
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, Ar_2, Ar_3 - 1)) [ Ar_3 > 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, Ar_2, Ar_3 - 1)) [ Ar_3 > 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, Ar_2, Ar_3 - 1)) [ Ar_3 > 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, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) with all transitions in problem 4, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 0 ]
We thus obtain the following problem:
5:	T:
		(Comp: 1, Cost: 2)       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 0 ] with all transitions in problem 5, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 2)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 ]
We thus obtain the following problem:
6:	T:
		(Comp: 1, Cost: 3)       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 2)) [ Ar_3 > 0 /\ Ar_3 - 1 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 2)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 ] with all transitions in problem 6, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 3)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 ]
We thus obtain the following problem:
7:	T:
		(Comp: 1, Cost: 4)       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 3)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 3)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 ] with all transitions in problem 7, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 4)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 ]
We thus obtain the following problem:
8:	T:
		(Comp: 1, Cost: 5)       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 4)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 4)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 ] with all transitions in problem 8, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 5)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 ]
We thus obtain the following problem:
9:	T:
		(Comp: 1, Cost: 6)       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 5)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 5)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 ] with all transitions in problem 9, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 6)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 ]
We thus obtain the following problem:
10:	T:
		(Comp: 1, Cost: 7)       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 6)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 6)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 ] with all transitions in problem 10, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 7)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 ]
We thus obtain the following problem:
11:	T:
		(Comp: 1, Cost: 8)       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 7)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 7)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 ] with all transitions in problem 11, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 8)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 ]
We thus obtain the following problem:
12:	T:
		(Comp: 1, Cost: 9)       l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 8)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 8)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 ] with all transitions in problem 12, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 9)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 ]
We thus obtain the following problem:
13:	T:
		(Comp: 1, Cost: 10)      l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 9)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 9)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 ] with all transitions in problem 13, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 10)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 ]
We thus obtain the following problem:
14:	T:
		(Comp: 1, Cost: 11)      l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 10)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 10)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 ] with all transitions in problem 14, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 11)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 ]
We thus obtain the following problem:
15:	T:
		(Comp: 1, Cost: 12)      l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 11)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 11)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 ] with all transitions in problem 15, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 12)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 /\ Ar_3 - 11 > 0 ]
We thus obtain the following problem:
16:	T:
		(Comp: 1, Cost: 13)      l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 12)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 /\ Ar_3 - 11 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 12)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 /\ Ar_3 - 11 > 0 ] with all transitions in problem 16, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 13)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 /\ Ar_3 - 11 > 0 /\ Ar_3 - 12 > 0 ]
We thus obtain the following problem:
17:	T:
		(Comp: 1, Cost: 14)      l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 13)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 /\ Ar_3 - 11 > 0 /\ Ar_3 - 12 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 13)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 /\ Ar_3 - 11 > 0 /\ Ar_3 - 12 > 0 ] with all transitions in problem 17, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 14)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 /\ Ar_3 - 11 > 0 /\ Ar_3 - 12 > 0 /\ Ar_3 - 13 > 0 ]
We thus obtain the following problem:
18:	T:
		(Comp: 1, Cost: 15)      l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 14)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 /\ Ar_3 - 11 > 0 /\ Ar_3 - 12 > 0 /\ Ar_3 - 13 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 14)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 /\ Ar_3 - 11 > 0 /\ Ar_3 - 12 > 0 /\ Ar_3 - 13 > 0 ] with all transitions in problem 18, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 15)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 /\ Ar_3 - 11 > 0 /\ Ar_3 - 12 > 0 /\ Ar_3 - 13 > 0 /\ Ar_3 - 14 > 0 ]
We thus obtain the following problem:
19:	T:
		(Comp: 1, Cost: 16)      l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 15)) [ Ar_3 > 0 /\ Ar_3 - 1 > 0 /\ Ar_3 - 2 > 0 /\ Ar_3 - 3 > 0 /\ Ar_3 - 4 > 0 /\ Ar_3 - 5 > 0 /\ Ar_3 - 6 > 0 /\ Ar_3 - 7 > 0 /\ Ar_3 - 8 > 0 /\ Ar_3 - 9 > 0 /\ Ar_3 - 10 > 0 /\ Ar_3 - 11 > 0 /\ Ar_3 - 12 > 0 /\ Ar_3 - 13 > 0 /\ Ar_3 - 14 > 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))
		(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: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) [ Ar_3 > 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 ?

Time: 0.297 sec (SMT: 0.241 sec)
