5.57/2.80	WORST_CASE(Omega(n^2), O(n^2))
5.57/2.81	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
5.57/2.81	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.57/2.81	
5.57/2.81	
5.57/2.81	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
5.57/2.81	
5.57/2.81	(0) CpxIntTrs
5.57/2.81	(1) Koat Proof [FINISHED, 221 ms]
5.57/2.81	(2) BOUNDS(1, n^2)
5.57/2.81	(3) Loat Proof [FINISHED, 936 ms]
5.57/2.81	(4) BOUNDS(n^2, INF)
5.57/2.81	
5.57/2.81	
5.57/2.81	----------------------------------------
5.57/2.81	
5.57/2.81	(0)
5.57/2.81	Obligation:
5.57/2.81	Complexity Int TRS consisting of the following rules:
5.57/2.81	evalrealbubblestart(A, B, C, D) -> Com_1(evalrealbubbleentryin(A, B, C, D)) :|: TRUE
5.57/2.81	evalrealbubbleentryin(A, B, C, D) -> Com_1(evalrealbubblebb7in(A - 1, B, C, D)) :|: TRUE
5.57/2.81	evalrealbubblebb7in(A, B, C, D) -> Com_1(evalrealbubblebb4in(A, 0, 0, D)) :|: A >= 1
5.57/2.81	evalrealbubblebb7in(A, B, C, D) -> Com_1(evalrealbubblereturnin(A, B, C, D)) :|: 0 >= A
5.57/2.81	evalrealbubblebb4in(A, B, C, D) -> Com_1(evalrealbubblebb1in(A, B, C, D)) :|: A >= B + 1
5.57/2.81	evalrealbubblebb4in(A, B, C, D) -> Com_1(evalrealbubblebb5in(A, B, C, D)) :|: B >= A
5.57/2.81	evalrealbubblebb1in(A, B, C, D) -> Com_1(evalrealbubblebb2in(A, B, C, D)) :|: E >= F + 1
5.57/2.81	evalrealbubblebb1in(A, B, C, D) -> Com_1(evalrealbubblebb3in(A, B, C, C)) :|: F >= E
5.57/2.81	evalrealbubblebb2in(A, B, C, D) -> Com_1(evalrealbubblebb3in(A, B, C, 1)) :|: TRUE
5.57/2.81	evalrealbubblebb3in(A, B, C, D) -> Com_1(evalrealbubblebb4in(A, B + 1, D, D)) :|: TRUE
5.57/2.81	evalrealbubblebb5in(A, B, C, D) -> Com_1(evalrealbubblereturnin(A, B, C, D)) :|: C >= 0 && C <= 0
5.57/2.81	evalrealbubblebb5in(A, B, C, D) -> Com_1(evalrealbubblebb6in(A, B, C, D)) :|: 0 >= C + 1
5.57/2.81	evalrealbubblebb5in(A, B, C, D) -> Com_1(evalrealbubblebb6in(A, B, C, D)) :|: C >= 1
5.57/2.81	evalrealbubblebb6in(A, B, C, D) -> Com_1(evalrealbubblebb7in(A - 1, B, C, D)) :|: TRUE
5.57/2.81	evalrealbubblereturnin(A, B, C, D) -> Com_1(evalrealbubblestop(A, B, C, D)) :|: TRUE
5.57/2.81	
5.57/2.81	The start-symbols are:[evalrealbubblestart_4]
5.57/2.81	
5.57/2.81	
5.57/2.81	----------------------------------------
5.57/2.81	
5.57/2.81	(1) Koat Proof (FINISHED)
5.57/2.81	YES(?, 115*ar_0 + 24*ar_0^2 + 8)
5.57/2.81	
5.57/2.81	
5.57/2.81	
5.57/2.81	Initial complexity problem:
5.57/2.81	
5.57/2.81	1:	T:
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.57/2.81	
5.57/2.81		start location:	koat_start
5.57/2.81	
5.57/2.81		leaf cost:	0
5.57/2.81	
5.57/2.81	
5.57/2.81	
5.57/2.81	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.57/2.81	
5.57/2.81	2:	T:
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 1)    evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 1)    evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.57/2.81	
5.57/2.81		start location:	koat_start
5.57/2.81	
5.57/2.81		leaf cost:	0
5.57/2.81	
5.57/2.81	
5.57/2.81	
5.57/2.81	A polynomial rank function with
5.57/2.81	
5.57/2.81		Pol(evalrealbubblestart) = 2
5.57/2.81	
5.57/2.81		Pol(evalrealbubbleentryin) = 2
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb7in) = 2
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb4in) = 2
5.57/2.81	
5.57/2.81		Pol(evalrealbubblereturnin) = 1
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb1in) = 2
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb5in) = 2
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb2in) = 2
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb3in) = 2
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb6in) = 2
5.57/2.81	
5.57/2.81		Pol(evalrealbubblestop) = 0
5.57/2.81	
5.57/2.81		Pol(koat_start) = 2
5.57/2.81	
5.57/2.81	orients all transitions weakly and the transitions
5.57/2.81	
5.57/2.81		evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81		evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.57/2.81	
5.57/2.81		evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
5.57/2.81	
5.57/2.81	strictly and produces the following problem:
5.57/2.81	
5.57/2.81	3:	T:
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 1)    evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 1)    evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]
5.57/2.81	
5.57/2.81			(Comp: 2, Cost: 1)    evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 2, Cost: 1)    evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)    evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 2, Cost: 1)    evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.57/2.81	
5.57/2.81		start location:	koat_start
5.57/2.81	
5.57/2.81		leaf cost:	0
5.57/2.81	
5.57/2.81	
5.57/2.81	
5.57/2.81	A polynomial rank function with
5.57/2.81	
5.57/2.81		Pol(evalrealbubblestart) = V_1
5.57/2.81	
5.57/2.81		Pol(evalrealbubbleentryin) = V_1
