
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]
		(Comp: ?, Cost: 1)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]
		(Comp: ?, Cost: 1)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(l0) = 1
	Pol(l1) = 1
	Pol(l2) = 0
	Pol(l3) = 0
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]
		(Comp: ?, Cost: 1)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(l0) = V_4
	Pol(l1) = V_4
	Pol(l2) = V_4
	Pol(l3) = V_4
	Pol(koat_start) = V_4
orients all transitions weakly and the transition
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)       l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: Ar_3, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(l3) = V_3 - 1
	Pol(l2) = V_3
and size complexities
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]", 0-0) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]", 0-1) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]", 0-2) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]", 0-3) = Ar_3
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]", 0-0) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]", 0-1) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]", 0-2) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]", 0-3) = Ar_3
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]", 0-0) = ?
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]", 0-1) = ?
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]", 0-2) = ?
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]", 0-3) = Ar_3
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]", 0-0) = Ar_0
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]", 0-1) = Ar_1
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]", 0-2) = Ar_2 + Ar_3 + Ar_3^2
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]", 0-3) = Ar_3
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]", 0-0) = Ar_0
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]", 0-1) = Ar_1
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]", 0-2) = Ar_2 + Ar_3 + Ar_3^2
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]", 0-3) = Ar_3
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3
orients the transitions
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]
	l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]
weakly and the transition
	l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)                       l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: Ar_3, Cost: 1)                    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]
		(Comp: ?, Cost: 1)                       l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)                       l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: 1, Cost: 0)                       koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(l3) = 1
	Pol(l2) = 0
and size complexities
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2
	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]", 0-0) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]", 0-1) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]", 0-2) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]", 0-3) = Ar_3
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]", 0-0) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]", 0-1) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]", 0-2) = ?
	S("l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]", 0-3) = Ar_3
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]", 0-0) = ?
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]", 0-1) = ?
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]", 0-2) = ?
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]", 0-3) = Ar_3
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]", 0-0) = Ar_0
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]", 0-1) = Ar_1
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]", 0-2) = Ar_2 + Ar_3 + Ar_3^2
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]", 0-3) = Ar_3
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]", 0-0) = Ar_0
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]", 0-1) = Ar_1
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]", 0-2) = Ar_2 + Ar_3 + Ar_3^2
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]", 0-3) = Ar_3
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2
	S("l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3
orients the transitions
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]
weakly and the transition
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]
strictly and produces the following problem:
6:	T:
		(Comp: 1, Cost: 1)                       l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: Ar_3, Cost: 1)                    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ Ar_2 > 0 ]
		(Comp: ?, Cost: 1)                       l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: 1, Cost: 0)                       koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 6 to obtain the following invariants:
  For symbol l2: -X_4 >= 0
  For symbol l3: -X_4 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_3 - 1 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 - X_2 >= 0


This yielded the following problem:
7:	T:
		(Comp: 1, Cost: 0)                       koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)                       l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)                       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: Ar_3, Cost: 1)                    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                       l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] with all transitions in problem 7, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
We thus obtain the following problem:
8:	T:
		(Comp: 1, Cost: 1)                       koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)                       l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)                       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: Ar_3, Cost: 1)                    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                       l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
	start location:	koat_start
	leaf cost:	0

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

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

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

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

By chaining the transition l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(3*Ar_2 - 4, Ar_2 - 3, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 ] with all transitions in problem 12, the following new transition is obtained:
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(4*Ar_2 - 7, Ar_2 - 4, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 ]
We thus obtain the following problem:
13:	T:
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 5)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(4*Ar_2 - 7, Ar_2 - 4, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 ]
		(Comp: ?, Cost: 1)                       l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 > 0 ]
		(Comp: Ar_3, Cost: 1)                    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: 1, Cost: 1)                       koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

