
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ Ar_0 >= 2 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f3(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)    f3(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ Ar_0 >= 2 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f3(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f3(Ar_0, Ar_1)) [ 0 <= 0 ] with all transitions in problem 2, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 <= 0 ]
We thus obtain the following problem:
3:	T:
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 3:
	f3(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
We thus obtain the following problem:
4:	T:
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 <= 0 ] with all transitions in problem 4, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 ]
We thus obtain the following problem:
5:	T:
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 5:
	f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ Ar_0 >= 2 ]
We thus obtain the following problem:
6:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 ] with all transitions in problem 6, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 2, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 ]
We thus obtain the following problem:
7:	T:
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 2, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 2, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 ] with all transitions in problem 7, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 3, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 ]
We thus obtain the following problem:
8:	T:
		(Comp: 1, Cost: 4)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 3, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 3, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 ] with all transitions in problem 8, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 4, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 ]
We thus obtain the following problem:
9:	T:
		(Comp: 1, Cost: 5)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 4, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 4, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 ] with all transitions in problem 9, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 5, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 ]
We thus obtain the following problem:
10:	T:
		(Comp: 1, Cost: 6)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 5, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 5, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 ] with all transitions in problem 10, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 6, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 ]
We thus obtain the following problem:
11:	T:
		(Comp: 1, Cost: 7)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 6, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 6, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 ] with all transitions in problem 11, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 7, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 ]
We thus obtain the following problem:
12:	T:
		(Comp: 1, Cost: 8)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 7, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 7, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 ] with all transitions in problem 12, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 8, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 ]
We thus obtain the following problem:
13:	T:
		(Comp: 1, Cost: 9)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 8, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 8, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 ] with all transitions in problem 13, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 9, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 ]
We thus obtain the following problem:
14:	T:
		(Comp: 1, Cost: 10)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 9, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)     koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 9, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 ] with all transitions in problem 14, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 10, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 ]
We thus obtain the following problem:
15:	T:
		(Comp: 1, Cost: 11)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 10, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)     koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 10, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 ] with all transitions in problem 15, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 11, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 /\ 1 >= Ar_0 - 10 ]
We thus obtain the following problem:
16:	T:
		(Comp: 1, Cost: 12)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 11, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 /\ 1 >= Ar_0 - 10 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)     koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 11, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 /\ 1 >= Ar_0 - 10 ] with all transitions in problem 16, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 12, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 /\ 1 >= Ar_0 - 10 /\ 1 >= Ar_0 - 11 ]
We thus obtain the following problem:
17:	T:
		(Comp: 1, Cost: 13)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 12, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 /\ 1 >= Ar_0 - 10 /\ 1 >= Ar_0 - 11 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)     koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 12, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 /\ 1 >= Ar_0 - 10 /\ 1 >= Ar_0 - 11 ] with all transitions in problem 17, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 13, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 /\ 1 >= Ar_0 - 10 /\ 1 >= Ar_0 - 11 /\ 1 >= Ar_0 - 12 ]
We thus obtain the following problem:
18:	T:
		(Comp: 1, Cost: 14)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 13, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 /\ 1 >= Ar_0 - 10 /\ 1 >= Ar_0 - 11 /\ 1 >= Ar_0 - 12 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)     koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 13, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 /\ 1 >= Ar_0 - 10 /\ 1 >= Ar_0 - 11 /\ 1 >= Ar_0 - 12 ] with all transitions in problem 18, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 14, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 /\ 1 >= Ar_0 - 10 /\ 1 >= Ar_0 - 11 /\ 1 >= Ar_0 - 12 /\ 1 >= Ar_0 - 13 ]
We thus obtain the following problem:
19:	T:
		(Comp: 1, Cost: 15)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 14, Ar_1)) [ 0 <= 0 /\ 1 >= Ar_0 /\ 1 >= Ar_0 - 1 /\ 1 >= Ar_0 - 2 /\ 1 >= Ar_0 - 3 /\ 1 >= Ar_0 - 4 /\ 1 >= Ar_0 - 5 /\ 1 >= Ar_0 - 6 /\ 1 >= Ar_0 - 7 /\ 1 >= Ar_0 - 8 /\ 1 >= Ar_0 - 9 /\ 1 >= Ar_0 - 10 /\ 1 >= Ar_0 - 11 /\ 1 >= Ar_0 - 12 /\ 1 >= Ar_0 - 13 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 1, Cost: 2)     koat_start(Ar_0, Ar_1) -> Com_1(f300(Ar_0 - 1, Fresh_0)) [ 0 <= 0 /\ Ar_0 >= 2 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.112 sec (SMT: 0.094 sec)