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb7in) = V_1 + 1
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb4in) = V_1
5.57/2.81	
5.57/2.81		Pol(evalrealbubblereturnin) = V_1
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb1in) = V_1
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb5in) = V_1
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb2in) = V_1
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb3in) = V_1
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb6in) = V_1
5.57/2.81	
5.57/2.81		Pol(evalrealbubblestop) = V_1
5.57/2.81	
5.57/2.81		Pol(koat_start) = V_1
5.57/2.81	
5.57/2.81	orients all transitions weakly and the transition
5.57/2.81	
5.57/2.81		evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]
5.57/2.81	
5.57/2.81	strictly and produces the following problem:
5.57/2.81	
5.57/2.81	4:	T:
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 1)       evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 1)       evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: ar_0, Cost: 1)    evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]
5.57/2.81	
5.57/2.81			(Comp: 2, Cost: 1)       evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)       evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)       evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)       evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)       evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)       evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)       evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 2, Cost: 1)       evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)       evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)       evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)       evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 2, Cost: 1)       evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.57/2.81	
5.57/2.81		start location:	koat_start
5.57/2.81	
5.57/2.81		leaf cost:	0
5.57/2.81	
5.57/2.81	
5.57/2.81	
5.57/2.81	A polynomial rank function with
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb6in) = 1
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb7in) = 0
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb5in) = 2
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb4in) = 3
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb1in) = 3
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb3in) = 3
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb2in) = 3
5.57/2.81	
5.57/2.81	and size complexities
5.57/2.81	
5.57/2.81		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.57/2.81	
5.57/2.81		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.57/2.81	
5.57/2.81		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.57/2.81	
5.57/2.81		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.57/2.81	
5.57/2.81		S("evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 + 1
5.57/2.81	
5.57/2.81		S("evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 + 2
5.57/2.81	
5.57/2.81		S("evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-1) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-2) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-3) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-1) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-2) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-3) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]", 0-1) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]", 0-2) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]", 0-3) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]", 0-1) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]", 0-2) = 0
5.57/2.81	
5.57/2.81		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]", 0-3) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))", 0-1) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))", 0-2) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))", 0-3) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))", 0-1) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))", 0-2) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))", 0-3) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]", 0-1) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]", 0-2) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]", 0-3) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]", 0-1) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]", 0-2) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]", 0-3) = ar_3 + 2
5.57/2.81	
5.57/2.81		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ar_3 + 2
5.57/2.81	
5.57/2.81		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2 + 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3 + 1
5.57/2.81	
5.57/2.81		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]", 0-0) = ?
