4.57/2.26	WORST_CASE(Omega(n^2), O(n^2))
4.57/2.27	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.57/2.27	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.57/2.27	
4.57/2.27	
4.57/2.27	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
4.57/2.27	
4.57/2.27	(0) CpxIntTrs
4.57/2.27	(1) Koat Proof [FINISHED, 25 ms]
4.57/2.27	(2) BOUNDS(1, n^2)
4.57/2.27	(3) Loat Proof [FINISHED, 629 ms]
4.57/2.27	(4) BOUNDS(n^2, INF)
4.57/2.27	
4.57/2.27	
4.57/2.27	----------------------------------------
4.57/2.27	
4.57/2.27	(0)
4.57/2.27	Obligation:
4.57/2.27	Complexity Int TRS consisting of the following rules:
4.57/2.27	evalfstart(A, B, C) -> Com_1(evalfentryin(A, B, C)) :|: TRUE
4.57/2.27	evalfentryin(A, B, C) -> Com_1(evalfbb4in(0, B, C)) :|: TRUE
4.57/2.27	evalfbb4in(A, B, C) -> Com_1(evalfbb2in(A, B, 0)) :|: B >= 1 + A
4.57/2.27	evalfbb4in(A, B, C) -> Com_1(evalfreturnin(A, B, C)) :|: A >= B
4.57/2.27	evalfbb2in(A, B, C) -> Com_1(evalfbb1in(A, B, C)) :|: A >= C
4.57/2.27	evalfbb2in(A, B, C) -> Com_1(evalfbb3in(A, B, C)) :|: C >= A + 1
4.57/2.27	evalfbb1in(A, B, C) -> Com_1(evalfbb2in(A, B, C + 1)) :|: TRUE
4.57/2.27	evalfbb3in(A, B, C) -> Com_1(evalfbb4in(A + 1, B, C)) :|: TRUE
4.57/2.27	evalfreturnin(A, B, C) -> Com_1(evalfstop(A, B, C)) :|: TRUE
4.57/2.27	
4.57/2.27	The start-symbols are:[evalfstart_3]
4.57/2.27	
4.57/2.27	
4.57/2.27	----------------------------------------
4.57/2.27	
4.57/2.27	(1) Koat Proof (FINISHED)
4.57/2.27	YES(?, 27*ar_1 + 4*ar_1^2 + 29)
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Initial complexity problem:
4.57/2.27	
4.57/2.27	1:	T:
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.57/2.27	
4.57/2.27		start location:	koat_start
4.57/2.27	
4.57/2.27		leaf cost:	0
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.57/2.27	
4.57/2.27	2:	T:
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.57/2.27	
4.57/2.27		start location:	koat_start
4.57/2.27	
4.57/2.27		leaf cost:	0
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	A polynomial rank function with
4.57/2.27	
4.57/2.27		Pol(evalfstart) = 2
4.57/2.27	
4.57/2.27		Pol(evalfentryin) = 2
4.57/2.27	
4.57/2.27		Pol(evalfbb4in) = 2
4.57/2.27	
4.57/2.27		Pol(evalfbb2in) = 2
4.57/2.27	
4.57/2.27		Pol(evalfreturnin) = 1
4.57/2.27	
4.57/2.27		Pol(evalfbb1in) = 2
4.57/2.27	
4.57/2.27		Pol(evalfbb3in) = 2
4.57/2.27	
4.57/2.27		Pol(evalfstop) = 0
4.57/2.27	
4.57/2.27		Pol(koat_start) = 2
4.57/2.27	
4.57/2.27	orients all transitions weakly and the transitions
4.57/2.27	
4.57/2.27		evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27		evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]
4.57/2.27	
4.57/2.27	strictly and produces the following problem:
4.57/2.27	
4.57/2.27	3:	T:
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: 2, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 2, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.57/2.27	
4.57/2.27		start location:	koat_start
4.57/2.27	
4.57/2.27		leaf cost:	0
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	A polynomial rank function with
4.57/2.27	
4.57/2.27		Pol(evalfstart) = V_2 + 1
4.57/2.27	
4.57/2.27		Pol(evalfentryin) = V_2 + 1
4.57/2.27	
4.57/2.27		Pol(evalfbb4in) = -V_1 + V_2 + 1
4.57/2.27	
4.57/2.27		Pol(evalfbb2in) = -V_1 + V_2
4.57/2.27	
4.57/2.27		Pol(evalfreturnin) = -V_1 + V_2
4.57/2.27	
4.57/2.27		Pol(evalfbb1in) = -V_1 + V_2
4.57/2.27	
4.57/2.27		Pol(evalfbb3in) = -V_1 + V_2
4.57/2.27	
4.57/2.27		Pol(evalfstop) = -V_1 + V_2
4.57/2.27	
4.57/2.27		Pol(koat_start) = V_2 + 1
4.57/2.27	
4.57/2.27	orients all transitions weakly and the transition
4.57/2.27	
4.57/2.27		evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27	strictly and produces the following problem:
4.57/2.27	
4.57/2.27	4:	T:
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 1)           evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 1)           evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: ar_1 + 1, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: 2, Cost: 1)           evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)           evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)           evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)           evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)           evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 2, Cost: 1)           evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.57/2.27	
4.57/2.27		start location:	koat_start
4.57/2.27	
4.57/2.27		leaf cost:	0
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	A polynomial rank function with
