MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f0(a, b) -> f1(a, a) [ a = b ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1)
		(?, 1)    f1(a, b) -> f2(a, b)
		(?, 1)    f1(a, b) -> f10000(a, b) [ a >= b + 1 ]
	start location:	f0
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem:
2:	T:
		(1, 1)    f0(a, b) -> f1(a, a) [ a = b ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1)
	start location:	f0
	leaf cost:	2

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


This yielded the following problem:
3:	T:
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
		(1, 1)    f0(a, b) -> f1(a, a) [ a = b ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a, a) [ a = b ] with all transitions in problem 3, the following new transition is obtained:
	f0(a, b) -> f1(a + 1, a + 1) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
4:	T:
		(1, 2)    f0(a, b) -> f1(a + 1, a + 1) [ a = b /\ 0 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 1, a + 1) [ a = b /\ 0 >= 0 ] with all transitions in problem 4, the following new transition is obtained:
	f0(a, b) -> f1(a + 2, a + 2) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
5:	T:
		(1, 3)    f0(a, b) -> f1(a + 2, a + 2) [ a = b /\ 0 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 2, a + 2) [ a = b /\ 0 >= 0 ] with all transitions in problem 5, the following new transition is obtained:
	f0(a, b) -> f1(a + 3, a + 3) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
6:	T:
		(1, 4)    f0(a, b) -> f1(a + 3, a + 3) [ a = b /\ 0 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 3, a + 3) [ a = b /\ 0 >= 0 ] with all transitions in problem 6, the following new transition is obtained:
	f0(a, b) -> f1(a + 4, a + 4) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
7:	T:
		(1, 5)    f0(a, b) -> f1(a + 4, a + 4) [ a = b /\ 0 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 4, a + 4) [ a = b /\ 0 >= 0 ] with all transitions in problem 7, the following new transition is obtained:
	f0(a, b) -> f1(a + 5, a + 5) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
8:	T:
		(1, 6)    f0(a, b) -> f1(a + 5, a + 5) [ a = b /\ 0 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 5, a + 5) [ a = b /\ 0 >= 0 ] with all transitions in problem 8, the following new transition is obtained:
	f0(a, b) -> f1(a + 6, a + 6) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
9:	T:
		(1, 7)    f0(a, b) -> f1(a + 6, a + 6) [ a = b /\ 0 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 6, a + 6) [ a = b /\ 0 >= 0 ] with all transitions in problem 9, the following new transition is obtained:
	f0(a, b) -> f1(a + 7, a + 7) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
10:	T:
		(1, 8)    f0(a, b) -> f1(a + 7, a + 7) [ a = b /\ 0 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 7, a + 7) [ a = b /\ 0 >= 0 ] with all transitions in problem 10, the following new transition is obtained:
	f0(a, b) -> f1(a + 8, a + 8) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
11:	T:
		(1, 9)    f0(a, b) -> f1(a + 8, a + 8) [ a = b /\ 0 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 8, a + 8) [ a = b /\ 0 >= 0 ] with all transitions in problem 11, the following new transition is obtained:
	f0(a, b) -> f1(a + 9, a + 9) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
12:	T:
		(1, 10)    f0(a, b) -> f1(a + 9, a + 9) [ a = b /\ 0 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 9, a + 9) [ a = b /\ 0 >= 0 ] with all transitions in problem 12, the following new transition is obtained:
	f0(a, b) -> f1(a + 10, a + 10) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
13:	T:
		(1, 11)    f0(a, b) -> f1(a + 10, a + 10) [ a = b /\ 0 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 10, a + 10) [ a = b /\ 0 >= 0 ] with all transitions in problem 13, the following new transition is obtained:
	f0(a, b) -> f1(a + 11, a + 11) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
14:	T:
		(1, 12)    f0(a, b) -> f1(a + 11, a + 11) [ a = b /\ 0 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 11, a + 11) [ a = b /\ 0 >= 0 ] with all transitions in problem 14, the following new transition is obtained:
	f0(a, b) -> f1(a + 12, a + 12) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
15:	T:
		(1, 13)    f0(a, b) -> f1(a + 12, a + 12) [ a = b /\ 0 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 12, a + 12) [ a = b /\ 0 >= 0 ] with all transitions in problem 15, the following new transition is obtained:
	f0(a, b) -> f1(a + 13, a + 13) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
16:	T:
		(1, 14)    f0(a, b) -> f1(a + 13, a + 13) [ a = b /\ 0 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 13, a + 13) [ a = b /\ 0 >= 0 ] with all transitions in problem 16, the following new transition is obtained:
	f0(a, b) -> f1(a + 14, a + 14) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
17:	T:
		(1, 15)    f0(a, b) -> f1(a + 14, a + 14) [ a = b /\ 0 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

By chaining the transition f0(a, b) -> f1(a + 14, a + 14) [ a = b /\ 0 >= 0 ] with all transitions in problem 17, the following new transition is obtained:
	f0(a, b) -> f1(a + 15, a + 15) [ a = b /\ 0 >= 0 ]
We thus obtain the following problem:
18:	T:
		(1, 16)    f0(a, b) -> f1(a + 15, a + 15) [ a = b /\ 0 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a + 1, b + 1) [ a - b >= 0 /\ -a + b >= 0 ]
	start location:	f0
	leaf cost:	2

Complexity upper bound ?

Time: 1.212 sec (SMT: 1.148 sec)