5.57/2.81	
5.57/2.81		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]", 0-1) = 0
5.57/2.81	
5.57/2.81		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]", 0-2) = 0
5.57/2.81	
5.57/2.81		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]", 0-3) = ar_3 + 1
5.57/2.81	
5.57/2.81		S("evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-0) = ar_0 + 1
5.57/2.81	
5.57/2.81		S("evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.57/2.81	
5.57/2.81		S("evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.57/2.81	
5.57/2.81		S("evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.57/2.81	
5.57/2.81		S("evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.57/2.81	
5.57/2.81		S("evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.57/2.81	
5.57/2.81		S("evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.57/2.81	
5.57/2.81		S("evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.57/2.81	
5.57/2.81	orients the transitions
5.57/2.81	
5.57/2.81		evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81		evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.57/2.81	
5.57/2.81		evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
5.57/2.81	
5.57/2.81		evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
5.57/2.81	
5.57/2.81		evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.57/2.81	
5.57/2.81		evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))
5.57/2.81	
5.57/2.81		evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))
5.57/2.81	
5.57/2.81		evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]
5.57/2.81	
5.57/2.81		evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]
5.57/2.81	
5.57/2.81	weakly and the transitions
5.57/2.81	
5.57/2.81		evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81		evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.57/2.81	
5.57/2.81		evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
5.57/2.81	
5.57/2.81		evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
5.57/2.81	
5.57/2.81	strictly and produces the following problem:
5.57/2.81	
5.57/2.81	5:	T:
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 1)         evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 1)         evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: ar_0, Cost: 1)      evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]
5.57/2.81	
5.57/2.81			(Comp: 2, Cost: 1)         evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)         evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.57/2.81	
5.57/2.81			(Comp: 3*ar_0, Cost: 1)    evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)         evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)         evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)         evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))
5.57/2.81	
5.57/2.81			(Comp: ?, Cost: 1)         evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 2, Cost: 1)         evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
5.57/2.81	
5.57/2.81			(Comp: 3*ar_0, Cost: 1)    evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
5.57/2.81	
5.57/2.81			(Comp: 3*ar_0, Cost: 1)    evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.57/2.81	
5.57/2.81			(Comp: 3*ar_0, Cost: 1)    evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 2, Cost: 1)         evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))
5.57/2.81	
5.57/2.81			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.57/2.81	
5.57/2.81		start location:	koat_start
5.57/2.81	
5.57/2.81		leaf cost:	0
5.57/2.81	
5.57/2.81	
5.57/2.81	
5.57/2.81	A polynomial rank function with
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb4in) = V_1 - V_2 + 1
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb1in) = V_1 - V_2
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb3in) = V_1 - V_2
5.57/2.81	
5.57/2.81		Pol(evalrealbubblebb2in) = V_1 - V_2
5.57/2.81	
5.57/2.81	and size complexities
5.57/2.81	
5.57/2.81		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.57/2.82	
5.57/2.82		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.57/2.82	
5.57/2.82		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.57/2.82	
5.57/2.82		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.57/2.82	
5.57/2.82		S("evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 4*ar_0 + 256
5.57/2.82	
5.57/2.82		S("evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
5.57/2.82	
5.57/2.82		S("evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 + 1
5.57/2.82	
5.57/2.82		S("evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 + 2
5.57/2.82	
5.57/2.82		S("evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-0) = 4*ar_0 + 16
5.57/2.82	
5.57/2.82		S("evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-1) = ?
5.57/2.82	
5.57/2.82		S("evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-2) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-3) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-0) = 4*ar_0 + 16
5.57/2.82	
5.57/2.82		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-1) = ?
5.57/2.82	
5.57/2.82		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-2) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-3) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]", 0-0) = 4*ar_0 + 16
5.57/2.82	
5.57/2.82		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]", 0-1) = ?
5.57/2.82	
5.57/2.82		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]", 0-2) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]", 0-3) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]", 0-0) = 4*ar_0 + 64
5.57/2.82	
5.57/2.82		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]", 0-1) = ?
5.57/2.82	
5.57/2.82		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]", 0-2) = 0
5.57/2.82	
5.57/2.82		S("evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]", 0-3) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))", 0-0) = 4*ar_0 + 16
5.57/2.82	
5.57/2.82		S("evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))", 0-1) = ?
5.57/2.82	
5.57/2.82		S("evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))", 0-2) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))", 0-3) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))", 0-0) = 4*ar_0 + 16
5.57/2.82	
5.57/2.82		S("evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))", 0-1) = ?
5.57/2.82	
5.57/2.82		S("evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))", 0-2) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))", 0-3) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]", 0-0) = 4*ar_0 + 16
5.57/2.82	
5.57/2.82		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]", 0-1) = ?
5.57/2.82	
5.57/2.82		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]", 0-2) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]", 0-3) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]", 0-0) = 4*ar_0 + 16
5.57/2.82	
5.57/2.82		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]", 0-1) = ?
5.57/2.82	
5.57/2.82		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]", 0-2) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]", 0-3) = ar_3 + 2
5.57/2.82	
5.57/2.82		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = 4*ar_0 + 16
5.57/2.82	
5.57/2.82		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ?
5.57/2.82	
5.57/2.82		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = 4*ar_0 + 16
5.57/2.82	
5.57/2.82		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ?
5.57/2.82	
5.57/2.82		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ar_3 + 2
5.57/2.82	
5.57/2.82		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = 4*ar_0 + 64
5.57/2.82	
5.57/2.82		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ?
