0.00/0.23	YES
0.00/0.23	
0.00/0.23	Problem 1: 
0.00/0.23	
0.00/0.23	(VAR v_NonEmpty:S x1:S)
0.00/0.23	(RULES
0.00/0.23	a(b(x1:S)) -> d(x1:S)
0.00/0.23	a(f(x1:S)) -> a(x1:S)
0.00/0.23	b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	)
0.00/0.23	
0.00/0.23	Problem 1: 
0.00/0.23	
0.00/0.23	Dependency Pairs Processor:
0.00/0.23	-> Pairs:
0.00/0.23	 A(b(x1:S)) -> D(x1:S)
0.00/0.23	 A(f(x1:S)) -> A(x1:S)
0.00/0.23	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.23	 B(a(x1:S)) -> B(x1:S)
0.00/0.23	 D(c(x1:S)) -> A(b(b(c(x1:S))))
0.00/0.23	 D(f(x1:S)) -> A(b(x1:S))
0.00/0.23	 D(f(x1:S)) -> B(x1:S)
0.00/0.23	-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	
0.00/0.23	Problem 1: 
0.00/0.23	
0.00/0.23	SCC Processor:
0.00/0.23	-> Pairs:
0.00/0.23	 A(b(x1:S)) -> D(x1:S)
0.00/0.23	 A(f(x1:S)) -> A(x1:S)
0.00/0.23	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.23	 B(a(x1:S)) -> B(x1:S)
0.00/0.23	 D(c(x1:S)) -> A(b(b(c(x1:S))))
0.00/0.23	 D(f(x1:S)) -> A(b(x1:S))
0.00/0.23	 D(f(x1:S)) -> B(x1:S)
0.00/0.23	-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	->Strongly Connected Components:
0.00/0.23	->->Cycle:
0.00/0.23	->->-> Pairs:
0.00/0.23	 A(b(x1:S)) -> D(x1:S)
0.00/0.23	 A(f(x1:S)) -> A(x1:S)
0.00/0.23	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.23	 B(a(x1:S)) -> B(x1:S)
0.00/0.23	 D(c(x1:S)) -> A(b(b(c(x1:S))))
0.00/0.23	 D(f(x1:S)) -> A(b(x1:S))
0.00/0.23	 D(f(x1:S)) -> B(x1:S)
0.00/0.23	->->-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	
0.00/0.23	Problem 1: 
0.00/0.23	
0.00/0.23	Reduction Pair Processor:
0.00/0.23	-> Pairs:
0.00/0.23	 A(b(x1:S)) -> D(x1:S)
0.00/0.23	 A(f(x1:S)) -> A(x1:S)
0.00/0.23	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.23	 B(a(x1:S)) -> B(x1:S)
0.00/0.23	 D(c(x1:S)) -> A(b(b(c(x1:S))))
0.00/0.23	 D(f(x1:S)) -> A(b(x1:S))
0.00/0.23	 D(f(x1:S)) -> B(x1:S)
0.00/0.23	-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	-> Usable rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	->Interpretation type:
0.00/0.23	 Linear
0.00/0.23	->Coefficients:
0.00/0.23	 Natural Numbers
0.00/0.23	->Dimension:
0.00/0.23	 1
0.00/0.23	->Bound:
0.00/0.23	 2
0.00/0.23	->Interpretation:
0.00/0.23	 
0.00/0.23	[a](X) = 2.X + 2
0.00/0.23	[b](X) = X
0.00/0.23	[d](X) = 2.X + 2
0.00/0.23	[c](X) = 2.X + 2
0.00/0.23	[f](X) = X
0.00/0.23	[A](X) = 2.X + 1
0.00/0.23	[B](X) = X
0.00/0.23	[D](X) = 2.X + 1
0.00/0.23	
0.00/0.23	Problem 1: 
0.00/0.23	
0.00/0.23	SCC Processor:
0.00/0.23	-> Pairs:
0.00/0.23	 A(b(x1:S)) -> D(x1:S)
0.00/0.23	 A(f(x1:S)) -> A(x1:S)
0.00/0.23	 B(a(x1:S)) -> B(x1:S)
0.00/0.23	 D(c(x1:S)) -> A(b(b(c(x1:S))))
0.00/0.23	 D(f(x1:S)) -> A(b(x1:S))
0.00/0.23	 D(f(x1:S)) -> B(x1:S)
0.00/0.23	-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	->Strongly Connected Components:
0.00/0.23	->->Cycle:
0.00/0.23	->->-> Pairs:
0.00/0.23	 B(a(x1:S)) -> B(x1:S)
0.00/0.23	->->-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	->->Cycle:
0.00/0.23	->->-> Pairs:
0.00/0.23	 A(b(x1:S)) -> D(x1:S)
0.00/0.23	 A(f(x1:S)) -> A(x1:S)
0.00/0.23	 D(c(x1:S)) -> A(b(b(c(x1:S))))
0.00/0.23	 D(f(x1:S)) -> A(b(x1:S))
0.00/0.23	->->-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	
0.00/0.23	
0.00/0.23	The problem is decomposed in 2 subproblems.
