
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ]
		(Comp: ?, Cost: 1)    l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ]
		(Comp: ?, Cost: 1)    l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l0(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(l0) = 2
	Pol(l1) = 2
	Pol(l2) = 1
	Pol(l3) = 0
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ]
	l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_2 >= 1 ]
		(Comp: 2, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ]
		(Comp: ?, Cost: 1)    l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l0(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(l0) = V_5
	Pol(l1) = V_5
	Pol(l2) = V_5
	Pol(l3) = V_5
	Pol(koat_start) = V_5
orients all transitions weakly and the transition
	l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)       l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
		(Comp: Ar_4, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_2 >= 1 ]
		(Comp: 2, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l0(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(l3) = V_2
	Pol(l2) = V_3
and size complexities
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 1 ]", 0-0) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 1 ]", 0-1) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 1 ]", 0-2) = Ar_2 + Ar_3 + Ar_4 + 2*Ar_4^2 + Ar_3*Ar_4 + Ar_4^3
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 1 ]", 0-3) = Ar_3 + Ar_4 + Ar_4^2
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 1 ]", 0-4) = Ar_4
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ]", 0-0) = Ar_0
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ]", 0-1) = Ar_1
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ]", 0-2) = Ar_2 + Ar_3 + Ar_4 + 2*Ar_4^2 + Ar_3*Ar_4 + Ar_4^3
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ]", 0-3) = Ar_3 + Ar_4 + Ar_4^2
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ]", 0-4) = Ar_4
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_2 >= 1 ]", 0-0) = Ar_0
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_2 >= 1 ]", 0-1) = Ar_1
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_2 >= 1 ]", 0-2) = Ar_2 + Ar_3 + Ar_4 + 2*Ar_4^2 + Ar_3*Ar_4 + Ar_4^3
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_2 >= 1 ]", 0-3) = Ar_3 + Ar_4 + Ar_4^2
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_2 >= 1 ]", 0-4) = Ar_4
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]", 0-0) = Ar_0
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]", 0-1) = Ar_1
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]", 0-2) = Ar_2 + Ar_3 + Ar_4 + 2*Ar_4^2 + Ar_3*Ar_4 + Ar_4^3
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]", 0-3) = Ar_3 + Ar_4 + Ar_4^2
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]", 0-4) = Ar_4
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]", 0-0) = Ar_0
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]", 0-1) = Ar_1
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]", 0-2) = Ar_2 + Ar_3 + Ar_4 + 2*Ar_4^2 + Ar_3*Ar_4 + Ar_4^3
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]", 0-3) = Ar_3 + Ar_4 + Ar_4^2
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]", 0-4) = Ar_4
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4
orients the transitions
	l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 1 ]
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_2 >= 1 ]
weakly and the transition
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_2 >= 1 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)                                                                        l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ Ar_2 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l0(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 l2: -X_5 >= 0
  For symbol l3: -X_5 >= 0 /\ -X_3 - X_5 >= 0 /\ -X_3 >= 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(l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 1, Cost: 1)                                                                        l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
	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(l0(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(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
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(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 1, Cost: 1)                                                                        l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 7:
	l0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))
We thus obtain the following problem:
8:	T:
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 ] with all transitions in problem 8, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
We thus obtain the following problem:
9:	T:
		(Comp: 2, Cost: 2)                                                                        l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ] with all transitions in problem 9, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 2*Ar_1 - 1, Ar_1 - 2, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 ]
We thus obtain the following problem:
10:	T:
		(Comp: 2, Cost: 3)                                                                        l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 2*Ar_1 - 1, Ar_1 - 2, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 2*Ar_1 - 1, Ar_1 - 2, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 ] with all transitions in problem 10, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 3*Ar_1 - 3, Ar_1 - 3, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 ]
We thus obtain the following problem:
11:	T:
		(Comp: 2, Cost: 4)                                                                        l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 3*Ar_1 - 3, Ar_1 - 3, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 3*Ar_1 - 3, Ar_1 - 3, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 ] with all transitions in problem 11, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 4*Ar_1 - 6, Ar_1 - 4, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 ]
We thus obtain the following problem:
12:	T:
		(Comp: 2, Cost: 5)                                                                        l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 4*Ar_1 - 6, Ar_1 - 4, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 4*Ar_1 - 6, Ar_1 - 4, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 ] with all transitions in problem 12, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 5*Ar_1 - 10, Ar_1 - 5, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 ]
We thus obtain the following problem:
13:	T:
		(Comp: 2, Cost: 6)                                                                        l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 5*Ar_1 - 10, Ar_1 - 5, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 5*Ar_1 - 10, Ar_1 - 5, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 ] with all transitions in problem 13, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 6*Ar_1 - 15, Ar_1 - 6, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 ]
We thus obtain the following problem:
14:	T:
		(Comp: 2, Cost: 7)                                                                        l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 6*Ar_1 - 15, Ar_1 - 6, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 6*Ar_1 - 15, Ar_1 - 6, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 ] with all transitions in problem 14, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 7*Ar_1 - 21, Ar_1 - 7, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 ]
We thus obtain the following problem:
15:	T:
		(Comp: 2, Cost: 8)                                                                        l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 7*Ar_1 - 21, Ar_1 - 7, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 7*Ar_1 - 21, Ar_1 - 7, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 ] with all transitions in problem 15, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 8*Ar_1 - 28, Ar_1 - 8, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 ]
We thus obtain the following problem:
16:	T:
		(Comp: 2, Cost: 9)                                                                        l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 8*Ar_1 - 28, Ar_1 - 8, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 8*Ar_1 - 28, Ar_1 - 8, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 ] with all transitions in problem 16, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 9*Ar_1 - 36, Ar_1 - 9, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 ]
We thus obtain the following problem:
17:	T:
		(Comp: 2, Cost: 10)                                                                       l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 9*Ar_1 - 36, Ar_1 - 9, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 9*Ar_1 - 36, Ar_1 - 9, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 ] with all transitions in problem 17, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 10*Ar_1 - 45, Ar_1 - 10, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 ]
We thus obtain the following problem:
18:	T:
		(Comp: 2, Cost: 11)                                                                       l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 10*Ar_1 - 45, Ar_1 - 10, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 10*Ar_1 - 45, Ar_1 - 10, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 ] with all transitions in problem 18, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 11*Ar_1 - 55, Ar_1 - 11, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 /\ Ar_0 + 10*Ar_1 - 45 >= 1 ]
We thus obtain the following problem:
19:	T:
		(Comp: 2, Cost: 12)                                                                       l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 11*Ar_1 - 55, Ar_1 - 11, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 /\ Ar_0 + 10*Ar_1 - 45 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 11*Ar_1 - 55, Ar_1 - 11, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 /\ Ar_0 + 10*Ar_1 - 45 >= 1 ] with all transitions in problem 19, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 12*Ar_1 - 66, Ar_1 - 12, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 /\ Ar_0 + 10*Ar_1 - 45 >= 1 /\ Ar_0 + 11*Ar_1 - 55 >= 1 ]
We thus obtain the following problem:
20:	T:
		(Comp: 2, Cost: 13)                                                                       l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 12*Ar_1 - 66, Ar_1 - 12, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 /\ Ar_0 + 10*Ar_1 - 45 >= 1 /\ Ar_0 + 11*Ar_1 - 55 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 12*Ar_1 - 66, Ar_1 - 12, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 /\ Ar_0 + 10*Ar_1 - 45 >= 1 /\ Ar_0 + 11*Ar_1 - 55 >= 1 ] with all transitions in problem 20, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 13*Ar_1 - 78, Ar_1 - 13, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 /\ Ar_0 + 10*Ar_1 - 45 >= 1 /\ Ar_0 + 11*Ar_1 - 55 >= 1 /\ Ar_0 + 12*Ar_1 - 66 >= 1 ]
We thus obtain the following problem:
21:	T:
		(Comp: 2, Cost: 14)                                                                       l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 13*Ar_1 - 78, Ar_1 - 13, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 /\ Ar_0 + 10*Ar_1 - 45 >= 1 /\ Ar_0 + 11*Ar_1 - 55 >= 1 /\ Ar_0 + 12*Ar_1 - 66 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 13*Ar_1 - 78, Ar_1 - 13, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 /\ Ar_0 + 10*Ar_1 - 45 >= 1 /\ Ar_0 + 11*Ar_1 - 55 >= 1 /\ Ar_0 + 12*Ar_1 - 66 >= 1 ] with all transitions in problem 21, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 14*Ar_1 - 91, Ar_1 - 14, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 /\ Ar_0 + 10*Ar_1 - 45 >= 1 /\ Ar_0 + 11*Ar_1 - 55 >= 1 /\ Ar_0 + 12*Ar_1 - 66 >= 1 /\ Ar_0 + 13*Ar_1 - 78 >= 1 ]
We thus obtain the following problem:
22:	T:
		(Comp: 2, Cost: 15)                                                                       l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + 14*Ar_1 - 91, Ar_1 - 14, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 < 1 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - 1 >= 1 /\ Ar_0 + 3*Ar_1 - 3 >= 1 /\ Ar_0 + 4*Ar_1 - 6 >= 1 /\ Ar_0 + 5*Ar_1 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15 >= 1 /\ Ar_0 + 7*Ar_1 - 21 >= 1 /\ Ar_0 + 8*Ar_1 - 28 >= 1 /\ Ar_0 + 9*Ar_1 - 36 >= 1 /\ Ar_0 + 10*Ar_1 - 45 >= 1 /\ Ar_0 + 11*Ar_1 - 55 >= 1 /\ Ar_0 + 12*Ar_1 - 66 >= 1 /\ Ar_0 + 13*Ar_1 - 78 >= 1 ]
		(Comp: ?, Cost: 1)                                                                        l3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ -Ar_2 - Ar_4 >= 0 /\ -Ar_2 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2*Ar_1 + 2*Ar_2 + 2*Ar_3 + 2*Ar_4 + 4*Ar_4^2 + 2*Ar_3*Ar_4 + 2*Ar_4^3, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_2 >= 1 ]
		(Comp: Ar_4, Cost: 1)                                                                     l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 + Ar_4, Ar_4 - 1)) [ Ar_4 >= 1 ]
		(Comp: 2, Cost: 1)                                                                        l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 < 1 ]
		(Comp: 1, Cost: 1)                                                                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.801 sec (SMT: 0.694 sec)
