0.00/0.46	YES
0.00/0.46	
0.00/0.46	Problem 1: 
0.00/0.46	
0.00/0.46	(VAR v_NonEmpty:S X:S X1:S X2:S X3:S Y:S)
0.00/0.46	(RULES
0.00/0.46	active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.46	active(div(0,s(Y:S))) -> mark(0)
0.00/0.46	active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.46	active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.46	active(geq(X:S,0)) -> mark(ttrue)
0.00/0.46	active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.46	active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.46	active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.46	active(minus(0,Y:S)) -> mark(0)
0.00/0.46	div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.46	div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.46	div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.46	div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.46	geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.46	geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.46	geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.46	geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.46	if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.46	if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.46	if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.46	if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.46	if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.46	if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.46	mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.46	mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.46	mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.46	mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.46	mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.46	mark(0) -> active(0)
0.00/0.46	mark(ffalse) -> active(ffalse)
0.00/0.46	mark(ttrue) -> active(ttrue)
0.00/0.46	minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.46	minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.46	minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.46	minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.46	s(active(X:S)) -> s(X:S)
0.00/0.46	s(mark(X:S)) -> s(X:S)
0.00/0.46	) 
0.00/0.46	(STRATEGY INNERMOST)
0.00/0.46	
0.00/0.46	Problem 1: 
0.00/0.46	
0.00/0.46	Dependency Pairs Processor:
0.00/0.46	-> Pairs:
0.00/0.46	 ACTIVE(div(s(X:S),s(Y:S))) -> DIV(minus(X:S,Y:S),s(Y:S))
0.00/0.46	 ACTIVE(div(s(X:S),s(Y:S))) -> GEQ(X:S,Y:S)
0.00/0.46	 ACTIVE(div(s(X:S),s(Y:S))) -> IF(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0)
0.00/0.46	 ACTIVE(div(s(X:S),s(Y:S))) -> MARK(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.46	 ACTIVE(div(s(X:S),s(Y:S))) -> MINUS(X:S,Y:S)
0.00/0.46	 ACTIVE(div(s(X:S),s(Y:S))) -> S(div(minus(X:S,Y:S),s(Y:S)))
0.00/0.46	 ACTIVE(div(0,s(Y:S))) -> MARK(0)
0.00/0.46	 ACTIVE(geq(s(X:S),s(Y:S))) -> GEQ(X:S,Y:S)
0.00/0.46	 ACTIVE(geq(s(X:S),s(Y:S))) -> MARK(geq(X:S,Y:S))
0.00/0.46	 ACTIVE(geq(0,s(Y:S))) -> MARK(ffalse)
0.00/0.46	 ACTIVE(geq(X:S,0)) -> MARK(ttrue)
0.00/0.46	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.00/0.46	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.46	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.46	 ACTIVE(minus(s(X:S),s(Y:S))) -> MINUS(X:S,Y:S)
0.00/0.46	 ACTIVE(minus(0,Y:S)) -> MARK(0)
0.00/0.46	 DIV(active(X1:S),X2:S) -> DIV(X1:S,X2:S)
0.00/0.46	 DIV(mark(X1:S),X2:S) -> DIV(X1:S,X2:S)
0.00/0.46	 DIV(X1:S,active(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.46	 DIV(X1:S,mark(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.46	 GEQ(active(X1:S),X2:S) -> GEQ(X1:S,X2:S)
0.00/0.46	 GEQ(mark(X1:S),X2:S) -> GEQ(X1:S,X2:S)
0.00/0.46	 GEQ(X1:S,active(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.46	 GEQ(X1:S,mark(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.46	 IF(active(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.46	 IF(mark(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.46	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.46	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.46	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.46	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.46	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.46	 MARK(div(X1:S,X2:S)) -> DIV(mark(X1:S),X2:S)
0.00/0.46	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.46	 MARK(geq(X1:S,X2:S)) -> ACTIVE(geq(X1:S,X2:S))
0.00/0.46	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.46	 MARK(if(X1:S,X2:S,X3:S)) -> IF(mark(X1:S),X2:S,X3:S)
0.00/0.46	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.46	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.46	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.46	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(s(X:S)) -> S(mark(X:S))
0.00/0.46	 MINUS(active(X1:S),X2:S) -> MINUS(X1:S,X2:S)
0.00/0.46	 MINUS(mark(X1:S),X2:S) -> MINUS(X1:S,X2:S)
0.00/0.46	 MINUS(X1:S,active(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.46	 MINUS(X1:S,mark(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.46	 S(active(X:S)) -> S(X:S)
0.00/0.46	 S(mark(X:S)) -> S(X:S)
0.00/0.46	-> Rules:
0.00/0.46	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.46	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.46	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.46	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.46	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.46	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.46	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.46	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.46	 active(minus(0,Y:S)) -> mark(0)
0.00/0.46	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.46	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.46	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.46	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.46	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.46	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.46	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.46	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.46	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.46	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.46	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.46	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.46	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.46	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.46	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.46	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.46	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.46	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.46	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.46	 mark(0) -> active(0)
0.00/0.46	 mark(ffalse) -> active(ffalse)
0.00/0.46	 mark(ttrue) -> active(ttrue)
0.00/0.46	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.46	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.46	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.46	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.46	 s(active(X:S)) -> s(X:S)
0.00/0.46	 s(mark(X:S)) -> s(X:S)
0.00/0.46	
0.00/0.46	Problem 1: 
0.00/0.46	
0.00/0.46	SCC Processor:
0.00/0.46	-> Pairs:
0.00/0.46	 ACTIVE(div(s(X:S),s(Y:S))) -> DIV(minus(X:S,Y:S),s(Y:S))
0.00/0.46	 ACTIVE(div(s(X:S),s(Y:S))) -> GEQ(X:S,Y:S)
0.00/0.46	 ACTIVE(div(s(X:S),s(Y:S))) -> IF(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0)
0.00/0.46	 ACTIVE(div(s(X:S),s(Y:S))) -> MARK(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.46	 ACTIVE(div(s(X:S),s(Y:S))) -> MINUS(X:S,Y:S)
0.00/0.46	 ACTIVE(div(s(X:S),s(Y:S))) -> S(div(minus(X:S,Y:S),s(Y:S)))
0.00/0.46	 ACTIVE(div(0,s(Y:S))) -> MARK(0)
0.00/0.46	 ACTIVE(geq(s(X:S),s(Y:S))) -> GEQ(X:S,Y:S)
0.00/0.46	 ACTIVE(geq(s(X:S),s(Y:S))) -> MARK(geq(X:S,Y:S))
0.00/0.46	 ACTIVE(geq(0,s(Y:S))) -> MARK(ffalse)
0.00/0.46	 ACTIVE(geq(X:S,0)) -> MARK(ttrue)
0.00/0.46	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.00/0.46	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.46	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.46	 ACTIVE(minus(s(X:S),s(Y:S))) -> MINUS(X:S,Y:S)
0.00/0.46	 ACTIVE(minus(0,Y:S)) -> MARK(0)
0.00/0.46	 DIV(active(X1:S),X2:S) -> DIV(X1:S,X2:S)
0.00/0.46	 DIV(mark(X1:S),X2:S) -> DIV(X1:S,X2:S)
0.00/0.46	 DIV(X1:S,active(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.46	 DIV(X1:S,mark(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.46	 GEQ(active(X1:S),X2:S) -> GEQ(X1:S,X2:S)
0.00/0.46	 GEQ(mark(X1:S),X2:S) -> GEQ(X1:S,X2:S)
0.00/0.46	 GEQ(X1:S,active(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.46	 GEQ(X1:S,mark(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.46	 IF(active(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.46	 IF(mark(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.46	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.46	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.46	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.46	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.46	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.46	 MARK(div(X1:S,X2:S)) -> DIV(mark(X1:S),X2:S)
0.00/0.46	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.46	 MARK(geq(X1:S,X2:S)) -> ACTIVE(geq(X1:S,X2:S))
0.00/0.46	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.46	 MARK(if(X1:S,X2:S,X3:S)) -> IF(mark(X1:S),X2:S,X3:S)
0.00/0.46	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.46	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.46	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.46	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.46	 MARK(s(X:S)) -> S(mark(X:S))
0.00/0.46	 MINUS(active(X1:S),X2:S) -> MINUS(X1:S,X2:S)
0.00/0.46	 MINUS(mark(X1:S),X2:S) -> MINUS(X1:S,X2:S)
0.00/0.46	 MINUS(X1:S,active(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.46	 MINUS(X1:S,mark(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.46	 S(active(X:S)) -> S(X:S)
0.00/0.46	 S(mark(X:S)) -> S(X:S)
0.00/0.46	-> Rules:
0.00/0.46	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.46	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.46	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.46	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.46	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.46	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.46	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.46	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.46	 active(minus(0,Y:S)) -> mark(0)