5.57/2.82	
5.57/2.82		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2 + 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3 + 1
5.57/2.82	
5.57/2.82		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]", 0-0) = 4*ar_0 + 16
5.57/2.82	
5.57/2.82		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]", 0-1) = 0
5.57/2.82	
5.57/2.82		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]", 0-2) = 0
5.57/2.82	
5.57/2.82		S("evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]", 0-3) = ar_3 + 1
5.57/2.82	
5.57/2.82		S("evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-0) = ar_0 + 1
5.57/2.82	
5.57/2.82		S("evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.57/2.82	
5.57/2.82		S("evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.57/2.82	
5.57/2.82		S("evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.57/2.82	
5.57/2.82		S("evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.57/2.82	
5.57/2.82		S("evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.57/2.82	
5.57/2.82		S("evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.57/2.82	
5.57/2.82		S("evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.57/2.82	
5.57/2.82	orients the transitions
5.57/2.82	
5.57/2.82		evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.57/2.82	
5.57/2.82		evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))
5.57/2.82	
5.57/2.82		evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))
5.57/2.82	
5.57/2.82		evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]
5.57/2.82	
5.57/2.82		evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]
5.57/2.82	
5.57/2.82	weakly and the transition
5.57/2.82	
5.57/2.82		evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.57/2.82	
5.57/2.82	strictly and produces the following problem:
5.57/2.82	
5.57/2.82	6:	T:
5.57/2.82	
5.57/2.82			(Comp: 1, Cost: 1)                     evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))
5.57/2.82	
5.57/2.82			(Comp: 1, Cost: 1)                     evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.82	
5.57/2.82			(Comp: ar_0, Cost: 1)                  evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]
5.57/2.82	
5.57/2.82			(Comp: 2, Cost: 1)                     evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.57/2.82	
5.57/2.82			(Comp: 4*ar_0^2 + 17*ar_0, Cost: 1)    evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.57/2.82	
5.57/2.82			(Comp: 3*ar_0, Cost: 1)                evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
5.57/2.82	
5.57/2.82			(Comp: ?, Cost: 1)                     evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]
5.57/2.82	
5.57/2.82			(Comp: ?, Cost: 1)                     evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]
5.57/2.82	
5.57/2.82			(Comp: ?, Cost: 1)                     evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))
5.57/2.82	
5.57/2.82			(Comp: ?, Cost: 1)                     evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))
5.57/2.82	
5.57/2.82			(Comp: 2, Cost: 1)                     evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
5.57/2.82	
5.57/2.82			(Comp: 3*ar_0, Cost: 1)                evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
5.57/2.82	
5.57/2.82			(Comp: 3*ar_0, Cost: 1)                evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.57/2.82	
5.57/2.82			(Comp: 3*ar_0, Cost: 1)                evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.82	
5.57/2.82			(Comp: 2, Cost: 1)                     evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))
5.57/2.82	
5.57/2.82			(Comp: 1, Cost: 0)                     koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.57/2.82	
5.57/2.82		start location:	koat_start
5.57/2.82	
5.57/2.82		leaf cost:	0
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Repeatedly propagating knowledge in problem 6 produces the following problem:
5.57/2.82	
5.57/2.82	7:	T:
5.57/2.82	
5.57/2.82			(Comp: 1, Cost: 1)                     evalrealbubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3))
5.57/2.82	
5.57/2.82			(Comp: 1, Cost: 1)                     evalrealbubbleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.82	
5.57/2.82			(Comp: ar_0, Cost: 1)                  evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, 0, 0, ar_3)) [ ar_0 >= 1 ]
5.57/2.82	
5.57/2.82			(Comp: 2, Cost: 1)                     evalrealbubblebb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.57/2.82	
5.57/2.82			(Comp: 4*ar_0^2 + 17*ar_0, Cost: 1)    evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.57/2.82	
