0.00/0.04	YES
0.00/0.04	
0.00/0.04	Problem 1: 
0.00/0.04	
0.00/0.04	(VAR v_NonEmpty:S x1:S)
0.00/0.04	(RULES
0.00/0.04	a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	)
0.00/0.04	
0.00/0.04	Problem 1: 
0.00/0.04	
0.00/0.04	Innermost Equivalent Processor:
0.00/0.04	-> Rules:
0.00/0.04	 a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
0.00/0.04	 
0.00/0.04	
0.00/0.04	Problem 1: 
0.00/0.04	
0.00/0.04	Dependency Pairs Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 A(b(x1:S)) -> A(x1:S)
0.00/0.04	 C(b(x1:S)) -> C(c(x1:S))
0.00/0.04	 C(b(x1:S)) -> C(x1:S)
0.00/0.04	-> Rules:
0.00/0.04	 a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	
0.00/0.04	Problem 1: 
0.00/0.04	
0.00/0.04	SCC Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 A(b(x1:S)) -> A(x1:S)
0.00/0.04	 C(b(x1:S)) -> C(c(x1:S))
0.00/0.04	 C(b(x1:S)) -> C(x1:S)
0.00/0.04	-> Rules:
0.00/0.04	 a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	->Strongly Connected Components:
0.00/0.04	->->Cycle:
0.00/0.04	->->-> Pairs:
0.00/0.04	 C(b(x1:S)) -> C(c(x1:S))
0.00/0.04	 C(b(x1:S)) -> C(x1:S)
0.00/0.04	->->-> Rules:
0.00/0.04	 a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	->->Cycle:
0.00/0.04	->->-> Pairs:
0.00/0.04	 A(b(x1:S)) -> A(x1:S)
0.00/0.04	->->-> Rules:
0.00/0.04	 a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	
0.00/0.04	
0.00/0.04	The problem is decomposed in 2 subproblems.
0.00/0.04	
0.00/0.04	Problem 1.1: 
0.00/0.04	
0.00/0.04	Reduction Pairs Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 C(b(x1:S)) -> C(c(x1:S))
0.00/0.04	 C(b(x1:S)) -> C(x1:S)
0.00/0.04	-> Rules:
0.00/0.04	 a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	-> Usable rules:
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	->Interpretation type:
0.00/0.04	 Linear
0.00/0.04	->Coefficients:
0.00/0.04	 Natural Numbers
0.00/0.04	->Dimension:
0.00/0.04	 1
0.00/0.04	->Bound:
0.00/0.04	 2
0.00/0.04	->Interpretation:
0.00/0.04	 
0.00/0.04	[a](X) = 0
0.00/0.04	[c](X) = X
0.00/0.04	[b](X) = X + 2
0.00/0.04	[fSNonEmpty] = 0
0.00/0.04	[A](X) = 0
0.00/0.04	[C](X) = 2.X
0.00/0.04	
0.00/0.04	Problem 1.1: 
0.00/0.04	
0.00/0.04	SCC Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 C(b(x1:S)) -> C(x1:S)
0.00/0.04	-> Rules:
0.00/0.04	 a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	->Strongly Connected Components:
0.00/0.04	->->Cycle:
0.00/0.04	->->-> Pairs:
0.00/0.04	 C(b(x1:S)) -> C(x1:S)
0.00/0.04	->->-> Rules:
0.00/0.04	 a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	
0.00/0.04	Problem 1.1: 
0.00/0.04	
0.00/0.04	Subterm Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 C(b(x1:S)) -> C(x1:S)
0.00/0.04	-> Rules:
0.00/0.04	 a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	->Projection:
0.00/0.04	 pi(C) = 1
0.00/0.04	
0.00/0.04	Problem 1.1: 
0.00/0.04	
0.00/0.04	SCC Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 Empty
0.00/0.04	-> Rules:
0.00/0.04	 a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	->Strongly Connected Components:
0.00/0.04	 There is no strongly connected component
0.00/0.04	
0.00/0.04	The problem is finite.
0.00/0.04	
0.00/0.04	Problem 1.2: 
0.00/0.04	
0.00/0.04	Subterm Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 A(b(x1:S)) -> A(x1:S)
0.00/0.04	-> Rules:
0.00/0.04	 a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	->Projection:
0.00/0.04	 pi(A) = 1
0.00/0.04	
0.00/0.04	Problem 1.2: 
0.00/0.04	
0.00/0.04	SCC Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 Empty
0.00/0.04	-> Rules:
0.00/0.04	 a(b(x1:S)) -> b(b(a(x1:S)))
0.00/0.04	 c(b(x1:S)) -> b(c(c(x1:S)))
0.00/0.04	->Strongly Connected Components:
0.00/0.04	 There is no strongly connected component
0.00/0.04	
0.00/0.04	The problem is finite.
0.00/0.04	EOF