0.00/0.46	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.46	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.46	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.46	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.46	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.46	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.46	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.46	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.46	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.46	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.46	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.46	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.46	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.46	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.46	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.46	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.46	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.46	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.46	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.46	 mark(0) -> active(0)
0.00/0.46	 mark(ffalse) -> active(ffalse)
0.00/0.46	 mark(ttrue) -> active(ttrue)
0.00/0.46	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.46	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.46	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.46	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.46	 s(active(X:S)) -> s(X:S)
0.00/0.46	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 S(active(X:S)) -> S(X:S)
0.00/0.47	 S(mark(X:S)) -> S(X:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 MINUS(active(X1:S),X2:S) -> MINUS(X1:S,X2:S)
0.00/0.47	 MINUS(mark(X1:S),X2:S) -> MINUS(X1:S,X2:S)
0.00/0.47	 MINUS(X1:S,active(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.47	 MINUS(X1:S,mark(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 IF(active(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(mark(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 GEQ(active(X1:S),X2:S) -> GEQ(X1:S,X2:S)
0.00/0.47	 GEQ(mark(X1:S),X2:S) -> GEQ(X1:S,X2:S)
0.00/0.47	 GEQ(X1:S,active(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.47	 GEQ(X1:S,mark(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 DIV(active(X1:S),X2:S) -> DIV(X1:S,X2:S)
0.00/0.47	 DIV(mark(X1:S),X2:S) -> DIV(X1:S,X2:S)
0.00/0.47	 DIV(X1:S,active(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.47	 DIV(X1:S,mark(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 ACTIVE(div(s(X:S),s(Y:S))) -> MARK(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 ACTIVE(geq(s(X:S),s(Y:S))) -> MARK(geq(X:S,Y:S))
0.00/0.47	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.00/0.47	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.47	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.47	 MARK(geq(X1:S,X2:S)) -> ACTIVE(geq(X1:S,X2:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.47	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.47	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.47	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	
0.00/0.47	
0.00/0.47	The problem is decomposed in 6 subproblems.
0.00/0.47	
0.00/0.47	Problem 1.1: 
0.00/0.47	
0.00/0.47	Subterm Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 S(active(X:S)) -> S(X:S)
0.00/0.47	 S(mark(X:S)) -> S(X:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Projection:
0.00/0.47	 pi(S) = 1
0.00/0.47	
0.00/0.47	Problem 1.1: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 Empty
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	 There is no strongly connected component
0.00/0.47	
0.00/0.47	The problem is finite.
0.00/0.47	
0.00/0.47	Problem 1.2: 
0.00/0.47	
0.00/0.47	Subterm Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 MINUS(active(X1:S),X2:S) -> MINUS(X1:S,X2:S)
0.00/0.47	 MINUS(mark(X1:S),X2:S) -> MINUS(X1:S,X2:S)
0.00/0.47	 MINUS(X1:S,active(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.47	 MINUS(X1:S,mark(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Projection:
0.00/0.47	 pi(MINUS) = 1
0.00/0.47	
0.00/0.47	Problem 1.2: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 MINUS(X1:S,active(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.47	 MINUS(X1:S,mark(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 MINUS(X1:S,active(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.47	 MINUS(X1:S,mark(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	
0.00/0.47	Problem 1.2: 
0.00/0.47	
0.00/0.47	Subterm Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 MINUS(X1:S,active(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.47	 MINUS(X1:S,mark(X2:S)) -> MINUS(X1:S,X2:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Projection:
0.00/0.47	 pi(MINUS) = 2
0.00/0.47	
0.00/0.47	Problem 1.2: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 Empty
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	 There is no strongly connected component
0.00/0.47	
0.00/0.47	The problem is finite.