5.57/2.82			(Comp: 3*ar_0, Cost: 1)                evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]
5.57/2.82	
5.57/2.82			(Comp: 4*ar_0^2 + 17*ar_0, Cost: 1)    evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ]
5.57/2.82	
5.57/2.82			(Comp: 4*ar_0^2 + 17*ar_0, Cost: 1)    evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_2)) [ e >= f ]
5.57/2.82	
5.57/2.82			(Comp: 4*ar_0^2 + 17*ar_0, Cost: 1)    evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, 1))
5.57/2.82	
5.57/2.82			(Comp: 8*ar_0^2 + 34*ar_0, Cost: 1)    evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb4in(ar_0, ar_1 + 1, ar_3, ar_3))
5.57/2.82	
5.57/2.82			(Comp: 2, Cost: 1)                     evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 = 0 ]
5.57/2.82	
5.57/2.82			(Comp: 3*ar_0, Cost: 1)                evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ]
5.57/2.82	
5.57/2.82			(Comp: 3*ar_0, Cost: 1)                evalrealbubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
5.57/2.82	
5.57/2.82			(Comp: 3*ar_0, Cost: 1)                evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblebb7in(ar_0 - 1, ar_1, ar_2, ar_3))
5.57/2.82	
5.57/2.82			(Comp: 2, Cost: 1)                     evalrealbubblereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestop(ar_0, ar_1, ar_2, ar_3))
5.57/2.82	
5.57/2.82			(Comp: 1, Cost: 0)                     koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealbubblestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.57/2.82	
5.57/2.82		start location:	koat_start
5.57/2.82	
5.57/2.82		leaf cost:	0
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Complexity upper bound 115*ar_0 + 24*ar_0^2 + 8
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Time: 0.196 sec (SMT: 0.152 sec)
5.57/2.82	
5.57/2.82	
5.57/2.82	----------------------------------------
5.57/2.82	
5.57/2.82	(2)
5.57/2.82	BOUNDS(1, n^2)
5.57/2.82	
5.57/2.82	----------------------------------------
5.57/2.82	
5.57/2.82	(3) Loat Proof (FINISHED)
5.57/2.82	
5.57/2.82	
5.57/2.82	### Pre-processing the ITS problem ###
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Initial linear ITS problem
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	      0: evalrealbubblestart -> evalrealbubbleentryin : [], cost: 1
5.57/2.82	
5.57/2.82	      1: evalrealbubbleentryin -> evalrealbubblebb7in : A'=-1+A, [], cost: 1
5.57/2.82	
5.57/2.82	      2: evalrealbubblebb7in -> evalrealbubblebb4in : B'=0, C'=0, [ A>=1 ], cost: 1
5.57/2.82	
5.57/2.82	      3: evalrealbubblebb7in -> evalrealbubblereturnin : [ 0>=A ], cost: 1
5.57/2.82	
5.57/2.82	      4: evalrealbubblebb4in -> evalrealbubblebb1in : [ A>=1+B ], cost: 1
5.57/2.82	
5.57/2.82	      5: evalrealbubblebb4in -> evalrealbubblebb5in : [ B>=A ], cost: 1
5.57/2.82	
5.57/2.82	      6: evalrealbubblebb1in -> evalrealbubblebb2in : [ free_1>=1+free ], cost: 1
5.57/2.82	
5.57/2.82	      7: evalrealbubblebb1in -> evalrealbubblebb3in : D'=C, [ free_3>=free_2 ], cost: 1
5.57/2.82	
5.57/2.82	      8: evalrealbubblebb2in -> evalrealbubblebb3in : D'=1, [], cost: 1
5.57/2.82	
5.57/2.82	      9: evalrealbubblebb3in -> evalrealbubblebb4in : B'=1+B, C'=D, [], cost: 1
5.57/2.82	
5.57/2.82	     10: evalrealbubblebb5in -> evalrealbubblereturnin : [ C==0 ], cost: 1
5.57/2.82	
5.57/2.82	     11: evalrealbubblebb5in -> evalrealbubblebb6in : [ 0>=1+C ], cost: 1
5.57/2.82	
5.57/2.82	     12: evalrealbubblebb5in -> evalrealbubblebb6in : [ C>=1 ], cost: 1
5.57/2.82	
5.57/2.82	     13: evalrealbubblebb6in -> evalrealbubblebb7in : A'=-1+A, [], cost: 1
5.57/2.82	
5.57/2.82	     14: evalrealbubblereturnin -> evalrealbubblestop : [], cost: 1
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Removed unreachable and leaf rules:
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	      0: evalrealbubblestart -> evalrealbubbleentryin : [], cost: 1
5.57/2.82	
5.57/2.82	      1: evalrealbubbleentryin -> evalrealbubblebb7in : A'=-1+A, [], cost: 1
5.57/2.82	
5.57/2.82	      2: evalrealbubblebb7in -> evalrealbubblebb4in : B'=0, C'=0, [ A>=1 ], cost: 1
5.57/2.82	
5.57/2.82	      4: evalrealbubblebb4in -> evalrealbubblebb1in : [ A>=1+B ], cost: 1
5.57/2.82	
5.57/2.82	      5: evalrealbubblebb4in -> evalrealbubblebb5in : [ B>=A ], cost: 1
5.57/2.82	
5.57/2.82	      6: evalrealbubblebb1in -> evalrealbubblebb2in : [ free_1>=1+free ], cost: 1
5.57/2.82	
5.57/2.82	      7: evalrealbubblebb1in -> evalrealbubblebb3in : D'=C, [ free_3>=free_2 ], cost: 1
5.57/2.82	
5.57/2.82	      8: evalrealbubblebb2in -> evalrealbubblebb3in : D'=1, [], cost: 1
5.57/2.82	