4.57/2.27	
4.57/2.27		Pol(evalfbb3in) = 1
4.57/2.27	
4.57/2.27		Pol(evalfbb4in) = 0
4.57/2.27	
4.57/2.27		Pol(evalfbb2in) = 2
4.57/2.27	
4.57/2.27		Pol(evalfbb1in) = 2
4.57/2.27	
4.57/2.27	and size complexities
4.57/2.27	
4.57/2.27		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
4.57/2.27	
4.57/2.27		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
4.57/2.27	
4.57/2.27		S("evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))", 0-0) = ?
4.57/2.27	
4.57/2.27		S("evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))", 0-2) = ?
4.57/2.27	
4.57/2.27		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))", 0-0) = ?
4.57/2.27	
4.57/2.27		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
4.57/2.27	
4.57/2.27		S("evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = ?
4.57/2.27	
4.57/2.27		S("evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ?
4.57/2.27	
4.57/2.27		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]", 0-0) = ?
4.57/2.27	
4.57/2.27		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ?
4.57/2.27	
4.57/2.27		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]", 0-0) = ?
4.57/2.27	
4.57/2.27		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]", 0-2) = ?
4.57/2.27	
4.57/2.27		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]", 0-0) = ?
4.57/2.27	
4.57/2.27		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]", 0-2) = ?
4.57/2.27	
4.57/2.27		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]", 0-0) = ?
4.57/2.27	
4.57/2.27		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]", 0-2) = 0
4.57/2.27	
4.57/2.27		S("evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))", 0-0) = 0
4.57/2.27	
4.57/2.27		S("evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))", 0-2) = ar_2
4.57/2.27	
4.57/2.27		S("evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))", 0-0) = ar_0
4.57/2.27	
4.57/2.27		S("evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))", 0-2) = ar_2
4.57/2.27	
4.57/2.27	orients the transitions
4.57/2.27	
4.57/2.27		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.57/2.27	
4.57/2.27		evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27		evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
4.57/2.27	
4.57/2.27		evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.57/2.27	
4.57/2.27	weakly and the transitions
4.57/2.27	
4.57/2.27		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.57/2.27	
4.57/2.27		evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27	strictly and produces the following problem:
4.57/2.27	
4.57/2.27	5:	T:
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 1)             evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 1)             evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: ar_1 + 1, Cost: 1)      evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: 2, Cost: 1)             evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)             evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
4.57/2.27	
4.57/2.27			(Comp: 2*ar_1 + 2, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)             evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.57/2.27	
4.57/2.27			(Comp: 2*ar_1 + 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 2, Cost: 1)             evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.57/2.27	
4.57/2.27		start location:	koat_start
4.57/2.27	
4.57/2.27		leaf cost:	0
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	A polynomial rank function with
4.57/2.27	
4.57/2.27		Pol(evalfbb2in) = V_1 - V_3 + 1
4.57/2.27	
4.57/2.27		Pol(evalfbb1in) = V_1 - V_3
4.57/2.27	
4.57/2.27	and size complexities
4.57/2.27	
4.57/2.27		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
4.57/2.27	
4.57/2.27		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
4.57/2.27	
4.57/2.27		S("evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))", 0-0) = 2*ar_1 + 32
4.57/2.27	
4.57/2.27		S("evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))", 0-2) = ?
4.57/2.27	
4.57/2.27		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))", 0-0) = 2*ar_1 + 8
4.57/2.27	
4.57/2.27		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))", 0-2) = ?
4.57/2.27	
4.57/2.27		S("evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = 2*ar_1 + 8
4.57/2.27	
4.57/2.27		S("evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ?
4.57/2.27	
4.57/2.27		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]", 0-0) = 2*ar_1 + 8
4.57/2.27	
4.57/2.27		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ?
