2.06/2.80	YES
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	(VAR v_NonEmpty:S x1:S)
2.06/2.80	(RULES
2.06/2.80	a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	)
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	Dependency Pairs Processor:
2.06/2.80	-> Pairs:
2.06/2.80	 A(d(x1:S)) -> B(d(x1:S))
2.06/2.80	 A(d(x1:S)) -> B(c(b(d(x1:S))))
2.06/2.80	 A(d(x1:S)) -> D(b(c(b(d(x1:S)))))
2.06/2.80	 A(x1:S) -> B(b(f(b(b(x1:S)))))
2.06/2.80	 A(x1:S) -> B(b(x1:S))
2.06/2.80	 A(x1:S) -> B(f(b(b(x1:S))))
2.06/2.80	 A(x1:S) -> B(x1:S)
2.06/2.80	 B(d(b(x1:S))) -> A(d(x1:S))
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	SCC Processor:
2.06/2.80	-> Pairs:
2.06/2.80	 A(d(x1:S)) -> B(d(x1:S))
2.06/2.80	 A(d(x1:S)) -> B(c(b(d(x1:S))))
2.06/2.80	 A(d(x1:S)) -> D(b(c(b(d(x1:S)))))
2.06/2.80	 A(x1:S) -> B(b(f(b(b(x1:S)))))
2.06/2.80	 A(x1:S) -> B(b(x1:S))
2.06/2.80	 A(x1:S) -> B(f(b(b(x1:S))))
2.06/2.80	 A(x1:S) -> B(x1:S)
2.06/2.80	 B(d(b(x1:S))) -> A(d(x1:S))
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	->Strongly Connected Components:
2.06/2.80	->->Cycle:
2.06/2.80	->->-> Pairs:
2.06/2.80	 A(d(x1:S)) -> B(d(x1:S))
2.06/2.80	 A(x1:S) -> B(b(x1:S))
2.06/2.80	 A(x1:S) -> B(x1:S)
2.06/2.80	 B(d(b(x1:S))) -> A(d(x1:S))
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	->->-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	Reduction Pair Processor:
2.06/2.80	-> Pairs:
2.06/2.80	 A(d(x1:S)) -> B(d(x1:S))
2.06/2.80	 A(x1:S) -> B(b(x1:S))
2.06/2.80	 A(x1:S) -> B(x1:S)
2.06/2.80	 B(d(b(x1:S))) -> A(d(x1:S))
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	-> Usable rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	->Interpretation type:
2.06/2.80	 Linear
2.06/2.80	->Coefficients:
2.06/2.80	 All rationals
2.06/2.80	->Dimension:
2.06/2.80	 1
2.06/2.80	->Bound:
2.06/2.80	 4
2.06/2.80	->Interpretation:
2.06/2.80	 
2.06/2.80	[a](X) = X + 3
2.06/2.80	[b](X) = X + 2/3
2.06/2.80	[d](X) = 4.X + 3
2.06/2.80	[c](X) = 0
2.06/2.80	[f](X) = X + 1/3
2.06/2.80	[A](X) = 1/2.X + 1/3
2.06/2.80	[B](X) = 1/2.X
2.06/2.80	[D](X) = 2.X + 4/3
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	SCC Processor:
2.06/2.80	-> Pairs:
2.06/2.80	 A(x1:S) -> B(b(x1:S))
2.06/2.80	 A(x1:S) -> B(x1:S)
2.06/2.80	 B(d(b(x1:S))) -> A(d(x1:S))
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	->Strongly Connected Components:
2.06/2.80	->->Cycle:
2.06/2.80	->->-> Pairs:
2.06/2.80	 A(x1:S) -> B(b(x1:S))
2.06/2.80	 A(x1:S) -> B(x1:S)
2.06/2.80	 B(d(b(x1:S))) -> A(d(x1:S))
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	->->-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	Reduction Pair Processor:
2.06/2.80	-> Pairs:
2.06/2.80	 A(x1:S) -> B(b(x1:S))
2.06/2.80	 A(x1:S) -> B(x1:S)
2.06/2.80	 B(d(b(x1:S))) -> A(d(x1:S))
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	-> Usable rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	->Interpretation type:
2.06/2.80	 Linear
2.06/2.80	->Coefficients:
2.06/2.80	 All rationals
2.06/2.80	->Dimension:
2.06/2.80	 1
2.06/2.80	->Bound:
2.06/2.80	 4
2.06/2.80	->Interpretation:
2.06/2.80	 
2.06/2.80	[a](X) = X + 3
2.06/2.80	[b](X) = X + 2/3
2.06/2.80	[d](X) = 4.X + 1/4
2.06/2.80	[c](X) = 0