0.00/0.47	
0.00/0.47	Problem 1.3: 
0.00/0.47	
0.00/0.47	Subterm Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 IF(active(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(mark(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Projection:
0.00/0.47	 pi(IF) = 1
0.00/0.47	
0.00/0.47	Problem 1.3: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	
0.00/0.47	Problem 1.3: 
0.00/0.47	
0.00/0.47	Subterm Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Projection:
0.00/0.47	 pi(IF) = 2
0.00/0.47	
0.00/0.47	Problem 1.3: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	
0.00/0.47	Problem 1.3: 
0.00/0.47	
0.00/0.47	Subterm Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Projection:
0.00/0.47	 pi(IF) = 3
0.00/0.47	
0.00/0.47	Problem 1.3: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 Empty
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	 There is no strongly connected component
0.00/0.47	
0.00/0.47	The problem is finite.
0.00/0.47	
0.00/0.47	Problem 1.4: 
0.00/0.47	
0.00/0.47	Subterm Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 GEQ(active(X1:S),X2:S) -> GEQ(X1:S,X2:S)
0.00/0.47	 GEQ(mark(X1:S),X2:S) -> GEQ(X1:S,X2:S)
0.00/0.47	 GEQ(X1:S,active(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.47	 GEQ(X1:S,mark(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Projection:
0.00/0.47	 pi(GEQ) = 1
0.00/0.47	
0.00/0.47	Problem 1.4: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 GEQ(X1:S,active(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.47	 GEQ(X1:S,mark(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 GEQ(X1:S,active(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.47	 GEQ(X1:S,mark(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	
0.00/0.47	Problem 1.4: 
0.00/0.47	
0.00/0.47	Subterm Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 GEQ(X1:S,active(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.47	 GEQ(X1:S,mark(X2:S)) -> GEQ(X1:S,X2:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Projection:
0.00/0.47	 pi(GEQ) = 2
0.00/0.47	
0.00/0.47	Problem 1.4: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 Empty
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	 There is no strongly connected component
0.00/0.47	
0.00/0.47	The problem is finite.
0.00/0.47	
0.00/0.47	Problem 1.5: 
0.00/0.47	
0.00/0.47	Subterm Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 DIV(active(X1:S),X2:S) -> DIV(X1:S,X2:S)
0.00/0.47	 DIV(mark(X1:S),X2:S) -> DIV(X1:S,X2:S)
0.00/0.47	 DIV(X1:S,active(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.47	 DIV(X1:S,mark(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Projection:
0.00/0.47	 pi(DIV) = 1
0.00/0.47	
0.00/0.47	Problem 1.5: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 DIV(X1:S,active(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.47	 DIV(X1:S,mark(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 DIV(X1:S,active(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.47	 DIV(X1:S,mark(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	
0.00/0.47	Problem 1.5: 
0.00/0.47	
0.00/0.47	Subterm Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 DIV(X1:S,active(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.47	 DIV(X1:S,mark(X2:S)) -> DIV(X1:S,X2:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Projection:
0.00/0.47	 pi(DIV) = 2
0.00/0.47	
0.00/0.47	Problem 1.5: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 Empty
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	 There is no strongly connected component
0.00/0.47	
0.00/0.47	The problem is finite.
