0.94/1.11	YES
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	(VAR v_NonEmpty:S x1:S)
0.94/1.11	(RULES
0.94/1.11	a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	a(x1:S) -> x1:S
0.94/1.11	b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	d(x1:S) -> x1:S
0.94/1.11	)
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	Dependency Pairs Processor:
0.94/1.11	-> Pairs:
0.94/1.11	 A(d(x1:S)) -> B(x1:S)
0.94/1.11	 A(d(x1:S)) -> D(b(x1:S))
0.94/1.11	 A(c(x1:S)) -> B(b(c(d(x1:S))))
0.94/1.11	 A(c(x1:S)) -> B(c(d(x1:S)))
0.94/1.11	 A(c(x1:S)) -> D(x1:S)
0.94/1.11	 A(x1:S) -> B(b(b(x1:S)))
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	 B(d(b(x1:S))) -> D(x1:S)
0.94/1.11	 B(c(x1:S)) -> D(d(x1:S))
0.94/1.11	 B(c(x1:S)) -> D(x1:S)
0.94/1.11	-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	SCC Processor:
0.94/1.11	-> Pairs:
0.94/1.11	 A(d(x1:S)) -> B(x1:S)
0.94/1.11	 A(d(x1:S)) -> D(b(x1:S))
0.94/1.11	 A(c(x1:S)) -> B(b(c(d(x1:S))))
0.94/1.11	 A(c(x1:S)) -> B(c(d(x1:S)))
0.94/1.11	 A(c(x1:S)) -> D(x1:S)
0.94/1.11	 A(x1:S) -> B(b(b(x1:S)))
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	 B(d(b(x1:S))) -> D(x1:S)
0.94/1.11	 B(c(x1:S)) -> D(d(x1:S))
0.94/1.11	 B(c(x1:S)) -> D(x1:S)
0.94/1.11	-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	->Strongly Connected Components:
0.94/1.11	->->Cycle:
0.94/1.11	->->-> Pairs:
0.94/1.11	 A(d(x1:S)) -> B(x1:S)
0.94/1.11	 A(c(x1:S)) -> B(b(c(d(x1:S))))
0.94/1.11	 A(x1:S) -> B(b(b(x1:S)))
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	->->-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	Reduction Pair Processor:
0.94/1.11	-> Pairs:
0.94/1.11	 A(d(x1:S)) -> B(x1:S)
0.94/1.11	 A(c(x1:S)) -> B(b(c(d(x1:S))))
0.94/1.11	 A(x1:S) -> B(b(b(x1:S)))
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	-> Usable rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	->Interpretation type:
0.94/1.11	 Linear
0.94/1.11	->Coefficients:
0.94/1.11	 Natural Numbers
0.94/1.11	->Dimension:
0.94/1.11	 1
0.94/1.11	->Bound:
0.94/1.11	 2
0.94/1.11	->Interpretation:
0.94/1.11	 
0.94/1.11	[a](X) = X
0.94/1.11	[b](X) = X
0.94/1.11	[d](X) = 2.X + 2
0.94/1.11	[c](X) = 2
0.94/1.11	[A](X) = 2.X
0.94/1.11	[B](X) = 2.X
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	SCC Processor:
0.94/1.11	-> Pairs:
0.94/1.11	 A(c(x1:S)) -> B(b(c(d(x1:S))))
0.94/1.11	 A(x1:S) -> B(b(b(x1:S)))
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	->Strongly Connected Components:
0.94/1.11	->->Cycle:
0.94/1.11	->->-> Pairs:
0.94/1.11	 A(c(x1:S)) -> B(b(c(d(x1:S))))
0.94/1.11	 A(x1:S) -> B(b(b(x1:S)))
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	->->-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	Reduction Pair Processor:
0.94/1.11	-> Pairs:
0.94/1.11	 A(c(x1:S)) -> B(b(c(d(x1:S))))
0.94/1.11	 A(x1:S) -> B(b(b(x1:S)))
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	-> Usable rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	->Interpretation type:
0.94/1.11	 Linear
0.94/1.11	->Coefficients:
0.94/1.11	 All rationals
0.94/1.11	->Dimension:
0.94/1.11	 1
0.94/1.11	->Bound:
0.94/1.11	 4
0.94/1.11	->Interpretation:
0.94/1.11	 
0.94/1.11	[a](X) = X + 4
0.94/1.11	[b](X) = X + 1
0.94/1.11	[d](X) = 4.X + 1
0.94/1.11	[c](X) = 0
0.94/1.11	[A](X) = 1/2.X + 3
