/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 124 ms]
(2) BOUNDS(1, n^1)
(3) Loat Proof [FINISHED, 543 ms]
(4) BOUNDS(n^1, INF)


----------------------------------------

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
evalwisestart(A, B) -> Com_1(evalwiseentryin(A, B)) :|: TRUE
evalwiseentryin(A, B) -> Com_1(evalwisereturnin(A, B)) :|: 0 >= A + 1
evalwiseentryin(A, B) -> Com_1(evalwisereturnin(A, B)) :|: 0 >= B + 1
evalwiseentryin(A, B) -> Com_1(evalwisebb6in(B, A)) :|: A >= 0 && B >= 0
evalwisebb6in(A, B) -> Com_1(evalwisebb3in(A, B)) :|: B >= A + 3
evalwisebb6in(A, B) -> Com_1(evalwisebb3in(A, B)) :|: A >= B + 3
evalwisebb6in(A, B) -> Com_1(evalwisereturnin(A, B)) :|: 2 + A >= B && 2 + B >= A
evalwisebb3in(A, B) -> Com_1(evalwisebb4in(A, B)) :|: A >= B + 1
evalwisebb3in(A, B) -> Com_1(evalwisebb5in(A, B)) :|: B >= A
evalwisebb4in(A, B) -> Com_1(evalwisebb6in(A, B + 1)) :|: TRUE
evalwisebb5in(A, B) -> Com_1(evalwisebb6in(A + 1, B)) :|: TRUE
evalwisereturnin(A, B) -> Com_1(evalwisestop(A, B)) :|: TRUE

The start-symbols are:[evalwisestart_2]


----------------------------------------

(1) Koat Proof (FINISHED)
YES(?, 18*Ar_1 + 18*Ar_0 + 20)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    evalwisestart(Ar_0, Ar_1) -> Com_1(evalwiseentryin(Ar_0, Ar_1))

		(Comp: ?, Cost: 1)    evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ]

		(Comp: ?, Cost: 1)    evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_1, Ar_0)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ]

		(Comp: ?, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 3 ]

		(Comp: ?, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 3 ]

		(Comp: ?, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ Ar_0 + 2 >= Ar_1 /\ Ar_1 + 2 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb4in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]

		(Comp: ?, Cost: 1)    evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwisebb4in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0, Ar_1 + 1))

		(Comp: ?, Cost: 1)    evalwisebb5in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0 + 1, Ar_1))

		(Comp: ?, Cost: 1)    evalwisereturnin(Ar_0, Ar_1) -> Com_1(evalwisestop(Ar_0, Ar_1))

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(evalwisestart(Ar_0, Ar_1)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 1 produces the following problem:

2:	T:

		(Comp: 1, Cost: 1)    evalwisestart(Ar_0, Ar_1) -> Com_1(evalwiseentryin(Ar_0, Ar_1))

		(Comp: 1, Cost: 1)    evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]

		(Comp: 1, Cost: 1)    evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ]

		(Comp: 1, Cost: 1)    evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_1, Ar_0)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ]

		(Comp: ?, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 3 ]

		(Comp: ?, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 3 ]

		(Comp: ?, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ Ar_0 + 2 >= Ar_1 /\ Ar_1 + 2 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb4in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]

		(Comp: ?, Cost: 1)    evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwisebb4in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0, Ar_1 + 1))

		(Comp: ?, Cost: 1)    evalwisebb5in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0 + 1, Ar_1))

		(Comp: ?, Cost: 1)    evalwisereturnin(Ar_0, Ar_1) -> Com_1(evalwisestop(Ar_0, Ar_1))

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(evalwisestart(Ar_0, Ar_1)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalwisestart) = 2

	Pol(evalwiseentryin) = 2

	Pol(evalwisereturnin) = 1

	Pol(evalwisebb6in) = 2

	Pol(evalwisebb3in) = 2

	Pol(evalwisebb4in) = 2

	Pol(evalwisebb5in) = 2

	Pol(evalwisestop) = 0

	Pol(koat_start) = 2

orients all transitions weakly and the transitions

	evalwisereturnin(Ar_0, Ar_1) -> Com_1(evalwisestop(Ar_0, Ar_1))

	evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ Ar_0 + 2 >= Ar_1 /\ Ar_1 + 2 >= Ar_0 ]

strictly and produces the following problem:

3:	T:

