4.49/2.07	WORST_CASE(Omega(n^2), O(n^2))
4.49/2.08	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.49/2.08	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.49/2.08	
4.49/2.08	
4.49/2.08	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
4.49/2.08	
4.49/2.08	(0) CpxIntTrs
4.49/2.08	(1) Koat Proof [FINISHED, 100 ms]
4.49/2.08	(2) BOUNDS(1, n^2)
4.49/2.08	(3) Loat Proof [FINISHED, 401 ms]
4.49/2.08	(4) BOUNDS(n^2, INF)
4.49/2.08	
4.49/2.08	
4.49/2.08	----------------------------------------
4.49/2.08	
4.49/2.08	(0)
4.49/2.08	Obligation:
4.49/2.08	Complexity Int TRS consisting of the following rules:
4.49/2.08	evalrealselectstart(A, B, C) -> Com_1(evalrealselectentryin(A, B, C)) :|: TRUE
4.49/2.08	evalrealselectentryin(A, B, C) -> Com_1(evalrealselectbb6in(0, B, C)) :|: TRUE
4.49/2.08	evalrealselectbb6in(A, B, C) -> Com_1(evalrealselectbbin(A, B, C)) :|: B >= 2 + A
4.49/2.08	evalrealselectbb6in(A, B, C) -> Com_1(evalrealselectreturnin(A, B, C)) :|: A + 1 >= B
4.49/2.08	evalrealselectbbin(A, B, C) -> Com_1(evalrealselectbb4in(A, B, A + 1)) :|: TRUE
4.49/2.08	evalrealselectbb4in(A, B, C) -> Com_1(evalrealselectbb1in(A, B, C)) :|: B >= C + 1
4.49/2.08	evalrealselectbb4in(A, B, C) -> Com_1(evalrealselectbb5in(A, B, C)) :|: C >= B
4.49/2.08	evalrealselectbb1in(A, B, C) -> Com_1(evalrealselectbb4in(A, B, C + 1)) :|: D >= E + 1
4.49/2.08	evalrealselectbb1in(A, B, C) -> Com_1(evalrealselectbb4in(A, B, C + 1)) :|: E >= D
4.49/2.08	evalrealselectbb5in(A, B, C) -> Com_1(evalrealselectbb6in(A + 1, B, C)) :|: TRUE
4.49/2.08	evalrealselectreturnin(A, B, C) -> Com_1(evalrealselectstop(A, B, C)) :|: TRUE
4.49/2.08	
4.49/2.08	The start-symbols are:[evalrealselectstart_3]
4.49/2.08	
4.49/2.08	
4.49/2.08	----------------------------------------
4.49/2.08	
4.49/2.08	(1) Koat Proof (FINISHED)
4.49/2.08	YES(?, 72*ar_1 + 9*ar_1^2 + 69)
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Initial complexity problem:
4.49/2.08	
4.49/2.08	1:	T:
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.49/2.08	
4.49/2.08		start location:	koat_start
4.49/2.08	
4.49/2.08		leaf cost:	0
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.49/2.08	
4.49/2.08	2:	T:
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)    evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)    evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.49/2.08	
4.49/2.08		start location:	koat_start
4.49/2.08	
4.49/2.08		leaf cost:	0
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	A polynomial rank function with
4.49/2.08	
4.49/2.08		Pol(evalrealselectstart) = 2
4.49/2.08	
4.49/2.08		Pol(evalrealselectentryin) = 2
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb6in) = 2
4.49/2.08	
4.49/2.08		Pol(evalrealselectbbin) = 2
4.49/2.08	
4.49/2.08		Pol(evalrealselectreturnin) = 1
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb4in) = 2
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb1in) = 2
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb5in) = 2
4.49/2.08	
4.49/2.08		Pol(evalrealselectstop) = 0
4.49/2.08	
4.49/2.08		Pol(koat_start) = 2
4.49/2.08	
4.49/2.08	orients all transitions weakly and the transitions
4.49/2.08	
4.49/2.08		evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08		evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]
4.49/2.08	
4.49/2.08	strictly and produces the following problem:
4.49/2.08	
4.49/2.08	3:	T:
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)    evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)    evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]
4.49/2.08	
4.49/2.08			(Comp: 2, Cost: 1)    evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)    evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 2, Cost: 1)    evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.49/2.08	
4.49/2.08		start location:	koat_start
4.49/2.08	
4.49/2.08		leaf cost:	0
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	A polynomial rank function with
4.49/2.08	
4.49/2.08		Pol(evalrealselectstart) = V_2 + 1
4.49/2.08	
4.49/2.08		Pol(evalrealselectentryin) = V_2 + 1
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb6in) = -V_1 + V_2 + 1
4.49/2.08	
4.49/2.08		Pol(evalrealselectbbin) = -V_1 + V_2
4.49/2.08	
4.49/2.08		Pol(evalrealselectreturnin) = -V_1 + V_2
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb4in) = -V_1 + V_2
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb1in) = -V_1 + V_2
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb5in) = -V_1 + V_2
4.49/2.08	
