MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f0(a, b) -> f1(3000, b)
		(?, 1)    f1(a, b) -> f1(a, b + 1000) [ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

Applied AI with 'oct' on problem 1 to obtain the following invariants:
  For symbol f1: -X_1 + 3000 >= 0 /\ X_1 - 3000 >= 0


This yielded the following problem:
2:	T:
		(?, 1)    f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
		(1, 1)    f0(a, b) -> f1(3000, b)
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b) with all transitions in problem 2, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 1000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 ]
We thus obtain the following problem:
3:	T:
		(1, 2)    f0(a, b) -> f1(3000, b + 1000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 ]
		(?, 1)    f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 1000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 ] with all transitions in problem 3, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 2000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 ]
We thus obtain the following problem:
4:	T:
		(1, 3)    f0(a, b) -> f1(3000, b + 2000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 2000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 ] with all transitions in problem 4, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 3000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 ]
We thus obtain the following problem:
5:	T:
		(1, 4)    f0(a, b) -> f1(3000, b + 3000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 3000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 ] with all transitions in problem 5, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 4000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 ]
We thus obtain the following problem:
6:	T:
		(1, 5)    f0(a, b) -> f1(3000, b + 4000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 4000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 ] with all transitions in problem 6, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 5000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 ]
We thus obtain the following problem:
7:	T:
		(1, 6)    f0(a, b) -> f1(3000, b + 5000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 5000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 ] with all transitions in problem 7, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 6000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 ]
We thus obtain the following problem:
8:	T:
		(1, 7)    f0(a, b) -> f1(3000, b + 6000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 6000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 ] with all transitions in problem 8, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 7000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 ]
We thus obtain the following problem:
9:	T:
		(1, 8)    f0(a, b) -> f1(3000, b + 7000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 7000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 ] with all transitions in problem 9, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 8000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 ]
We thus obtain the following problem:
10:	T:
		(1, 9)    f0(a, b) -> f1(3000, b + 8000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 ]
		(?, 1)    f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 8000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 ] with all transitions in problem 10, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 9000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 ]
We thus obtain the following problem:
11:	T:
		(1, 10)    f0(a, b) -> f1(3000, b + 9000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 9000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 ] with all transitions in problem 11, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 10000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 ]
We thus obtain the following problem:
12:	T:
		(1, 11)    f0(a, b) -> f1(3000, b + 10000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 10000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 ] with all transitions in problem 12, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 11000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 ]
We thus obtain the following problem:
13:	T:
		(1, 12)    f0(a, b) -> f1(3000, b + 11000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 11000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 ] with all transitions in problem 13, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 12000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 /\ b + 11889 >= 0 ]
We thus obtain the following problem:
14:	T:
		(1, 13)    f0(a, b) -> f1(3000, b + 12000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 /\ b + 11889 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 12000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 /\ b + 11889 >= 0 ] with all transitions in problem 14, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 13000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 /\ b + 11889 >= 0 /\ b + 12889 >= 0 ]
We thus obtain the following problem:
15:	T:
		(1, 14)    f0(a, b) -> f1(3000, b + 13000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 /\ b + 11889 >= 0 /\ b + 12889 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 13000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 /\ b + 11889 >= 0 /\ b + 12889 >= 0 ] with all transitions in problem 15, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 14000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 /\ b + 11889 >= 0 /\ b + 12889 >= 0 /\ b + 13889 >= 0 ]
We thus obtain the following problem:
16:	T:
		(1, 15)    f0(a, b) -> f1(3000, b + 14000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 /\ b + 11889 >= 0 /\ b + 12889 >= 0 /\ b + 13889 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

By chaining the transition f0(a, b) -> f1(3000, b + 14000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 /\ b + 11889 >= 0 /\ b + 12889 >= 0 /\ b + 13889 >= 0 ] with all transitions in problem 16, the following new transition is obtained:
	f0(a, b) -> f1(3000, b + 15000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 /\ b + 11889 >= 0 /\ b + 12889 >= 0 /\ b + 13889 >= 0 /\ b + 14889 >= 0 ]
We thus obtain the following problem:
17:	T:
		(1, 16)    f0(a, b) -> f1(3000, b + 15000) [ 0 >= 0 /\ b + 889 >= 0 /\ 3999 >= 3000 /\ b + 1889 >= 0 /\ b + 2889 >= 0 /\ b + 3889 >= 0 /\ b + 4889 >= 0 /\ b + 5889 >= 0 /\ b + 6889 >= 0 /\ b + 7889 >= 0 /\ b + 8889 >= 0 /\ b + 9889 >= 0 /\ b + 10889 >= 0 /\ b + 11889 >= 0 /\ b + 12889 >= 0 /\ b + 13889 >= 0 /\ b + 14889 >= 0 ]
		(?, 1)     f1(a, b) -> f1(a, b + 1000) [ -a + 3000 >= 0 /\ a - 3000 >= 0 /\ b + 889 >= 0 /\ 3999 >= a ]
	start location:	f0
	leaf cost:	0

Complexity upper bound ?

Time: 1.390 sec (SMT: 1.311 sec)