0.00/0.17	YES
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	(VAR v_NonEmpty:S M:S N:S X:S X1:S X2:S)
0.00/0.17	(RULES
0.00/0.17	a__and(tt,X:S) -> mark(X:S)
0.00/0.17	a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	a__plus(N:S,0) -> mark(N:S)
0.00/0.17	a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	mark(0) -> 0
0.00/0.17	mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	mark(tt) -> tt
0.00/0.17	) 
0.00/0.17	(STRATEGY INNERMOST)
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	Dependency Pairs Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 A__AND(tt,X:S) -> MARK(X:S)
0.00/0.17	 A__PLUS(N:S,0) -> MARK(N:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> A__PLUS(mark(N:S),mark(M:S))
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	SCC Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 A__AND(tt,X:S) -> MARK(X:S)
0.00/0.17	 A__PLUS(N:S,0) -> MARK(N:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> A__PLUS(mark(N:S),mark(M:S))
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Strongly Connected Components:
0.00/0.17	->->Cycle:
0.00/0.17	->->-> Pairs:
0.00/0.17	 A__AND(tt,X:S) -> MARK(X:S)
0.00/0.17	 A__PLUS(N:S,0) -> MARK(N:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> A__PLUS(mark(N:S),mark(M:S))
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	->->-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	Reduction Pairs Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 A__AND(tt,X:S) -> MARK(X:S)
0.00/0.17	 A__PLUS(N:S,0) -> MARK(N:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> A__PLUS(mark(N:S),mark(M:S))
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	-> Usable rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Interpretation type:
0.00/0.17	 Linear
0.00/0.17	->Coefficients:
0.00/0.17	 Natural Numbers
0.00/0.17	->Dimension:
0.00/0.17	 1
0.00/0.17	->Bound:
0.00/0.17	 2
0.00/0.17	->Interpretation:
0.00/0.17	 
0.00/0.17	[a__and](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[a__plus](X1,X2) = X1 + 2.X2 + 1
0.00/0.17	[mark](X) = X
0.00/0.17	[0] = 1
0.00/0.17	[and](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[fSNonEmpty] = 0
0.00/0.17	[plus](X1,X2) = X1 + 2.X2 + 1
0.00/0.17	[s](X) = X + 2
0.00/0.17	[tt] = 2
0.00/0.17	[A__AND](X1,X2) = 2.X1 + 2.X2
0.00/0.17	[A__PLUS](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[MARK](X) = 2.X + 2
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	SCC Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 A__PLUS(N:S,0) -> MARK(N:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> A__PLUS(mark(N:S),mark(M:S))
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Strongly Connected Components:
0.00/0.17	->->Cycle:
0.00/0.17	->->-> Pairs:
0.00/0.17	 A__PLUS(N:S,0) -> MARK(N:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> A__PLUS(mark(N:S),mark(M:S))
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	->->-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	Reduction Pairs Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 A__PLUS(N:S,0) -> MARK(N:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> A__PLUS(mark(N:S),mark(M:S))
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	-> Usable rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Interpretation type:
0.00/0.17	 Linear
0.00/0.17	->Coefficients:
0.00/0.17	 Natural Numbers
0.00/0.17	->Dimension:
0.00/0.17	 1
0.00/0.17	->Bound:
0.00/0.17	 2
0.00/0.17	->Interpretation:
0.00/0.17	 
0.00/0.17	[a__and](X1,X2) = 2.X1 + 2.X2
0.00/0.17	[a__plus](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[mark](X) = X
0.00/0.17	[0] = 1
0.00/0.17	[and](X1,X2) = 2.X1 + 2.X2
0.00/0.17	[fSNonEmpty] = 0
0.00/0.17	[plus](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[s](X) = X
0.00/0.17	[tt] = 2
0.00/0.17	[A__AND](X1,X2) = 0
0.00/0.17	[A__PLUS](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[MARK](X) = 2.X
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	SCC Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> A__PLUS(mark(N:S),mark(M:S))
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Strongly Connected Components:
0.00/0.17	->->Cycle:
0.00/0.17	->->-> Pairs:
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> A__PLUS(mark(N:S),mark(M:S))
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	->->-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	Reduction Pairs Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> A__PLUS(mark(N:S),mark(M:S))