4.49/2.08		Pol(evalrealselectstop) = -V_1 + V_2
4.49/2.08	
4.49/2.08		Pol(koat_start) = V_2 + 1
4.49/2.08	
4.49/2.08	orients all transitions weakly and the transition
4.49/2.08	
4.49/2.08		evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]
4.49/2.08	
4.49/2.08	strictly and produces the following problem:
4.49/2.08	
4.49/2.08	4:	T:
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)           evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)           evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: ar_1 + 1, Cost: 1)    evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]
4.49/2.08	
4.49/2.08			(Comp: 2, Cost: 1)           evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)           evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)           evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)           evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)           evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)           evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)           evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 2, Cost: 1)           evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.49/2.08	
4.49/2.08		start location:	koat_start
4.49/2.08	
4.49/2.08		leaf cost:	0
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Repeatedly propagating knowledge in problem 4 produces the following problem:
4.49/2.08	
4.49/2.08	5:	T:
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)           evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)           evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: ar_1 + 1, Cost: 1)    evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]
4.49/2.08	
4.49/2.08			(Comp: 2, Cost: 1)           evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ar_1 + 1, Cost: 1)    evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)           evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)           evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)           evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)           evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)           evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 2, Cost: 1)           evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.49/2.08	
4.49/2.08		start location:	koat_start
4.49/2.08	
4.49/2.08		leaf cost:	0
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	A polynomial rank function with
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb5in) = 1
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb6in) = 0
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb4in) = 2
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb1in) = 2
4.49/2.08	
4.49/2.08	and size complexities
4.49/2.08	
4.49/2.08		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
4.49/2.08	
4.49/2.08		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
4.49/2.08	
4.49/2.08		S("evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))", 0-0) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))", 0-0) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]", 0-0) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]", 0-0) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-0) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-0) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))", 0-0) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]", 0-0) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]", 0-0) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))", 0-0) = 0
4.49/2.08	
4.49/2.08		S("evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))", 0-2) = ar_2
4.49/2.08	
4.49/2.08		S("evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))", 0-0) = ar_0
4.49/2.08	
4.49/2.08		S("evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))", 0-2) = ar_2
4.49/2.08	
4.49/2.08	orients the transitions
4.49/2.08	
4.49/2.08		evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))
4.49/2.08	
4.49/2.08		evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
4.49/2.08	
4.49/2.08		evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
4.49/2.08	
4.49/2.08		evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]
4.49/2.08	
4.49/2.08		evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]
4.49/2.08	
4.49/2.08	weakly and the transitions
4.49/2.08	
4.49/2.08		evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))
4.49/2.08	
4.49/2.08		evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
