WORST_CASE(?, O(n^1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    evalspeedpldi4start(Ar_0, Ar_1) -> Com_1(evalspeedpldi4entryin(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb2in(Ar_0, Ar_1)) [ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb4in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb3in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - 1))
		(Comp: ?, Cost: 1)    evalspeedpldi4bb4in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - Ar_0))
		(Comp: ?, Cost: 1)    evalspeedpldi4returnin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(evalspeedpldi4start(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)    evalspeedpldi4start(Ar_0, Ar_1) -> Com_1(evalspeedpldi4entryin(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)    evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ]
		(Comp: 1, Cost: 1)    evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb2in(Ar_0, Ar_1)) [ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb4in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb3in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - 1))
		(Comp: ?, Cost: 1)    evalspeedpldi4bb4in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - Ar_0))
		(Comp: ?, Cost: 1)    evalspeedpldi4returnin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(evalspeedpldi4start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(evalspeedpldi4start) = 2
	Pol(evalspeedpldi4entryin) = 2
	Pol(evalspeedpldi4returnin) = 1
	Pol(evalspeedpldi4bb5in) = 2
	Pol(evalspeedpldi4bb2in) = 2
	Pol(evalspeedpldi4bb3in) = 2
	Pol(evalspeedpldi4bb4in) = 2
	Pol(evalspeedpldi4stop) = 0
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	evalspeedpldi4returnin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4stop(Ar_0, Ar_1))
	evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ 0 >= Ar_1 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    evalspeedpldi4start(Ar_0, Ar_1) -> Com_1(evalspeedpldi4entryin(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)    evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ]
		(Comp: 1, Cost: 1)    evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb2in(Ar_0, Ar_1)) [ Ar_1 >= 1 ]
		(Comp: 2, Cost: 1)    evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb4in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb3in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - 1))
		(Comp: ?, Cost: 1)    evalspeedpldi4bb4in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - Ar_0))
		(Comp: 2, Cost: 1)    evalspeedpldi4returnin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(evalspeedpldi4start(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 evalspeedpldi4bb2in: X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
  For symbol evalspeedpldi4bb3in: X_1 - X_2 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 2 >= 0
  For symbol evalspeedpldi4bb4in: X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0
  For symbol evalspeedpldi4bb5in: X_1 - 1 >= 0


This yielded the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(evalspeedpldi4start(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 2, Cost: 1)    evalspeedpldi4returnin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4stop(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    evalspeedpldi4bb4in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - Ar_0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb3in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb4in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb3in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 2, Cost: 1)    evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb2in(Ar_0, Ar_1)) [ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ]
		(Comp: 1, Cost: 1)    evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)    evalspeedpldi4start(Ar_0, Ar_1) -> Com_1(evalspeedpldi4entryin(Ar_0, Ar_1))
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(koat_start) = 3*V_2
	Pol(evalspeedpldi4start) = 3*V_2
	Pol(evalspeedpldi4returnin) = 3*V_2
	Pol(evalspeedpldi4stop) = 3*V_2
	Pol(evalspeedpldi4bb4in) = 3*V_2 - 2
	Pol(evalspeedpldi4bb5in) = 3*V_2
	Pol(evalspeedpldi4bb3in) = 3*V_2 - 2
	Pol(evalspeedpldi4bb2in) = 3*V_2 - 1
	Pol(evalspeedpldi4entryin) = 3*V_2
orients all transitions weakly and the transitions
	evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb2in(Ar_0, Ar_1)) [ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ]
	evalspeedpldi4bb4in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - Ar_0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ]
	evalspeedpldi4bb3in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]
	evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb3in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 0)         koat_start(Ar_0, Ar_1) -> Com_1(evalspeedpldi4start(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 2, Cost: 1)         evalspeedpldi4returnin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4stop(Ar_0, Ar_1))
		(Comp: 3*Ar_1, Cost: 1)    evalspeedpldi4bb4in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - Ar_0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ]
		(Comp: 3*Ar_1, Cost: 1)    evalspeedpldi4bb3in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]
		(Comp: ?, Cost: 1)         evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb4in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_0 ]
		(Comp: 3*Ar_1, Cost: 1)    evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb3in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 2, Cost: 1)         evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_1 ]
		(Comp: 3*Ar_1, Cost: 1)    evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb2in(Ar_0, Ar_1)) [ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)         evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)         evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ]
		(Comp: 1, Cost: 1)         evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)         evalspeedpldi4start(Ar_0, Ar_1) -> Com_1(evalspeedpldi4entryin(Ar_0, Ar_1))
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 5 produces the following problem:
6:	T:
		(Comp: 1, Cost: 0)         koat_start(Ar_0, Ar_1) -> Com_1(evalspeedpldi4start(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 2, Cost: 1)         evalspeedpldi4returnin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4stop(Ar_0, Ar_1))
		(Comp: 3*Ar_1, Cost: 1)    evalspeedpldi4bb4in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - Ar_0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ]
		(Comp: 3*Ar_1, Cost: 1)    evalspeedpldi4bb3in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1 - 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]
		(Comp: 3*Ar_1, Cost: 1)    evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb4in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_0 ]
		(Comp: 3*Ar_1, Cost: 1)    evalspeedpldi4bb2in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb3in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 2, Cost: 1)         evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ Ar_0 - 1 >= 0 /\ 0 >= Ar_1 ]
		(Comp: 3*Ar_1, Cost: 1)    evalspeedpldi4bb5in(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb2in(Ar_0, Ar_1)) [ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)         evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4bb5in(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)         evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 ]
		(Comp: 1, Cost: 1)         evalspeedpldi4entryin(Ar_0, Ar_1) -> Com_1(evalspeedpldi4returnin(Ar_0, Ar_1)) [ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)         evalspeedpldi4start(Ar_0, Ar_1) -> Com_1(evalspeedpldi4entryin(Ar_0, Ar_1))
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 15*Ar_1 + 8

Time: 1.778 sec (SMT: 1.729 sec)