5.57/2.82	      9: evalrealbubblebb3in -> evalrealbubblebb4in : B'=1+B, C'=D, [], cost: 1
5.57/2.82	
5.57/2.82	     11: evalrealbubblebb5in -> evalrealbubblebb6in : [ 0>=1+C ], cost: 1
5.57/2.82	
5.57/2.82	     12: evalrealbubblebb5in -> evalrealbubblebb6in : [ C>=1 ], cost: 1
5.57/2.82	
5.57/2.82	     13: evalrealbubblebb6in -> evalrealbubblebb7in : A'=-1+A, [], cost: 1
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Simplified all rules, resulting in:
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	      0: evalrealbubblestart -> evalrealbubbleentryin : [], cost: 1
5.57/2.82	
5.57/2.82	      1: evalrealbubbleentryin -> evalrealbubblebb7in : A'=-1+A, [], cost: 1
5.57/2.82	
5.57/2.82	      2: evalrealbubblebb7in -> evalrealbubblebb4in : B'=0, C'=0, [ A>=1 ], cost: 1
5.57/2.82	
5.57/2.82	      4: evalrealbubblebb4in -> evalrealbubblebb1in : [ A>=1+B ], cost: 1
5.57/2.82	
5.57/2.82	      5: evalrealbubblebb4in -> evalrealbubblebb5in : [ B>=A ], cost: 1
5.57/2.82	
5.57/2.82	      6: evalrealbubblebb1in -> evalrealbubblebb2in : [], cost: 1
5.57/2.82	
5.57/2.82	      7: evalrealbubblebb1in -> evalrealbubblebb3in : D'=C, [], cost: 1
5.57/2.82	
5.57/2.82	      8: evalrealbubblebb2in -> evalrealbubblebb3in : D'=1, [], cost: 1
5.57/2.82	
5.57/2.82	      9: evalrealbubblebb3in -> evalrealbubblebb4in : B'=1+B, C'=D, [], cost: 1
5.57/2.82	
5.57/2.82	     11: evalrealbubblebb5in -> evalrealbubblebb6in : [ 0>=1+C ], cost: 1
5.57/2.82	
5.57/2.82	     12: evalrealbubblebb5in -> evalrealbubblebb6in : [ C>=1 ], cost: 1
5.57/2.82	
5.57/2.82	     13: evalrealbubblebb6in -> evalrealbubblebb7in : A'=-1+A, [], cost: 1
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	### Simplification by acceleration and chaining ###
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Eliminated locations (on linear paths):
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	     15: evalrealbubblestart -> evalrealbubblebb7in : A'=-1+A, [], cost: 2
5.57/2.82	
5.57/2.82	      2: evalrealbubblebb7in -> evalrealbubblebb4in : B'=0, C'=0, [ A>=1 ], cost: 1
5.57/2.82	
5.57/2.82	      4: evalrealbubblebb4in -> evalrealbubblebb1in : [ A>=1+B ], cost: 1
5.57/2.82	
5.57/2.82	      5: evalrealbubblebb4in -> evalrealbubblebb5in : [ B>=A ], cost: 1
5.57/2.82	
5.57/2.82	      7: evalrealbubblebb1in -> evalrealbubblebb3in : D'=C, [], cost: 1
5.57/2.82	
5.57/2.82	     16: evalrealbubblebb1in -> evalrealbubblebb3in : D'=1, [], cost: 2
5.57/2.82	
5.57/2.82	      9: evalrealbubblebb3in -> evalrealbubblebb4in : B'=1+B, C'=D, [], cost: 1
5.57/2.82	
5.57/2.82	     11: evalrealbubblebb5in -> evalrealbubblebb6in : [ 0>=1+C ], cost: 1
5.57/2.82	
5.57/2.82	     12: evalrealbubblebb5in -> evalrealbubblebb6in : [ C>=1 ], cost: 1
5.57/2.82	
5.57/2.82	     13: evalrealbubblebb6in -> evalrealbubblebb7in : A'=-1+A, [], cost: 1
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Eliminated locations (on tree-shaped paths):
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	     15: evalrealbubblestart -> evalrealbubblebb7in : A'=-1+A, [], cost: 2
5.57/2.82	
5.57/2.82	      2: evalrealbubblebb7in -> evalrealbubblebb4in : B'=0, C'=0, [ A>=1 ], cost: 1
5.57/2.82	
5.57/2.82	     17: evalrealbubblebb4in -> evalrealbubblebb3in : D'=C, [ A>=1+B ], cost: 2
5.57/2.82	
5.57/2.82	     18: evalrealbubblebb4in -> evalrealbubblebb3in : D'=1, [ A>=1+B ], cost: 3
5.57/2.82	
5.57/2.82	     19: evalrealbubblebb4in -> evalrealbubblebb6in : [ B>=A && 0>=1+C ], cost: 2
5.57/2.82	
5.57/2.82	     20: evalrealbubblebb4in -> evalrealbubblebb6in : [ B>=A && C>=1 ], cost: 2
5.57/2.82	
5.57/2.82	      9: evalrealbubblebb3in -> evalrealbubblebb4in : B'=1+B, C'=D, [], cost: 1
5.57/2.82	
5.57/2.82	     13: evalrealbubblebb6in -> evalrealbubblebb7in : A'=-1+A, [], cost: 1
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Eliminated locations (on tree-shaped paths):
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	     15: evalrealbubblestart -> evalrealbubblebb7in : A'=-1+A, [], cost: 2
5.57/2.82	
5.57/2.82	      2: evalrealbubblebb7in -> evalrealbubblebb4in : B'=0, C'=0, [ A>=1 ], cost: 1
5.57/2.82	
5.57/2.82	     21: evalrealbubblebb4in -> evalrealbubblebb4in : B'=1+B, C'=C, D'=C, [ A>=1+B ], cost: 3
5.57/2.82	
5.57/2.82	     22: evalrealbubblebb4in -> evalrealbubblebb4in : B'=1+B, C'=1, D'=1, [ A>=1+B ], cost: 4
5.57/2.82	
5.57/2.82	     23: evalrealbubblebb4in -> evalrealbubblebb7in : A'=-1+A, [ B>=A && 0>=1+C ], cost: 3
5.57/2.82	
5.57/2.82	     24: evalrealbubblebb4in -> evalrealbubblebb7in : A'=-1+A, [ B>=A && C>=1 ], cost: 3
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Accelerating simple loops of location 3.
