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

Time: 0.071 sec (SMT: 0.065 sec)