4.49/2.08	
4.49/2.08	strictly and produces the following problem:
4.49/2.08	
4.49/2.08	6:	T:
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)             evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)             evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: ar_1 + 1, Cost: 1)      evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]
4.49/2.08	
4.49/2.08			(Comp: 2, Cost: 1)             evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ar_1 + 1, Cost: 1)      evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)             evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
4.49/2.08	
4.49/2.08			(Comp: 2*ar_1 + 2, Cost: 1)    evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)             evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)             evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]
4.49/2.08	
4.49/2.08			(Comp: 2*ar_1 + 2, Cost: 1)    evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 2, Cost: 1)             evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.49/2.08	
4.49/2.08		start location:	koat_start
4.49/2.08	
4.49/2.08		leaf cost:	0
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	A polynomial rank function with
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb4in) = V_2 - V_3 + 1
4.49/2.08	
4.49/2.08		Pol(evalrealselectbb1in) = V_2 - V_3
4.49/2.08	
4.49/2.08	and size complexities
4.49/2.08	
4.49/2.08		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
4.49/2.08	
4.49/2.08		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
4.49/2.08	
4.49/2.08		S("evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))", 0-0) = 2*ar_1 + 32
4.49/2.08	
4.49/2.08		S("evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))", 0-0) = 2*ar_1 + 8
4.49/2.08	
4.49/2.08		S("evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]", 0-0) = 2*ar_1 + 8
4.49/2.08	
4.49/2.08		S("evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]", 0-0) = 2*ar_1 + 8
4.49/2.08	
4.49/2.08		S("evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-0) = 2*ar_1 + 8
4.49/2.08	
4.49/2.08		S("evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-0) = 2*ar_1 + 8
4.49/2.08	
4.49/2.08		S("evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))", 0-0) = 2*ar_1 + 8
4.49/2.08	
4.49/2.08		S("evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))", 0-2) = 2*ar_1 + 18
4.49/2.08	
4.49/2.08		S("evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]", 0-0) = 2*ar_1 + 16
4.49/2.08	
4.49/2.08		S("evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]", 0-0) = 2*ar_1 + 8
4.49/2.08	
4.49/2.08		S("evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]", 0-2) = ?
4.49/2.08	
4.49/2.08		S("evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))", 0-0) = 0
4.49/2.08	
4.49/2.08		S("evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))", 0-2) = ar_2
4.49/2.08	
4.49/2.08		S("evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))", 0-0) = ar_0
4.49/2.08	
4.49/2.08		S("evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))", 0-1) = ar_1
4.49/2.08	
4.49/2.08		S("evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))", 0-2) = ar_2
4.49/2.08	
4.49/2.08	orients the transitions
4.49/2.08	
4.49/2.08		evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
4.49/2.08	
4.49/2.08		evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]
4.49/2.08	
4.49/2.08		evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]
4.49/2.08	
4.49/2.08	weakly and the transition
4.49/2.08	
4.49/2.08		evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
4.49/2.08	
4.49/2.08	strictly and produces the following problem:
4.49/2.08	
4.49/2.08	7:	T:
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)                          evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)                          evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: ar_1 + 1, Cost: 1)                   evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]
4.49/2.08	
4.49/2.08			(Comp: 2, Cost: 1)                          evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ar_1 + 1, Cost: 1)                   evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))
4.49/2.08	
4.49/2.08			(Comp: 3*ar_1^2 + 22*ar_1 + 19, Cost: 1)    evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
4.49/2.08	
4.49/2.08			(Comp: 2*ar_1 + 2, Cost: 1)                 evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)                          evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]
