4.26/2.01	WORST_CASE(Omega(n^2), O(n^2))
4.34/2.36	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.34/2.36	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.34/2.36	
4.34/2.36	
4.34/2.36	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
4.34/2.36	
4.34/2.36	(0) CpxIntTrs
4.34/2.36	(1) Koat Proof [FINISHED, 23 ms]
4.34/2.36	(2) BOUNDS(1, n^2)
4.34/2.36	(3) Loat Proof [FINISHED, 320 ms]
4.34/2.36	(4) BOUNDS(n^2, INF)
4.34/2.36	
4.34/2.36	
4.34/2.36	----------------------------------------
4.34/2.36	
4.34/2.36	(0)
4.34/2.36	Obligation:
4.34/2.36	Complexity Int TRS consisting of the following rules:
4.34/2.36	evalfstart(A, B, C) -> Com_1(evalfentryin(A, B, C)) :|: TRUE
4.34/2.36	evalfentryin(A, B, C) -> Com_1(evalfbb4in(1, B, C)) :|: TRUE
4.34/2.36	evalfbb4in(A, B, C) -> Com_1(evalfbb2in(A, B, A)) :|: B >= A
4.34/2.36	evalfbb4in(A, B, C) -> Com_1(evalfreturnin(A, B, C)) :|: A >= B + 1
4.34/2.36	evalfbb2in(A, B, C) -> Com_1(evalfbb1in(A, B, C)) :|: B >= C
4.34/2.36	evalfbb2in(A, B, C) -> Com_1(evalfbb3in(A, B, C)) :|: C >= B + 1
4.34/2.36	evalfbb1in(A, B, C) -> Com_1(evalfbb2in(A, B, C + 1)) :|: TRUE
4.34/2.36	evalfbb3in(A, B, C) -> Com_1(evalfbb4in(A + 1, B, C)) :|: TRUE
4.34/2.36	evalfreturnin(A, B, C) -> Com_1(evalfstop(A, B, C)) :|: TRUE
4.34/2.36	
4.34/2.36	The start-symbols are:[evalfstart_3]
4.34/2.36	
4.34/2.36	
4.34/2.36	----------------------------------------
4.34/2.36	
4.34/2.36	(1) Koat Proof (FINISHED)
4.34/2.36	YES(?, 27*ar_1 + 6*ar_1^2 + 6)
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Initial complexity problem:
4.34/2.36	
4.34/2.36	1:	T:
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.34/2.36	
4.34/2.36		start location:	koat_start
4.34/2.36	
4.34/2.36		leaf cost:	0
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.34/2.36	
4.34/2.36	2:	T:
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.34/2.36	
4.34/2.36		start location:	koat_start
4.34/2.36	
4.34/2.36		leaf cost:	0
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	A polynomial rank function with
4.34/2.36	
4.34/2.36		Pol(evalfstart) = 2
4.34/2.36	
4.34/2.36		Pol(evalfentryin) = 2
4.34/2.36	
4.34/2.36		Pol(evalfbb4in) = 2
4.34/2.36	
4.34/2.36		Pol(evalfbb2in) = 2
4.34/2.36	
4.34/2.36		Pol(evalfreturnin) = 1
4.34/2.36	
4.34/2.36		Pol(evalfbb1in) = 2
4.34/2.36	
4.34/2.36		Pol(evalfbb3in) = 2
4.34/2.36	
4.34/2.36		Pol(evalfstop) = 0
4.34/2.36	
4.34/2.36		Pol(koat_start) = 2
4.34/2.36	
4.34/2.36	orients all transitions weakly and the transitions
4.34/2.36	
4.34/2.36		evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36		evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36	strictly and produces the following problem:
4.34/2.36	
4.34/2.36	3:	T:
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]
4.34/2.36	
4.34/2.36			(Comp: 2, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 2, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.34/2.36	
4.34/2.36		start location:	koat_start
4.34/2.36	
4.34/2.36		leaf cost:	0
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	A polynomial rank function with
4.34/2.36	
4.34/2.36		Pol(evalfstart) = V_2
4.34/2.36	
4.34/2.36		Pol(evalfentryin) = V_2
4.34/2.36	
4.34/2.36		Pol(evalfbb4in) = -V_1 + V_2 + 1
4.34/2.36	
4.34/2.36		Pol(evalfbb2in) = -V_1 + V_2
4.34/2.36	
4.34/2.36		Pol(evalfreturnin) = -V_1 + V_2
4.34/2.36	
4.34/2.36		Pol(evalfbb1in) = -V_1 + V_2
4.34/2.36	
4.34/2.36		Pol(evalfbb3in) = -V_1 + V_2
4.34/2.36	
4.34/2.36		Pol(evalfstop) = -V_1 + V_2
4.34/2.36	
4.34/2.36		Pol(koat_start) = V_2
4.34/2.36	
4.34/2.36	orients all transitions weakly and the transition
4.34/2.36	
4.34/2.36		evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]
4.34/2.36	
4.34/2.36	strictly and produces the following problem:
4.34/2.36	
4.34/2.36	4:	T:
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 1)       evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 1)       evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: ar_1, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]
4.34/2.36	
