
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    evalcyclicstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 = Ar_0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ D >= 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstart(Ar_0, Ar_1, Ar_2)) [ 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)    evalcyclicstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 = Ar_0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ D >= 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(evalcyclicstart) = 2
	Pol(evalcyclicentryin) = 2
	Pol(evalcyclicbb3in) = 2
	Pol(evalcyclicreturnin) = 1
	Pol(evalcyclicbb4in) = 2
	Pol(evalcyclicbbin) = 2
	Pol(evalcyclicstop) = 0
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	evalcyclicreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2))
	evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2))
	evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 = Ar_0 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    evalcyclicstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 2, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_2 = Ar_0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ D >= 1 ]
		(Comp: 2, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: 2, Cost: 1)    evalcyclicreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 3 to obtain the following invariants:
  For symbol evalcyclicbb3in: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0
  For symbol evalcyclicbb4in: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0
  For symbol evalcyclicbbin: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0
  For symbol evalcyclicreturnin: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0


This yielded the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 2, Cost: 1)    evalcyclicreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ]
		(Comp: 2, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ D >= 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: 2, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ]
		(Comp: 1, Cost: 1)    evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    evalcyclicstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2))
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
We thus obtain the following problem:
5:	T:
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 2, Cost: 1)    evalcyclicreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ]
		(Comp: 2, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ D >= 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: 2, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ]
		(Comp: 1, Cost: 1)    evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    evalcyclicstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2))
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 5:
	evalcyclicstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2))
We thus obtain the following problem:
6:	T:
		(Comp: 2, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: 2, Cost: 1)    evalcyclicreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ D >= 1 ]
		(Comp: 2, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ] with all transitions in problem 6, the following new transition is obtained:
	evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ]
We thus obtain the following problem:
7:	T:
		(Comp: 2, Cost: 2)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: 2, Cost: 1)    evalcyclicreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ D >= 1 ]
		(Comp: 2, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] with all transitions in problem 7, the following new transition is obtained:
	evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
We thus obtain the following problem:
8:	T:
		(Comp: 2, Cost: 2)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: 2, Cost: 2)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: 2, Cost: 1)    evalcyclicreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ D >= 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 8:
	evalcyclicreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
We thus obtain the following problem:
9:	T:
		(Comp: 2, Cost: 2)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: 2, Cost: 2)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ D >= 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] with all transitions in problem 9, the following new transition is obtained:
	evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 + 1 >= Ar_0 + 1 ]
We thus obtain the following problem:
10:	T:
		(Comp: 1, Cost: 2)    evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 + 1 >= Ar_0 + 1 ]
		(Comp: 2, Cost: 2)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: 2, Cost: 2)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ D >= 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicentryin(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] with all transitions in problem 10, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 + 1 >= Ar_0 + 1 ]
We thus obtain the following problem:
11:	T:
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 + 1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 2)    evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 + 1 >= Ar_0 + 1 ]
		(Comp: 2, Cost: 2)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: 2, Cost: 2)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ D >= 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 1 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 11:
	evalcyclicentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 + 1 >= Ar_0 + 1 ]
We thus obtain the following problem:
12:	T:
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 2, Cost: 2)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: 2, Cost: 2)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ D >= 1 ]
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 + 1 >= Ar_0 + 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ] with all transitions in problem 12, the following new transitions are obtained:
	evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 /\ 0 = Ar_0 ]
	evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 /\ Ar_0 >= 1 ]
We thus obtain the following problem:
13:	T:
		(Comp: ?, Cost: 3)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 /\ 0 = Ar_0 ]
		(Comp: ?, Cost: 2)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 2, Cost: 2)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ]
		(Comp: 2, Cost: 2)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ D >= 1 ]
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 + 1 >= Ar_0 + 1 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(evalcyclicbbin) = 1
	Pol(evalcyclicstop) = 0
	Pol(evalcyclicbb4in) = 1
	Pol(evalcyclicbb3in) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 /\ 0 = Ar_0 ]
strictly and produces the following problem:
14:	T:
		(Comp: 1, Cost: 3)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 /\ 0 = Ar_0 ]
		(Comp: ?, Cost: 2)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, 0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 2, Cost: 2)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 = Ar_0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbbin(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ]
		(Comp: 2, Cost: 2)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicstop(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= D + 1 ]
		(Comp: ?, Cost: 1)    evalcyclicbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbbin(Ar_0, Ar_1, Ar_2)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ D >= 1 ]
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalcyclicbb4in(Ar_0, Ar_1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 + 1 >= Ar_0 + 1 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.227 sec (SMT: 0.184 sec)
