MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f20(a, b) -> f1(0, 0)
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1)
		(?, 1)    f1(a, b) -> f30(a, b) [ a >= b + 1 ]
	start location:	f20
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem:
2:	T:
		(1, 1)    f20(a, b) -> f1(0, 0)
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1)
	start location:	f20
	leaf cost:	1

Applied AI with 'oct' on problem 2 to obtain the following invariants:
  For symbol f1: X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0


This yielded the following problem:
3:	T:
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
		(1, 1)    f20(a, b) -> f1(0, 0)
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(0, 0) with all transitions in problem 3, the following new transition is obtained:
	f20(a, b) -> f1(1, 1) [ 0 >= 0 ]
We thus obtain the following problem:
4:	T:
		(1, 2)    f20(a, b) -> f1(1, 1) [ 0 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(1, 1) [ 0 >= 0 ] with all transitions in problem 4, the following new transition is obtained:
	f20(a, b) -> f1(2, 2) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 ]
We thus obtain the following problem:
5:	T:
		(1, 3)    f20(a, b) -> f1(2, 2) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(2, 2) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 ] with all transitions in problem 5, the following new transition is obtained:
	f20(a, b) -> f1(3, 3) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 ]
We thus obtain the following problem:
6:	T:
		(1, 4)    f20(a, b) -> f1(3, 3) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(3, 3) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 ] with all transitions in problem 6, the following new transition is obtained:
	f20(a, b) -> f1(4, 4) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 ]
We thus obtain the following problem:
7:	T:
		(1, 5)    f20(a, b) -> f1(4, 4) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(4, 4) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 ] with all transitions in problem 7, the following new transition is obtained:
	f20(a, b) -> f1(5, 5) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 ]
We thus obtain the following problem:
8:	T:
		(1, 6)    f20(a, b) -> f1(5, 5) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(5, 5) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 ] with all transitions in problem 8, the following new transition is obtained:
	f20(a, b) -> f1(6, 6) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 ]
We thus obtain the following problem:
9:	T:
		(1, 7)    f20(a, b) -> f1(6, 6) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(6, 6) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 ] with all transitions in problem 9, the following new transition is obtained:
	f20(a, b) -> f1(7, 7) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 ]
We thus obtain the following problem:
10:	T:
		(1, 8)    f20(a, b) -> f1(7, 7) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(7, 7) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 ] with all transitions in problem 10, the following new transition is obtained:
	f20(a, b) -> f1(8, 8) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 ]
We thus obtain the following problem:
11:	T:
		(1, 9)    f20(a, b) -> f1(8, 8) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(8, 8) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 ] with all transitions in problem 11, the following new transition is obtained:
	f20(a, b) -> f1(9, 9) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 ]
We thus obtain the following problem:
12:	T:
		(1, 10)    f20(a, b) -> f1(9, 9) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(9, 9) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 ] with all transitions in problem 12, the following new transition is obtained:
	f20(a, b) -> f1(10, 10) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 ]
We thus obtain the following problem:
13:	T:
		(1, 11)    f20(a, b) -> f1(10, 10) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(10, 10) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 ] with all transitions in problem 13, the following new transition is obtained:
	f20(a, b) -> f1(11, 11) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 ]
We thus obtain the following problem:
14:	T:
		(1, 12)    f20(a, b) -> f1(11, 11) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(11, 11) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 ] with all transitions in problem 14, the following new transition is obtained:
	f20(a, b) -> f1(12, 12) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 /\ 11 >= 0 /\ 22 >= 0 ]
We thus obtain the following problem:
15:	T:
		(1, 13)    f20(a, b) -> f1(12, 12) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 /\ 11 >= 0 /\ 22 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(12, 12) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 /\ 11 >= 0 /\ 22 >= 0 ] with all transitions in problem 15, the following new transition is obtained:
	f20(a, b) -> f1(13, 13) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 /\ 11 >= 0 /\ 22 >= 0 /\ 24 >= 0 ]
We thus obtain the following problem:
16:	T:
		(1, 14)    f20(a, b) -> f1(13, 13) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 /\ 11 >= 0 /\ 22 >= 0 /\ 24 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(13, 13) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 /\ 11 >= 0 /\ 22 >= 0 /\ 24 >= 0 ] with all transitions in problem 16, the following new transition is obtained:
	f20(a, b) -> f1(14, 14) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 /\ 11 >= 0 /\ 22 >= 0 /\ 24 >= 0 /\ 13 >= 0 /\ 26 >= 0 ]
We thus obtain the following problem:
17:	T:
		(1, 15)    f20(a, b) -> f1(14, 14) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 /\ 11 >= 0 /\ 22 >= 0 /\ 24 >= 0 /\ 13 >= 0 /\ 26 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

By chaining the transition f20(a, b) -> f1(14, 14) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 /\ 11 >= 0 /\ 22 >= 0 /\ 24 >= 0 /\ 13 >= 0 /\ 26 >= 0 ] with all transitions in problem 17, the following new transition is obtained:
	f20(a, b) -> f1(15, 15) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 /\ 11 >= 0 /\ 22 >= 0 /\ 24 >= 0 /\ 13 >= 0 /\ 26 >= 0 /\ 28 >= 0 ]
We thus obtain the following problem:
18:	T:
		(1, 16)    f20(a, b) -> f1(15, 15) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 4 >= 0 /\ 3 >= 0 /\ 6 >= 0 /\ 8 >= 0 /\ 5 >= 0 /\ 10 >= 0 /\ 12 >= 0 /\ 7 >= 0 /\ 14 >= 0 /\ 16 >= 0 /\ 9 >= 0 /\ 18 >= 0 /\ 20 >= 0 /\ 11 >= 0 /\ 22 >= 0 /\ 24 >= 0 /\ 13 >= 0 /\ 26 >= 0 /\ 28 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ]
	start location:	f20
	leaf cost:	1

Complexity upper bound ?

Time: 0.707 sec (SMT: 0.652 sec)