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 X:S X1:S X2:S X3:S)
0.00/0.04	(RULES
0.00/0.04	a__b -> a
0.00/0.04	a__b -> b
0.00/0.04	a__f(a,X:S,X:S) -> a__f(X:S,a__b,b)
0.00/0.04	a__f(X1:S,X2:S,X3:S) -> f(X1:S,X2:S,X3:S)
0.00/0.04	mark(a) -> a
0.00/0.04	mark(b) -> a__b
0.00/0.04	mark(f(X1:S,X2:S,X3:S)) -> a__f(X1:S,mark(X2:S),X3:S)
0.00/0.04	) 
0.00/0.04	(STRATEGY INNERMOST)
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__F(a,X:S,X:S) -> A__B
0.00/0.04	 A__F(a,X:S,X:S) -> A__F(X:S,a__b,b)
0.00/0.04	 MARK(b) -> A__B
0.00/0.04	 MARK(f(X1:S,X2:S,X3:S)) -> A__F(X1:S,mark(X2:S),X3:S)
0.00/0.04	 MARK(f(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.04	-> Rules:
0.00/0.04	 a__b -> a
0.00/0.04	 a__b -> b
0.00/0.04	 a__f(a,X:S,X:S) -> a__f(X:S,a__b,b)
0.00/0.04	 a__f(X1:S,X2:S,X3:S) -> f(X1:S,X2:S,X3:S)
0.00/0.04	 mark(a) -> a
0.00/0.04	 mark(b) -> a__b
0.00/0.04	 mark(f(X1:S,X2:S,X3:S)) -> a__f(X1:S,mark(X2:S),X3: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__F(a,X:S,X:S) -> A__B
0.00/0.04	 A__F(a,X:S,X:S) -> A__F(X:S,a__b,b)
0.00/0.04	 MARK(b) -> A__B
0.00/0.04	 MARK(f(X1:S,X2:S,X3:S)) -> A__F(X1:S,mark(X2:S),X3:S)
0.00/0.04	 MARK(f(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.04	-> Rules:
0.00/0.04	 a__b -> a
0.00/0.04	 a__b -> b
0.00/0.04	 a__f(a,X:S,X:S) -> a__f(X:S,a__b,b)
0.00/0.04	 a__f(X1:S,X2:S,X3:S) -> f(X1:S,X2:S,X3:S)
0.00/0.04	 mark(a) -> a
0.00/0.04	 mark(b) -> a__b
0.00/0.04	 mark(f(X1:S,X2:S,X3:S)) -> a__f(X1:S,mark(X2:S),X3:S)
0.00/0.04	->Strongly Connected Components:
0.00/0.04	->->Cycle:
0.00/0.04	->->-> Pairs:
0.00/0.04	 A__F(a,X:S,X:S) -> A__F(X:S,a__b,b)
0.00/0.04	->->-> Rules:
0.00/0.04	 a__b -> a
0.00/0.04	 a__b -> b
0.00/0.04	 a__f(a,X:S,X:S) -> a__f(X:S,a__b,b)
0.00/0.04	 a__f(X1:S,X2:S,X3:S) -> f(X1:S,X2:S,X3:S)
0.00/0.04	 mark(a) -> a
0.00/0.04	 mark(b) -> a__b
0.00/0.04	 mark(f(X1:S,X2:S,X3:S)) -> a__f(X1:S,mark(X2:S),X3:S)
0.00/0.04	->->Cycle:
0.00/0.04	->->-> Pairs:
0.00/0.04	 MARK(f(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.04	->->-> Rules:
0.00/0.04	 a__b -> a
0.00/0.04	 a__b -> b
0.00/0.04	 a__f(a,X:S,X:S) -> a__f(X:S,a__b,b)
0.00/0.04	 a__f(X1:S,X2:S,X3:S) -> f(X1:S,X2:S,X3:S)
0.00/0.04	 mark(a) -> a
0.00/0.04	 mark(b) -> a__b
0.00/0.04	 mark(f(X1:S,X2:S,X3:S)) -> a__f(X1:S,mark(X2:S),X3: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	 A__F(a,X:S,X:S) -> A__F(X:S,a__b,b)
0.00/0.04	-> Rules:
0.00/0.04	 a__b -> a
0.00/0.04	 a__b -> b
0.00/0.04	 a__f(a,X:S,X:S) -> a__f(X:S,a__b,b)
0.00/0.04	 a__f(X1:S,X2:S,X3:S) -> f(X1:S,X2:S,X3:S)
0.00/0.04	 mark(a) -> a
0.00/0.04	 mark(b) -> a__b
0.00/0.04	 mark(f(X1:S,X2:S,X3:S)) -> a__f(X1:S,mark(X2:S),X3:S)
0.00/0.04	-> Usable rules:
0.00/0.04	 a__b -> a
0.00/0.04	 a__b -> b
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__b] = 1
0.00/0.04	[a__f](X1,X2,X3) = 0
0.00/0.04	[mark](X) = 0
0.00/0.04	[a] = 1
0.00/0.04	[b] = 0
0.00/0.04	[f](X1,X2,X3) = 0
0.00/0.04	[fSNonEmpty] = 0
0.00/0.04	[A__B] = 0
0.00/0.04	[A__F](X1,X2,X3) = 2.X1 + X2 + 2.X3
0.00/0.04	[MARK](X) = 0
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 -> a
0.00/0.04	 a__b -> b
0.00/0.04	 a__f(a,X:S,X:S) -> a__f(X:S,a__b,b)
0.00/0.04	 a__f(X1:S,X2:S,X3:S) -> f(X1:S,X2:S,X3:S)
0.00/0.04	 mark(a) -> a
0.00/0.04	 mark(b) -> a__b
0.00/0.04	 mark(f(X1:S,X2:S,X3:S)) -> a__f(X1:S,mark(X2:S),X3: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	 MARK(f(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.04	-> Rules:
0.00/0.04	 a__b -> a
0.00/0.04	 a__b -> b
0.00/0.04	 a__f(a,X:S,X:S) -> a__f(X:S,a__b,b)
0.00/0.04	 a__f(X1:S,X2:S,X3:S) -> f(X1:S,X2:S,X3:S)
0.00/0.04	 mark(a) -> a
0.00/0.04	 mark(b) -> a__b
0.00/0.04	 mark(f(X1:S,X2:S,X3:S)) -> a__f(X1:S,mark(X2:S),X3:S)
0.00/0.04	->Projection:
0.00/0.04	 pi(MARK) = 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 -> a
0.00/0.04	 a__b -> b
0.00/0.04	 a__f(a,X:S,X:S) -> a__f(X:S,a__b,b)
0.00/0.04	 a__f(X1:S,X2:S,X3:S) -> f(X1:S,X2:S,X3:S)
0.00/0.04	 mark(a) -> a
0.00/0.04	 mark(b) -> a__b
0.00/0.04	 mark(f(X1:S,X2:S,X3:S)) -> a__f(X1:S,mark(X2:S),X3: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