0.00/0.47	
0.00/0.47	Problem 1.6: 
0.00/0.47	
0.00/0.47	Reduction Pairs Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 ACTIVE(div(s(X:S),s(Y:S))) -> MARK(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 ACTIVE(geq(s(X:S),s(Y:S))) -> MARK(geq(X:S,Y:S))
0.00/0.47	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.00/0.47	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.47	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.47	 MARK(geq(X1:S,X2:S)) -> ACTIVE(geq(X1:S,X2:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.47	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.47	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.47	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	-> Usable rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Interpretation type:
0.00/0.47	 Linear
0.00/0.47	->Coefficients:
0.00/0.47	 Natural Numbers
0.00/0.47	->Dimension:
0.00/0.47	 1
0.00/0.47	->Bound:
0.00/0.47	 2
0.00/0.47	->Interpretation:
0.00/0.47	 
0.00/0.47	[active](X) = X
0.00/0.47	[div](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.47	[geq](X1,X2) = 0
0.00/0.47	[if](X1,X2,X3) = 2.X1 + X2 + X3
0.00/0.47	[mark](X) = X
0.00/0.47	[minus](X1,X2) = X1
0.00/0.47	[s](X) = X + 1
0.00/0.47	[0] = 0
0.00/0.47	[fSNonEmpty] = 0
0.00/0.47	[false] = 0
0.00/0.47	[true] = 0
0.00/0.47	[ACTIVE](X) = 2.X + 2
0.00/0.47	[DIV](X1,X2) = 0
0.00/0.47	[GEQ](X1,X2) = 0
0.00/0.47	[IF](X1,X2,X3) = 0
0.00/0.47	[MARK](X) = 2.X + 2
0.00/0.47	[MINUS](X1,X2) = 0
0.00/0.47	[S](X) = 0
0.00/0.47	
0.00/0.47	Problem 1.6: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 ACTIVE(geq(s(X:S),s(Y:S))) -> MARK(geq(X:S,Y:S))
0.00/0.47	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.00/0.47	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.47	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.47	 MARK(geq(X1:S,X2:S)) -> ACTIVE(geq(X1:S,X2:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.47	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.47	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.47	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 ACTIVE(geq(s(X:S),s(Y:S))) -> MARK(geq(X:S,Y:S))
0.00/0.47	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.00/0.47	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.47	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.47	 MARK(geq(X1:S,X2:S)) -> ACTIVE(geq(X1:S,X2:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.47	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.47	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.47	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	
0.00/0.47	Problem 1.6: 
0.00/0.47	
0.00/0.47	Reduction Pairs Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 ACTIVE(geq(s(X:S),s(Y:S))) -> MARK(geq(X:S,Y:S))
0.00/0.47	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.00/0.47	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.47	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.47	 MARK(geq(X1:S,X2:S)) -> ACTIVE(geq(X1:S,X2:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.47	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.47	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.47	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	-> Usable rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Interpretation type:
0.00/0.47	 Linear
0.00/0.47	->Coefficients:
0.00/0.47	 Natural Numbers
0.00/0.47	->Dimension:
0.00/0.47	 1
0.00/0.47	->Bound:
0.00/0.47	 2
0.00/0.47	->Interpretation:
0.00/0.47	 
0.00/0.47	[active](X) = X
0.00/0.47	[div](X1,X2) = 2.X1
0.00/0.47	[geq](X1,X2) = 2.X1 + 1
0.00/0.47	[if](X1,X2,X3) = X1 + X2 + X3 + 1
0.00/0.47	[mark](X) = X
0.00/0.47	[minus](X1,X2) = 0
0.00/0.47	[s](X) = 2.X + 2
0.00/0.47	[0] = 0
0.00/0.47	[fSNonEmpty] = 0
0.00/0.47	[false] = 1
0.00/0.47	[true] = 0
0.00/0.47	[ACTIVE](X) = 2.X + 2
0.00/0.47	[DIV](X1,X2) = 0
0.00/0.47	[GEQ](X1,X2) = 0
0.00/0.47	[IF](X1,X2,X3) = 0
0.00/0.47	[MARK](X) = 2.X + 2
0.00/0.47	[MINUS](X1,X2) = 0
0.00/0.47	[S](X) = 0
0.00/0.47	
0.00/0.47	Problem 1.6: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.00/0.47	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.47	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.47	 MARK(geq(X1:S,X2:S)) -> ACTIVE(geq(X1:S,X2:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.47	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.47	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.47	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.00/0.47	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.47	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.47	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.47	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.47	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	
0.00/0.47	Problem 1.6: 
0.00/0.47	
0.00/0.47	Reduction Pairs Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.00/0.47	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.47	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.47	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.47	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.47	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	-> Usable rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Interpretation type:
0.00/0.47	 Linear
0.00/0.47	->Coefficients:
0.00/0.47	 Natural Numbers
0.00/0.47	->Dimension:
0.00/0.47	 1
0.00/0.47	->Bound:
0.00/0.47	 2
0.00/0.47	->Interpretation:
0.00/0.47	 
0.00/0.47	[active](X) = X
0.00/0.47	[div](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.47	[geq](X1,X2) = 0
