c(b(x1:S))
0.55/0.85	b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	b(c(x1:S)) -> a(x1:S)
0.55/0.85	c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	)
0.55/0.85	
0.55/0.85	Problem 1: 
0.55/0.85	
0.55/0.85	Dependency Pairs Processor:
0.55/0.85	-> Pairs:
0.55/0.85	 A(x1:S) -> B(x1:S)
0.55/0.85	 A(x1:S) -> C(b(x1:S))
0.55/0.85	 B(b(x1:S)) -> A(c(x1:S))
0.55/0.85	 B(b(x1:S)) -> C(x1:S)
0.55/0.85	 B(c(x1:S)) -> A(x1:S)
0.55/0.85	 C(c(c(x1:S))) -> B(x1:S)
0.55/0.85	-> Rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	
0.55/0.85	Problem 1: 
0.55/0.85	
0.55/0.85	SCC Processor:
0.55/0.85	-> Pairs:
0.55/0.85	 A(x1:S) -> B(x1:S)
0.55/0.85	 A(x1:S) -> C(b(x1:S))
0.55/0.85	 B(b(x1:S)) -> A(c(x1:S))
0.55/0.85	 B(b(x1:S)) -> C(x1:S)
0.55/0.85	 B(c(x1:S)) -> A(x1:S)
0.55/0.85	 C(c(c(x1:S))) -> B(x1:S)
0.55/0.85	-> Rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	->Strongly Connected Components:
0.55/0.85	->->Cycle:
0.55/0.85	->->-> Pairs:
0.55/0.85	 A(x1:S) -> B(x1:S)
0.55/0.85	 A(x1:S) -> C(b(x1:S))
0.55/0.85	 B(b(x1:S)) -> A(c(x1:S))
0.55/0.85	 B(b(x1:S)) -> C(x1:S)
0.55/0.85	 B(c(x1:S)) -> A(x1:S)
0.55/0.85	 C(c(c(x1:S))) -> B(x1:S)
0.55/0.85	->->-> Rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	
0.55/0.85	Problem 1: 
0.55/0.85	
0.55/0.85	Reduction Pair Processor:
0.55/0.85	-> Pairs:
0.55/0.85	 A(x1:S) -> B(x1:S)
0.55/0.85	 A(x1:S) -> C(b(x1:S))
0.55/0.85	 B(b(x1:S)) -> A(c(x1:S))
0.55/0.85	 B(b(x1:S)) -> C(x1:S)
0.55/0.85	 B(c(x1:S)) -> A(x1:S)
0.55/0.85	 C(c(c(x1:S))) -> B(x1:S)
0.55/0.85	-> Rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	-> Usable rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	->Interpretation type:
0.55/0.85	 Linear
0.55/0.85	->Coefficients:
0.55/0.85	 All rationals
0.55/0.85	->Dimension:
0.55/0.85	 1
0.55/0.85	->Bound:
0.55/0.85	 4
0.55/0.85	->Interpretation:
0.55/0.85	 
0.55/0.85	[a](X) = X + 3/2
0.55/0.85	[b](X) = X + 1
0.55/0.85	[c](X) = X + 1/2
0.55/0.85	[A](X) = 4.X + 4
0.55/0.85	[B](X) = 4.X + 3
0.55/0.85	[C](X) = 4.X
0.55/0.85	
0.55/0.85	Problem 1: 
0.55/0.85	
0.55/0.85	SCC Processor:
0.55/0.85	-> Pairs:
0.55/0.85	 A(x1:S) -> C(b(x1:S))
0.55/0.85	 B(b(x1:S)) -> A(c(x1:S))
0.55/0.85	 B(b(x1:S)) -> C(x1:S)
0.55/0.85	 B(c(x1:S)) -> A(x1:S)
0.55/0.85	 C(c(c(x1:S))) -> B(x1:S)
0.55/0.85	-> Rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	->Strongly Connected Components:
0.55/0.85	->->Cycle:
0.55/0.85	->->-> Pairs:
0.55/0.85	 A(x1:S) -> C(b(x1:S))
0.55/0.85	 B(b(x1:S)) -> A(c(x1:S))
0.55/0.85	 B(b(x1:S)) -> C(x1:S)
0.55/0.85	 B(c(x1:S)) -> A(x1:S)
0.55/0.85	 C(c(c(x1:S))) -> B(x1:S)
0.55/0.85	->->-> Rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	
0.55/0.85	Problem 1: 
0.55/0.85	
0.55/0.85	Reduction Pair Processor:
0.55/0.85	-> Pairs:
0.55/0.85	 A(x1:S) -> C(b(x1:S))
0.55/0.85	 B(b(x1:S)) -> A(c(x1:S))
0.55/0.85	 B(b(x1:S)) -> C(x1:S)
0.55/0.85	 B(c(x1:S)) -> A(x1:S)
0.55/0.85	 C(c(c(x1:S))) -> B(x1:S)
0.55/0.85	-> Rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	-> Usable rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	->Interpretation type:
0.55/0.85	 Linear
0.55/0.85	->Coefficients:
0.55/0.85	 All rationals
0.55/0.85	->Dimension:
0.55/0.85	 1
0.55/0.85	->Bound:
0.55/0.85	 4
0.55/0.85	->Interpretation:
0.55/0.85	 
0.55/0.85	[a](X) = X + 3/2
0.55/0.85	[b](X) = X + 1
0.55/0.85	[c](X) = X + 1/2
0.55/0.85	[A](X) = 3.X + 4
0.55/0.85	[B](X) = 3.X + 3
0.55/0.85	[C](X) = 3.X + 2/3
0.55/0.85	
0.55/0.85	Problem 1: 
0.55/0.85	
0.55/0.85	SCC Processor:
0.55/0.85	-> Pairs:
0.55/0.85	 B(b(x1:S)) -> A(c(x1:S))
0.55/0.85	 B(b(x1:S)) -> C(x1:S)
0.55/0.85	 B(c(x1:S)) -> A(x1:S)
0.55/0.85	 C(c(c(x1:S))) -> B(x1:S)
0.55/0.85	-> Rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	->Strongly Connected Components:
0.55/0.85	->->Cycle:
0.55/0.85	->->-> Pairs:
0.55/0.85	 B(b(x1:S)) -> C(x1:S)
0.55/0.85	 C(c(c(x1:S))) -> B(x1:S)
0.55/0.85	->->-> Rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	
0.55/0.85	Problem 1: 
0.55/0.85	
0.55/0.85	Subterm Processor:
0.55/0.85	-> Pairs:
0.55/0.85	 B(b(x1:S)) -> C(x1:S)
0.55/0.85	 C(c(c(x1:S))) -> B(x1:S)
0.55/0.85	-> Rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	->Projection:
0.55/0.85	 pi(B) = 1
0.55/0.85	 pi(C) = 1
0.55/0.85	
0.55/0.85	Problem 1: 
0.55/0.85	
0.55/0.85	SCC Processor:
0.55/0.85	-> Pairs:
0.55/0.85	 Empty
0.55/0.85	-> Rules:
0.55/0.85	 a(x1:S) -> c(b(x1:S))
0.55/0.85	 b(b(x1:S)) -> a(c(x1:S))
0.55/0.85	 b(c(x1:S)) -> a(x1:S)
0.55/0.85	 c(c(c(x1:S))) -> b(x1:S)
0.55/0.85	->Strongly Connected Components:
0.55/0.85	 There is no strongly connected component
0.55/0.85	
0.55/0.85	The problem is finite.
0.55/0.85	EOF