MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f3(a, b) -> f1(a, b)
		(?, 1)    f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
		(?, 1)    f1(a, b) -> f300(a, c) [ 0 >= a + 1 ]
	start location:	f3
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem:
2:	T:
		(1, 1)    f3(a, b) -> f1(a, b)
		(?, 1)    f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a, b) with all transitions in problem 2, the following new transition is obtained:
	f3(a, b) -> f1(a + 1, b) [ a >= 0 ]
We thus obtain the following problem:
3:	T:
		(1, 2)    f3(a, b) -> f1(a + 1, b) [ a >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 1, b) [ a >= 0 ] with all transitions in problem 3, the following new transition is obtained:
	f3(a, b) -> f1(a + 2, b) [ a >= 0 /\ a + 1 >= 0 ]
We thus obtain the following problem:
4:	T:
		(1, 3)    f3(a, b) -> f1(a + 2, b) [ a >= 0 /\ a + 1 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 2, b) [ a >= 0 /\ a + 1 >= 0 ] with all transitions in problem 4, the following new transition is obtained:
	f3(a, b) -> f1(a + 3, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 ]
We thus obtain the following problem:
5:	T:
		(1, 4)    f3(a, b) -> f1(a + 3, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 3, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 ] with all transitions in problem 5, the following new transition is obtained:
	f3(a, b) -> f1(a + 4, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 ]
We thus obtain the following problem:
6:	T:
		(1, 5)    f3(a, b) -> f1(a + 4, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 4, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 ] with all transitions in problem 6, the following new transition is obtained:
	f3(a, b) -> f1(a + 5, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 ]
We thus obtain the following problem:
7:	T:
		(1, 6)    f3(a, b) -> f1(a + 5, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 5, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 ] with all transitions in problem 7, the following new transition is obtained:
	f3(a, b) -> f1(a + 6, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 ]
We thus obtain the following problem:
8:	T:
		(1, 7)    f3(a, b) -> f1(a + 6, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 6, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 ] with all transitions in problem 8, the following new transition is obtained:
	f3(a, b) -> f1(a + 7, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 ]
We thus obtain the following problem:
9:	T:
		(1, 8)    f3(a, b) -> f1(a + 7, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 7, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 ] with all transitions in problem 9, the following new transition is obtained:
	f3(a, b) -> f1(a + 8, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 ]
We thus obtain the following problem:
10:	T:
		(1, 9)    f3(a, b) -> f1(a + 8, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 8, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 ] with all transitions in problem 10, the following new transition is obtained:
	f3(a, b) -> f1(a + 9, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 ]
We thus obtain the following problem:
11:	T:
		(1, 10)    f3(a, b) -> f1(a + 9, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 9, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 ] with all transitions in problem 11, the following new transition is obtained:
	f3(a, b) -> f1(a + 10, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 ]
We thus obtain the following problem:
12:	T:
		(1, 11)    f3(a, b) -> f1(a + 10, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 10, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 ] with all transitions in problem 12, the following new transition is obtained:
	f3(a, b) -> f1(a + 11, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 ]
We thus obtain the following problem:
13:	T:
		(1, 12)    f3(a, b) -> f1(a + 11, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 11, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 ] with all transitions in problem 13, the following new transition is obtained:
	f3(a, b) -> f1(a + 12, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 /\ a + 11 >= 0 ]
We thus obtain the following problem:
14:	T:
		(1, 13)    f3(a, b) -> f1(a + 12, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 /\ a + 11 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 12, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 /\ a + 11 >= 0 ] with all transitions in problem 14, the following new transition is obtained:
	f3(a, b) -> f1(a + 13, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 /\ a + 11 >= 0 /\ a + 12 >= 0 ]
We thus obtain the following problem:
15:	T:
		(1, 14)    f3(a, b) -> f1(a + 13, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 /\ a + 11 >= 0 /\ a + 12 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 13, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 /\ a + 11 >= 0 /\ a + 12 >= 0 ] with all transitions in problem 15, the following new transition is obtained:
	f3(a, b) -> f1(a + 14, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 /\ a + 11 >= 0 /\ a + 12 >= 0 /\ a + 13 >= 0 ]
We thus obtain the following problem:
16:	T:
		(1, 15)    f3(a, b) -> f1(a + 14, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 /\ a + 11 >= 0 /\ a + 12 >= 0 /\ a + 13 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

By chaining the transition f3(a, b) -> f1(a + 14, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 /\ a + 11 >= 0 /\ a + 12 >= 0 /\ a + 13 >= 0 ] with all transitions in problem 16, the following new transition is obtained:
	f3(a, b) -> f1(a + 15, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 /\ a + 11 >= 0 /\ a + 12 >= 0 /\ a + 13 >= 0 /\ a + 14 >= 0 ]
We thus obtain the following problem:
17:	T:
		(1, 16)    f3(a, b) -> f1(a + 15, b) [ a >= 0 /\ a + 1 >= 0 /\ a + 2 >= 0 /\ a + 3 >= 0 /\ a + 4 >= 0 /\ a + 5 >= 0 /\ a + 6 >= 0 /\ a + 7 >= 0 /\ a + 8 >= 0 /\ a + 9 >= 0 /\ a + 10 >= 0 /\ a + 11 >= 0 /\ a + 12 >= 0 /\ a + 13 >= 0 /\ a + 14 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b) [ a >= 0 ]
	start location:	f3
	leaf cost:	1

Complexity upper bound ?

Time: 0.923 sec (SMT: 0.862 sec)