0.00/0.47	[if](X1,X2,X3) = 2.X1 + X2 + X3 + 1
0.00/0.47	[mark](X) = X
0.00/0.47	[minus](X1,X2) = X1
0.00/0.47	[s](X) = X + 2
0.00/0.47	[0] = 1
0.00/0.47	[fSNonEmpty] = 0
0.00/0.47	[false] = 0
0.00/0.47	[true] = 0
0.00/0.47	[ACTIVE](X) = 2.X
0.00/0.47	[DIV](X1,X2) = 0
0.00/0.47	[GEQ](X1,X2) = 0
0.00/0.47	[IF](X1,X2,X3) = 0
0.00/0.47	[MARK](X) = 2.X
0.00/0.47	[MINUS](X1,X2) = 0
0.00/0.47	[S](X) = 0
0.00/0.47	
0.00/0.47	Problem 1.6: 
0.00/0.47	
0.00/0.47	SCC Processor:
0.00/0.47	-> Pairs:
0.00/0.47	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.47	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.47	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.47	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.47	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.47	-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.47	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.47	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.47	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.47	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.47	 mark(0) -> active(0)
0.00/0.47	 mark(ffalse) -> active(ffalse)
0.00/0.47	 mark(ttrue) -> active(ttrue)
0.00/0.47	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.47	 s(active(X:S)) -> s(X:S)
0.00/0.47	 s(mark(X:S)) -> s(X:S)
0.00/0.47	->Strongly Connected Components:
0.00/0.47	->->Cycle:
0.00/0.47	->->-> Pairs:
0.00/0.47	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.47	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.47	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.47	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.47	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.47	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.47	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.47	->->-> Rules:
0.00/0.47	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.47	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.47	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.47	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.47	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.47	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.47	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.47	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.47	 active(minus(0,Y:S)) -> mark(0)
0.00/0.47	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.47	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.47	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.48	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.48	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(0) -> active(0)
0.00/0.48	 mark(ffalse) -> active(ffalse)
0.00/0.48	 mark(ttrue) -> active(ttrue)
0.00/0.48	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	
0.00/0.48	Problem 1.6: 
0.00/0.48	
0.00/0.48	Reduction Pairs Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.00/0.48	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.48	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.48	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.48	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.48	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.48	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.48	-> Rules:
0.00/0.48	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.48	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.48	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.48	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.48	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.48	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.48	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.48	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.48	 active(minus(0,Y:S)) -> mark(0)
0.00/0.48	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.48	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.48	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(0) -> active(0)
0.00/0.48	 mark(ffalse) -> active(ffalse)
0.00/0.48	 mark(ttrue) -> active(ttrue)
0.00/0.48	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	-> Usable rules:
0.00/0.48	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.48	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.48	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.48	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.48	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.48	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.48	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.48	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.48	 active(minus(0,Y:S)) -> mark(0)
0.00/0.48	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.48	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.48	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(0) -> active(0)
0.00/0.48	 mark(ffalse) -> active(ffalse)
0.00/0.48	 mark(ttrue) -> active(ttrue)
0.00/0.48	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	->Interpretation type:
0.00/0.48	 Linear
0.00/0.48	->Coefficients:
0.00/0.48	 Natural Numbers
0.00/0.48	->Dimension:
0.00/0.48	 1
0.00/0.48	->Bound:
0.00/0.48	 2
0.00/0.48	->Interpretation:
0.00/0.48	 
0.00/0.48	[active](X) = X
0.00/0.48	[div](X1,X2) = 2.X1 + 1
0.00/0.48	[geq](X1,X2) = 0
0.00/0.48	[if](X1,X2,X3) = 2.X1 + X2 + 2.X3 + 1
0.00/0.48	[mark](X) = X
0.00/0.48	[minus](X1,X2) = 0
0.00/0.48	[s](X) = 2.X + 2
0.00/0.48	[0] = 0
0.00/0.48	[fSNonEmpty] = 0
0.00/0.48	[false] = 0
0.00/0.48	[true] = 0
0.00/0.48	[ACTIVE](X) = 2.X
0.00/0.48	[DIV](X1,X2) = 0
0.00/0.48	[GEQ](X1,X2) = 0