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	-> Usable rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Interpretation type:
0.00/0.17	 Linear
0.00/0.17	->Coefficients:
0.00/0.17	 Natural Numbers
0.00/0.17	->Dimension:
0.00/0.17	 1
0.00/0.17	->Bound:
0.00/0.17	 2
0.00/0.17	->Interpretation:
0.00/0.17	 
0.00/0.17	[a__and](X1,X2) = X1 + X2
0.00/0.17	[a__plus](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[mark](X) = X
0.00/0.17	[0] = 2
0.00/0.17	[and](X1,X2) = X1 + X2
0.00/0.17	[fSNonEmpty] = 0
0.00/0.17	[plus](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[s](X) = X + 2
0.00/0.17	[tt] = 2
0.00/0.17	[A__AND](X1,X2) = 0
0.00/0.17	[A__PLUS](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[MARK](X) = 2.X + 2
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	SCC Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Strongly Connected Components:
0.00/0.17	->->Cycle:
0.00/0.17	->->-> Pairs:
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	->->-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	Reduction Pairs Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(M:S)
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	-> Usable rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Interpretation type:
0.00/0.17	 Linear
0.00/0.17	->Coefficients:
0.00/0.17	 Natural Numbers
0.00/0.17	->Dimension:
0.00/0.17	 1
0.00/0.17	->Bound:
0.00/0.17	 2
0.00/0.17	->Interpretation:
0.00/0.17	 
0.00/0.17	[a__and](X1,X2) = 2.X1 + X2 + 2
0.00/0.17	[a__plus](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[mark](X) = X
0.00/0.17	[0] = 2
0.00/0.17	[and](X1,X2) = 2.X1 + X2 + 2
0.00/0.17	[fSNonEmpty] = 0
0.00/0.17	[plus](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[s](X) = X + 2
0.00/0.17	[tt] = 1
0.00/0.17	[A__AND](X1,X2) = 0
0.00/0.17	[A__PLUS](X1,X2) = 2.X1 + 2.X2
0.00/0.17	[MARK](X) = 2.X
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	SCC Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Strongly Connected Components:
0.00/0.17	->->Cycle:
0.00/0.17	->->-> Pairs:
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	->->-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	Reduction Pairs Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 A__PLUS(N:S,s(M:S)) -> MARK(N:S)
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	-> Usable rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Interpretation type:
0.00/0.17	 Linear
0.00/0.17	->Coefficients:
0.00/0.17	 Natural Numbers
0.00/0.17	->Dimension:
0.00/0.17	 1
0.00/0.17	->Bound:
0.00/0.17	 2
0.00/0.17	->Interpretation:
0.00/0.17	 
0.00/0.17	[a__and](X1,X2) = 2.X1 + 2.X2
0.00/0.17	[a__plus](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[mark](X) = X
0.00/0.17	[0] = 2
0.00/0.17	[and](X1,X2) = 2.X1 + 2.X2
0.00/0.17	[fSNonEmpty] = 0
0.00/0.17	[plus](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.17	[s](X) = X
0.00/0.17	[tt] = 0
0.00/0.17	[A__AND](X1,X2) = 0
0.00/0.17	[A__PLUS](X1,X2) = 2.X1 + 2
0.00/0.17	[MARK](X) = 2.X + 1
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	SCC Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S))
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Strongly Connected Components:
0.00/0.17	->->Cycle:
0.00/0.17	->->-> Pairs:
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	->->-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	Subterm Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.17	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.17	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Projection:
0.00/0.17	 pi(MARK) = 1
0.00/0.17	
0.00/0.17	Problem 1: 
0.00/0.17	
0.00/0.17	SCC Processor:
0.00/0.17	-> Pairs:
0.00/0.17	 Empty
0.00/0.17	-> Rules:
0.00/0.17	 a__and(tt,X:S) -> mark(X:S)
0.00/0.17	 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
0.00/0.17	 a__plus(N:S,0) -> mark(N:S)
0.00/0.17	 a__plus(N:S,s(M:S)) -> s(a__plus(mark(N:S),mark(M:S)))
0.00/0.17	 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S)
0.00/0.17	 mark(0) -> 0
0.00/0.17	 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
0.00/0.17	 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S))
0.00/0.17	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.17	 mark(tt) -> tt
0.00/0.17	->Strongly Connected Components:
0.00/0.17	 There is no strongly connected component
0.00/0.17	
0.00/0.17	The problem is finite.
0.00/0.17	EOF