0.00/0.10	YES
0.00/0.10	
0.00/0.10	Problem 1: 
0.00/0.10	
0.00/0.10	(VAR v_NonEmpty:S x1:S)
0.00/0.10	(RULES
0.00/0.10	L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	)
0.00/0.10	
0.00/0.10	Problem 1: 
0.00/0.10	
0.00/0.10	Dependency Pairs Processor:
0.00/0.10	-> Pairs:
0.00/0.10	 L#(a(a(x1:S))) -> L#(a(b(c(x1:S))))
0.00/0.10	 L#(a(a(x1:S))) -> B(c(x1:S))
0.00/0.10	 L#(a(a(x1:S))) -> C(x1:S)
0.00/0.10	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.10	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.10	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.10	 C(a(x1:S)) -> C(x1:S)
0.00/0.10	-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	
0.00/0.10	Problem 1: 
0.00/0.10	
0.00/0.10	SCC Processor:
0.00/0.10	-> Pairs:
0.00/0.10	 L#(a(a(x1:S))) -> L#(a(b(c(x1:S))))
0.00/0.10	 L#(a(a(x1:S))) -> B(c(x1:S))
0.00/0.10	 L#(a(a(x1:S))) -> C(x1:S)
0.00/0.10	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.10	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.10	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.10	 C(a(x1:S)) -> C(x1:S)
0.00/0.10	-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	->Strongly Connected Components:
0.00/0.10	->->Cycle:
0.00/0.10	->->-> Pairs:
0.00/0.10	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.10	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.10	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.10	 C(a(x1:S)) -> C(x1:S)
0.00/0.10	->->-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	->->Cycle:
0.00/0.10	->->-> Pairs:
0.00/0.10	 L#(a(a(x1:S))) -> L#(a(b(c(x1:S))))
0.00/0.10	->->-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	
0.00/0.10	
0.00/0.10	The problem is decomposed in 2 subproblems.
0.00/0.10	
0.00/0.10	Problem 1.1: 
0.00/0.10	
0.00/0.10	Reduction Pair Processor:
0.00/0.10	-> Pairs:
0.00/0.10	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.10	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.10	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.10	 C(a(x1:S)) -> C(x1:S)
0.00/0.10	-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	-> Usable rules:
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	->Interpretation type:
0.00/0.10	 Linear
0.00/0.10	->Coefficients:
0.00/0.10	 Natural Numbers
0.00/0.10	->Dimension:
0.00/0.10	 1
0.00/0.10	->Bound:
0.00/0.10	 2
0.00/0.10	->Interpretation:
0.00/0.10	 
0.00/0.10	[b](X) = X
0.00/0.10	[c](X) = 2.X + 2
0.00/0.10	[R](X) = 2.X + 2
0.00/0.10	[a](X) = 2.X + 2
0.00/0.10	[B](X) = X
0.00/0.10	[C](X) = 2.X + 2
0.00/0.10	
0.00/0.10	Problem 1.1: 
0.00/0.10	
0.00/0.10	SCC Processor:
0.00/0.10	-> Pairs:
0.00/0.10	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.10	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.10	 C(a(x1:S)) -> C(x1:S)
0.00/0.10	-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	->Strongly Connected Components:
0.00/0.10	->->Cycle:
0.00/0.10	->->-> Pairs:
0.00/0.10	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.10	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.10	 C(a(x1:S)) -> C(x1:S)
0.00/0.10	->->-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	
0.00/0.10	Problem 1.1: 
0.00/0.10	
0.00/0.10	Reduction Pair Processor:
0.00/0.10	-> Pairs:
0.00/0.10	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.10	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.10	 C(a(x1:S)) -> C(x1:S)
0.00/0.10	-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	-> Usable rules:
0.00/0.10	 Empty
0.00/0.10	->Interpretation type:
0.00/0.10	 Linear
0.00/0.10	->Coefficients:
0.00/0.10	 Natural Numbers
0.00/0.10	->Dimension:
0.00/0.10	 1
0.00/0.10	->Bound:
0.00/0.10	 2
0.00/0.10	->Interpretation:
0.00/0.10	 
0.00/0.10	[b](X) = X + 2
0.00/0.10	[a](X) = 2.X + 2
0.00/0.10	[B](X) = X + 2
0.00/0.10	[C](X) = 2.X + 2
0.00/0.10	
0.00/0.10	Problem 1.1: 
0.00/0.10	
0.00/0.10	SCC Processor:
0.00/0.10	-> Pairs:
0.00/0.10	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.10	 C(a(x1:S)) -> C(x1:S)
0.00/0.10	-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	->Strongly Connected Components:
0.00/0.10	->->Cycle:
0.00/0.10	->->-> Pairs:
0.00/0.10	 C(a(x1:S)) -> C(x1:S)
0.00/0.10	->->-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	
0.00/0.10	Problem 1.1: 
0.00/0.10	
0.00/0.10	Subterm Processor:
0.00/0.10	-> Pairs:
0.00/0.10	 C(a(x1:S)) -> C(x1:S)
0.00/0.10	-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	->Projection:
0.00/0.10	 pi(C) = 1
0.00/0.10	
0.00/0.10	Problem 1.1: 
0.00/0.10	
0.00/0.10	SCC Processor:
0.00/0.10	-> Pairs:
0.00/0.10	 Empty
0.00/0.10	-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	->Strongly Connected Components:
0.00/0.10	 There is no strongly connected component
0.00/0.10	
0.00/0.10	The problem is finite.
0.00/0.10	
0.00/0.10	Problem 1.2: 
0.00/0.10	
0.00/0.10	Reduction Pair Processor:
0.00/0.10	-> Pairs:
0.00/0.10	 L#(a(a(x1:S))) -> L#(a(b(c(x1:S))))
0.00/0.10	-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	-> Usable rules:
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	->Interpretation type:
0.00/0.10	 Linear
0.00/0.10	->Coefficients:
0.00/0.10	 All rationals
0.00/0.10	->Dimension:
0.00/0.10	 1
0.00/0.10	->Bound:
0.00/0.10	 2
0.00/0.10	->Interpretation:
0.00/0.10	 
0.00/0.10	[b](X) = 1/2.X
0.00/0.10	[c](X) = 2.X + 1
0.00/0.10	[R](X) = 1/2
0.00/0.10	[a](X) = 2.X + 2
0.00/0.10	[L#](X) = 2.X
0.00/0.10	
0.00/0.10	Problem 1.2: 
0.00/0.10	
0.00/0.10	SCC Processor:
0.00/0.10	-> Pairs:
0.00/0.10	 Empty
0.00/0.10	-> Rules:
0.00/0.10	 L(a(a(x1:S))) -> L(a(b(c(x1:S))))
0.00/0.10	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.10	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.10	 c(R(x1:S)) -> b(a(R(x1:S)))
0.00/0.10	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.10	->Strongly Connected Components:
0.00/0.10	 There is no strongly connected component
0.00/0.10	
0.00/0.10	The problem is finite.
0.00/0.10	EOF