0.00/0.48	[IF](X1,X2,X3) = 0
0.00/0.48	[MARK](X) = 2.X
0.00/0.48	[MINUS](X1,X2) = 0
0.00/0.48	[S](X) = 0
0.00/0.48	
0.00/0.48	Problem 1.6: 
0.00/0.48	
0.00/0.48	SCC Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.48	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.48	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.48	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.48	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.48	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.48	-> Rules:
0.00/0.48	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.48	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.48	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.48	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.48	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.48	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.48	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.48	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.48	 active(minus(0,Y:S)) -> mark(0)
0.00/0.48	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.48	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.48	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(0) -> active(0)
0.00/0.48	 mark(ffalse) -> active(ffalse)
0.00/0.48	 mark(ttrue) -> active(ttrue)
0.00/0.48	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	->Strongly Connected Components:
0.00/0.48	->->Cycle:
0.00/0.48	->->-> Pairs:
0.00/0.48	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.48	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.48	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.48	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.48	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.48	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.48	->->-> Rules:
0.00/0.48	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.48	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.48	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.48	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.48	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.48	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.48	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.48	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.48	 active(minus(0,Y:S)) -> mark(0)
0.00/0.48	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.48	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.48	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(0) -> active(0)
0.00/0.48	 mark(ffalse) -> active(ffalse)
0.00/0.48	 mark(ttrue) -> active(ttrue)
0.00/0.48	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	
0.00/0.48	Problem 1.6: 
0.00/0.48	
0.00/0.48	Reduction Pairs Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 ACTIVE(minus(s(X:S),s(Y:S))) -> MARK(minus(X:S,Y:S))
0.00/0.48	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.48	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.48	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.48	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.48	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.48	-> Rules:
0.00/0.48	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.48	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.48	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.48	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.48	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.48	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.48	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.48	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.48	 active(minus(0,Y:S)) -> mark(0)
0.00/0.48	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.48	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.48	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(0) -> active(0)
0.00/0.48	 mark(ffalse) -> active(ffalse)
0.00/0.48	 mark(ttrue) -> active(ttrue)
0.00/0.48	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	-> Usable rules:
0.00/0.48	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.48	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.48	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.48	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.48	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.48	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.48	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.48	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.48	 active(minus(0,Y:S)) -> mark(0)
0.00/0.48	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.48	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.48	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(0) -> active(0)
0.00/0.48	 mark(ffalse) -> active(ffalse)
0.00/0.48	 mark(ttrue) -> active(ttrue)
0.00/0.48	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	->Interpretation type:
0.00/0.48	 Linear
0.00/0.48	->Coefficients:
0.00/0.48	 Natural Numbers
0.00/0.48	->Dimension:
0.00/0.48	 1
0.00/0.48	->Bound:
0.00/0.48	 2
0.00/0.48	->Interpretation:
0.00/0.48	 
0.00/0.48	[active](X) = X
0.00/0.48	[div](X1,X2) = 2.X1
0.00/0.48	[geq](X1,X2) = 2
0.00/0.48	[if](X1,X2,X3) = X1 + X2 + 2.X3
0.00/0.48	[mark](X) = X
0.00/0.48	[minus](X1,X2) = X1
0.00/0.48	[s](X) = 2.X + 2
0.00/0.48	[0] = 0
0.00/0.48	[fSNonEmpty] = 0
0.00/0.48	[false] = 1
0.00/0.48	[true] = 2
0.00/0.48	[ACTIVE](X) = 2.X
0.00/0.48	[DIV](X1,X2) = 0
0.00/0.48	[GEQ](X1,X2) = 0
0.00/0.48	[IF](X1,X2,X3) = 0
0.00/0.48	[MARK](X) = 2.X + 2
0.00/0.48	[MINUS](X1,X2) = 0
0.00/0.48	[S](X) = 0
0.00/0.48	
0.00/0.48	Problem 1.6: 
0.00/0.48	