4.34/2.36			(Comp: 2, Cost: 1)       evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)       evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)       evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)       evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)       evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 2, Cost: 1)       evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.34/2.36	
4.34/2.36		start location:	koat_start
4.34/2.36	
4.34/2.36		leaf cost:	0
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	A polynomial rank function with
4.34/2.36	
4.34/2.36		Pol(evalfbb3in) = 1
4.34/2.36	
4.34/2.36		Pol(evalfbb4in) = 0
4.34/2.36	
4.34/2.36		Pol(evalfbb2in) = 2
4.34/2.36	
4.34/2.36		Pol(evalfbb1in) = 2
4.34/2.36	
4.34/2.36	and size complexities
4.34/2.36	
4.34/2.36		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
4.34/2.36	
4.34/2.36		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
4.34/2.36	
4.34/2.36		S("evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))", 0-0) = ?
4.34/2.36	
4.34/2.36		S("evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))", 0-0) = ?
4.34/2.36	
4.34/2.36		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = ?
4.34/2.36	
4.34/2.36		S("evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-0) = ?
4.34/2.36	
4.34/2.36		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-0) = ?
4.34/2.36	
4.34/2.36		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ?
4.34/2.36	
4.34/2.36		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]", 0-0) = ?
4.34/2.36	
4.34/2.36		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))", 0-0) = 1
4.34/2.36	
4.34/2.36		S("evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))", 0-2) = ar_2
4.34/2.36	
4.34/2.36		S("evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))", 0-0) = ar_0
4.34/2.36	
4.34/2.36		S("evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))", 0-2) = ar_2
4.34/2.36	
4.34/2.36	orients the transitions
4.34/2.36	
4.34/2.36		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.34/2.36	
4.34/2.36		evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36		evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
4.34/2.36	
4.34/2.36		evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.34/2.36	
4.34/2.36	weakly and the transitions
4.34/2.36	
4.34/2.36		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.34/2.36	
4.34/2.36		evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36	strictly and produces the following problem:
4.34/2.36	
4.34/2.36	5:	T:
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 1)         evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 1)         evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: ar_1, Cost: 1)      evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]
4.34/2.36	
4.34/2.36			(Comp: 2, Cost: 1)         evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)         evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
4.34/2.36	
4.34/2.36			(Comp: 2*ar_1, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)         evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.34/2.36	
4.34/2.36			(Comp: 2*ar_1, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 2, Cost: 1)         evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.34/2.36	
4.34/2.36		start location:	koat_start
4.34/2.36	
4.34/2.36		leaf cost:	0
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	A polynomial rank function with
4.34/2.36	
4.34/2.36		Pol(evalfbb2in) = V_2 - V_3 + 1
4.34/2.36	
4.34/2.36		Pol(evalfbb1in) = V_2 - V_3
4.34/2.36	
4.34/2.36	and size complexities
4.34/2.36	
4.34/2.36		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
4.34/2.36	
4.34/2.36		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
4.34/2.36	
4.34/2.36		S("evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))", 0-0) = 2*ar_1 + 20
4.34/2.36	
4.34/2.36		S("evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))", 0-0) = 2*ar_1 + 4
4.34/2.36	
4.34/2.36		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = 2*ar_1 + 4
4.34/2.36	
4.34/2.36		S("evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-0) = 2*ar_1 + 4
4.34/2.36	
4.34/2.36		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-0) = 2*ar_1 + 4
4.34/2.36	
4.34/2.36		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-0) = 2*ar_1 + 10
4.34/2.36	
4.34/2.36		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ?