4.49/2.08	
4.49/2.08			(Comp: ?, Cost: 1)                          evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]
4.49/2.08	
4.49/2.08			(Comp: 2*ar_1 + 2, Cost: 1)                 evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 2, Cost: 1)                          evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 0)                          koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.49/2.08	
4.49/2.08		start location:	koat_start
4.49/2.08	
4.49/2.08		leaf cost:	0
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Repeatedly propagating knowledge in problem 7 produces the following problem:
4.49/2.08	
4.49/2.08	8:	T:
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)                          evalrealselectstart(ar_0, ar_1, ar_2) -> Com_1(evalrealselectentryin(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 1)                          evalrealselectentryin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: ar_1 + 1, Cost: 1)                   evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbbin(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 2 ]
4.49/2.08	
4.49/2.08			(Comp: 2, Cost: 1)                          evalrealselectbb6in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectreturnin(ar_0, ar_1, ar_2)) [ ar_0 + 1 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: ar_1 + 1, Cost: 1)                   evalrealselectbbin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_0 + 1))
4.49/2.08	
4.49/2.08			(Comp: 3*ar_1^2 + 22*ar_1 + 19, Cost: 1)    evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
4.49/2.08	
4.49/2.08			(Comp: 2*ar_1 + 2, Cost: 1)                 evalrealselectbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
4.49/2.08	
4.49/2.08			(Comp: 3*ar_1^2 + 22*ar_1 + 19, Cost: 1)    evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e + 1 ]
4.49/2.08	
4.49/2.08			(Comp: 3*ar_1^2 + 22*ar_1 + 19, Cost: 1)    evalrealselectbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb4in(ar_0, ar_1, ar_2 + 1)) [ d >= e ]
4.49/2.08	
4.49/2.08			(Comp: 2*ar_1 + 2, Cost: 1)                 evalrealselectbb5in(ar_0, ar_1, ar_2) -> Com_1(evalrealselectbb6in(ar_0 + 1, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 2, Cost: 1)                          evalrealselectreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2))
4.49/2.08	
4.49/2.08			(Comp: 1, Cost: 0)                          koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrealselectstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.49/2.08	
4.49/2.08		start location:	koat_start
4.49/2.08	
4.49/2.08		leaf cost:	0
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Complexity upper bound 72*ar_1 + 9*ar_1^2 + 69
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Time: 0.121 sec (SMT: 0.105 sec)
4.49/2.08	
4.49/2.08	
4.49/2.08	----------------------------------------
4.49/2.08	
4.49/2.08	(2)
4.49/2.08	BOUNDS(1, n^2)
4.49/2.08	
4.49/2.08	----------------------------------------
4.49/2.08	
4.49/2.08	(3) Loat Proof (FINISHED)
4.49/2.08	
4.49/2.08	
4.49/2.08	### Pre-processing the ITS problem ###
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Initial linear ITS problem
4.49/2.08	
4.49/2.08	   Start location: evalrealselectstart
4.49/2.08	
4.49/2.08	      0: evalrealselectstart -> evalrealselectentryin : [], cost: 1
4.49/2.08	
4.49/2.08	      1: evalrealselectentryin -> evalrealselectbb6in : A'=0, [], cost: 1
4.49/2.08	
4.49/2.08	      2: evalrealselectbb6in -> evalrealselectbbin : [ B>=2+A ], cost: 1
4.49/2.08	
4.49/2.08	      3: evalrealselectbb6in -> evalrealselectreturnin : [ 1+A>=B ], cost: 1
4.49/2.08	
4.49/2.08	      4: evalrealselectbbin -> evalrealselectbb4in : C'=1+A, [], cost: 1
4.49/2.08	
4.49/2.08	      5: evalrealselectbb4in -> evalrealselectbb1in : [ B>=1+C ], cost: 1
4.49/2.08	
4.49/2.08	      6: evalrealselectbb4in -> evalrealselectbb5in : [ C>=B ], cost: 1
4.49/2.08	
4.49/2.08	      7: evalrealselectbb1in -> evalrealselectbb4in : C'=1+C, [ free>=1+free_1 ], cost: 1
4.49/2.08	
4.49/2.08	      8: evalrealselectbb1in -> evalrealselectbb4in : C'=1+C, [ free_2>=free_3 ], cost: 1
4.49/2.08	
4.49/2.08	      9: evalrealselectbb5in -> evalrealselectbb6in : A'=1+A, [], cost: 1
4.49/2.08	
4.49/2.08	     10: evalrealselectreturnin -> evalrealselectstop : [], cost: 1
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Removed unreachable and leaf rules:
4.49/2.08	
4.49/2.08	   Start location: evalrealselectstart
4.49/2.08	