		(Comp: 1, Cost: 1)    evalwisestart(Ar_0, Ar_1) -> Com_1(evalwiseentryin(Ar_0, Ar_1))

		(Comp: 1, Cost: 1)    evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]

		(Comp: 1, Cost: 1)    evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ]

		(Comp: 1, Cost: 1)    evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_1, Ar_0)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ]

		(Comp: ?, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 3 ]

		(Comp: ?, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 3 ]

		(Comp: 2, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ Ar_0 + 2 >= Ar_1 /\ Ar_1 + 2 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb4in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]

		(Comp: ?, Cost: 1)    evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwisebb4in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0, Ar_1 + 1))

		(Comp: ?, Cost: 1)    evalwisebb5in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0 + 1, Ar_1))

		(Comp: 2, Cost: 1)    evalwisereturnin(Ar_0, Ar_1) -> Com_1(evalwisestop(Ar_0, Ar_1))

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(evalwisestart(Ar_0, Ar_1)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Applied AI with 'oct' on problem 3 to obtain the following invariants:

  For symbol evalwisebb3in: X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 >= 0

  For symbol evalwisebb4in: X_1 - X_2 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 2 >= 0

  For symbol evalwisebb5in: X_2 - 1 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0

  For symbol evalwisebb6in: X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0





This yielded the following problem:

4:	T:

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(evalwisestart(Ar_0, Ar_1)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)    evalwisereturnin(Ar_0, Ar_1) -> Com_1(evalwisestop(Ar_0, Ar_1))

		(Comp: ?, Cost: 1)    evalwisebb5in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ]

		(Comp: ?, Cost: 1)    evalwisebb4in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0, Ar_1 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]

		(Comp: ?, Cost: 1)    evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb5in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb4in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ]

		(Comp: 2, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 + 2 >= Ar_1 /\ Ar_1 + 2 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 3 ]

		(Comp: ?, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 3 ]

		(Comp: 1, Cost: 1)    evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_1, Ar_0)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ]

		(Comp: 1, Cost: 1)    evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ]

		(Comp: 1, Cost: 1)    evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]

		(Comp: 1, Cost: 1)    evalwisestart(Ar_0, Ar_1) -> Com_1(evalwiseentryin(Ar_0, Ar_1))

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalwisebb5in) = -3*V_1 + 3*V_2 + 1

	Pol(evalwisebb6in) = -3*V_1 + 3*V_2 + 3

	Pol(evalwisebb3in) = -3*V_1 + 3*V_2 + 2

and size complexities

	S("evalwisestart(Ar_0, Ar_1) -> Com_1(evalwiseentryin(Ar_0, Ar_1))", 0-0) = Ar_0

	S("evalwisestart(Ar_0, Ar_1) -> Com_1(evalwiseentryin(Ar_0, Ar_1))", 0-1) = Ar_1

	S("evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0

	S("evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1

	S("evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0

	S("evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1

	S("evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_1, Ar_0)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-0) = Ar_1

	S("evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_1, Ar_0)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-1) = Ar_0

	S("evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 3 ]", 0-0) = ?

	S("evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 3 ]", 0-1) = Ar_0

	S("evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 3 ]", 0-0) = Ar_1

	S("evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 3 ]", 0-1) = Ar_0 + Ar_1

	S("evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 + 2 >= Ar_1 /\\ Ar_1 + 2 >= Ar_0 ]", 0-0) = ?

	S("evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 + 2 >= Ar_1 /\\ Ar_1 + 2 >= Ar_0 ]", 0-1) = Ar_0 + Ar_1

	S("evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb4in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_1

	S("evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb4in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_0 + Ar_1

	S("evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb5in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-0) = ?

	S("evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb5in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-1) = Ar_0

	S("evalwisebb4in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0, Ar_1 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-0) = Ar_1

	S("evalwisebb4in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0, Ar_1 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-1) = Ar_1

	S("evalwisebb5in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = ?

	S("evalwisebb5in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_0

	S("evalwisereturnin(Ar_0, Ar_1) -> Com_1(evalwisestop(Ar_0, Ar_1))", 0-0) = ?

