
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 - 1, 3*Ar_1 + 2*Ar_2, -5*Ar_1 - 3*Ar_2, Ar_0^2 + Ar_3)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3)) [ Ar_1 + Ar_2 > 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 - 1, 3*Ar_1 + 2*Ar_2, -5*Ar_1 - 3*Ar_2, Ar_0^2 + Ar_3)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3)) [ Ar_1 + Ar_2 > 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(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))
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 - 1, 3*Ar_1 + 2*Ar_2, -5*Ar_1 - 3*Ar_2, Ar_0^2 + Ar_3)) [ Ar_0 > 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))
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3)) [ Ar_1 + Ar_2 > 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_1
	Pol(l1) = V_1
	Pol(l2) = V_1
	Pol(koat_start) = V_1
orients all transitions weakly and the transition
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0 - 1, 3*Ar_1 + 2*Ar_2, -5*Ar_1 - 3*Ar_2, Ar_0^2 + Ar_3)) [ Ar_0 > 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_0, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0 - 1, 3*Ar_1 + 2*Ar_2, -5*Ar_1 - 3*Ar_2, Ar_0^2 + Ar_3)) [ Ar_0 > 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))
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3)) [ Ar_1 + Ar_2 > 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(l2) = V_2 + 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("l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3)) [ Ar_1 + Ar_2 > 0 ]", 0-0) = Ar_0
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3)) [ Ar_1 + Ar_2 > 0 ]", 0-1) = ?
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3)) [ Ar_1 + Ar_2 > 0 ]", 0-2) = ?
	S("l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3)) [ Ar_1 + Ar_2 > 0 ]", 0-3) = ?
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3))", 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))", 0-1) = pow(3, Ar_0) * pow(5, Ar_0) * pow(2, 2*Ar_0) * (Ar_1 + Ar_2) + Ar_1
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = pow(3, Ar_0) * pow(5, Ar_0) * pow(2, 2*Ar_0) * (Ar_1 + Ar_2) + Ar_2
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ?
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0 - 1, 3*Ar_1 + 2*Ar_2, -5*Ar_1 - 3*Ar_2, Ar_0^2 + Ar_3)) [ Ar_0 > 0 ]", 0-0) = Ar_0
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0 - 1, 3*Ar_1 + 2*Ar_2, -5*Ar_1 - 3*Ar_2, Ar_0^2 + Ar_3)) [ Ar_0 > 0 ]", 0-1) = pow(3, Ar_0) * pow(5, Ar_0) * pow(2, 2*Ar_0) * (Ar_1 + Ar_2)
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0 - 1, 3*Ar_1 + 2*Ar_2, -5*Ar_1 - 3*Ar_2, Ar_0^2 + Ar_3)) [ Ar_0 > 0 ]", 0-2) = pow(3, Ar_0) * pow(5, Ar_0) * pow(2, 2*Ar_0) * (Ar_1 + Ar_2)
	S("l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0 - 1, 3*Ar_1 + 2*Ar_2, -5*Ar_1 - 3*Ar_2, Ar_0^2 + Ar_3)) [ Ar_0 > 0 ]", 0-3) = ?
	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
	l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3)) [ Ar_1 + Ar_2 > 0 ]
weakly and the transition
	l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3)) [ Ar_1 + 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_0, Cost: 1)                                                                              l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0 - 1, 3*Ar_1 + 2*Ar_2, -5*Ar_1 - 3*Ar_2, Ar_0^2 + Ar_3)) [ Ar_0 > 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))
		(Comp: 2 * pow(3, Ar_0) * pow(5, Ar_0) * pow(2, 2*Ar_0) * (Ar_1 + Ar_2) + Ar_1 + Ar_2, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3)) [ Ar_1 + Ar_2 > 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

Complexity upper bound 2 * pow(3, Ar_0) * pow(5, Ar_0) * pow(2, 2*Ar_0) * (Ar_1 + Ar_2) + Ar_0 + Ar_1 + Ar_2 + 2

Time: 0.071 sec (SMT: 0.064 sec)