5.57/2.82	
5.57/2.82	   Simplified some of the simple loops (and removed duplicate rules).
5.57/2.82	
5.57/2.82	   Accelerating the following rules:
5.57/2.82	
5.57/2.82	     21: evalrealbubblebb4in -> evalrealbubblebb4in : B'=1+B, D'=C, [ A>=1+B ], cost: 3
5.57/2.82	
5.57/2.82	     22: evalrealbubblebb4in -> evalrealbubblebb4in : B'=1+B, C'=1, D'=1, [ A>=1+B ], cost: 4
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	   Accelerated rule 21 with metering function A-B, yielding the new rule 25.
5.57/2.82	
5.57/2.82	   Accelerated rule 22 with metering function A-B, yielding the new rule 26.
5.57/2.82	
5.57/2.82	   Removing the simple loops: 21 22.
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Accelerated all simple loops using metering functions (where possible):
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	     15: evalrealbubblestart -> evalrealbubblebb7in : A'=-1+A, [], cost: 2
5.57/2.82	
5.57/2.82	      2: evalrealbubblebb7in -> evalrealbubblebb4in : B'=0, C'=0, [ A>=1 ], cost: 1
5.57/2.82	
5.57/2.82	     23: evalrealbubblebb4in -> evalrealbubblebb7in : A'=-1+A, [ B>=A && 0>=1+C ], cost: 3
5.57/2.82	
5.57/2.82	     24: evalrealbubblebb4in -> evalrealbubblebb7in : A'=-1+A, [ B>=A && C>=1 ], cost: 3
5.57/2.82	
5.57/2.82	     25: evalrealbubblebb4in -> evalrealbubblebb4in : B'=A, D'=C, [ A>=1+B ], cost: 3*A-3*B
5.57/2.82	
5.57/2.82	     26: evalrealbubblebb4in -> evalrealbubblebb4in : B'=A, C'=1, D'=1, [ A>=1+B ], cost: 4*A-4*B
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Chained accelerated rules (with incoming rules):
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	     15: evalrealbubblestart -> evalrealbubblebb7in : A'=-1+A, [], cost: 2
5.57/2.82	
5.57/2.82	      2: evalrealbubblebb7in -> evalrealbubblebb4in : B'=0, C'=0, [ A>=1 ], cost: 1
5.57/2.82	
5.57/2.82	     27: evalrealbubblebb7in -> evalrealbubblebb4in : B'=A, C'=0, D'=0, [ A>=1 ], cost: 1+3*A
5.57/2.82	
5.57/2.82	     28: evalrealbubblebb7in -> evalrealbubblebb4in : B'=A, C'=1, D'=1, [ A>=1 ], cost: 1+4*A
5.57/2.82	
5.57/2.82	     23: evalrealbubblebb4in -> evalrealbubblebb7in : A'=-1+A, [ B>=A && 0>=1+C ], cost: 3
5.57/2.82	
5.57/2.82	     24: evalrealbubblebb4in -> evalrealbubblebb7in : A'=-1+A, [ B>=A && C>=1 ], cost: 3
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Eliminated locations (on tree-shaped paths):
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	     15: evalrealbubblestart -> evalrealbubblebb7in : A'=-1+A, [], cost: 2
5.57/2.82	
5.57/2.82	     29: evalrealbubblebb7in -> evalrealbubblebb7in : A'=-1+A, B'=A, C'=1, D'=1, [ A>=1 ], cost: 4+4*A
5.57/2.82	
5.57/2.82	     30: evalrealbubblebb7in -> [12] : [ A>=1 ], cost: 1+3*A
5.57/2.82	
5.57/2.82	     31: evalrealbubblebb7in -> [12] : [ A>=1 ], cost: 1+4*A
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Accelerating simple loops of location 2.
5.57/2.82	
5.57/2.82	   Accelerating the following rules:
5.57/2.82	
5.57/2.82	     29: evalrealbubblebb7in -> evalrealbubblebb7in : A'=-1+A, B'=A, C'=1, D'=1, [ A>=1 ], cost: 4+4*A
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	   Accelerated rule 29 with metering function A, yielding the new rule 32.
5.57/2.82	
5.57/2.82	   Removing the simple loops: 29.
