0.89/1.17	YES
0.89/1.17	
0.89/1.17	Problem 1: 
0.89/1.17	
0.89/1.17	(VAR v_NonEmpty:S x1:S)
0.89/1.17	(RULES
0.89/1.17	a(l(x1:S)) -> l(a(x1:S))
0.89/1.17	b(l(x1:S)) -> b(a(r(x1:S)))
0.89/1.17	r(a(a(x1:S))) -> a(a(r(x1:S)))
0.89/1.17	r(b(x1:S)) -> l(b(x1:S))
0.89/1.17	)
0.89/1.17	
0.89/1.17	Problem 1: 
0.89/1.17	
0.89/1.17	Dependency Pairs Processor:
0.89/1.17	-> Pairs:
0.89/1.17	 A(l(x1:S)) -> A(x1:S)
0.89/1.17	 B(l(x1:S)) -> A(r(x1:S))
0.89/1.17	 B(l(x1:S)) -> B(a(r(x1:S)))
0.89/1.17	 B(l(x1:S)) -> R(x1:S)
0.89/1.17	 R(a(a(x1:S))) -> A(a(r(x1:S)))
0.89/1.17	 R(a(a(x1:S))) -> A(r(x1:S))
0.89/1.17	 R(a(a(x1:S))) -> R(x1:S)
0.89/1.17	-> Rules:
0.89/1.17	 a(l(x1:S)) -> l(a(x1:S))
0.89/1.17	 b(l(x1:S)) -> b(a(r(x1:S)))
0.89/1.17	 r(a(a(x1:S))) -> a(a(r(x1:S)))
0.89/1.17	 r(b(x1:S)) -> l(b(x1:S))
0.89/1.17	
0.89/1.17	Problem 1: 
0.89/1.17	
0.89/1.17	SCC Processor:
0.89/1.17	-> Pairs:
0.89/1.17	 A(l(x1:S)) -> A(x1:S)
0.89/1.17	 B(l(x1:S)) -> A(r(x1:S))
0.89/1.17	 B(l(x1:S)) -> B(a(r(x1:S)))
0.89/1.17	 B(l(x1:S)) -> R(x1:S)
0.89/1.17	 R(a(a(x1:S))) -> A(a(r(x1:S)))
0.89/1.17	 R(a(a(x1:S))) -> A(r(x1:S))
0.89/1.17	 R(a(a(x1:S))) -> R(x1:S)
0.89/1.17	-> Rules:
0.89/1.17	 a(l(x1:S)) -> l(a(x1:S))
0.89/1.17	 b(l(x1:S)) -> b(a(r(x1:S)))
0.89/1.17	 r(a(a(x1:S))) -> a(a(r(x1:S)))
0.89/1.17	 r(b(x1:S)) -> l(b(x1:S))
0.89/1.17	->Strongly Connected Components:
0.89/1.17	->->Cycle:
0.89/1.17	->->-> Pairs:
0.89/1.17	 A(l(x1:S)) -> A(x1:S)
0.89/1.17	->->-> Rules:
0.89/1.17	 a(l(x1:S)) -> l(a(x1:S))
0.89/1.17	 b(l(x1:S)) -> b(a(r(x1:S)))
0.89/1.17	 r(a(a(x1:S))) -> a(a(r(x1:S)))
0.89/1.17	 r(b(x1:S)) -> l(b(x1:S))
0.89/1.17	->->Cycle:
0.89/1.17	->->-> Pairs:
0.89/1.17	 R(a(a(x1:S))) -> R(x1:S)
0.89/1.17	->->-> Rules:
0.89/1.17	 a(l(x1:S)) -> l(a(x1:S))
0.89/1.17	 b(l(x1:S)) -> b(a(r(x1:S)))
0.89/1.17	 r(a(a(x1:S))) -> a(a(r(x1:S)))
0.89/1.17	 r(b(x1:S)) -> l(b(x1:S))
0.89/1.17	->->Cycle:
0.89/1.17	->->-> Pairs:
0.89/1.17	 B(l(x1:S)) -> B(a(r(x1:S)))
0.89/1.17	->->-> Rules:
0.89/1.17	 a(l(x1:S)) -> l(a(x1:S))
0.89/1.17	 b(l(x1:S)) -> b(a(r(x1:S)))
0.89/1.17	 r(a(a(x1:S))) -> a(a(r(x1:S)))
0.89/1.17	 r(b(x1:S)) -> l(b(x1:S))
0.89/1.17	
0.89/1.17	
0.89/1.17	The problem is decomposed in 3 subproblems.