4.34/2.36	
4.34/2.36		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]", 0-0) = 2*ar_1 + 4
4.34/2.36	
4.34/2.36		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]", 0-2) = 2*ar_1 + 10
4.34/2.36	
4.34/2.36		S("evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))", 0-0) = 1
4.34/2.36	
4.34/2.36		S("evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))", 0-2) = ar_2
4.34/2.36	
4.34/2.36		S("evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))", 0-0) = ar_0
4.34/2.36	
4.34/2.36		S("evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))", 0-1) = ar_1
4.34/2.36	
4.34/2.36		S("evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))", 0-2) = ar_2
4.34/2.36	
4.34/2.36	orients the transitions
4.34/2.36	
4.34/2.36		evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
4.34/2.36	
4.34/2.36		evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.34/2.36	
4.34/2.36	weakly and the transition
4.34/2.36	
4.34/2.36		evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
4.34/2.36	
4.34/2.36	strictly and produces the following problem:
4.34/2.36	
4.34/2.36	6:	T:
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 1)                     evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 1)                     evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: ar_1, Cost: 1)                  evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]
4.34/2.36	
4.34/2.36			(Comp: 2, Cost: 1)                     evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: 3*ar_1^2 + 11*ar_1, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
4.34/2.36	
4.34/2.36			(Comp: 2*ar_1, Cost: 1)                evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: ?, Cost: 1)                     evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.34/2.36	
4.34/2.36			(Comp: 2*ar_1, Cost: 1)                evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 2, Cost: 1)                     evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 0)                     koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.34/2.36	
4.34/2.36		start location:	koat_start
4.34/2.36	
4.34/2.36		leaf cost:	0
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Repeatedly propagating knowledge in problem 6 produces the following problem:
4.34/2.36	
4.34/2.36	7:	T:
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 1)                     evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 1)                     evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: ar_1, Cost: 1)                  evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]
4.34/2.36	
4.34/2.36			(Comp: 2, Cost: 1)                     evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: 3*ar_1^2 + 11*ar_1, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]
4.34/2.36	
4.34/2.36			(Comp: 2*ar_1, Cost: 1)                evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]
4.34/2.36	
4.34/2.36			(Comp: 3*ar_1^2 + 11*ar_1, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.34/2.36	
4.34/2.36			(Comp: 2*ar_1, Cost: 1)                evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 2, Cost: 1)                     evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.34/2.36	
4.34/2.36			(Comp: 1, Cost: 0)                     koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.34/2.36	
4.34/2.36		start location:	koat_start
4.34/2.36	
4.34/2.36		leaf cost:	0
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Complexity upper bound 27*ar_1 + 6*ar_1^2 + 6
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Time: 0.092 sec (SMT: 0.082 sec)
4.34/2.36	
4.34/2.36	
4.34/2.36	----------------------------------------
4.34/2.36	
4.34/2.36	(2)
4.34/2.36	BOUNDS(1, n^2)
4.34/2.36	
4.34/2.36	----------------------------------------
4.34/2.36	
4.34/2.36	(3) Loat Proof (FINISHED)
4.34/2.36	
4.34/2.36	
4.34/2.36	### Pre-processing the ITS problem ###