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Accelerated all simple loops using metering functions (where possible):
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	     15: evalrealbubblestart -> evalrealbubblebb7in : A'=-1+A, [], cost: 2
5.57/2.82	
5.57/2.82	     30: evalrealbubblebb7in -> [12] : [ A>=1 ], cost: 1+3*A
5.57/2.82	
5.57/2.82	     31: evalrealbubblebb7in -> [12] : [ A>=1 ], cost: 1+4*A
5.57/2.82	
5.57/2.82	     32: evalrealbubblebb7in -> evalrealbubblebb7in : A'=0, B'=1, C'=1, D'=1, [ A>=1 ], cost: 6*A+2*A^2
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Chained accelerated rules (with incoming rules):
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	     15: evalrealbubblestart -> evalrealbubblebb7in : A'=-1+A, [], cost: 2
5.57/2.82	
5.57/2.82	     33: evalrealbubblestart -> evalrealbubblebb7in : A'=0, B'=1, C'=1, D'=1, [ -1+A>=1 ], cost: -4+6*A+2*(-1+A)^2
5.57/2.82	
5.57/2.82	     30: evalrealbubblebb7in -> [12] : [ A>=1 ], cost: 1+3*A
5.57/2.82	
5.57/2.82	     31: evalrealbubblebb7in -> [12] : [ A>=1 ], cost: 1+4*A
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Eliminated locations (on tree-shaped paths):
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	     34: evalrealbubblestart -> [12] : A'=-1+A, [ -1+A>=1 ], cost: 3*A
5.57/2.82	
5.57/2.82	     35: evalrealbubblestart -> [12] : A'=-1+A, [ -1+A>=1 ], cost: -1+4*A
5.57/2.82	
5.57/2.82	     36: evalrealbubblestart -> [14] : [ -1+A>=1 ], cost: -4+6*A+2*(-1+A)^2
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	### Computing asymptotic complexity ###
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Fully simplified ITS problem
5.57/2.82	
5.57/2.82	   Start location: evalrealbubblestart
5.57/2.82	
5.57/2.82	     34: evalrealbubblestart -> [12] : A'=-1+A, [ -1+A>=1 ], cost: 3*A
5.57/2.82	
5.57/2.82	     35: evalrealbubblestart -> [12] : A'=-1+A, [ -1+A>=1 ], cost: -1+4*A
5.57/2.82	
5.57/2.82	     36: evalrealbubblestart -> [14] : [ -1+A>=1 ], cost: -4+6*A+2*(-1+A)^2
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Computing asymptotic complexity for rule 34
5.57/2.82	
5.57/2.82	   Solved the limit problem by the following transformations:
5.57/2.82	
5.57/2.82	      Created initial limit problem:
5.57/2.82	
5.57/2.82	      -1+A (+/+!), 3*A (+) [not solved]
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	      removing all constraints (solved by SMT)
5.57/2.82	
5.57/2.82	      resulting limit problem: [solved]
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	      applying transformation rule (C) using substitution {A==n}
5.57/2.82	
5.57/2.82	      resulting limit problem:
5.57/2.82	
5.57/2.82	      [solved]
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	   Solution:
5.57/2.82	
5.57/2.82	      A / n
5.57/2.82	
5.57/2.82	   Resulting cost 3*n has complexity: Poly(n^1)
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Found new complexity Poly(n^1).
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Computing asymptotic complexity for rule 36
5.57/2.82	
5.57/2.82	   Solved the limit problem by the following transformations:
5.57/2.82	
5.57/2.82	      Created initial limit problem:
5.57/2.82	
5.57/2.82	      -1+A (+/+!), -2+2*A+2*A^2 (+) [not solved]
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	      removing all constraints (solved by SMT)
5.57/2.82	
5.57/2.82	      resulting limit problem: [solved]
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	      applying transformation rule (C) using substitution {A==n}
5.57/2.82	
5.57/2.82	      resulting limit problem:
5.57/2.82	
5.57/2.82	      [solved]
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	   Solution:
5.57/2.82	
5.57/2.82	      A / n
5.57/2.82	
5.57/2.82	   Resulting cost -2+2*n+2*n^2 has complexity: Poly(n^2)
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Found new complexity Poly(n^2).
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	Obtained the following overall complexity (w.r.t. the length of the input n):
5.57/2.82	
5.57/2.82	   Complexity:  Poly(n^2)
5.57/2.82	
5.57/2.82	   Cpx degree:  2
5.57/2.82	
5.57/2.82	   Solved cost: -2+2*n+2*n^2
5.57/2.82	
5.57/2.82	   Rule cost:   -4+6*A+2*(-1+A)^2
5.57/2.82	
5.57/2.82	   Rule guard:  [ -1+A>=1 ]
5.57/2.82	
5.57/2.82	
5.57/2.82	
5.57/2.82	WORST_CASE(Omega(n^2),?)
5.57/2.82	
5.57/2.82	
5.57/2.82	----------------------------------------
5.57/2.82	
5.57/2.82	(4)
5.57/2.82	BOUNDS(n^2, INF)
5.57/2.84	EOF