
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ Ar_0 < Ar_1^2 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(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)    l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ Ar_0 < Ar_1^2 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(l0) = 1
	Pol(l1) = 1
	Pol(l2) = 0
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ Ar_0 < Ar_1^2 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(l0) = V_3
	Pol(l1) = V_3
	Pol(l2) = V_3
	Pol(koat_start) = V_3
orients all transitions weakly and the transition
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)       l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ Ar_0 < Ar_1^2 ]
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 4 to obtain the following invariants:
  For symbol l1: X_1 - 1 >= 0
  For symbol l2: -X_3 >= 0


This yielded the following problem:
5:	T:
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: 1, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] with all transitions in problem 5, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
We thus obtain the following problem:
6:	T:
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: 1, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 6:
	l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
We thus obtain the following problem:
7:	T:
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ] with all transitions in problem 7, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
We thus obtain the following problem:
8:	T:
		(Comp: 1, Cost: 2)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ] with all transitions in problem 8, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(25*Ar_0 + 6*Ar_2^2, 4*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 ]
We thus obtain the following problem:
9:	T:
		(Comp: 1, Cost: 3)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(25*Ar_0 + 6*Ar_2^2, 4*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(25*Ar_0 + 6*Ar_2^2, 4*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 ] with all transitions in problem 9, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(125*Ar_0 + 31*Ar_2^2, 8*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 ]
We thus obtain the following problem:
10:	T:
		(Comp: 1, Cost: 4)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(125*Ar_0 + 31*Ar_2^2, 8*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(125*Ar_0 + 31*Ar_2^2, 8*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 ] with all transitions in problem 10, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(625*Ar_0 + 156*Ar_2^2, 16*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 ]
We thus obtain the following problem:
11:	T:
		(Comp: 1, Cost: 5)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(625*Ar_0 + 156*Ar_2^2, 16*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(625*Ar_0 + 156*Ar_2^2, 16*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 ] with all transitions in problem 11, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(3125*Ar_0 + 781*Ar_2^2, 32*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 ]
We thus obtain the following problem:
12:	T:
		(Comp: 1, Cost: 6)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(3125*Ar_0 + 781*Ar_2^2, 32*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(3125*Ar_0 + 781*Ar_2^2, 32*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 ] with all transitions in problem 12, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(15625*Ar_0 + 3906*Ar_2^2, 64*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 ]
We thus obtain the following problem:
13:	T:
		(Comp: 1, Cost: 7)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(15625*Ar_0 + 3906*Ar_2^2, 64*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(15625*Ar_0 + 3906*Ar_2^2, 64*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 ] with all transitions in problem 13, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(78125*Ar_0 + 19531*Ar_2^2, 128*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 ]
We thus obtain the following problem:
14:	T:
		(Comp: 1, Cost: 8)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(78125*Ar_0 + 19531*Ar_2^2, 128*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(78125*Ar_0 + 19531*Ar_2^2, 128*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 ] with all transitions in problem 14, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(390625*Ar_0 + 97656*Ar_2^2, 256*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 ]
We thus obtain the following problem:
15:	T:
		(Comp: 1, Cost: 9)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(390625*Ar_0 + 97656*Ar_2^2, 256*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(390625*Ar_0 + 97656*Ar_2^2, 256*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 ] with all transitions in problem 15, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(1953125*Ar_0 + 488281*Ar_2^2, 512*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 ]