0.94/1.11	[B](X) = 1/2.X + 4/3
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	SCC Processor:
0.94/1.11	-> Pairs:
0.94/1.11	 A(x1:S) -> B(b(b(x1:S)))
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	->Strongly Connected Components:
0.94/1.11	->->Cycle:
0.94/1.11	->->-> Pairs:
0.94/1.11	 A(x1:S) -> B(b(b(x1:S)))
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	->->-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	Reduction Pair Processor:
0.94/1.11	-> Pairs:
0.94/1.11	 A(x1:S) -> B(b(b(x1:S)))
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	-> Usable rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	->Interpretation type:
0.94/1.11	 Linear
0.94/1.11	->Coefficients:
0.94/1.11	 All rationals
0.94/1.11	->Dimension:
0.94/1.11	 1
0.94/1.11	->Bound:
0.94/1.11	 4
0.94/1.11	->Interpretation:
0.94/1.11	 
0.94/1.11	[a](X) = X + 3
0.94/1.11	[b](X) = X + 1
0.94/1.11	[d](X) = 3.X + 2
0.94/1.11	[c](X) = 2
0.94/1.11	[A](X) = 4/3.X + 4
0.94/1.11	[B](X) = 4/3.X
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	SCC Processor:
0.94/1.11	-> Pairs:
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	->Strongly Connected Components:
0.94/1.11	->->Cycle:
0.94/1.11	->->-> Pairs:
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	->->-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	Reduction Pair Processor:
0.94/1.11	-> Pairs:
0.94/1.11	 A(x1:S) -> B(b(x1:S))
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	-> Usable rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	->Interpretation type:
0.94/1.11	 Linear
0.94/1.11	->Coefficients:
0.94/1.11	 All rationals
0.94/1.11	->Dimension:
0.94/1.11	 1
0.94/1.11	->Bound:
0.94/1.11	 4
0.94/1.11	->Interpretation:
0.94/1.11	 
0.94/1.11	[a](X) = X + 3/4
0.94/1.11	[b](X) = X + 1/4
0.94/1.11	[d](X) = 2.X + 1/2
0.94/1.11	[c](X) = 3
0.94/1.11	[A](X) = 4.X + 4/3
0.94/1.11	[B](X) = 4.X
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	SCC Processor:
0.94/1.11	-> Pairs:
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	->Strongly Connected Components:
0.94/1.11	->->Cycle:
0.94/1.11	->->-> Pairs:
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	->->-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	Reduction Pair Processor:
0.94/1.11	-> Pairs:
0.94/1.11	 A(x1:S) -> B(x1:S)
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	-> Usable rules:
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	->Interpretation type:
0.94/1.11	 Linear
0.94/1.11	->Coefficients:
0.94/1.11	 Natural Numbers
0.94/1.11	->Dimension:
0.94/1.11	 1
0.94/1.11	->Bound:
0.94/1.11	 2
0.94/1.11	->Interpretation:
0.94/1.11	 
0.94/1.11	[b](X) = 2.X + 2
0.94/1.11	[d](X) = 2.X + 2
0.94/1.11	[A](X) = 2.X + 2
0.94/1.11	[B](X) = 2.X + 1
0.94/1.11	
0.94/1.11	Problem 1: 
0.94/1.11	
0.94/1.11	SCC Processor:
0.94/1.11	-> Pairs:
0.94/1.11	 B(d(b(x1:S))) -> A(d(x1:S))
0.94/1.11	-> Rules:
0.94/1.11	 a(d(x1:S)) -> d(b(x1:S))
0.94/1.11	 a(c(x1:S)) -> b(b(c(d(x1:S))))
0.94/1.11	 a(x1:S) -> b(b(b(x1:S)))
0.94/1.11	 a(x1:S) -> x1:S
0.94/1.11	 b(d(b(x1:S))) -> a(d(x1:S))
0.94/1.11	 b(c(x1:S)) -> c(d(d(x1:S)))
0.94/1.11	 d(x1:S) -> x1:S
0.94/1.11	->Strongly Connected Components:
0.94/1.11	 There is no strongly connected component
0.94/1.11	
0.94/1.11	The problem is finite.
0.94/1.11	EOF