0.00/0.20	YES
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	(VAR v_NonEmpty:S x1:S)
0.00/0.20	(RULES
0.00/0.20	a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	)
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Dependency Pairs Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(c(x1:S)) -> A(x1:S)
0.00/0.20	 A(c(x1:S)) -> C(a(x1:S))
0.00/0.20	 A(l(x1:S)) -> A(x1:S)
0.00/0.20	 A(l(x1:S)) -> L(a(x1:S))
0.00/0.20	 C(a(r(x1:S))) -> A(x1:S)
0.00/0.20	 L(r(a(x1:S))) -> A(l(c(c(r(x1:S)))))
0.00/0.20	-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(c(x1:S)) -> A(x1:S)
0.00/0.20	 A(c(x1:S)) -> C(a(x1:S))
0.00/0.20	 A(l(x1:S)) -> A(x1:S)
0.00/0.20	 A(l(x1:S)) -> L(a(x1:S))
0.00/0.20	 C(a(r(x1:S))) -> A(x1:S)
0.00/0.20	 L(r(a(x1:S))) -> A(l(c(c(r(x1:S)))))
0.00/0.20	-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 A(c(x1:S)) -> A(x1:S)
0.00/0.20	 A(c(x1:S)) -> C(a(x1:S))
0.00/0.20	 A(l(x1:S)) -> A(x1:S)
0.00/0.20	 A(l(x1:S)) -> L(a(x1:S))
0.00/0.20	 C(a(r(x1:S))) -> A(x1:S)
0.00/0.20	 L(r(a(x1:S))) -> A(l(c(c(r(x1:S)))))
0.00/0.20	->->-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pair Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(c(x1:S)) -> A(x1:S)
0.00/0.20	 A(c(x1:S)) -> C(a(x1:S))
0.00/0.20	 A(l(x1:S)) -> A(x1:S)
0.00/0.20	 A(l(x1:S)) -> L(a(x1:S))
0.00/0.20	 C(a(r(x1:S))) -> A(x1:S)
0.00/0.20	 L(r(a(x1:S))) -> A(l(c(c(r(x1:S)))))
0.00/0.20	-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	-> Usable rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a](X) = 2.X + 1
0.00/0.20	[c](X) = X
0.00/0.20	[l](X) = 2.X + 1
0.00/0.20	[r](X) = 2.X + 1
0.00/0.20	[A](X) = 2.X + 2
0.00/0.20	[C](X) = X
0.00/0.20	[L](X) = 2.X + 2
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(c(x1:S)) -> A(x1:S)
0.00/0.20	 A(l(x1:S)) -> A(x1:S)
0.00/0.20	 A(l(x1:S)) -> L(a(x1:S))
0.00/0.20	 C(a(r(x1:S))) -> A(x1:S)
0.00/0.20	 L(r(a(x1:S))) -> A(l(c(c(r(x1:S)))))
0.00/0.20	-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 A(c(x1:S)) -> A(x1:S)
0.00/0.20	 A(l(x1:S)) -> A(x1:S)
0.00/0.20	 A(l(x1:S)) -> L(a(x1:S))
0.00/0.20	 L(r(a(x1:S))) -> A(l(c(c(r(x1:S)))))
0.00/0.20	->->-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pair Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(c(x1:S)) -> A(x1:S)
0.00/0.20	 A(l(x1:S)) -> A(x1:S)
0.00/0.20	 A(l(x1:S)) -> L(a(x1:S))
0.00/0.20	 L(r(a(x1:S))) -> A(l(c(c(r(x1:S)))))
0.00/0.20	-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	-> Usable rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a](X) = 2.X + 2
0.00/0.20	[c](X) = X
0.00/0.20	[l](X) = 2.X + 2
0.00/0.20	[r](X) = 2.X + 2
0.00/0.20	[A](X) = 2.X + 2
0.00/0.20	[L](X) = 2.X + 2
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(c(x1:S)) -> A(x1:S)
0.00/0.20	 A(l(x1:S)) -> L(a(x1:S))
0.00/0.20	 L(r(a(x1:S))) -> A(l(c(c(r(x1:S)))))
0.00/0.20	-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 A(l(x1:S)) -> L(a(x1:S))
0.00/0.20	 L(r(a(x1:S))) -> A(l(c(c(r(x1:S)))))
0.00/0.20	->->-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 A(c(x1:S)) -> A(x1:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	
0.00/0.20	
0.00/0.20	The problem is decomposed in 2 subproblems.
0.00/0.20	
0.00/0.20	Problem 1.1: 
0.00/0.20	
0.00/0.20	Reduction Pair Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(l(x1:S)) -> L(a(x1:S))
0.00/0.20	 L(r(a(x1:S))) -> A(l(c(c(r(x1:S)))))
0.00/0.20	-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	-> Usable rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 All rationals
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a](X) = 2.X
0.00/0.20	[c](X) = 1/2.X
0.00/0.20	[l](X) = 1/2.X
0.00/0.20	[r](X) = 2
0.00/0.20	[A](X) = 2.X + 1/2
0.00/0.20	[L](X) = 1/2.X
0.00/0.20	
0.00/0.20	Problem 1.1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 L(r(a(x1:S))) -> A(l(c(c(r(x1:S)))))
0.00/0.20	-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	 There is no strongly connected component
0.00/0.20	
0.00/0.20	The problem is finite.
0.00/0.20	
0.00/0.20	Problem 1.2: 
0.00/0.20	
0.00/0.20	Subterm Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(c(x1:S)) -> A(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	->Projection:
0.00/0.20	 pi(A) = 1
0.00/0.20	
0.00/0.20	Problem 1.2: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 Empty
0.00/0.20	-> Rules:
0.00/0.20	 a(c(x1:S)) -> c(a(x1:S))
0.00/0.20	 a(l(x1:S)) -> l(a(x1:S))
0.00/0.20	 c(a(r(x1:S))) -> r(a(x1:S))
0.00/0.20	 l(r(a(x1:S))) -> a(l(c(c(r(x1:S)))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	 There is no strongly connected component
0.00/0.20	
0.00/0.20	The problem is finite.
0.00/0.20	EOF