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

By chaining the transition l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(5*Ar_2 - 11, Ar_2 - 5, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 ] with all transitions in problem 14, the following new transition is obtained:
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(6*Ar_2 - 16, Ar_2 - 6, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 ]
We thus obtain the following problem:
15:	T:
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 7)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(6*Ar_2 - 16, Ar_2 - 6, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 ]
		(Comp: ?, Cost: 1)                       l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 > 0 ]
		(Comp: Ar_3, Cost: 1)                    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: 1, Cost: 1)                       koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(6*Ar_2 - 16, Ar_2 - 6, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 ] with all transitions in problem 15, the following new transition is obtained:
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(7*Ar_2 - 22, Ar_2 - 7, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 ]
We thus obtain the following problem:
16:	T:
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 8)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(7*Ar_2 - 22, Ar_2 - 7, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 ]
		(Comp: ?, Cost: 1)                       l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 > 0 ]
		(Comp: Ar_3, Cost: 1)                    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: 1, Cost: 1)                       koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(7*Ar_2 - 22, Ar_2 - 7, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 ] with all transitions in problem 16, the following new transition is obtained:
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(8*Ar_2 - 29, Ar_2 - 8, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 ]
We thus obtain the following problem:
17:	T:
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 9)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(8*Ar_2 - 29, Ar_2 - 8, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 ]
		(Comp: ?, Cost: 1)                       l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 > 0 ]
		(Comp: Ar_3, Cost: 1)                    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: 1, Cost: 1)                       koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(8*Ar_2 - 29, Ar_2 - 8, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 ] with all transitions in problem 17, the following new transition is obtained:
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(9*Ar_2 - 37, Ar_2 - 9, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 ]
We thus obtain the following problem:
18:	T:
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 10)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(9*Ar_2 - 37, Ar_2 - 9, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 ]
		(Comp: ?, Cost: 1)                        l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 > 0 ]
		(Comp: Ar_3, Cost: 1)                     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                        l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: 1, Cost: 1)                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(9*Ar_2 - 37, Ar_2 - 9, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 ] with all transitions in problem 18, the following new transition is obtained:
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(10*Ar_2 - 46, Ar_2 - 10, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 ]
We thus obtain the following problem:
19:	T:
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 11)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(10*Ar_2 - 46, Ar_2 - 10, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 ]
		(Comp: ?, Cost: 1)                        l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 > 0 ]
		(Comp: Ar_3, Cost: 1)                     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                        l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: 1, Cost: 1)                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(10*Ar_2 - 46, Ar_2 - 10, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 ] with all transitions in problem 19, the following new transition is obtained:
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(11*Ar_2 - 56, Ar_2 - 11, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 /\ 9 >= 0 /\ 9*Ar_2 - 36 >= 0 /\ 10*Ar_2 - 46 > 0 ]
We thus obtain the following problem:
20:	T:
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 12)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(11*Ar_2 - 56, Ar_2 - 11, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 /\ 9 >= 0 /\ 9*Ar_2 - 36 >= 0 /\ 10*Ar_2 - 46 > 0 ]
