MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f3(a, b) -> f0(1, 1)
		(?, 1)    f0(a, b) -> f0(a + 1, b)
	start location:	f3
	leaf cost:	0

Applied AI with 'oct' on problem 1 to obtain the following invariants:
  For symbol f0: -X_2 + 1 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0


This yielded the following problem:
2:	T:
		(?, 1)    f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
		(1, 1)    f3(a, b) -> f0(1, 1)
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(1, 1) with all transitions in problem 2, the following new transition is obtained:
	f3(a, b) -> f0(2, 1) [ 0 >= 0 ]
We thus obtain the following problem:
3:	T:
		(1, 2)    f3(a, b) -> f0(2, 1) [ 0 >= 0 ]
		(?, 1)    f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(2, 1) [ 0 >= 0 ] with all transitions in problem 3, the following new transition is obtained:
	f3(a, b) -> f0(3, 1) [ 0 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
4:	T:
		(1, 3)    f3(a, b) -> f0(3, 1) [ 0 >= 0 /\ 1 >= 0 ]
		(?, 1)    f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(3, 1) [ 0 >= 0 /\ 1 >= 0 ] with all transitions in problem 4, the following new transition is obtained:
	f3(a, b) -> f0(4, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 ]
We thus obtain the following problem:
5:	T:
		(1, 4)    f3(a, b) -> f0(4, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 ]
		(?, 1)    f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(4, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 ] with all transitions in problem 5, the following new transition is obtained:
	f3(a, b) -> f0(5, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 ]
We thus obtain the following problem:
6:	T:
		(1, 5)    f3(a, b) -> f0(5, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 ]
		(?, 1)    f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(5, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 ] with all transitions in problem 6, the following new transition is obtained:
	f3(a, b) -> f0(6, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 ]
We thus obtain the following problem:
7:	T:
		(1, 6)    f3(a, b) -> f0(6, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 ]
		(?, 1)    f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(6, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 ] with all transitions in problem 7, the following new transition is obtained:
	f3(a, b) -> f0(7, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 ]
We thus obtain the following problem:
8:	T:
		(1, 7)    f3(a, b) -> f0(7, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 ]
		(?, 1)    f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(7, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 ] with all transitions in problem 8, the following new transition is obtained:
	f3(a, b) -> f0(8, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 ]
We thus obtain the following problem:
9:	T:
		(1, 8)    f3(a, b) -> f0(8, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 ]
		(?, 1)    f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(8, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 ] with all transitions in problem 9, the following new transition is obtained:
	f3(a, b) -> f0(9, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 ]
We thus obtain the following problem:
10:	T:
		(1, 9)    f3(a, b) -> f0(9, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 ]
		(?, 1)    f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(9, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 ] with all transitions in problem 10, the following new transition is obtained:
	f3(a, b) -> f0(10, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 ]
We thus obtain the following problem:
11:	T:
		(1, 10)    f3(a, b) -> f0(10, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 ]
		(?, 1)     f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(10, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 ] with all transitions in problem 11, the following new transition is obtained:
	f3(a, b) -> f0(11, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 ]
We thus obtain the following problem:
12:	T:
		(1, 11)    f3(a, b) -> f0(11, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 ]
		(?, 1)     f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(11, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 ] with all transitions in problem 12, the following new transition is obtained:
	f3(a, b) -> f0(12, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 ]
We thus obtain the following problem:
13:	T:
		(1, 12)    f3(a, b) -> f0(12, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 ]
		(?, 1)     f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(12, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 ] with all transitions in problem 13, the following new transition is obtained:
	f3(a, b) -> f0(13, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 ]
We thus obtain the following problem:
14:	T:
		(1, 13)    f3(a, b) -> f0(13, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 ]
		(?, 1)     f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(13, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 ] with all transitions in problem 14, the following new transition is obtained:
	f3(a, b) -> f0(14, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 ]
We thus obtain the following problem:
15:	T:
		(1, 14)    f3(a, b) -> f0(14, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 ]
		(?, 1)     f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(14, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 ] with all transitions in problem 15, the following new transition is obtained:
	f3(a, b) -> f0(15, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 /\ 13 >= 0 ]
We thus obtain the following problem:
16:	T:
		(1, 15)    f3(a, b) -> f0(15, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 /\ 13 >= 0 ]
		(?, 1)     f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

By chaining the transition f3(a, b) -> f0(15, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 /\ 13 >= 0 ] with all transitions in problem 16, the following new transition is obtained:
	f3(a, b) -> f0(16, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 /\ 13 >= 0 /\ 14 >= 0 ]
We thus obtain the following problem:
17:	T:
		(1, 16)    f3(a, b) -> f0(16, 1) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 /\ 13 >= 0 /\ 14 >= 0 ]
		(?, 1)     f0(a, b) -> f0(a + 1, b) [ -b + 1 >= 0 /\ a - b >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ a - 1 >= 0 ]
	start location:	f3
	leaf cost:	0

Complexity upper bound ?

Time: 0.625 sec (SMT: 0.577 sec)