	S("evalwisereturnin(Ar_0, Ar_1) -> Com_1(evalwisestop(Ar_0, Ar_1))", 0-1) = Ar_0 + Ar_1

	S("koat_start(Ar_0, Ar_1) -> Com_1(evalwisestart(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0

	S("koat_start(Ar_0, Ar_1) -> Com_1(evalwisestart(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1

orients the transitions

	evalwisebb5in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ]

	evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb5in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ]

	evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 3 ]

weakly and the transitions

	evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 3 ]

	evalwisebb5in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ]

	evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb5in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ]

strictly and produces the following problem:

5:	T:

		(Comp: 1, Cost: 0)                      koat_start(Ar_0, Ar_1) -> Com_1(evalwisestart(Ar_0, Ar_1)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)                      evalwisereturnin(Ar_0, Ar_1) -> Com_1(evalwisestop(Ar_0, Ar_1))

		(Comp: 3*Ar_1 + 3*Ar_0 + 3, Cost: 1)    evalwisebb5in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ]

		(Comp: ?, Cost: 1)                      evalwisebb4in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0, Ar_1 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]

		(Comp: 3*Ar_1 + 3*Ar_0 + 3, Cost: 1)    evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb5in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ]

		(Comp: ?, Cost: 1)                      evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb4in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ]

		(Comp: 2, Cost: 1)                      evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 + 2 >= Ar_1 /\ Ar_1 + 2 >= Ar_0 ]

		(Comp: ?, Cost: 1)                      evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 3 ]

		(Comp: 3*Ar_1 + 3*Ar_0 + 3, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 3 ]

		(Comp: 1, Cost: 1)                      evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_1, Ar_0)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ]

		(Comp: 1, Cost: 1)                      evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ]

		(Comp: 1, Cost: 1)                      evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]

		(Comp: 1, Cost: 1)                      evalwisestart(Ar_0, Ar_1) -> Com_1(evalwiseentryin(Ar_0, Ar_1))

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalwisebb6in) = 3*V_1 - 3*V_2 + 1

	Pol(evalwisebb3in) = 3*V_1 - 3*V_2

	Pol(evalwisebb4in) = 3*V_1 - 3*V_2 - 1

and size complexities

	S("evalwisestart(Ar_0, Ar_1) -> Com_1(evalwiseentryin(Ar_0, Ar_1))", 0-0) = Ar_0

	S("evalwisestart(Ar_0, Ar_1) -> Com_1(evalwiseentryin(Ar_0, Ar_1))", 0-1) = Ar_1

	S("evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0

	S("evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1

	S("evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0

	S("evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1

	S("evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_1, Ar_0)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-0) = Ar_1

	S("evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_1, Ar_0)) [ Ar_0 >= 0 /\\ Ar_1 >= 0 ]", 0-1) = Ar_0

	S("evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 3 ]", 0-0) = 4*Ar_0 + 4*Ar_1 + 48

	S("evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 3 ]", 0-1) = Ar_0

	S("evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 3 ]", 0-0) = Ar_1

	S("evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 3 ]", 0-1) = Ar_0 + Ar_1

	S("evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 + 2 >= Ar_1 /\\ Ar_1 + 2 >= Ar_0 ]", 0-0) = 4*Ar_0 + 4*Ar_1 + 192

	S("evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 + 2 >= Ar_1 /\\ Ar_1 + 2 >= Ar_0 ]", 0-1) = Ar_0 + Ar_1

	S("evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb4in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_1

	S("evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb4in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_0 + Ar_1

	S("evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb5in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-0) = 4*Ar_0 + 4*Ar_1 + 48

	S("evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb5in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-1) = Ar_0

	S("evalwisebb4in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0, Ar_1 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-0) = Ar_1

	S("evalwisebb4in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0, Ar_1 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-1) = Ar_1

	S("evalwisebb5in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = 4*Ar_0 + 4*Ar_1 + 48

	S("evalwisebb5in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_0

	S("evalwisereturnin(Ar_0, Ar_1) -> Com_1(evalwisestop(Ar_0, Ar_1))", 0-0) = 4*Ar_0 + 4*Ar_1 + 768

	S("evalwisereturnin(Ar_0, Ar_1) -> Com_1(evalwisestop(Ar_0, Ar_1))", 0-1) = Ar_0 + Ar_1

	S("koat_start(Ar_0, Ar_1) -> Com_1(evalwisestart(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0

	S("koat_start(Ar_0, Ar_1) -> Com_1(evalwisestart(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1

orients the transitions

	evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 3 ]

	evalwisebb4in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0, Ar_1 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]

	evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb4in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ]

weakly and the transitions

	evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 3 ]

	evalwisebb4in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0, Ar_1 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]

	evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb4in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ]

strictly and produces the following problem:

