0.00/0.07	YES
0.00/0.07	
0.00/0.07	Problem 1: 
0.00/0.07	
0.00/0.07	(VAR v_NonEmpty:S x1:S)
0.00/0.07	(RULES
0.00/0.07	a(b(a(a(x1:S)))) -> c(b(a(b(a(x1:S)))))
0.00/0.07	a(c(b(x1:S))) -> a(a(b(c(b(a(x1:S))))))
0.00/0.07	)
0.00/0.07	
0.00/0.07	Problem 1: 
0.00/0.07	
0.00/0.07	Dependency Pairs Processor:
0.00/0.07	-> Pairs:
0.00/0.07	 A(b(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.07	 A(c(b(x1:S))) -> A(a(b(c(b(a(x1:S))))))
0.00/0.07	 A(c(b(x1:S))) -> A(b(c(b(a(x1:S)))))
0.00/0.07	 A(c(b(x1:S))) -> A(x1:S)
0.00/0.07	-> Rules:
0.00/0.07	 a(b(a(a(x1:S)))) -> c(b(a(b(a(x1:S)))))
0.00/0.07	 a(c(b(x1:S))) -> a(a(b(c(b(a(x1:S))))))
0.00/0.07	
0.00/0.07	Problem 1: 
0.00/0.07	
0.00/0.07	SCC Processor:
0.00/0.07	-> Pairs:
0.00/0.07	 A(b(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.07	 A(c(b(x1:S))) -> A(a(b(c(b(a(x1:S))))))
0.00/0.07	 A(c(b(x1:S))) -> A(b(c(b(a(x1:S)))))
0.00/0.07	 A(c(b(x1:S))) -> A(x1:S)
0.00/0.07	-> Rules:
0.00/0.07	 a(b(a(a(x1:S)))) -> c(b(a(b(a(x1:S)))))
0.00/0.07	 a(c(b(x1:S))) -> a(a(b(c(b(a(x1:S))))))
0.00/0.07	->Strongly Connected Components:
0.00/0.07	->->Cycle:
0.00/0.07	->->-> Pairs:
0.00/0.07	 A(b(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.07	->->-> Rules:
0.00/0.07	 a(b(a(a(x1:S)))) -> c(b(a(b(a(x1:S)))))
0.00/0.07	 a(c(b(x1:S))) -> a(a(b(c(b(a(x1:S))))))
0.00/0.07	->->Cycle:
0.00/0.07	->->-> Pairs:
0.00/0.07	 A(c(b(x1:S))) -> A(x1:S)
0.00/0.07	->->-> Rules:
0.00/0.07	 a(b(a(a(x1:S)))) -> c(b(a(b(a(x1:S)))))
0.00/0.07	 a(c(b(x1:S))) -> a(a(b(c(b(a(x1:S))))))
0.00/0.07	
0.00/0.07	
0.00/0.07	The problem is decomposed in 2 subproblems.
0.00/0.07	
0.00/0.07	Problem 1.1: 
0.00/0.07	
0.00/0.07	Reduction Pair Processor:
0.00/0.07	-> Pairs:
0.00/0.07	 A(b(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.07	-> Rules:
0.00/0.07	 a(b(a(a(x1:S)))) -> c(b(a(b(a(x1:S)))))
0.00/0.07	 a(c(b(x1:S))) -> a(a(b(c(b(a(x1:S))))))
0.00/0.07	-> Usable rules:
0.00/0.07	 a(b(a(a(x1:S)))) -> c(b(a(b(a(x1:S)))))
0.00/0.07	 a(c(b(x1:S))) -> a(a(b(c(b(a(x1:S))))))
0.00/0.07	->Interpretation type:
0.00/0.07	 Linear
0.00/0.07	->Coefficients:
0.00/0.07	 All rationals
0.00/0.07	->Dimension:
0.00/0.07	 1
0.00/0.07	->Bound:
0.00/0.07	 2
0.00/0.07	->Interpretation:
0.00/0.07	 
0.00/0.07	[a](X) = X + 1/2
0.00/0.07	[b](X) = 1/2.X
0.00/0.07	[c](X) = 1
0.00/0.07	[A](X) = 1/2.X
0.00/0.07	
0.00/0.07	Problem 1.1: 
0.00/0.07	
0.00/0.07	SCC Processor:
0.00/0.07	-> Pairs:
0.00/0.07	 Empty
0.00/0.07	-> Rules:
0.00/0.07	 a(b(a(a(x1:S)))) -> c(b(a(b(a(x1:S)))))
0.00/0.07	 a(c(b(x1:S))) -> a(a(b(c(b(a(x1:S))))))
0.00/0.07	->Strongly Connected Components:
0.00/0.07	 There is no strongly connected component
0.00/0.07	
0.00/0.07	The problem is finite.
0.00/0.07	
0.00/0.07	Problem 1.2: 
0.00/0.07	
0.00/0.07	Subterm Processor:
0.00/0.07	-> Pairs:
0.00/0.07	 A(c(b(x1:S))) -> A(x1:S)
0.00/0.07	-> Rules:
0.00/0.07	 a(b(a(a(x1:S)))) -> c(b(a(b(a(x1:S)))))
0.00/0.07	 a(c(b(x1:S))) -> a(a(b(c(b(a(x1:S))))))
0.00/0.07	->Projection:
0.00/0.07	 pi(A) = 1
0.00/0.07	
0.00/0.07	Problem 1.2: 
0.00/0.07	
0.00/0.07	SCC Processor:
0.00/0.07	-> Pairs:
0.00/0.07	 Empty
0.00/0.07	-> Rules:
0.00/0.07	 a(b(a(a(x1:S)))) -> c(b(a(b(a(x1:S)))))
0.00/0.07	 a(c(b(x1:S))) -> a(a(b(c(b(a(x1:S))))))
0.00/0.08	->Strongly Connected Components:
0.00/0.08	 There is no strongly connected component
0.00/0.08	
0.00/0.08	The problem is finite.
0.06/0.08	EOF