4.57/2.27	
4.57/2.27		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]", 0-0) = 2*ar_1 + 8
4.57/2.27	
4.57/2.27		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]", 0-2) = ?
4.57/2.27	
4.57/2.27		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]", 0-0) = 2*ar_1 + 16
4.57/2.27	
4.57/2.27		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]", 0-2) = ?
4.57/2.27	
4.57/2.27		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]", 0-0) = 2*ar_1 + 8
4.57/2.27	
4.57/2.27		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]", 0-2) = 0
4.57/2.27	
4.57/2.27		S("evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))", 0-0) = 0
4.57/2.27	
4.57/2.27		S("evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))", 0-2) = ar_2
4.57/2.27	
4.57/2.27		S("evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))", 0-0) = ar_0
4.57/2.27	
4.57/2.27		S("evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))", 0-1) = ar_1
4.57/2.27	
4.57/2.27		S("evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))", 0-2) = ar_2
4.57/2.27	
4.57/2.27	orients the transitions
4.57/2.27	
4.57/2.27		evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
4.57/2.27	
4.57/2.27		evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.57/2.27	
4.57/2.27	weakly and the transition
4.57/2.27	
4.57/2.27		evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
4.57/2.27	
4.57/2.27	strictly and produces the following problem:
4.57/2.27	
4.57/2.27	6:	T:
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 1)                         evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 1)                         evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: ar_1 + 1, Cost: 1)                  evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: 2, Cost: 1)                         evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]
4.57/2.27	
4.57/2.27			(Comp: 2*ar_1^2 + 11*ar_1 + 9, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
4.57/2.27	
4.57/2.27			(Comp: 2*ar_1 + 2, Cost: 1)                evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: ?, Cost: 1)                         evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.57/2.27	
4.57/2.27			(Comp: 2*ar_1 + 2, Cost: 1)                evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 2, Cost: 1)                         evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 0)                         koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.57/2.27	
4.57/2.27		start location:	koat_start
4.57/2.27	
4.57/2.27		leaf cost:	0
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Repeatedly propagating knowledge in problem 6 produces the following problem:
4.57/2.27	
4.57/2.27	7:	T:
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 1)                         evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 1)                         evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: ar_1 + 1, Cost: 1)                  evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, 0)) [ ar_1 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: 2, Cost: 1)                         evalfbb4in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ]
4.57/2.27	
4.57/2.27			(Comp: 2*ar_1^2 + 11*ar_1 + 9, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 ]
4.57/2.27	
4.57/2.27			(Comp: 2*ar_1 + 2, Cost: 1)                evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
4.57/2.27	
4.57/2.27			(Comp: 2*ar_1^2 + 11*ar_1 + 9, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1))
4.57/2.27	
4.57/2.27			(Comp: 2*ar_1 + 2, Cost: 1)                evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb4in(ar_0 + 1, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 2, Cost: 1)                         evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
4.57/2.27	
4.57/2.27			(Comp: 1, Cost: 0)                         koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.57/2.27	
4.57/2.27		start location:	koat_start
4.57/2.27	
4.57/2.27		leaf cost:	0
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Complexity upper bound 27*ar_1 + 4*ar_1^2 + 29
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Time: 0.090 sec (SMT: 0.079 sec)
4.57/2.27	
4.57/2.27	
4.57/2.27	----------------------------------------