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Initial linear ITS problem
4.34/2.36	
4.34/2.36	   Start location: evalfstart
4.34/2.36	
4.34/2.36	      0: evalfstart -> evalfentryin : [], cost: 1
4.34/2.36	
4.34/2.36	      1: evalfentryin -> evalfbb4in : A'=1, [], cost: 1
4.34/2.36	
4.34/2.36	      2: evalfbb4in -> evalfbb2in : C'=A, [ B>=A ], cost: 1
4.34/2.36	
4.34/2.36	      3: evalfbb4in -> evalfreturnin : [ A>=1+B ], cost: 1
4.34/2.36	
4.34/2.36	      4: evalfbb2in -> evalfbb1in : [ B>=C ], cost: 1
4.34/2.36	
4.34/2.36	      5: evalfbb2in -> evalfbb3in : [ C>=1+B ], cost: 1
4.34/2.36	
4.34/2.36	      6: evalfbb1in -> evalfbb2in : C'=1+C, [], cost: 1
4.34/2.36	
4.34/2.36	      7: evalfbb3in -> evalfbb4in : A'=1+A, [], cost: 1
4.34/2.36	
4.34/2.36	      8: evalfreturnin -> evalfstop : [], cost: 1
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Removed unreachable and leaf rules:
4.34/2.36	
4.34/2.36	   Start location: evalfstart
4.34/2.36	
4.34/2.36	      0: evalfstart -> evalfentryin : [], cost: 1
4.34/2.36	
4.34/2.36	      1: evalfentryin -> evalfbb4in : A'=1, [], cost: 1
4.34/2.36	
4.34/2.36	      2: evalfbb4in -> evalfbb2in : C'=A, [ B>=A ], cost: 1
4.34/2.36	
4.34/2.36	      4: evalfbb2in -> evalfbb1in : [ B>=C ], cost: 1
4.34/2.36	
4.34/2.36	      5: evalfbb2in -> evalfbb3in : [ C>=1+B ], cost: 1
4.34/2.36	
4.34/2.36	      6: evalfbb1in -> evalfbb2in : C'=1+C, [], cost: 1
4.34/2.36	
4.34/2.36	      7: evalfbb3in -> evalfbb4in : A'=1+A, [], cost: 1
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	### Simplification by acceleration and chaining ###
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Eliminated locations (on linear paths):
4.34/2.36	
4.34/2.36	   Start location: evalfstart
4.34/2.36	
4.34/2.36	      9: evalfstart -> evalfbb4in : A'=1, [], cost: 2
4.34/2.36	
4.34/2.36	      2: evalfbb4in -> evalfbb2in : C'=A, [ B>=A ], cost: 1
4.34/2.36	
4.34/2.36	     10: evalfbb2in -> evalfbb2in : C'=1+C, [ B>=C ], cost: 2
4.34/2.36	
4.34/2.36	     11: evalfbb2in -> evalfbb4in : A'=1+A, [ C>=1+B ], cost: 2
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Accelerating simple loops of location 3.
4.34/2.36	
4.34/2.36	   Accelerating the following rules:
4.34/2.36	
4.34/2.36	     10: evalfbb2in -> evalfbb2in : C'=1+C, [ B>=C ], cost: 2
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	   Accelerated rule 10 with metering function 1-C+B, yielding the new rule 12.
4.34/2.36	
4.34/2.36	   Removing the simple loops: 10.
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Accelerated all simple loops using metering functions (where possible):
4.34/2.36	
4.34/2.36	   Start location: evalfstart
4.34/2.36	
4.34/2.36	      9: evalfstart -> evalfbb4in : A'=1, [], cost: 2
4.34/2.36	
4.34/2.36	      2: evalfbb4in -> evalfbb2in : C'=A, [ B>=A ], cost: 1
4.34/2.36	
4.34/2.36	     11: evalfbb2in -> evalfbb4in : A'=1+A, [ C>=1+B ], cost: 2
4.34/2.36	
4.34/2.36	     12: evalfbb2in -> evalfbb2in : C'=1+B, [ B>=C ], cost: 2-2*C+2*B
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Chained accelerated rules (with incoming rules):
4.34/2.36	
4.34/2.36	   Start location: evalfstart
4.34/2.36	
4.34/2.36	      9: evalfstart -> evalfbb4in : A'=1, [], cost: 2
4.34/2.36	
4.34/2.36	      2: evalfbb4in -> evalfbb2in : C'=A, [ B>=A ], cost: 1
4.34/2.36	
4.34/2.36	     13: evalfbb4in -> evalfbb2in : C'=1+B, [ B>=A ], cost: 3-2*A+2*B
4.34/2.36	
4.34/2.36	     11: evalfbb2in -> evalfbb4in : A'=1+A, [ C>=1+B ], cost: 2
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Eliminated locations (on tree-shaped paths):
4.34/2.36	
4.34/2.36	   Start location: evalfstart
4.34/2.36	
4.34/2.36	      9: evalfstart -> evalfbb4in : A'=1, [], cost: 2
4.34/2.36	
4.34/2.36	     14: evalfbb4in -> evalfbb4in : A'=1+A, C'=1+B, [ B>=A ], cost: 5-2*A+2*B
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Accelerating simple loops of location 2.