We thus obtain the following problem:
16:	T:
		(Comp: 1, Cost: 10)      l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(1953125*Ar_0 + 488281*Ar_2^2, 512*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(1953125*Ar_0 + 488281*Ar_2^2, 512*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 ] with all transitions in problem 16, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(9765625*Ar_0 + 2441406*Ar_2^2, 1024*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 ]
We thus obtain the following problem:
17:	T:
		(Comp: 1, Cost: 11)      l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(9765625*Ar_0 + 2441406*Ar_2^2, 1024*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(9765625*Ar_0 + 2441406*Ar_2^2, 1024*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 ] with all transitions in problem 17, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(48828125*Ar_0 + 12207031*Ar_2^2, 2048*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 /\ 9765625*Ar_0 + 2441406*Ar_2^2 < 1048576*Ar_1^2 ]
We thus obtain the following problem:
18:	T:
		(Comp: 1, Cost: 12)      l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(48828125*Ar_0 + 12207031*Ar_2^2, 2048*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 /\ 9765625*Ar_0 + 2441406*Ar_2^2 < 1048576*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(48828125*Ar_0 + 12207031*Ar_2^2, 2048*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 /\ 9765625*Ar_0 + 2441406*Ar_2^2 < 1048576*Ar_1^2 ] with all transitions in problem 18, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(244140625*Ar_0 + 61035156*Ar_2^2, 4096*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 /\ 9765625*Ar_0 + 2441406*Ar_2^2 < 1048576*Ar_1^2 /\ 48828125*Ar_0 + 12207031*Ar_2^2 < 4194304*Ar_1^2 ]
We thus obtain the following problem:
19:	T:
		(Comp: 1, Cost: 13)      l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(244140625*Ar_0 + 61035156*Ar_2^2, 4096*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 /\ 9765625*Ar_0 + 2441406*Ar_2^2 < 1048576*Ar_1^2 /\ 48828125*Ar_0 + 12207031*Ar_2^2 < 4194304*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(244140625*Ar_0 + 61035156*Ar_2^2, 4096*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 /\ 9765625*Ar_0 + 2441406*Ar_2^2 < 1048576*Ar_1^2 /\ 48828125*Ar_0 + 12207031*Ar_2^2 < 4194304*Ar_1^2 ] with all transitions in problem 19, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(1220703125*Ar_0 + 305175781*Ar_2^2, 8192*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 /\ 9765625*Ar_0 + 2441406*Ar_2^2 < 1048576*Ar_1^2 /\ 48828125*Ar_0 + 12207031*Ar_2^2 < 4194304*Ar_1^2 /\ 244140625*Ar_0 + 61035156*Ar_2^2 < 16777216*Ar_1^2 ]
We thus obtain the following problem:
20:	T:
		(Comp: 1, Cost: 14)      l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(1220703125*Ar_0 + 305175781*Ar_2^2, 8192*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 /\ 9765625*Ar_0 + 2441406*Ar_2^2 < 1048576*Ar_1^2 /\ 48828125*Ar_0 + 12207031*Ar_2^2 < 4194304*Ar_1^2 /\ 244140625*Ar_0 + 61035156*Ar_2^2 < 16777216*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(1220703125*Ar_0 + 305175781*Ar_2^2, 8192*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 /\ 9765625*Ar_0 + 2441406*Ar_2^2 < 1048576*Ar_1^2 /\ 48828125*Ar_0 + 12207031*Ar_2^2 < 4194304*Ar_1^2 /\ 244140625*Ar_0 + 61035156*Ar_2^2 < 16777216*Ar_1^2 ] with all transitions in problem 20, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(6103515625*Ar_0 + 1525878906*Ar_2^2, 16384*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 /\ 9765625*Ar_0 + 2441406*Ar_2^2 < 1048576*Ar_1^2 /\ 48828125*Ar_0 + 12207031*Ar_2^2 < 4194304*Ar_1^2 /\ 244140625*Ar_0 + 61035156*Ar_2^2 < 16777216*Ar_1^2 /\ 1220703125*Ar_0 + 305175781*Ar_2^2 < 67108864*Ar_1^2 ]
We thus obtain the following problem:
21:	T:
		(Comp: 1, Cost: 15)      l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(6103515625*Ar_0 + 1525878906*Ar_2^2, 16384*Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 /\ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 /\ 5*Ar_0 + Ar_2^2 < 4*Ar_1^2 /\ 25*Ar_0 + 6*Ar_2^2 < 16*Ar_1^2 /\ 125*Ar_0 + 31*Ar_2^2 < 64*Ar_1^2 /\ 625*Ar_0 + 156*Ar_2^2 < 256*Ar_1^2 /\ 3125*Ar_0 + 781*Ar_2^2 < 1024*Ar_1^2 /\ 15625*Ar_0 + 3906*Ar_2^2 < 4096*Ar_1^2 /\ 78125*Ar_0 + 19531*Ar_2^2 < 16384*Ar_1^2 /\ 390625*Ar_0 + 97656*Ar_2^2 < 65536*Ar_1^2 /\ 1953125*Ar_0 + 488281*Ar_2^2 < 262144*Ar_1^2 /\ 9765625*Ar_0 + 2441406*Ar_2^2 < 1048576*Ar_1^2 /\ 48828125*Ar_0 + 12207031*Ar_2^2 < 4194304*Ar_1^2 /\ 244140625*Ar_0 + 61035156*Ar_2^2 < 16777216*Ar_1^2 /\ 1220703125*Ar_0 + 305175781*Ar_2^2 < 67108864*Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(5*Ar_0 + Ar_2^2, 2*Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.307 sec (SMT: 0.242 sec)