4.57/2.27	
4.57/2.27	(2)
4.57/2.27	BOUNDS(1, n^2)
4.57/2.27	
4.57/2.27	----------------------------------------
4.57/2.27	
4.57/2.27	(3) Loat Proof (FINISHED)
4.57/2.27	
4.57/2.27	
4.57/2.27	### Pre-processing the ITS problem ###
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Initial linear ITS problem
4.57/2.27	
4.57/2.27	   Start location: evalfstart
4.57/2.27	
4.57/2.27	      0: evalfstart -> evalfentryin : [], cost: 1
4.57/2.27	
4.57/2.27	      1: evalfentryin -> evalfbb4in : A'=0, [], cost: 1
4.57/2.27	
4.57/2.27	      2: evalfbb4in -> evalfbb2in : C'=0, [ B>=1+A ], cost: 1
4.57/2.27	
4.57/2.27	      3: evalfbb4in -> evalfreturnin : [ A>=B ], cost: 1
4.57/2.27	
4.57/2.27	      4: evalfbb2in -> evalfbb1in : [ A>=C ], cost: 1
4.57/2.27	
4.57/2.27	      5: evalfbb2in -> evalfbb3in : [ C>=1+A ], cost: 1
4.57/2.27	
4.57/2.27	      6: evalfbb1in -> evalfbb2in : C'=1+C, [], cost: 1
4.57/2.27	
4.57/2.27	      7: evalfbb3in -> evalfbb4in : A'=1+A, [], cost: 1
4.57/2.27	
4.57/2.27	      8: evalfreturnin -> evalfstop : [], cost: 1
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Removed unreachable and leaf rules:
4.57/2.27	
4.57/2.27	   Start location: evalfstart
4.57/2.27	
4.57/2.27	      0: evalfstart -> evalfentryin : [], cost: 1
4.57/2.27	
4.57/2.27	      1: evalfentryin -> evalfbb4in : A'=0, [], cost: 1
4.57/2.27	
4.57/2.27	      2: evalfbb4in -> evalfbb2in : C'=0, [ B>=1+A ], cost: 1
4.57/2.27	
4.57/2.27	      4: evalfbb2in -> evalfbb1in : [ A>=C ], cost: 1
4.57/2.27	
4.57/2.27	      5: evalfbb2in -> evalfbb3in : [ C>=1+A ], cost: 1
4.57/2.27	
4.57/2.27	      6: evalfbb1in -> evalfbb2in : C'=1+C, [], cost: 1
4.57/2.27	
4.57/2.27	      7: evalfbb3in -> evalfbb4in : A'=1+A, [], cost: 1
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	### Simplification by acceleration and chaining ###
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Eliminated locations (on linear paths):
4.57/2.27	
4.57/2.27	   Start location: evalfstart
4.57/2.27	
4.57/2.27	      9: evalfstart -> evalfbb4in : A'=0, [], cost: 2
4.57/2.27	
4.57/2.27	      2: evalfbb4in -> evalfbb2in : C'=0, [ B>=1+A ], cost: 1
4.57/2.27	
4.57/2.27	     10: evalfbb2in -> evalfbb2in : C'=1+C, [ A>=C ], cost: 2
4.57/2.27	
4.57/2.27	     11: evalfbb2in -> evalfbb4in : A'=1+A, [ C>=1+A ], cost: 2
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Accelerating simple loops of location 3.
4.57/2.27	
4.57/2.27	   Accelerating the following rules:
4.57/2.27	
4.57/2.27	     10: evalfbb2in -> evalfbb2in : C'=1+C, [ A>=C ], cost: 2
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	   Accelerated rule 10 with metering function 1-C+A, yielding the new rule 12.
4.57/2.27	
4.57/2.27	   Removing the simple loops: 10.
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Accelerated all simple loops using metering functions (where possible):
4.57/2.27	
4.57/2.27	   Start location: evalfstart
4.57/2.27	
4.57/2.27	      9: evalfstart -> evalfbb4in : A'=0, [], cost: 2
4.57/2.27	
4.57/2.27	      2: evalfbb4in -> evalfbb2in : C'=0, [ B>=1+A ], cost: 1
4.57/2.27	
4.57/2.27	     11: evalfbb2in -> evalfbb4in : A'=1+A, [ C>=1+A ], cost: 2
4.57/2.27	
4.57/2.27	     12: evalfbb2in -> evalfbb2in : C'=1+A, [ A>=C ], cost: 2-2*C+2*A
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Chained accelerated rules (with incoming rules):
4.57/2.27	
4.57/2.27	   Start location: evalfstart
4.57/2.27	
4.57/2.27	      9: evalfstart -> evalfbb4in : A'=0, [], cost: 2
4.57/2.27	
4.57/2.27	      2: evalfbb4in -> evalfbb2in : C'=0, [ B>=1+A ], cost: 1
4.57/2.27	
4.57/2.27	     13: evalfbb4in -> evalfbb2in : C'=1+A, [ B>=1+A && A>=0 ], cost: 3+2*A
4.57/2.27	
4.57/2.27	     11: evalfbb2in -> evalfbb4in : A'=1+A, [ C>=1+A ], cost: 2
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Eliminated locations (on tree-shaped paths):
4.57/2.27	
4.57/2.27	   Start location: evalfstart
4.57/2.27	
4.57/2.27	      9: evalfstart -> evalfbb4in : A'=0, [], cost: 2
4.57/2.27	
4.57/2.27	     14: evalfbb4in -> evalfbb4in : A'=1+A, C'=0, [ B>=1+A && 0>=1+A ], cost: 3
4.57/2.27	
4.57/2.27	     15: evalfbb4in -> evalfbb4in : A'=1+A, C'=1+A, [ B>=1+A && A>=0 ], cost: 5+2*A
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Accelerating simple loops of location 2.