4.34/2.36	
4.34/2.36	   Accelerating the following rules:
4.34/2.36	
4.34/2.36	     14: evalfbb4in -> evalfbb4in : A'=1+A, C'=1+B, [ B>=A ], cost: 5-2*A+2*B
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	   Accelerated rule 14 with metering function 1-A+B, yielding the new rule 15.
4.34/2.36	
4.34/2.36	   Removing the simple loops: 14.
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Accelerated all simple loops using metering functions (where possible):
4.34/2.36	
4.34/2.36	   Start location: evalfstart
4.34/2.36	
4.34/2.36	      9: evalfstart -> evalfbb4in : A'=1, [], cost: 2
4.34/2.36	
4.34/2.36	     15: evalfbb4in -> evalfbb4in : A'=1+B, C'=1+B, [ B>=A ], cost: 6+2*(-1+A-B)*A-6*A-2*(-1+A-B)*B-(-1+A-B)^2+6*B
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Chained accelerated rules (with incoming rules):
4.34/2.36	
4.34/2.36	   Start location: evalfstart
4.34/2.36	
4.34/2.36	      9: evalfstart -> evalfbb4in : A'=1, [], cost: 2
4.34/2.36	
4.34/2.36	     16: evalfstart -> evalfbb4in : A'=1+B, C'=1+B, [ B>=1 ], cost: 2+B^2+4*B
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Removed unreachable locations (and leaf rules with constant cost):
4.34/2.36	
4.34/2.36	   Start location: evalfstart
4.34/2.36	
4.34/2.36	     16: evalfstart -> evalfbb4in : A'=1+B, C'=1+B, [ B>=1 ], cost: 2+B^2+4*B
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	### Computing asymptotic complexity ###
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Fully simplified ITS problem
4.34/2.36	
4.34/2.36	   Start location: evalfstart
4.34/2.36	
4.34/2.36	     16: evalfstart -> evalfbb4in : A'=1+B, C'=1+B, [ B>=1 ], cost: 2+B^2+4*B
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Computing asymptotic complexity for rule 16
4.34/2.36	
4.34/2.36	   Solved the limit problem by the following transformations:
4.34/2.36	
4.34/2.36	      Created initial limit problem:
4.34/2.36	
4.34/2.36	      2+B^2+4*B (+), B (+/+!) [not solved]
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	      removing all constraints (solved by SMT)
4.34/2.36	
4.34/2.36	      resulting limit problem: [solved]
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	      applying transformation rule (C) using substitution {B==n}
4.34/2.36	
4.34/2.36	      resulting limit problem:
4.34/2.36	
4.34/2.36	      [solved]
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	   Solution:
4.34/2.36	
4.34/2.36	      B / n
4.34/2.36	
4.34/2.36	   Resulting cost 2+n^2+4*n has complexity: Poly(n^2)
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Found new complexity Poly(n^2).
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	Obtained the following overall complexity (w.r.t. the length of the input n):
4.34/2.36	
4.34/2.36	   Complexity:  Poly(n^2)
4.34/2.36	
4.34/2.36	   Cpx degree:  2
4.34/2.36	
4.34/2.36	   Solved cost: 2+n^2+4*n
4.34/2.36	
4.34/2.36	   Rule cost:   2+B^2+4*B
4.34/2.36	
4.34/2.36	   Rule guard:  [ B>=1 ]
4.34/2.36	
4.34/2.36	
4.34/2.36	
4.34/2.36	WORST_CASE(Omega(n^2),?)
4.34/2.36	
4.34/2.36	
4.34/2.36	----------------------------------------
4.34/2.36	
4.34/2.36	(4)
4.34/2.36	BOUNDS(n^2, INF)
4.34/2.44	EOF