
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 29 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_0 >= 30 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 19 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 1 produces the following problem:
2:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 29 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_0 >= 30 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 19 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = 1
	Pol(f300) = 1
	Pol(f1) = 0
	Pol(f3) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
strictly and produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 29 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_0 >= 30 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 19 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 3 to obtain the following invariants:
  For symbol f2: -X_2 + 19 >= 0


This yielded the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 19 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
We thus obtain the following problem:
5:	T:
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 19 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 5:
	f3(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))
We thus obtain the following problem:
6:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 19 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 ] with all transitions in problem 6, the following new transition is obtained:
	f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
We thus obtain the following problem:
7:	T:
		(Comp: ?, Cost: 2)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 19 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 7 produces the following problem:
8:	T:
		(Comp: ?, Cost: 2)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 19 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 19 >= Ar_1 ] with all transitions in problem 8, the following new transitions are obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
We thus obtain the following problem:
9:	T:
		(Comp: 1, Cost: 3)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: 1, Cost: 2)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ] with all transitions in problem 9, the following new transition is obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 2, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 ]
We thus obtain the following problem:
10:	T:
		(Comp: 1, Cost: 5)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 2, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 ]
		(Comp: 1, Cost: 2)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 2, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 ] with all transitions in problem 10, the following new transition is obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 3, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 ]
We thus obtain the following problem:
11:	T:
		(Comp: 1, Cost: 7)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 3, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 ]
		(Comp: 1, Cost: 2)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 3, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 ] with all transitions in problem 11, the following new transition is obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 4, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 ]
We thus obtain the following problem:
12:	T:
		(Comp: 1, Cost: 9)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 4, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 ]
		(Comp: 1, Cost: 2)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 4, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 ] with all transitions in problem 12, the following new transition is obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 5, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 ]
We thus obtain the following problem:
13:	T:
		(Comp: 1, Cost: 11)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 5, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 ]
		(Comp: 1, Cost: 2)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 5, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 ] with all transitions in problem 13, the following new transition is obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 6, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 ]
We thus obtain the following problem:
14:	T:
		(Comp: 1, Cost: 13)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 6, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 ]
		(Comp: 1, Cost: 2)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 6, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 ] with all transitions in problem 14, the following new transition is obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 7, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 ]
We thus obtain the following problem:
15:	T:
		(Comp: 1, Cost: 15)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 7, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 ]
		(Comp: 1, Cost: 2)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 7, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 ] with all transitions in problem 15, the following new transition is obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 8, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 ]
We thus obtain the following problem:
16:	T:
		(Comp: 1, Cost: 17)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 8, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 ]
		(Comp: 1, Cost: 2)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 8, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 ] with all transitions in problem 16, the following new transition is obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 9, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 ]
We thus obtain the following problem:
17:	T:
		(Comp: 1, Cost: 19)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 9, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 ]
		(Comp: 1, Cost: 2)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 9, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 ] with all transitions in problem 17, the following new transition is obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 10, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 /\ -Ar_1 + 28 >= 0 /\ 19 >= Ar_1 - 10 ]
We thus obtain the following problem:
18:	T:
		(Comp: 1, Cost: 21)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 10, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 /\ -Ar_1 + 28 >= 0 /\ 19 >= Ar_1 - 10 ]
		(Comp: 1, Cost: 2)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 10, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 /\ -Ar_1 + 28 >= 0 /\ 19 >= Ar_1 - 10 ] with all transitions in problem 18, the following new transition is obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 11, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 /\ -Ar_1 + 28 >= 0 /\ 19 >= Ar_1 - 10 /\ -Ar_1 + 29 >= 0 /\ 19 >= Ar_1 - 11 ]
We thus obtain the following problem:
19:	T:
		(Comp: 1, Cost: 23)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 11, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 /\ -Ar_1 + 28 >= 0 /\ 19 >= Ar_1 - 10 /\ -Ar_1 + 29 >= 0 /\ 19 >= Ar_1 - 11 ]
		(Comp: 1, Cost: 2)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 11, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 /\ -Ar_1 + 28 >= 0 /\ 19 >= Ar_1 - 10 /\ -Ar_1 + 29 >= 0 /\ 19 >= Ar_1 - 11 ] with all transitions in problem 19, the following new transition is obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 12, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 /\ -Ar_1 + 28 >= 0 /\ 19 >= Ar_1 - 10 /\ -Ar_1 + 29 >= 0 /\ 19 >= Ar_1 - 11 /\ -Ar_1 + 30 >= 0 /\ 19 >= Ar_1 - 12 ]
We thus obtain the following problem:
20:	T:
		(Comp: 1, Cost: 25)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 12, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 /\ -Ar_1 + 28 >= 0 /\ 19 >= Ar_1 - 10 /\ -Ar_1 + 29 >= 0 /\ 19 >= Ar_1 - 11 /\ -Ar_1 + 30 >= 0 /\ 19 >= Ar_1 - 12 ]
		(Comp: 1, Cost: 2)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 12, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 /\ -Ar_1 + 28 >= 0 /\ 19 >= Ar_1 - 10 /\ -Ar_1 + 29 >= 0 /\ 19 >= Ar_1 - 11 /\ -Ar_1 + 30 >= 0 /\ 19 >= Ar_1 - 12 ] with all transitions in problem 20, the following new transition is obtained:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 13, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 /\ -Ar_1 + 28 >= 0 /\ 19 >= Ar_1 - 10 /\ -Ar_1 + 29 >= 0 /\ 19 >= Ar_1 - 11 /\ -Ar_1 + 30 >= 0 /\ 19 >= Ar_1 - 12 /\ -Ar_1 + 31 >= 0 /\ 19 >= Ar_1 - 13 ]
We thus obtain the following problem:
21:	T:
		(Comp: 1, Cost: 27)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 13, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 /\ -Ar_1 + 20 >= 0 /\ 19 >= Ar_1 - 2 /\ -Ar_1 + 21 >= 0 /\ 19 >= Ar_1 - 3 /\ -Ar_1 + 22 >= 0 /\ 19 >= Ar_1 - 4 /\ -Ar_1 + 23 >= 0 /\ 19 >= Ar_1 - 5 /\ -Ar_1 + 24 >= 0 /\ 19 >= Ar_1 - 6 /\ -Ar_1 + 25 >= 0 /\ 19 >= Ar_1 - 7 /\ -Ar_1 + 26 >= 0 /\ 19 >= Ar_1 - 8 /\ -Ar_1 + 27 >= 0 /\ 19 >= Ar_1 - 9 /\ -Ar_1 + 28 >= 0 /\ 19 >= Ar_1 - 10 /\ -Ar_1 + 29 >= 0 /\ 19 >= Ar_1 - 11 /\ -Ar_1 + 30 >= 0 /\ 19 >= Ar_1 - 12 /\ -Ar_1 + 31 >= 0 /\ 19 >= Ar_1 - 13 ]
		(Comp: 1, Cost: 2)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ 19 >= Ar_1 /\ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: ?, Cost: 2)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ Ar_0 >= 30 /\ 19 >= Ar_1 - 1 ]
		(Comp: ?, Cost: 1)     f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_1 + 19 >= 0 /\ 29 >= Ar_0 ]
		(Comp: 1, Cost: 1)     f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_1 >= 20 ]
		(Comp: 1, Cost: 1)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.221 sec (SMT: 0.182 sec)