0.89/1.17	
0.89/1.17	Problem 1.1: 
0.89/1.17	
0.89/1.17	Subterm Processor:
0.89/1.17	-> Pairs:
0.89/1.17	 A(l(x1:S)) -> A(x1:S)
0.89/1.17	-> Rules:
0.89/1.17	 a(l(x1:S)) -> l(a(x1:S))
0.89/1.17	 b(l(x1:S)) -> b(a(r(x1:S)))
0.89/1.17	 r(a(a(x1:S))) -> a(a(r(x1:S)))
0.89/1.17	 r(b(x1:S)) -> l(b(x1:S))
0.89/1.17	->Projection:
0.89/1.17	 pi(A) = 1
0.89/1.17	
0.89/1.17	Problem 1.1: 
0.89/1.17	
0.89/1.17	SCC Processor:
0.89/1.17	-> Pairs:
0.89/1.17	 Empty
0.89/1.17	-> Rules:
0.89/1.17	 a(l(x1:S)) -> l(a(x1:S))
0.89/1.17	 b(l(x1:S)) -> b(a(r(x1:S)))
0.89/1.17	 r(a(a(x1:S))) -> a(a(r(x1:S)))
0.89/1.17	 r(b(x1:S)) -> l(b(x1:S))
0.89/1.17	->Strongly Connected Components:
0.89/1.17	 There is no strongly connected component
0.89/1.17	
0.89/1.17	The problem is finite.
0.89/1.17	
0.89/1.17	Problem 1.2: 
0.89/1.17	
0.89/1.17	Subterm Processor:
0.89/1.17	-> Pairs:
0.89/1.17	 R(a(a(x1:S))) -> R(x1:S)
0.89/1.17	-> Rules:
0.89/1.17	 a(l(x1:S)) -> l(a(x1:S))
0.89/1.17	 b(l(x1:S)) -> b(a(r(x1:S)))
0.89/1.17	 r(a(a(x1:S))) -> a(a(r(x1:S)))
0.89/1.17	 r(b(x1:S)) -> l(b(x1:S))
0.89/1.17	->Projection:
0.89/1.17	 pi(R) = 1
0.89/1.17	
0.89/1.17	Problem 1.2: 
0.89/1.17	
0.89/1.17	SCC Processor:
0.89/1.17	-> Pairs:
0.89/1.17	 Empty
0.89/1.17	-> Rules:
0.89/1.17	 a(l(x1:S)) -> l(a(x1:S))
0.89/1.17	 b(l(x1:S)) -> b(a(r(x1:S)))
0.89/1.17	 r(a(a(x1:S))) -> a(a(r(x1:S)))
0.89/1.17	 r(b(x1:S)) -> l(b(x1:S))
0.89/1.17	->Strongly Connected Components:
0.89/1.17	 There is no strongly connected component
0.89/1.17	
0.89/1.17	The problem is finite.
0.89/1.17	
0.89/1.17	Problem 1.3: 
0.89/1.17	
0.89/1.17	Reduction Pair Processor:
0.89/1.17	-> Pairs:
0.89/1.17	 B(l(x1:S)) -> B(a(r(x1:S)))
0.89/1.17	-> Rules:
0.89/1.17	 a(l(x1:S)) -> l(a(x1:S))
0.89/1.17	 b(l(x1:S)) -> b(a(r(x1:S)))
0.89/1.17	 r(a(a(x1:S))) -> a(a(r(x1:S)))
0.89/1.17	 r(b(x1:S)) -> l(b(x1:S))
0.89/1.17	-> Usable rules:
0.89/1.17	 a(l(x1:S)) -> l(a(x1:S))
0.89/1.17	 b(l(x1:S)) -> b(a(r(x1:S)))
0.89/1.17	 r(a(a(x1:S))) -> a(a(r(x1:S)))
0.89/1.17	 r(b(x1:S)) -> l(b(x1:S))
0.89/1.17	->Interpretation type:
0.89/1.17	 Linear
0.89/1.17	->Coefficients:
0.89/1.17	 Natural Numbers
0.89/1.17	->Dimension:
0.89/1.17	 2
0.89/1.17	->Bound:
0.89/1.17	 1
0.89/1.17	->Interpretation:
0.89/1.17	 
0.89/1.17	[a](X) = [0 1;1 0].X
0.89/1.17	[b](X) = [0 1;0 1].X + [1;0]
0.89/1.17	[r](X) = [1 0;1 0].X + [0;1]
0.89/1.17	[l](X) = [0 1;1 0].X + [1;1]
0.89/1.17	[B](X) = [0 1;0 0].X
0.89/1.17	
0.89/1.17	Problem 1.3: 
0.89/1.17	
0.89/1.17	SCC Processor:
0.89/1.17	-> Pairs:
0.99/1.17	 Empty
0.99/1.17	-> Rules:
0.99/1.17	 a(l(x1:S)) -> l(a(x1:S))
0.99/1.17	 b(l(x1:S)) -> b(a(r(x1:S)))
0.99/1.17	 r(a(a(x1:S))) -> a(a(r(x1:S)))
0.99/1.17	 r(b(x1:S)) -> l(b(x1:S))
0.99/1.17	->Strongly Connected Components:
0.99/1.17	 There is no strongly connected component
0.99/1.17	
0.99/1.17	The problem is finite.
0.99/1.17	EOF