WORST_CASE(?, O(n^2))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1))
		(Comp: ?, Cost: 1)    evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1))
		(Comp: ?, Cost: 1)    evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(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)    evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)    evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1))
		(Comp: ?, Cost: 1)    evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1))
		(Comp: ?, Cost: 1)    evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(evalloopsstart) = 2
	Pol(evalloopsentryin) = 2
	Pol(evalloopsbb6in) = 2
	Pol(evalloopsreturnin) = 1
	Pol(evalloopsbb1in) = 2
	Pol(evalloopsbb4in) = 2
	Pol(evalloopsbb5in) = 2
	Pol(evalloopsbb3in) = 2
	Pol(evalloopsstop) = 0
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1))
	evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)    evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 2, Cost: 1)    evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1))
		(Comp: ?, Cost: 1)    evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1))
		(Comp: 2, Cost: 1)    evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(evalloopsstart) = 2*V_1 + 1
	Pol(evalloopsentryin) = 2*V_1 + 1
	Pol(evalloopsbb6in) = 2*V_1 + 1
	Pol(evalloopsreturnin) = 2*V_1
	Pol(evalloopsbb1in) = 2*V_1 - 1
	Pol(evalloopsbb4in) = 2*V_1 - 1
	Pol(evalloopsbb5in) = 2*V_1 - 1
	Pol(evalloopsbb3in) = 2*V_1 - 1
	Pol(evalloopsstop) = 2*V_1
	Pol(koat_start) = 2*V_1 + 1
orients all transitions weakly and the transition
	evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)             evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)             evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)    evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 2, Cost: 1)             evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)             evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)             evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)             evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)             evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)             evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1))
		(Comp: ?, Cost: 1)             evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1))
		(Comp: 2, Cost: 1)             evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)             koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 4 produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)             evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)             evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)    evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 2, Cost: 1)             evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)    evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 2 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)    evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)             evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)             evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)             evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1))
		(Comp: ?, Cost: 1)             evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1))
		(Comp: 2, Cost: 1)             evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)             koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(evalloopsbb5in) = 1
	Pol(evalloopsbb6in) = 0
	Pol(evalloopsbb4in) = 2
	Pol(evalloopsbb3in) = 2
and size complexities
	S("koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1))", 0-0) = ?
	S("evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1))", 0-1) = ?
	S("evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1))", 0-0) = ?
	S("evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1))", 0-1) = ?
	S("evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1))", 0-0) = ?
	S("evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1))", 0-1) = ?
	S("evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]", 0-0) = ?
	S("evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]", 0-1) = ?
	S("evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = ?
	S("evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = ?
	S("evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ 1 >= Ar_0 ]", 0-0) = ?
	S("evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ 1 >= Ar_0 ]", 0-1) = ?
	S("evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 2 ]", 0-0) = ?
	S("evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 2 ]", 0-1) = 1
	S("evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-0) = ?
	S("evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-1) = ?
	S("evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]", 0-0) = ?
	S("evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]", 0-1) = ?
	S("evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0
	S("evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1
	S("evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]", 0-0) = Ar_0
	S("evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]", 0-1) = Ar_1
	S("evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))", 0-0) = Ar_0
	S("evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))", 0-1) = Ar_1
orients the transitions
	evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1))
	evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
	evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
	evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1))
weakly and the transitions
	evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1))
	evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
strictly and produces the following problem:
6:	T:
		(Comp: 1, Cost: 1)             evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)             evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)    evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 2, Cost: 1)             evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)    evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 2 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)    evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)             evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: 6*Ar_0 + 3, Cost: 1)    evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)             evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1))
		(Comp: 6*Ar_0 + 3, Cost: 1)    evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1))
		(Comp: 2, Cost: 1)             evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)             koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 6 to obtain the following invariants:
  For symbol evalloopsbb1in: X_1 >= 0
  For symbol evalloopsbb3in: X_1 - X_2 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 2 >= 0
  For symbol evalloopsbb4in: X_2 - 1 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 2 >= 0
  For symbol evalloopsbb5in: X_1 >= 0
  For symbol evalloopsreturnin: -X_1 - 1 >= 0


This yielded the following problem:
7:	T:
		(Comp: 1, Cost: 0)             koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 2, Cost: 1)             evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1)) [ -Ar_0 - 1 >= 0 ]
		(Comp: 6*Ar_0 + 3, Cost: 1)    evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)             evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]
		(Comp: 6*Ar_0 + 3, Cost: 1)    evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)             evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)    evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ Ar_0 >= 0 /\ 1 >= Ar_0 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)    evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 0 /\ Ar_0 >= 2 ]
		(Comp: 2, Cost: 1)             evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)    evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)             evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)             evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)             evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(evalloopsbb4in) = 6*V_1 - 6*V_2 - 5
	Pol(evalloopsbb3in) = 6*V_1 - 12*V_2 - 3
and size complexities
	S("evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))", 0-0) = Ar_0
	S("evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))", 0-1) = Ar_1
	S("evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]", 0-0) = Ar_0
	S("evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]", 0-1) = Ar_1
	S("evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0
	S("evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1
	S("evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]", 0-0) = Ar_0 + 2
	S("evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]", 0-1) = ?