6:	T:

		(Comp: 1, Cost: 0)                      koat_start(Ar_0, Ar_1) -> Com_1(evalwisestart(Ar_0, Ar_1)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)                      evalwisereturnin(Ar_0, Ar_1) -> Com_1(evalwisestop(Ar_0, Ar_1))

		(Comp: 3*Ar_1 + 3*Ar_0 + 3, Cost: 1)    evalwisebb5in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0 + 1, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ]

		(Comp: 3*Ar_1 + 3*Ar_0 + 1, Cost: 1)    evalwisebb4in(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_0, Ar_1 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]

		(Comp: 3*Ar_1 + 3*Ar_0 + 3, Cost: 1)    evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb5in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 ]

		(Comp: 3*Ar_1 + 3*Ar_0 + 1, Cost: 1)    evalwisebb3in(Ar_0, Ar_1) -> Com_1(evalwisebb4in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 1 ]

		(Comp: 2, Cost: 1)                      evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 + 2 >= Ar_1 /\ Ar_1 + 2 >= Ar_0 ]

		(Comp: 3*Ar_1 + 3*Ar_0 + 1, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 + 3 ]

		(Comp: 3*Ar_1 + 3*Ar_0 + 3, Cost: 1)    evalwisebb6in(Ar_0, Ar_1) -> Com_1(evalwisebb3in(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 3 ]

		(Comp: 1, Cost: 1)                      evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisebb6in(Ar_1, Ar_0)) [ Ar_0 >= 0 /\ Ar_1 >= 0 ]

		(Comp: 1, Cost: 1)                      evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_1 + 1 ]

		(Comp: 1, Cost: 1)                      evalwiseentryin(Ar_0, Ar_1) -> Com_1(evalwisereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]

		(Comp: 1, Cost: 1)                      evalwisestart(Ar_0, Ar_1) -> Com_1(evalwiseentryin(Ar_0, Ar_1))

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 18*Ar_1 + 18*Ar_0 + 20



Time: 0.178 sec (SMT: 0.149 sec)


----------------------------------------

(2)
BOUNDS(1, n^1)

----------------------------------------

(3) Loat Proof (FINISHED)


### Pre-processing the ITS problem ###



Initial linear ITS problem

   Start location: evalwisestart

      0: evalwisestart -> evalwiseentryin : [], cost: 1

      1: evalwiseentryin -> evalwisereturnin : [ 0>=1+A ], cost: 1

      2: evalwiseentryin -> evalwisereturnin : [ 0>=1+B ], cost: 1

      3: evalwiseentryin -> evalwisebb6in : A'=B, B'=A, [ A>=0 && B>=0 ], cost: 1

      4: evalwisebb6in -> evalwisebb3in : [ B>=3+A ], cost: 1

      5: evalwisebb6in -> evalwisebb3in : [ A>=3+B ], cost: 1

      6: evalwisebb6in -> evalwisereturnin : [ 2+A>=B && 2+B>=A ], cost: 1

      7: evalwisebb3in -> evalwisebb4in : [ A>=1+B ], cost: 1

      8: evalwisebb3in -> evalwisebb5in : [ B>=A ], cost: 1

      9: evalwisebb4in -> evalwisebb6in : B'=1+B, [], cost: 1

     10: evalwisebb5in -> evalwisebb6in : A'=1+A, [], cost: 1

     11: evalwisereturnin -> evalwisestop : [], cost: 1



Checking for constant complexity:

   The following rule is satisfiable with cost >= 1, yielding constant complexity:

      0: evalwisestart -> evalwiseentryin : [], cost: 1



Removed unreachable and leaf rules:

   Start location: evalwisestart

      0: evalwisestart -> evalwiseentryin : [], cost: 1

      3: evalwiseentryin -> evalwisebb6in : A'=B, B'=A, [ A>=0 && B>=0 ], cost: 1

      4: evalwisebb6in -> evalwisebb3in : [ B>=3+A ], cost: 1

      5: evalwisebb6in -> evalwisebb3in : [ A>=3+B ], cost: 1

      7: evalwisebb3in -> evalwisebb4in : [ A>=1+B ], cost: 1

      8: evalwisebb3in -> evalwisebb5in : [ B>=A ], cost: 1

      9: evalwisebb4in -> evalwisebb6in : B'=1+B, [], cost: 1

     10: evalwisebb5in -> evalwisebb6in : A'=1+A, [], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on linear paths):