4.57/2.27	
4.57/2.27	   Accelerating the following rules:
4.57/2.27	
4.57/2.27	     14: evalfbb4in -> evalfbb4in : A'=1+A, C'=0, [ B>=1+A && 0>=1+A ], cost: 3
4.57/2.27	
4.57/2.27	     15: evalfbb4in -> evalfbb4in : A'=1+A, C'=1+A, [ B>=1+A && A>=0 ], cost: 5+2*A
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	   Accelerated rule 14 with backward acceleration, yielding the new rule 16.
4.57/2.27	
4.57/2.27	   Accelerated rule 14 with backward acceleration, yielding the new rule 17.
4.57/2.27	
4.57/2.27	   Accelerated rule 15 with metering function -A+B, yielding the new rule 18.
4.57/2.27	
4.57/2.27	   Removing the simple loops: 14 15.
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Accelerated all simple loops using metering functions (where possible):
4.57/2.27	
4.57/2.27	   Start location: evalfstart
4.57/2.27	
4.57/2.27	      9: evalfstart -> evalfbb4in : A'=0, [], cost: 2
4.57/2.27	
4.57/2.27	     16: evalfbb4in -> evalfbb4in : A'=B, C'=0, [ B>=1+A && 0>=1+A && 0>=B ], cost: -3*A+3*B
4.57/2.27	
4.57/2.27	     17: evalfbb4in -> evalfbb4in : A'=0, C'=0, [ B>=1+A && 0>=1+A && B>=0 ], cost: -3*A
4.57/2.27	
4.57/2.27	     18: evalfbb4in -> evalfbb4in : A'=B, C'=B, [ B>=1+A && A>=0 ], cost: (A-B)^2-4*A-2*A*(A-B)+4*B
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Chained accelerated rules (with incoming rules):
4.57/2.27	
4.57/2.27	   Start location: evalfstart
4.57/2.27	
4.57/2.27	      9: evalfstart -> evalfbb4in : A'=0, [], cost: 2
4.57/2.27	
4.57/2.27	     19: evalfstart -> evalfbb4in : A'=B, C'=B, [ B>=1 ], cost: 2+B^2+4*B
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Removed unreachable locations (and leaf rules with constant cost):
4.57/2.27	
4.57/2.27	   Start location: evalfstart
4.57/2.27	
4.57/2.27	     19: evalfstart -> evalfbb4in : A'=B, C'=B, [ B>=1 ], cost: 2+B^2+4*B
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	### Computing asymptotic complexity ###
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Fully simplified ITS problem
4.57/2.27	
4.57/2.27	   Start location: evalfstart
4.57/2.27	
4.57/2.27	     19: evalfstart -> evalfbb4in : A'=B, C'=B, [ B>=1 ], cost: 2+B^2+4*B
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Computing asymptotic complexity for rule 19
4.57/2.27	
4.57/2.27	   Solved the limit problem by the following transformations:
4.57/2.27	
4.57/2.27	      Created initial limit problem:
4.57/2.27	
4.57/2.27	      2+B^2+4*B (+), B (+/+!) [not solved]
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	      removing all constraints (solved by SMT)
4.57/2.27	
4.57/2.27	      resulting limit problem: [solved]
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	      applying transformation rule (C) using substitution {B==n}
4.57/2.27	
4.57/2.27	      resulting limit problem:
4.57/2.27	
4.57/2.27	      [solved]
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	   Solution:
4.57/2.27	
4.57/2.27	      B / n
4.57/2.27	
4.57/2.27	   Resulting cost 2+n^2+4*n has complexity: Poly(n^2)
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Found new complexity Poly(n^2).
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	Obtained the following overall complexity (w.r.t. the length of the input n):
4.57/2.27	
4.57/2.27	   Complexity:  Poly(n^2)
4.57/2.27	
4.57/2.27	   Cpx degree:  2
4.57/2.27	
4.57/2.27	   Solved cost: 2+n^2+4*n
4.57/2.27	
4.57/2.27	   Rule cost:   2+B^2+4*B
4.57/2.27	
4.57/2.27	   Rule guard:  [ B>=1 ]
4.57/2.27	
4.57/2.27	
4.57/2.27	
4.57/2.27	WORST_CASE(Omega(n^2),?)
4.57/2.27	
4.57/2.27	
4.57/2.27	----------------------------------------
4.57/2.27	
4.57/2.27	(4)
4.57/2.27	BOUNDS(n^2, INF)
4.57/2.29	EOF