	S("evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-0) = Ar_0 + 2
	S("evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-1) = ?
	S("evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 0 /\\ Ar_0 >= 2 ]", 0-0) = Ar_0 + 2
	S("evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 0 /\\ Ar_0 >= 2 ]", 0-1) = 1
	S("evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ Ar_0 >= 0 /\\ 1 >= Ar_0 ]", 0-0) = 1
	S("evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ Ar_0 >= 0 /\\ 1 >= Ar_0 ]", 0-1) = ?
	S("evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_0 + 2
	S("evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-1) = ?
	S("evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-0) = Ar_0 + 2
	S("evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-1) = ?
	S("evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-0) = Ar_0 + 2
	S("evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-1) = ?
	S("evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1)) [ Ar_0 >= 0 ]", 0-0) = Ar_0 + 2
	S("evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1)) [ Ar_0 >= 0 ]", 0-1) = ?
	S("evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1)) [ -Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 + 2
	S("evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1)) [ -Ar_0 - 1 >= 0 ]", 0-1) = ?
	S("koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
orients the transitions
	evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_0 >= Ar_1 + 1 ]
	evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]
weakly and the transition
	evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_0 >= Ar_1 + 1 ]
strictly and produces the following problem:
8:	T:
		(Comp: 1, Cost: 0)                           koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 2, Cost: 1)                           evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1)) [ -Ar_0 - 1 >= 0 ]
		(Comp: 6*Ar_0 + 3, Cost: 1)                  evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)                           evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]
		(Comp: 6*Ar_0 + 3, Cost: 1)                  evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_1 >= Ar_0 ]
		(Comp: 12*Ar_0^2 + 52*Ar_0 + 23, Cost: 1)    evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)                  evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ Ar_0 >= 0 /\ 1 >= Ar_0 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)                  evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 0 /\ Ar_0 >= 2 ]
		(Comp: 2, Cost: 1)                           evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)                  evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)                           evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)                           evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)                           evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 8 produces the following problem:
9:	T:
		(Comp: 1, Cost: 0)                           koat_start(Ar_0, Ar_1) -> Com_1(evalloopsstart(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 2, Cost: 1)                           evalloopsreturnin(Ar_0, Ar_1) -> Com_1(evalloopsstop(Ar_0, Ar_1)) [ -Ar_0 - 1 >= 0 ]
		(Comp: 6*Ar_0 + 3, Cost: 1)                  evalloopsbb5in(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0 - 1, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 12*Ar_0^2 + 52*Ar_0 + 23, Cost: 1)    evalloopsbb3in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 2*Ar_1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ]
		(Comp: 6*Ar_0 + 3, Cost: 1)                  evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_1 >= Ar_0 ]
		(Comp: 12*Ar_0^2 + 52*Ar_0 + 23, Cost: 1)    evalloopsbb4in(Ar_0, Ar_1) -> Com_1(evalloopsbb3in(Ar_0, Ar_1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)                  evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb5in(Ar_0, Fresh_0)) [ Ar_0 >= 0 /\ 1 >= Ar_0 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)                  evalloopsbb1in(Ar_0, Ar_1) -> Com_1(evalloopsbb4in(Ar_0, 1)) [ Ar_0 >= 0 /\ Ar_0 >= 2 ]
		(Comp: 2, Cost: 1)                           evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: 2*Ar_0 + 1, Cost: 1)                  evalloopsbb6in(Ar_0, Ar_1) -> Com_1(evalloopsbb1in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)                           evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsreturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)                           evalloopsentryin(Ar_0, Ar_1) -> Com_1(evalloopsbb6in(Ar_0, Ar_1)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)                           evalloopsstart(Ar_0, Ar_1) -> Com_1(evalloopsentryin(Ar_0, Ar_1))
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 122*Ar_0 + 24*Ar_0^2 + 62

Time: 2.393 sec (SMT: 2.323 sec)