   Start location: evalwisestart

     12: evalwisestart -> evalwisebb6in : A'=B, B'=A, [ A>=0 && B>=0 ], cost: 2

      4: evalwisebb6in -> evalwisebb3in : [ B>=3+A ], cost: 1

      5: evalwisebb6in -> evalwisebb3in : [ A>=3+B ], cost: 1

     13: evalwisebb3in -> evalwisebb6in : B'=1+B, [ A>=1+B ], cost: 2

     14: evalwisebb3in -> evalwisebb6in : A'=1+A, [ B>=A ], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: evalwisestart

     12: evalwisestart -> evalwisebb6in : A'=B, B'=A, [ A>=0 && B>=0 ], cost: 2

     15: evalwisebb6in -> evalwisebb6in : A'=1+A, [ B>=3+A ], cost: 3

     16: evalwisebb6in -> evalwisebb6in : B'=1+B, [ A>=3+B ], cost: 3



Accelerating simple loops of location 2.

   Accelerating the following rules:

     15: evalwisebb6in -> evalwisebb6in : A'=1+A, [ B>=3+A ], cost: 3

     16: evalwisebb6in -> evalwisebb6in : B'=1+B, [ A>=3+B ], cost: 3



   Accelerated rule 15 with metering function -2-A+B, yielding the new rule 17.

   Accelerated rule 16 with metering function -2+A-B, yielding the new rule 18.

   Removing the simple loops: 15 16.



Accelerated all simple loops using metering functions (where possible):

   Start location: evalwisestart

     12: evalwisestart -> evalwisebb6in : A'=B, B'=A, [ A>=0 && B>=0 ], cost: 2

     17: evalwisebb6in -> evalwisebb6in : A'=-2+B, [ B>=3+A ], cost: -6-3*A+3*B

     18: evalwisebb6in -> evalwisebb6in : B'=-2+A, [ A>=3+B ], cost: -6+3*A-3*B



Chained accelerated rules (with incoming rules):

   Start location: evalwisestart

     12: evalwisestart -> evalwisebb6in : A'=B, B'=A, [ A>=0 && B>=0 ], cost: 2

     19: evalwisestart -> evalwisebb6in : A'=-2+A, B'=A, [ A>=0 && B>=0 && A>=3+B ], cost: -4+3*A-3*B

     20: evalwisestart -> evalwisebb6in : A'=B, B'=-2+B, [ A>=0 && B>=0 && B>=3+A ], cost: -4-3*A+3*B



Removed unreachable locations (and leaf rules with constant cost):

   Start location: evalwisestart

     19: evalwisestart -> evalwisebb6in : A'=-2+A, B'=A, [ A>=0 && B>=0 && A>=3+B ], cost: -4+3*A-3*B

     20: evalwisestart -> evalwisebb6in : A'=B, B'=-2+B, [ A>=0 && B>=0 && B>=3+A ], cost: -4-3*A+3*B



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalwisestart

     19: evalwisestart -> evalwisebb6in : A'=-2+A, B'=A, [ A>=0 && B>=0 && A>=3+B ], cost: -4+3*A-3*B

     20: evalwisestart -> evalwisebb6in : A'=B, B'=-2+B, [ A>=0 && B>=0 && B>=3+A ], cost: -4-3*A+3*B



Computing asymptotic complexity for rule 19

   Simplified the guard:

     19: evalwisestart -> evalwisebb6in : A'=-2+A, B'=A, [ B>=0 && A>=3+B ], cost: -4+3*A-3*B

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      1+B (+/+!), -4+3*A-3*B (+), -2+A-B (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {A==2*n,B==n}

      resulting limit problem:

      [solved]



   Solution:

      A / 2*n

      B / n

   Resulting cost -4+3*n has complexity: Poly(n^1)



Found new complexity Poly(n^1).



Obtained the following overall complexity (w.r.t. the length of the input n):

   Complexity:  Poly(n^1)

   Cpx degree:  1

   Solved cost: -4+3*n

   Rule cost:   -4+3*A-3*B

   Rule guard:  [ B>=0 && A>=3+B ]



WORST_CASE(Omega(n^1),?)


----------------------------------------

(4)
BOUNDS(n^1, INF)