		(Comp: ?, Cost: 1)                        l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 > 0 ]
		(Comp: Ar_3, Cost: 1)                     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                        l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: 1, Cost: 1)                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(11*Ar_2 - 56, Ar_2 - 11, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 /\ 9 >= 0 /\ 9*Ar_2 - 36 >= 0 /\ 10*Ar_2 - 46 > 0 ] with all transitions in problem 20, the following new transition is obtained:
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(12*Ar_2 - 67, Ar_2 - 12, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 /\ 9 >= 0 /\ 9*Ar_2 - 36 >= 0 /\ 10*Ar_2 - 46 > 0 /\ 10 >= 0 /\ 10*Ar_2 - 45 >= 0 /\ 11*Ar_2 - 56 > 0 ]
We thus obtain the following problem:
21:	T:
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 13)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(12*Ar_2 - 67, Ar_2 - 12, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 /\ 9 >= 0 /\ 9*Ar_2 - 36 >= 0 /\ 10*Ar_2 - 46 > 0 /\ 10 >= 0 /\ 10*Ar_2 - 45 >= 0 /\ 11*Ar_2 - 56 > 0 ]
		(Comp: ?, Cost: 1)                        l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 > 0 ]
		(Comp: Ar_3, Cost: 1)                     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                        l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: 1, Cost: 1)                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(12*Ar_2 - 67, Ar_2 - 12, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 /\ 9 >= 0 /\ 9*Ar_2 - 36 >= 0 /\ 10*Ar_2 - 46 > 0 /\ 10 >= 0 /\ 10*Ar_2 - 45 >= 0 /\ 11*Ar_2 - 56 > 0 ] with all transitions in problem 21, the following new transition is obtained:
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(13*Ar_2 - 79, Ar_2 - 13, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 /\ 9 >= 0 /\ 9*Ar_2 - 36 >= 0 /\ 10*Ar_2 - 46 > 0 /\ 10 >= 0 /\ 10*Ar_2 - 45 >= 0 /\ 11*Ar_2 - 56 > 0 /\ 11 >= 0 /\ 11*Ar_2 - 55 >= 0 /\ 12*Ar_2 - 67 > 0 ]
We thus obtain the following problem:
22:	T:
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 14)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(13*Ar_2 - 79, Ar_2 - 13, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 /\ 9 >= 0 /\ 9*Ar_2 - 36 >= 0 /\ 10*Ar_2 - 46 > 0 /\ 10 >= 0 /\ 10*Ar_2 - 45 >= 0 /\ 11*Ar_2 - 56 > 0 /\ 11 >= 0 /\ 11*Ar_2 - 55 >= 0 /\ 12*Ar_2 - 67 > 0 ]
		(Comp: ?, Cost: 1)                        l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 > 0 ]
		(Comp: Ar_3, Cost: 1)                     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                        l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: 1, Cost: 1)                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(13*Ar_2 - 79, Ar_2 - 13, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 /\ 9 >= 0 /\ 9*Ar_2 - 36 >= 0 /\ 10*Ar_2 - 46 > 0 /\ 10 >= 0 /\ 10*Ar_2 - 45 >= 0 /\ 11*Ar_2 - 56 > 0 /\ 11 >= 0 /\ 11*Ar_2 - 55 >= 0 /\ 12*Ar_2 - 67 > 0 ] with all transitions in problem 22, the following new transition is obtained:
	l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(14*Ar_2 - 92, Ar_2 - 14, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 /\ 9 >= 0 /\ 9*Ar_2 - 36 >= 0 /\ 10*Ar_2 - 46 > 0 /\ 10 >= 0 /\ 10*Ar_2 - 45 >= 0 /\ 11*Ar_2 - 56 > 0 /\ 11 >= 0 /\ 11*Ar_2 - 55 >= 0 /\ 12*Ar_2 - 67 > 0 /\ 12 >= 0 /\ 12*Ar_2 - 66 >= 0 /\ 13*Ar_2 - 79 > 0 ]
We thus obtain the following problem:
23:	T:
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 15)    l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(14*Ar_2 - 92, Ar_2 - 14, Ar_2 - 1, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 <= 0 /\ Ar_2 - 1 > 0 /\ Ar_2 - Ar_3 - 2 >= 0 /\ Ar_2 - 2 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ Ar_2 >= 0 /\ 2*Ar_2 - 2 > 0 /\ 2 >= 0 /\ 2*Ar_2 - 1 >= 0 /\ 3*Ar_2 - 4 > 0 /\ 3 >= 0 /\ 3*Ar_2 - 3 >= 0 /\ 4*Ar_2 - 7 > 0 /\ 4 >= 0 /\ 4*Ar_2 - 6 >= 0 /\ 5*Ar_2 - 11 > 0 /\ 5 >= 0 /\ 5*Ar_2 - 10 >= 0 /\ 6*Ar_2 - 16 > 0 /\ 6 >= 0 /\ 6*Ar_2 - 15 >= 0 /\ 7*Ar_2 - 22 > 0 /\ 7 >= 0 /\ 7*Ar_2 - 21 >= 0 /\ 8*Ar_2 - 29 > 0 /\ 8 >= 0 /\ 8*Ar_2 - 28 >= 0 /\ 9*Ar_2 - 37 > 0 /\ 9 >= 0 /\ 9*Ar_2 - 36 >= 0 /\ 10*Ar_2 - 46 > 0 /\ 10 >= 0 /\ 10*Ar_2 - 45 >= 0 /\ 11*Ar_2 - 56 > 0 /\ 11 >= 0 /\ 11*Ar_2 - 55 >= 0 /\ 12*Ar_2 - 67 > 0 /\ 12 >= 0 /\ 12*Ar_2 - 66 >= 0 /\ 13*Ar_2 - 79 > 0 ]
		(Comp: ?, Cost: 1)                        l3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_0 + Ar_1, Ar_1 - 1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 > 0 ]
		(Comp: Ar_2 + Ar_3 + Ar_3^2, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l3(Ar_2, Ar_2, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 > 0 ]
		(Comp: Ar_3, Cost: 1)                     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - 1)) [ Ar_3 > 0 ]
		(Comp: 1, Cost: 1)                        l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 <= 0 ]
		(Comp: 1, Cost: 1)                        koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.881 sec (SMT: 0.721 sec)