2.06/2.80	[f](X) = X + 1/4
2.06/2.80	[A](X) = 1/3.X + 3/2
2.06/2.80	[B](X) = 1/3.X + 1
2.06/2.80	[D](X) = 4/3.X + 4/3
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	SCC Processor:
2.06/2.80	-> Pairs:
2.06/2.80	 A(x1:S) -> B(x1:S)
2.06/2.80	 B(d(b(x1:S))) -> A(d(x1:S))
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	->Strongly Connected Components:
2.06/2.80	->->Cycle:
2.06/2.80	->->-> Pairs:
2.06/2.80	 A(x1:S) -> B(x1:S)
2.06/2.80	 B(d(b(x1:S))) -> A(d(x1:S))
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	->->-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	Reduction Pair Processor:
2.06/2.80	-> Pairs:
2.06/2.80	 A(x1:S) -> B(x1:S)
2.06/2.80	 B(d(b(x1:S))) -> A(d(x1:S))
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	-> Usable rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	->Interpretation type:
2.06/2.80	 Linear
2.06/2.80	->Coefficients:
2.06/2.80	 All rationals
2.06/2.80	->Dimension:
2.06/2.80	 1
2.06/2.80	->Bound:
2.06/2.80	 4
2.06/2.80	->Interpretation:
2.06/2.80	 
2.06/2.80	[a](X) = X + 3
2.06/2.80	[b](X) = X + 2/3
2.06/2.80	[d](X) = 4.X + 3/2
2.06/2.80	[c](X) = 0
2.06/2.80	[f](X) = X + 1/4
2.06/2.80	[A](X) = 1/2.X + 4/3
2.06/2.80	[B](X) = 1/2.X + 3/4
2.06/2.80	[D](X) = 2.X + 4/3
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	SCC Processor:
2.06/2.80	-> Pairs:
2.06/2.80	 B(d(b(x1:S))) -> A(d(x1:S))
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	->Strongly Connected Components:
2.06/2.80	->->Cycle:
2.06/2.80	->->-> Pairs:
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	->->-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	Reduction Pair Processor:
2.06/2.80	-> Pairs:
2.06/2.80	 B(d(b(x1:S))) -> D(x1:S)
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	-> Usable rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	->Interpretation type:
2.06/2.80	 Linear
2.06/2.80	->Coefficients:
2.06/2.80	 All rationals
2.06/2.80	->Dimension:
2.06/2.80	 1
2.06/2.80	->Bound:
2.06/2.80	 4
2.06/2.80	->Interpretation:
2.06/2.80	 
2.06/2.80	[a](X) = 1/2.X + 4/3
2.06/2.80	[b](X) = 3/4.X + 1/3
2.06/2.80	[d](X) = 4.X
2.06/2.80	[c](X) = 0
2.06/2.80	[f](X) = 4/3.X + 1/2
2.06/2.80	[B](X) = 1/3.X + 4
2.06/2.80	[D](X) = X + 4
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	SCC Processor:
2.06/2.80	-> Pairs:
2.06/2.80	 D(f(x1:S)) -> B(d(x1:S))
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	->Strongly Connected Components:
2.06/2.80	->->Cycle:
2.06/2.80	->->-> Pairs:
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	->->-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	Subterm Processor:
2.06/2.80	-> Pairs:
2.06/2.80	 D(f(x1:S)) -> D(x1:S)
2.06/2.80	-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	->Projection:
2.06/2.80	 pi(D) = 1
2.06/2.80	
2.06/2.80	Problem 1: 
2.06/2.80	
2.06/2.80	SCC Processor:
2.06/2.80	-> Pairs:
2.06/2.80	 Empty
2.06/2.80	-> Rules:
2.06/2.80	 a(d(x1:S)) -> d(b(c(b(d(x1:S)))))
2.06/2.80	 a(x1:S) -> b(b(f(b(b(x1:S)))))
2.06/2.80	 b(d(b(x1:S))) -> a(d(x1:S))
2.06/2.80	 d(f(x1:S)) -> b(d(x1:S))
2.06/2.80	->Strongly Connected Components:
2.06/2.80	 There is no strongly connected component
2.06/2.80	
2.06/2.80	The problem is finite.
2.06/2.80	EOF