0.00/0.48	SCC Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 MARK(div(X1:S,X2:S)) -> ACTIVE(div(mark(X1:S),X2:S))
0.00/0.48	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.48	 MARK(minus(X1:S,X2:S)) -> ACTIVE(minus(X1:S,X2:S))
0.00/0.48	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.48	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.48	-> Rules:
0.00/0.48	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.48	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.48	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.48	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.48	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.48	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.48	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.48	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.48	 active(minus(0,Y:S)) -> mark(0)
0.00/0.48	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.48	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.48	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(0) -> active(0)
0.00/0.48	 mark(ffalse) -> active(ffalse)
0.00/0.48	 mark(ttrue) -> active(ttrue)
0.00/0.48	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	->Strongly Connected Components:
0.00/0.48	->->Cycle:
0.00/0.48	->->-> Pairs:
0.00/0.48	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.48	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.48	->->-> Rules:
0.00/0.48	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.48	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.48	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.48	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.48	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.48	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.48	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.48	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.48	 active(minus(0,Y:S)) -> mark(0)
0.00/0.48	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.48	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.48	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(0) -> active(0)
0.00/0.48	 mark(ffalse) -> active(ffalse)
0.00/0.48	 mark(ttrue) -> active(ttrue)
0.00/0.48	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	
0.00/0.48	Problem 1.6: 
0.00/0.48	
0.00/0.48	Subterm Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 MARK(div(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.48	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.48	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.48	-> Rules:
0.00/0.48	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.48	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.48	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.48	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.48	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.48	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.48	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.48	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.48	 active(minus(0,Y:S)) -> mark(0)
0.00/0.48	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.48	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.48	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(0) -> active(0)
0.00/0.48	 mark(ffalse) -> active(ffalse)
0.00/0.48	 mark(ttrue) -> active(ttrue)
0.00/0.48	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	->Projection:
0.00/0.48	 pi(MARK) = 1
0.00/0.48	
0.00/0.48	Problem 1.6: 
0.00/0.48	
0.00/0.48	SCC Processor:
0.00/0.48	-> Pairs:
0.00/0.48	 Empty
0.00/0.48	-> Rules:
0.00/0.48	 active(div(s(X:S),s(Y:S))) -> mark(if(geq(X:S,Y:S),s(div(minus(X:S,Y:S),s(Y:S))),0))
0.00/0.48	 active(div(0,s(Y:S))) -> mark(0)
0.00/0.48	 active(geq(s(X:S),s(Y:S))) -> mark(geq(X:S,Y:S))
0.00/0.48	 active(geq(0,s(Y:S))) -> mark(ffalse)
0.00/0.48	 active(geq(X:S,0)) -> mark(ttrue)
0.00/0.48	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.00/0.48	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.00/0.48	 active(minus(s(X:S),s(Y:S))) -> mark(minus(X:S,Y:S))
0.00/0.48	 active(minus(0,Y:S)) -> mark(0)
0.00/0.48	 div(active(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(mark(X1:S),X2:S) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,active(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 div(X1:S,mark(X2:S)) -> div(X1:S,X2:S)
0.00/0.48	 geq(active(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(mark(X1:S),X2:S) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,active(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 geq(X1:S,mark(X2:S)) -> geq(X1:S,X2:S)
0.00/0.48	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.00/0.48	 mark(div(X1:S,X2:S)) -> active(div(mark(X1:S),X2:S))
0.00/0.48	 mark(geq(X1:S,X2:S)) -> active(geq(X1:S,X2:S))
0.00/0.48	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.00/0.48	 mark(minus(X1:S,X2:S)) -> active(minus(X1:S,X2:S))
0.00/0.48	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.48	 mark(0) -> active(0)
0.00/0.48	 mark(ffalse) -> active(ffalse)
0.00/0.48	 mark(ttrue) -> active(ttrue)
0.00/0.48	 minus(active(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(mark(X1:S),X2:S) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,active(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 minus(X1:S,mark(X2:S)) -> minus(X1:S,X2:S)
0.00/0.48	 s(active(X:S)) -> s(X:S)
0.00/0.48	 s(mark(X:S)) -> s(X:S)
0.00/0.48	->Strongly Connected Components:
0.00/0.48	 There is no strongly connected component
0.00/0.48	
0.00/0.48	The problem is finite.
0.00/0.48	EOF