0.41/0.60	YES
0.41/0.60	
0.41/0.60	Problem 1: 
0.41/0.60	
0.41/0.60	(VAR v_NonEmpty:S x1:S)
0.41/0.60	(RULES
0.41/0.60	a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	c(x1:S) -> d(x1:S)
0.41/0.60	)
0.41/0.60	
0.41/0.60	Problem 1: 
0.41/0.60	
0.41/0.60	Dependency Pairs Processor:
0.41/0.60	-> Pairs:
0.41/0.60	 A(d(x1:S)) -> B(x1:S)
0.41/0.60	 A(x1:S) -> B(b(b(x1:S)))
0.41/0.60	 A(x1:S) -> B(b(x1:S))
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	 B(d(b(x1:S))) -> C(x1:S)
0.41/0.60	-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	
0.41/0.60	Problem 1: 
0.41/0.60	
0.41/0.60	SCC Processor:
0.41/0.60	-> Pairs:
0.41/0.60	 A(d(x1:S)) -> B(x1:S)
0.41/0.60	 A(x1:S) -> B(b(b(x1:S)))
0.41/0.60	 A(x1:S) -> B(b(x1:S))
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	 B(d(b(x1:S))) -> C(x1:S)
0.41/0.60	-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	->Strongly Connected Components:
0.41/0.60	->->Cycle:
0.41/0.60	->->-> Pairs:
0.41/0.60	 A(d(x1:S)) -> B(x1:S)
0.41/0.60	 A(x1:S) -> B(b(b(x1:S)))
0.41/0.60	 A(x1:S) -> B(b(x1:S))
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	->->-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	
0.41/0.60	Problem 1: 
0.41/0.60	
0.41/0.60	Reduction Pair Processor:
0.41/0.60	-> Pairs:
0.41/0.60	 A(d(x1:S)) -> B(x1:S)
0.41/0.60	 A(x1:S) -> B(b(b(x1:S)))
0.41/0.60	 A(x1:S) -> B(b(x1:S))
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	-> Usable rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	->Interpretation type:
0.41/0.60	 Linear
0.41/0.60	->Coefficients:
0.41/0.60	 Natural Numbers
0.41/0.60	->Dimension:
0.41/0.60	 1
0.41/0.60	->Bound:
0.41/0.60	 2
0.41/0.60	->Interpretation:
0.41/0.60	 
0.41/0.60	[a](X) = X
0.41/0.60	[b](X) = X
0.41/0.60	[c](X) = X + 2
0.41/0.60	[d](X) = X + 2
0.41/0.60	[A](X) = X + 1
0.41/0.60	[B](X) = X + 1
0.41/0.60	
0.41/0.60	Problem 1: 
0.41/0.60	
0.41/0.60	SCC Processor:
0.41/0.60	-> Pairs:
0.41/0.60	 A(x1:S) -> B(b(b(x1:S)))
0.41/0.60	 A(x1:S) -> B(b(x1:S))
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	->Strongly Connected Components:
0.41/0.60	->->Cycle:
0.41/0.60	->->-> Pairs:
0.41/0.60	 A(x1:S) -> B(b(b(x1:S)))
0.41/0.60	 A(x1:S) -> B(b(x1:S))
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	->->-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	
0.41/0.60	Problem 1: 
0.41/0.60	
0.41/0.60	Reduction Pair Processor:
0.41/0.60	-> Pairs:
0.41/0.60	 A(x1:S) -> B(b(b(x1:S)))
0.41/0.60	 A(x1:S) -> B(b(x1:S))
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	-> Usable rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	->Interpretation type:
0.41/0.60	 Linear
0.41/0.60	->Coefficients:
0.41/0.60	 All rationals
0.41/0.60	->Dimension:
0.41/0.60	 1
0.41/0.60	->Bound:
0.41/0.60	 4
0.41/0.60	->Interpretation:
0.41/0.60	 
0.41/0.60	[a](X) = X + 3/4
0.41/0.60	[b](X) = X + 1/4
0.41/0.60	[c](X) = 3.X + 3/4
0.41/0.60	[d](X) = 3.X + 3/4
0.41/0.60	[A](X) = 4.X + 4
0.41/0.60	[B](X) = 4.X + 1
0.41/0.60	
0.41/0.60	Problem 1: 
0.41/0.60	
0.41/0.60	SCC Processor:
0.41/0.60	-> Pairs:
0.41/0.60	 A(x1:S) -> B(b(x1:S))
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	->Strongly Connected Components:
0.41/0.60	->->Cycle:
0.41/0.60	->->-> Pairs:
0.41/0.60	 A(x1:S) -> B(b(x1:S))
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	->->-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	
0.41/0.60	Problem 1: 
0.41/0.60	
0.41/0.60	Reduction Pair Processor:
0.41/0.60	-> Pairs:
0.41/0.60	 A(x1:S) -> B(b(x1:S))
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	-> Usable rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	->Interpretation type:
0.41/0.60	 Linear
0.41/0.60	->Coefficients:
0.41/0.60	 All rationals
0.41/0.60	->Dimension:
0.41/0.60	 1
0.41/0.60	->Bound:
0.41/0.60	 4
0.41/0.60	->Interpretation:
0.41/0.60	 
0.41/0.60	[a](X) = X + 3
0.41/0.60	[b](X) = X + 1
0.41/0.60	[c](X) = 2.X
0.41/0.60	[d](X) = 2.X
0.41/0.60	[A](X) = 2.X + 3
0.41/0.60	[B](X) = 2.X + 1/2
0.41/0.60	
0.41/0.60	Problem 1: 
0.41/0.60	
0.41/0.60	SCC Processor:
0.41/0.60	-> Pairs:
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	->Strongly Connected Components:
0.41/0.60	->->Cycle:
0.41/0.60	->->-> Pairs:
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	->->-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	
0.41/0.60	Problem 1: 
0.41/0.60	
0.41/0.60	Reduction Pair Processor:
0.41/0.60	-> Pairs:
0.41/0.60	 A(x1:S) -> B(x1:S)
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	-> Usable rules:
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	->Interpretation type:
0.41/0.60	 Linear
0.41/0.60	->Coefficients:
0.41/0.60	 Natural Numbers
0.41/0.60	->Dimension:
0.41/0.60	 1
0.41/0.60	->Bound:
0.41/0.60	 2
0.41/0.60	->Interpretation:
0.41/0.60	 
0.41/0.60	[b](X) = X + 2
0.41/0.60	[c](X) = 2.X + 2
0.41/0.60	[d](X) = 2.X
0.41/0.60	[A](X) = 2.X + 1
0.41/0.60	[B](X) = 2.X
0.41/0.60	
0.41/0.60	Problem 1: 
0.41/0.60	
0.41/0.60	SCC Processor:
0.41/0.60	-> Pairs:
0.41/0.60	 B(d(b(x1:S))) -> A(c(x1:S))
0.41/0.60	-> Rules:
0.41/0.60	 a(d(x1:S)) -> d(b(x1:S))
0.41/0.60	 a(x1:S) -> b(b(b(x1:S)))
0.41/0.60	 b(d(b(x1:S))) -> a(c(x1:S))
0.41/0.60	 c(x1:S) -> d(x1:S)
0.41/0.60	->Strongly Connected Components:
0.41/0.60	 There is no strongly connected component
0.41/0.60	
0.41/0.60	The problem is finite.
0.41/0.60	EOF