
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1 - 1, Ar_2 + 1, Fresh_2, Ar_4)) [ Ar_0 >= 1 /\ Fresh_2 >= 1 ]
		(Comp: ?, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1, Ar_2, Fresh_1, Ar_4)) [ 0 >= Fresh_1 /\ Ar_0 >= 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
		(Comp: ?, Cost: 1)    f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f26(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
		(Comp: ?, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(8, Fresh_0, 0, Ar_3, 8)) [ Fresh_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 1:
	f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f26(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
We thus obtain the following problem:
2:	T:
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
		(Comp: ?, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1, Ar_2, Fresh_1, Ar_4)) [ 0 >= Fresh_1 /\ Ar_0 >= 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1 - 1, Ar_2 + 1, Fresh_2, Ar_4)) [ Ar_0 >= 1 /\ Fresh_2 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(8, Fresh_0, 0, Ar_3, 8)) [ Fresh_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
		(Comp: ?, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1, Ar_2, Fresh_1, Ar_4)) [ 0 >= Fresh_1 /\ Ar_0 >= 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1 - 1, Ar_2 + 1, Fresh_2, Ar_4)) [ Ar_0 >= 1 /\ Fresh_2 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(8, Fresh_0, 0, Ar_3, 8)) [ Fresh_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f21) = 0
	Pol(f11) = 1
	Pol(f0) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ]
strictly and produces the following problem:
4:	T:
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
		(Comp: 1, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1, Ar_2, Fresh_1, Ar_4)) [ 0 >= Fresh_1 /\ Ar_0 >= 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1 - 1, Ar_2 + 1, Fresh_2, Ar_4)) [ Ar_0 >= 1 /\ Fresh_2 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(8, Fresh_0, 0, Ar_3, 8)) [ Fresh_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f21) = V_1
	Pol(f11) = V_1
	Pol(f0) = 8
	Pol(koat_start) = 8
orients all transitions weakly and the transitions
	f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1, Ar_2, Fresh_1, Ar_4)) [ 0 >= Fresh_1 /\ Ar_0 >= 1 /\ Ar_0 >= Ar_1 + 1 ]
	f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1 - 1, Ar_2 + 1, Fresh_2, Ar_4)) [ Ar_0 >= 1 /\ Fresh_2 >= 1 ]
strictly and produces the following problem:
5:	T:
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
		(Comp: 1, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_0 ]
		(Comp: 8, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1, Ar_2, Fresh_1, Ar_4)) [ 0 >= Fresh_1 /\ Ar_0 >= 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 8, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1 - 1, Ar_2 + 1, Fresh_2, Ar_4)) [ Ar_0 >= 1 /\ Fresh_2 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(8, Fresh_0, 0, Ar_3, 8)) [ Fresh_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 5 to obtain the following invariants:
  For symbol f11: -X_5 + 8 >= 0 /\ X_3 - X_5 + 8 >= 0 /\ -X_1 - X_5 + 16 >= 0 /\ X_5 - 8 >= 0 /\ X_3 + X_5 - 8 >= 0 /\ -X_1 + X_5 >= 0 /\ -X_1 - X_3 + 8 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_1 + X_3 + 8 >= 0 /\ -X_1 + X_2 + 7 >= 0 /\ -X_1 + 8 >= 0
  For symbol f21: -X_5 + 8 >= 0 /\ X_3 - X_5 + 8 >= 0 /\ -X_1 - X_5 + 8 >= 0 /\ X_5 - 8 >= 0 /\ X_3 + X_5 - 8 >= 0 /\ -X_1 + X_5 - 8 >= 0 /\ -X_1 - X_3 + 8 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_1 + X_3 >= 0 /\ -X_1 + X_2 + 7 >= 0 /\ -X_1 >= 0


This yielded the following problem:
6:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(8, Fresh_0, 0, Ar_3, 8)) [ Fresh_0 >= 1 ]
		(Comp: 8, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1 - 1, Ar_2 + 1, Fresh_2, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ Ar_0 >= 1 /\ Fresh_2 >= 1 ]
		(Comp: 8, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1, Ar_2, Fresh_1, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ 0 >= Fresh_1 /\ Ar_0 >= 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 8 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 - 8 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] with all transitions in problem 6, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(8, Fresh_0, 0, Ar_3, 8)) [ 0 <= 0 /\ Fresh_0 >= 1 ]
We thus obtain the following problem:
7:	T:
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(8, Fresh_0, 0, Ar_3, 8)) [ 0 <= 0 /\ Fresh_0 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(8, Fresh_0, 0, Ar_3, 8)) [ Fresh_0 >= 1 ]
		(Comp: 8, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1 - 1, Ar_2 + 1, Fresh_2, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ Ar_0 >= 1 /\ Fresh_2 >= 1 ]
		(Comp: 8, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1, Ar_2, Fresh_1, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ 0 >= Fresh_1 /\ Ar_0 >= 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 8 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 - 8 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 >= 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 7:
	f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(8, Fresh_0, 0, Ar_3, 8)) [ Fresh_0 >= 1 ]
We thus obtain the following problem:
8:	T:
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 8 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 - 8 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ 0 >= Ar_0 ]
		(Comp: 8, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1, Ar_2, Fresh_1, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ 0 >= Fresh_1 /\ Ar_0 >= 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 8, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1 - 1, Ar_2 + 1, Fresh_2, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ Ar_0 >= 1 /\ Fresh_2 >= 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(8, Fresh_0, 0, Ar_3, 8)) [ 0 <= 0 /\ Fresh_0 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ 0 >= Ar_0 ] with all transitions in problem 8, the following new transition is obtained:
	f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ 0 >= Ar_0 /\ -Ar_0 - Ar_4 + 8 >= 0 /\ -Ar_0 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ -Ar_0 >= 0 ]
We thus obtain the following problem:
9:	T:
		(Comp: 1, Cost: 2)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ 0 >= Ar_0 /\ -Ar_0 - Ar_4 + 8 >= 0 /\ -Ar_0 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ -Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 8 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 - 8 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 >= 0 ]
		(Comp: 8, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1, Ar_2, Fresh_1, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ 0 >= Fresh_1 /\ Ar_0 >= 1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 8, Cost: 1)    f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(Ar_0 - 1, Ar_1 - 1, Ar_2 + 1, Fresh_2, Ar_4)) [ -Ar_4 + 8 >= 0 /\ Ar_2 - Ar_4 + 8 >= 0 /\ -Ar_0 - Ar_4 + 16 >= 0 /\ Ar_4 - 8 >= 0 /\ Ar_2 + Ar_4 - 8 >= 0 /\ -Ar_0 + Ar_4 >= 0 /\ -Ar_0 - Ar_2 + 8 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 + 8 >= 0 /\ -Ar_0 + Ar_1 + 7 >= 0 /\ -Ar_0 + 8 >= 0 /\ Ar_0 >= 1 /\ Fresh_2 >= 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f11(8, Fresh_0, 0, Ar_3, 8)) [ 0 <= 0 /\ Fresh_0 >= 1 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.183 sec (SMT: 0.150 sec)
