0.48/0.62	YES
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	(VAR v_NonEmpty:S x1:S)
0.48/0.62	(RULES
0.48/0.62	a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	)
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	Dependency Pairs Processor:
0.48/0.62	-> Pairs:
0.48/0.62	 A(c(x1:S)) -> A(x1:S)
0.48/0.62	 A(c(x1:S)) -> C(a(x1:S))
0.48/0.62	 A(l(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 C(a(r(x1:S))) -> A(x1:S)
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	SCC Processor:
0.48/0.62	-> Pairs:
0.48/0.62	 A(c(x1:S)) -> A(x1:S)
0.48/0.62	 A(c(x1:S)) -> C(a(x1:S))
0.48/0.62	 A(l(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 C(a(r(x1:S))) -> A(x1:S)
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	->Strongly Connected Components:
0.48/0.62	->->Cycle:
0.48/0.62	->->-> Pairs:
0.48/0.62	 A(c(x1:S)) -> A(x1:S)
0.48/0.62	 A(c(x1:S)) -> C(a(x1:S))
0.48/0.62	 A(l(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 C(a(r(x1:S))) -> A(x1:S)
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	->->-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	Reduction Pair Processor:
0.48/0.62	-> Pairs:
0.48/0.62	 A(c(x1:S)) -> A(x1:S)
0.48/0.62	 A(c(x1:S)) -> C(a(x1:S))
0.48/0.62	 A(l(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 C(a(r(x1:S))) -> A(x1:S)
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	-> Usable rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	->Interpretation type:
0.48/0.62	 Linear
0.48/0.62	->Coefficients:
0.48/0.62	 Natural Numbers
0.48/0.62	->Dimension:
0.48/0.62	 1
0.48/0.62	->Bound:
0.48/0.62	 2
0.48/0.62	->Interpretation:
0.48/0.62	 
0.48/0.62	[a](X) = 2.X + 1
0.48/0.62	[c](X) = X
0.48/0.62	[l](X) = 2.X + 1
0.48/0.62	[r](X) = 2.X + 1
0.48/0.62	[A](X) = 2.X + 2
0.48/0.62	[C](X) = X
0.48/0.62	[L](X) = 2.X + 2
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	SCC Processor:
0.48/0.62	-> Pairs:
0.48/0.62	 A(c(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 C(a(r(x1:S))) -> A(x1:S)
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	->Strongly Connected Components:
0.48/0.62	->->Cycle:
0.48/0.62	->->-> Pairs:
0.48/0.62	 A(c(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	->->-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	Reduction Pair Processor:
0.48/0.62	-> Pairs:
0.48/0.62	 A(c(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	-> Usable rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	->Interpretation type:
0.48/0.62	 Linear
0.48/0.62	->Coefficients:
0.48/0.62	 Natural Numbers
0.48/0.62	->Dimension:
0.48/0.62	 1
0.48/0.62	->Bound:
0.48/0.62	 2
0.48/0.62	->Interpretation:
0.48/0.62	 
0.48/0.62	[a](X) = 2.X + 2
0.48/0.62	[c](X) = X
0.48/0.62	[l](X) = 2.X + 2
0.48/0.62	[r](X) = 2.X + 2
0.48/0.62	[A](X) = 2.X + 2
0.48/0.62	[L](X) = 2.X + 2
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	SCC Processor:
0.48/0.62	-> Pairs:
0.48/0.62	 A(c(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	->Strongly Connected Components:
0.48/0.62	->->Cycle:
0.48/0.62	->->-> Pairs:
0.48/0.62	 A(c(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	->->-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	Reduction Pair Processor:
0.48/0.62	-> Pairs:
0.48/0.62	 A(c(x1:S)) -> A(x1:S)
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	-> Usable rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	->Interpretation type:
0.48/0.62	 Linear
0.48/0.62	->Coefficients:
0.48/0.62	 Natural Numbers
0.48/0.62	->Dimension:
0.48/0.62	 1
0.48/0.62	->Bound:
0.48/0.62	 2
0.48/0.62	->Interpretation:
0.48/0.62	 
0.48/0.62	[a](X) = 2.X
0.48/0.62	[c](X) = 2.X + 2
0.48/0.62	[l](X) = 0
0.48/0.62	[r](X) = 2.X
0.48/0.62	[A](X) = 2.X + 2
0.48/0.62	[L](X) = 2
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	SCC Processor:
0.48/0.62	-> Pairs:
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	->Strongly Connected Components:
0.48/0.62	->->Cycle:
0.48/0.62	->->-> Pairs:
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	->->-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	Reduction Pair Processor:
0.48/0.62	-> Pairs:
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(l(c(c(c(r(x1:S))))))
0.48/0.62	-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	-> Usable rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	->Interpretation type:
0.48/0.62	 Linear
0.48/0.62	->Coefficients:
0.48/0.62	 Natural Numbers
0.48/0.62	->Dimension:
0.48/0.62	 1
0.48/0.62	->Bound:
0.48/0.62	 2
0.48/0.62	->Interpretation:
0.48/0.62	 
0.48/0.62	[a](X) = 2.X + 2
0.48/0.62	[c](X) = X
0.48/0.62	[l](X) = 2.X + 2
0.48/0.62	[r](X) = 2.X + 2
0.48/0.62	[A](X) = 2.X
0.48/0.62	[L](X) = 2.X
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	SCC Processor:
0.48/0.62	-> Pairs:
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	->Strongly Connected Components:
0.48/0.62	->->Cycle:
0.48/0.62	->->-> Pairs:
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	->->-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	Reduction Pair Processor:
0.48/0.62	-> Pairs:
0.48/0.62	 A(l(x1:S)) -> L(a(x1:S))
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	-> Usable rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	->Interpretation type:
0.48/0.62	 Linear
0.48/0.62	->Coefficients:
0.48/0.62	 All rationals
0.48/0.62	->Dimension:
0.48/0.62	 1
0.48/0.62	->Bound:
0.48/0.62	 2
0.48/0.62	->Interpretation:
0.48/0.62	 
0.48/0.62	[a](X) = 2.X
0.48/0.62	[c](X) = 1/2.X
0.48/0.62	[l](X) = 2.X + 1/2
0.48/0.62	[r](X) = 2
0.48/0.62	[A](X) = X
0.48/0.62	[L](X) = X
0.48/0.62	
0.48/0.62	Problem 1: 
0.48/0.62	
0.48/0.62	SCC Processor:
0.48/0.62	-> Pairs:
0.48/0.62	 L(r(a(a(x1:S)))) -> A(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	-> Rules:
0.48/0.62	 a(c(x1:S)) -> c(a(x1:S))
0.48/0.62	 a(l(x1:S)) -> l(a(x1:S))
0.48/0.62	 c(a(r(x1:S))) -> r(a(x1:S))
0.48/0.62	 l(r(a(a(x1:S)))) -> a(a(l(c(c(c(r(x1:S)))))))
0.48/0.62	->Strongly Connected Components:
0.48/0.62	 There is no strongly connected component
0.48/0.62	
0.48/0.62	The problem is finite.
0.48/0.62	EOF