4.49/2.08	      0: evalrealselectstart -> evalrealselectentryin : [], cost: 1
4.49/2.08	
4.49/2.08	      1: evalrealselectentryin -> evalrealselectbb6in : A'=0, [], cost: 1
4.49/2.08	
4.49/2.08	      2: evalrealselectbb6in -> evalrealselectbbin : [ B>=2+A ], cost: 1
4.49/2.08	
4.49/2.08	      4: evalrealselectbbin -> evalrealselectbb4in : C'=1+A, [], cost: 1
4.49/2.08	
4.49/2.08	      5: evalrealselectbb4in -> evalrealselectbb1in : [ B>=1+C ], cost: 1
4.49/2.08	
4.49/2.08	      6: evalrealselectbb4in -> evalrealselectbb5in : [ C>=B ], cost: 1
4.49/2.08	
4.49/2.08	      7: evalrealselectbb1in -> evalrealselectbb4in : C'=1+C, [ free>=1+free_1 ], cost: 1
4.49/2.08	
4.49/2.08	      8: evalrealselectbb1in -> evalrealselectbb4in : C'=1+C, [ free_2>=free_3 ], cost: 1
4.49/2.08	
4.49/2.08	      9: evalrealselectbb5in -> evalrealselectbb6in : A'=1+A, [], cost: 1
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Simplified all rules, resulting in:
4.49/2.08	
4.49/2.08	   Start location: evalrealselectstart
4.49/2.08	
4.49/2.08	      0: evalrealselectstart -> evalrealselectentryin : [], cost: 1
4.49/2.08	
4.49/2.08	      1: evalrealselectentryin -> evalrealselectbb6in : A'=0, [], cost: 1
4.49/2.08	
4.49/2.08	      2: evalrealselectbb6in -> evalrealselectbbin : [ B>=2+A ], cost: 1
4.49/2.08	
4.49/2.08	      4: evalrealselectbbin -> evalrealselectbb4in : C'=1+A, [], cost: 1
4.49/2.08	
4.49/2.08	      5: evalrealselectbb4in -> evalrealselectbb1in : [ B>=1+C ], cost: 1
4.49/2.08	
4.49/2.08	      6: evalrealselectbb4in -> evalrealselectbb5in : [ C>=B ], cost: 1
4.49/2.08	
4.49/2.08	      8: evalrealselectbb1in -> evalrealselectbb4in : C'=1+C, [], cost: 1
4.49/2.08	
4.49/2.08	      9: evalrealselectbb5in -> evalrealselectbb6in : A'=1+A, [], cost: 1
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	### Simplification by acceleration and chaining ###
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Eliminated locations (on linear paths):
4.49/2.08	
4.49/2.08	   Start location: evalrealselectstart
4.49/2.08	
4.49/2.08	     11: evalrealselectstart -> evalrealselectbb6in : A'=0, [], cost: 2
4.49/2.08	
4.49/2.08	     12: evalrealselectbb6in -> evalrealselectbb4in : C'=1+A, [ B>=2+A ], cost: 2
4.49/2.08	
4.49/2.08	     13: evalrealselectbb4in -> evalrealselectbb4in : C'=1+C, [ B>=1+C ], cost: 2
4.49/2.08	
4.49/2.08	     14: evalrealselectbb4in -> evalrealselectbb6in : A'=1+A, [ C>=B ], cost: 2
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Accelerating simple loops of location 4.
4.49/2.08	
4.49/2.08	   Accelerating the following rules:
4.49/2.08	
4.49/2.08	     13: evalrealselectbb4in -> evalrealselectbb4in : C'=1+C, [ B>=1+C ], cost: 2
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	   Accelerated rule 13 with metering function -C+B, yielding the new rule 15.
4.49/2.08	
4.49/2.08	   Removing the simple loops: 13.
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Accelerated all simple loops using metering functions (where possible):
4.49/2.08	
4.49/2.08	   Start location: evalrealselectstart
4.49/2.08	
4.49/2.08	     11: evalrealselectstart -> evalrealselectbb6in : A'=0, [], cost: 2
4.49/2.08	
4.49/2.08	     12: evalrealselectbb6in -> evalrealselectbb4in : C'=1+A, [ B>=2+A ], cost: 2
4.49/2.08	
4.49/2.08	     14: evalrealselectbb4in -> evalrealselectbb6in : A'=1+A, [ C>=B ], cost: 2
4.49/2.08	
4.49/2.08	     15: evalrealselectbb4in -> evalrealselectbb4in : C'=B, [ B>=1+C ], cost: -2*C+2*B
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Chained accelerated rules (with incoming rules):
4.49/2.08	
4.49/2.08	   Start location: evalrealselectstart
4.49/2.08	
4.49/2.08	     11: evalrealselectstart -> evalrealselectbb6in : A'=0, [], cost: 2
4.49/2.08	
4.49/2.08	     12: evalrealselectbb6in -> evalrealselectbb4in : C'=1+A, [ B>=2+A ], cost: 2
4.49/2.08	
4.49/2.08	     16: evalrealselectbb6in -> evalrealselectbb4in : C'=B, [ B>=2+A ], cost: -2*A+2*B
4.49/2.08	
4.49/2.08	     14: evalrealselectbb4in -> evalrealselectbb6in : A'=1+A, [ C>=B ], cost: 2
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Eliminated locations (on tree-shaped paths):
4.49/2.08	
4.49/2.08	   Start location: evalrealselectstart
4.49/2.08	
4.49/2.08	     11: evalrealselectstart -> evalrealselectbb6in : A'=0, [], cost: 2
4.49/2.08	
4.49/2.08	     17: evalrealselectbb6in -> evalrealselectbb6in : A'=1+A, C'=B, [ B>=2+A ], cost: 2-2*A+2*B
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Accelerating simple loops of location 2.