0.00/0.23	
0.00/0.23	Problem 1.1: 
0.00/0.23	
0.00/0.23	Subterm Processor:
0.00/0.23	-> Pairs:
0.00/0.23	 B(a(x1:S)) -> B(x1:S)
0.00/0.23	-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	->Projection:
0.00/0.23	 pi(B) = 1
0.00/0.23	
0.00/0.23	Problem 1.1: 
0.00/0.23	
0.00/0.23	SCC Processor:
0.00/0.23	-> Pairs:
0.00/0.23	 Empty
0.00/0.23	-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	->Strongly Connected Components:
0.00/0.23	 There is no strongly connected component
0.00/0.23	
0.00/0.23	The problem is finite.
0.00/0.23	
0.00/0.23	Problem 1.2: 
0.00/0.23	
0.00/0.23	Reduction Pair Processor:
0.00/0.23	-> Pairs:
0.00/0.23	 A(b(x1:S)) -> D(x1:S)
0.00/0.23	 A(f(x1:S)) -> A(x1:S)
0.00/0.23	 D(c(x1:S)) -> A(b(b(c(x1:S))))
0.00/0.23	 D(f(x1:S)) -> A(b(x1:S))
0.00/0.23	-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	-> Usable rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	->Interpretation type:
0.00/0.23	 Linear
0.00/0.23	->Coefficients:
0.00/0.23	 All rationals
0.00/0.23	->Dimension:
0.00/0.23	 1
0.00/0.23	->Bound:
0.00/0.23	 2
0.00/0.23	->Interpretation:
0.00/0.23	 
0.00/0.23	[a](X) = 2.X
0.00/0.23	[b](X) = 1/2.X
0.00/0.23	[d](X) = X
0.00/0.23	[c](X) = 2
0.00/0.23	[f](X) = X + 1
0.00/0.23	[A](X) = X + 1
0.00/0.23	[D](X) = 1/2.X + 1/2
0.00/0.23	
0.00/0.23	Problem 1.2: 
0.00/0.23	
0.00/0.23	SCC Processor:
0.00/0.23	-> Pairs:
0.00/0.23	 A(f(x1:S)) -> A(x1:S)
0.00/0.23	 D(c(x1:S)) -> A(b(b(c(x1:S))))
0.00/0.23	 D(f(x1:S)) -> A(b(x1:S))
0.00/0.23	-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	->Strongly Connected Components:
0.00/0.23	->->Cycle:
0.00/0.23	->->-> Pairs:
0.00/0.23	 A(f(x1:S)) -> A(x1:S)
0.00/0.23	->->-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	
0.00/0.23	Problem 1.2: 
0.00/0.23	
0.00/0.23	Subterm Processor:
0.00/0.23	-> Pairs:
0.00/0.23	 A(f(x1:S)) -> A(x1:S)
0.00/0.23	-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	->Projection:
0.00/0.23	 pi(A) = 1
0.00/0.23	
0.00/0.23	Problem 1.2: 
0.00/0.23	
0.00/0.23	SCC Processor:
0.00/0.23	-> Pairs:
0.00/0.23	 Empty
0.00/0.23	-> Rules:
0.00/0.23	 a(b(x1:S)) -> d(x1:S)
0.00/0.23	 a(f(x1:S)) -> a(x1:S)
0.00/0.23	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.23	 d(c(x1:S)) -> f(a(b(b(c(x1:S)))))
0.00/0.23	 d(f(x1:S)) -> f(a(b(x1:S)))
0.00/0.23	->Strongly Connected Components:
0.00/0.23	 There is no strongly connected component
0.00/0.23	
0.00/0.23	The problem is finite.
0.00/0.23	EOF