0.95/1.26	YES
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	(VAR v_NonEmpty:S x1:S)
0.95/1.26	(RULES
0.95/1.26	b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	)
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	Dependency Pairs Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(c(d(d(c(x1:S)))))
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> C(x1:S)
0.95/1.26	 B(d(d(x1:S))) -> D(c(x1:S))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	SCC Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(c(d(d(c(x1:S)))))
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> C(x1:S)
0.95/1.26	 B(d(d(x1:S))) -> D(c(x1:S))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Strongly Connected Components:
0.95/1.26	->->Cycle:
0.95/1.26	->->-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(c(d(d(c(x1:S)))))
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> C(x1:S)
0.95/1.26	 B(d(d(x1:S))) -> D(c(x1:S))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	->->-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	Reduction Pair Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(c(d(d(c(x1:S)))))
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> C(x1:S)
0.95/1.26	 B(d(d(x1:S))) -> D(c(x1:S))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	-> Usable rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Interpretation type:
0.95/1.26	 Linear
0.95/1.26	->Coefficients:
0.95/1.26	 Natural Numbers
0.95/1.26	->Dimension:
0.95/1.26	 1
0.95/1.26	->Bound:
0.95/1.26	 2
0.95/1.26	->Interpretation:
0.95/1.26	 
0.95/1.26	[b](X) = X
0.95/1.26	[c](X) = X
0.95/1.26	[d](X) = 2.X + 2
0.95/1.26	[a](X) = X
0.95/1.26	[B](X) = X
0.95/1.26	[C](X) = X
0.95/1.26	[D](X) = 2.X + 2
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	SCC Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(c(d(d(c(x1:S)))))
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> D(c(x1:S))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Strongly Connected Components:
0.95/1.26	->->Cycle:
0.95/1.26	->->-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(c(d(d(c(x1:S)))))
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> D(c(x1:S))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	->->-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	Reduction Pair Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(c(d(d(c(x1:S)))))
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> D(c(x1:S))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	-> Usable rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Interpretation type:
0.95/1.26	 Linear
0.95/1.26	->Coefficients:
0.95/1.26	 Natural Numbers
0.95/1.26	->Dimension:
0.95/1.26	 1
0.95/1.26	->Bound:
0.95/1.26	 2
0.95/1.26	->Interpretation:
0.95/1.26	 
0.95/1.26	[b](X) = 2
0.95/1.26	[c](X) = 0
0.95/1.26	[d](X) = 2
0.95/1.26	[a](X) = 0
0.95/1.26	[B](X) = 2
0.95/1.26	[C](X) = X
0.95/1.26	[D](X) = 2
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	SCC Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> D(c(x1:S))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Strongly Connected Components:
0.95/1.26	->->Cycle:
0.95/1.26	->->-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> D(c(x1:S))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	->->-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	Reduction Pair Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> D(c(x1:S))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	-> Usable rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Interpretation type:
0.95/1.26	 Linear
0.95/1.26	->Coefficients:
0.95/1.26	 Natural Numbers
0.95/1.26	->Dimension:
0.95/1.26	 1
0.95/1.26	->Bound:
0.95/1.26	 2
0.95/1.26	->Interpretation:
0.95/1.26	 
0.95/1.26	[b](X) = X
0.95/1.26	[c](X) = X
0.95/1.26	[d](X) = 2.X + 2
0.95/1.26	[a](X) = X
0.95/1.26	[B](X) = X
0.95/1.26	[C](X) = X
0.95/1.26	[D](X) = 2.X + 2
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	SCC Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Strongly Connected Components:
0.95/1.26	->->Cycle:
0.95/1.26	->->-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	->->-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	Reduction Pair Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> C(d(d(c(x1:S))))
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	-> Usable rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Interpretation type:
0.95/1.26	 Linear
0.95/1.26	->Coefficients:
0.95/1.26	 All rationals
0.95/1.26	->Dimension:
0.95/1.26	 1
0.95/1.26	->Bound:
0.95/1.26	 4
0.95/1.26	->Interpretation:
0.95/1.26	 
0.95/1.26	[b](X) = X + 4
0.95/1.26	[c](X) = X + 1/3
0.95/1.26	[d](X) = 3.X + 1/4
0.95/1.26	[a](X) = X + 4/3
0.95/1.26	[B](X) = 1/2.X + 3
0.95/1.26	[C](X) = 1/2.X + 4/3
0.95/1.26	[D](X) = 3/2.X + 3/2
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	SCC Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 C(d(c(x1:S))) -> D(x1:S)
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Strongly Connected Components:
0.95/1.26	->->Cycle:
0.95/1.26	->->-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	->->-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	Reduction Pair Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 B(d(d(x1:S))) -> D(d(c(x1:S)))
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	-> Usable rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Interpretation type:
0.95/1.26	 Linear
0.95/1.26	->Coefficients:
0.95/1.26	 All rationals
0.95/1.26	->Dimension:
0.95/1.26	 1
0.95/1.26	->Bound:
0.95/1.26	 4
0.95/1.26	->Interpretation:
0.95/1.26	 
0.95/1.26	[b](X) = X + 4
0.95/1.26	[c](X) = X + 1/3
0.95/1.26	[d](X) = 3.X + 1
0.95/1.26	[a](X) = X + 4/3
0.95/1.26	[B](X) = 1/3.X + 2
0.95/1.26	[D](X) = X + 1
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	SCC Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 D(a(x1:S)) -> B(d(x1:S))
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Strongly Connected Components:
0.95/1.26	->->Cycle:
0.95/1.26	->->-> Pairs:
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	->->-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	Subterm Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 D(a(x1:S)) -> D(x1:S)
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Projection:
0.95/1.26	 pi(D) = 1
0.95/1.26	
0.95/1.26	Problem 1: 
0.95/1.26	
0.95/1.26	SCC Processor:
0.95/1.26	-> Pairs:
0.95/1.26	 Empty
0.95/1.26	-> Rules:
0.95/1.26	 b(d(d(x1:S))) -> c(c(d(d(c(x1:S)))))
0.95/1.26	 b(x1:S) -> a(a(a(x1:S)))
0.95/1.26	 c(d(c(x1:S))) -> a(d(x1:S))
0.95/1.26	 d(a(x1:S)) -> b(d(x1:S))
0.95/1.26	->Strongly Connected Components:
0.95/1.26	 There is no strongly connected component
0.95/1.26	
0.95/1.26	The problem is finite.
0.95/1.26	EOF