4.49/2.08	
4.49/2.08	   Accelerating the following rules:
4.49/2.08	
4.49/2.08	     17: evalrealselectbb6in -> evalrealselectbb6in : A'=1+A, C'=B, [ B>=2+A ], cost: 2-2*A+2*B
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	   Accelerated rule 17 with metering function -1-A+B, yielding the new rule 18.
4.49/2.08	
4.49/2.08	   Removing the simple loops: 17.
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Accelerated all simple loops using metering functions (where possible):
4.49/2.08	
4.49/2.08	   Start location: evalrealselectstart
4.49/2.08	
4.49/2.08	     11: evalrealselectstart -> evalrealselectbb6in : A'=0, [], cost: 2
4.49/2.08	
4.49/2.08	     18: evalrealselectbb6in -> evalrealselectbb6in : A'=-1+B, C'=B, [ B>=2+A ], cost: -3-(1+A-B)^2-3*A-2*(1+A-B)*B+2*A*(1+A-B)+3*B
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Chained accelerated rules (with incoming rules):
4.49/2.08	
4.49/2.08	   Start location: evalrealselectstart
4.49/2.08	
4.49/2.08	     11: evalrealselectstart -> evalrealselectbb6in : A'=0, [], cost: 2
4.49/2.08	
4.49/2.08	     19: evalrealselectstart -> evalrealselectbb6in : A'=-1+B, C'=B, [ B>=2 ], cost: -1+2*(-1+B)*B-(-1+B)^2+3*B
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Removed unreachable locations (and leaf rules with constant cost):
4.49/2.08	
4.49/2.08	   Start location: evalrealselectstart
4.49/2.08	
4.49/2.08	     19: evalrealselectstart -> evalrealselectbb6in : A'=-1+B, C'=B, [ B>=2 ], cost: -1+2*(-1+B)*B-(-1+B)^2+3*B
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	### Computing asymptotic complexity ###
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Fully simplified ITS problem
4.49/2.08	
4.49/2.08	   Start location: evalrealselectstart
4.49/2.08	
4.49/2.08	     19: evalrealselectstart -> evalrealselectbb6in : A'=-1+B, C'=B, [ B>=2 ], cost: -1+2*(-1+B)*B-(-1+B)^2+3*B
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Computing asymptotic complexity for rule 19
4.49/2.08	
4.49/2.08	   Solved the limit problem by the following transformations:
4.49/2.08	
4.49/2.08	      Created initial limit problem:
4.49/2.08	
4.49/2.08	      -2+B^2+3*B (+), -1+B (+/+!) [not solved]
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	      removing all constraints (solved by SMT)
4.49/2.08	
4.49/2.08	      resulting limit problem: [solved]
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	      applying transformation rule (C) using substitution {B==n}
4.49/2.08	
4.49/2.08	      resulting limit problem:
4.49/2.08	
4.49/2.08	      [solved]
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	   Solution:
4.49/2.08	
4.49/2.08	      B / n
4.49/2.08	
4.49/2.08	   Resulting cost -2+3*n+n^2 has complexity: Poly(n^2)
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Found new complexity Poly(n^2).
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	Obtained the following overall complexity (w.r.t. the length of the input n):
4.49/2.08	
4.49/2.08	   Complexity:  Poly(n^2)
4.49/2.08	
4.49/2.08	   Cpx degree:  2
4.49/2.08	
4.49/2.08	   Solved cost: -2+3*n+n^2
4.49/2.08	
4.49/2.08	   Rule cost:   -1+2*(-1+B)*B-(-1+B)^2+3*B
4.49/2.08	
4.49/2.08	   Rule guard:  [ B>=2 ]
4.49/2.08	
4.49/2.08	
4.49/2.08	
4.49/2.08	WORST_CASE(Omega(n^2),?)
4.49/2.08	
4.49/2.08	
4.49/2.08	----------------------------------------
4.49/2.08	
4.49/2.08	(4)
4.49/2.08	BOUNDS(n^2, INF)
4.59/2.11	EOF