
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    l0(Ar_0, Ar_1) -> Com_1(l1(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1) -> Com_1(l1(2*Ar_0, 3*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(l0(Ar_0, Ar_1)) [ 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) -> Com_1(l1(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1) -> Com_1(l1(2*Ar_0, 3*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(l0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l0(Ar_0, Ar_1) -> Com_1(l1(Ar_0, Ar_1)) with all transitions in problem 2, the following new transition is obtained:
	l0(Ar_0, Ar_1) -> Com_1(l1(2*Ar_0, 3*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
We thus obtain the following problem:
3:	T:
		(Comp: 1, Cost: 2)    l0(Ar_0, Ar_1) -> Com_1(l1(2*Ar_0, 3*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1) -> Com_1(l1(2*Ar_0, 3*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(l0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l0(Ar_0, Ar_1) -> Com_1(l1(2*Ar_0, 3*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ] with all transitions in problem 3, the following new transition is obtained:
	l0(Ar_0, Ar_1) -> Com_1(l1(4*Ar_0, 9*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 /\ 12*Ar_1 >= 2*Ar_0 /\ 2*Ar_0 >= 3*Ar_1 /\ 2*Ar_0 >= 1 /\ 3*Ar_1 >= 1 ]
We thus obtain the following problem:
4:	T:
		(Comp: 1, Cost: 3)    l0(Ar_0, Ar_1) -> Com_1(l1(4*Ar_0, 9*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 /\ 12*Ar_1 >= 2*Ar_0 /\ 2*Ar_0 >= 3*Ar_1 /\ 2*Ar_0 >= 1 /\ 3*Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1) -> Com_1(l1(2*Ar_0, 3*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(l0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l0(Ar_0, Ar_1) -> Com_1(l1(4*Ar_0, 9*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 /\ 12*Ar_1 >= 2*Ar_0 /\ 2*Ar_0 >= 3*Ar_1 /\ 2*Ar_0 >= 1 /\ 3*Ar_1 >= 1 ] with all transitions in problem 4, the following new transition is obtained:
	l0(Ar_0, Ar_1) -> Com_1(l1(8*Ar_0, 27*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 /\ 12*Ar_1 >= 2*Ar_0 /\ 2*Ar_0 >= 3*Ar_1 /\ 2*Ar_0 >= 1 /\ 3*Ar_1 >= 1 /\ 36*Ar_1 >= 4*Ar_0 /\ 4*Ar_0 >= 9*Ar_1 /\ 4*Ar_0 >= 1 /\ 9*Ar_1 >= 1 ]
We thus obtain the following problem:
5:	T:
		(Comp: 1, Cost: 4)    l0(Ar_0, Ar_1) -> Com_1(l1(8*Ar_0, 27*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 /\ 12*Ar_1 >= 2*Ar_0 /\ 2*Ar_0 >= 3*Ar_1 /\ 2*Ar_0 >= 1 /\ 3*Ar_1 >= 1 /\ 36*Ar_1 >= 4*Ar_0 /\ 4*Ar_0 >= 9*Ar_1 /\ 4*Ar_0 >= 1 /\ 9*Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1) -> Com_1(l1(2*Ar_0, 3*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(l0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l0(Ar_0, Ar_1) -> Com_1(l1(8*Ar_0, 27*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 /\ 12*Ar_1 >= 2*Ar_0 /\ 2*Ar_0 >= 3*Ar_1 /\ 2*Ar_0 >= 1 /\ 3*Ar_1 >= 1 /\ 36*Ar_1 >= 4*Ar_0 /\ 4*Ar_0 >= 9*Ar_1 /\ 4*Ar_0 >= 1 /\ 9*Ar_1 >= 1 ] with all transitions in problem 5, the following new transition is obtained:
	l0(Ar_0, Ar_1) -> Com_1(l1(16*Ar_0, 81*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 /\ 12*Ar_1 >= 2*Ar_0 /\ 2*Ar_0 >= 3*Ar_1 /\ 2*Ar_0 >= 1 /\ 3*Ar_1 >= 1 /\ 36*Ar_1 >= 4*Ar_0 /\ 4*Ar_0 >= 9*Ar_1 /\ 4*Ar_0 >= 1 /\ 9*Ar_1 >= 1 /\ 108*Ar_1 >= 8*Ar_0 /\ 8*Ar_0 >= 27*Ar_1 /\ 8*Ar_0 >= 1 /\ 27*Ar_1 >= 1 ]
We thus obtain the following problem:
6:	T:
		(Comp: 1, Cost: 5)    l0(Ar_0, Ar_1) -> Com_1(l1(16*Ar_0, 81*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 /\ 12*Ar_1 >= 2*Ar_0 /\ 2*Ar_0 >= 3*Ar_1 /\ 2*Ar_0 >= 1 /\ 3*Ar_1 >= 1 /\ 36*Ar_1 >= 4*Ar_0 /\ 4*Ar_0 >= 9*Ar_1 /\ 4*Ar_0 >= 1 /\ 9*Ar_1 >= 1 /\ 108*Ar_1 >= 8*Ar_0 /\ 8*Ar_0 >= 27*Ar_1 /\ 8*Ar_0 >= 1 /\ 27*Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1) -> Com_1(l1(2*Ar_0, 3*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(l0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 6:
	l1(Ar_0, Ar_1) -> Com_1(l1(2*Ar_0, 3*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
We thus obtain the following problem:
7:	T:
		(Comp: 1, Cost: 5)    l0(Ar_0, Ar_1) -> Com_1(l1(16*Ar_0, 81*Ar_1)) [ 4*Ar_1 >= Ar_0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 /\ 12*Ar_1 >= 2*Ar_0 /\ 2*Ar_0 >= 3*Ar_1 /\ 2*Ar_0 >= 1 /\ 3*Ar_1 >= 1 /\ 36*Ar_1 >= 4*Ar_0 /\ 4*Ar_0 >= 9*Ar_1 /\ 4*Ar_0 >= 1 /\ 9*Ar_1 >= 1 /\ 108*Ar_1 >= 8*Ar_0 /\ 8*Ar_0 >= 27*Ar_1 /\ 8*Ar_0 >= 1 /\ 27*Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(l0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 5

Time: 0.181 sec (SMT: 0.167 sec)
