MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f300(a) -> f3(a)
		(?, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)    f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

A polynomial rank function with
	Pol(f300) = 2*V_1 - 3
	Pol(f3) = 2*V_1 - 3
orients all transitions weakly and the transition
	f3(a) -> f3(a - 1) [ a >= 2 ]
strictly and produces the following problem:
2:	T:
		(1, 1)          f300(a) -> f3(a)
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a) with all transitions in problem 2, the following new transitions are obtained:
	f300(a) -> f3(a - 1) [ 1 >= a ]
	f300(a) -> f3(a - 1) [ a >= 2 ]
We thus obtain the following problem:
3:	T:
		(1, 2)          f300(a) -> f3(a - 1) [ 1 >= a ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 1) [ 1 >= a ] with all transitions in problem 3, the following new transition is obtained:
	f300(a) -> f3(a - 2) [ 1 >= a /\ 1 >= a - 1 ]
We thus obtain the following problem:
4:	T:
		(1, 3)          f300(a) -> f3(a - 2) [ 1 >= a /\ 1 >= a - 1 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 2) [ 1 >= a /\ 1 >= a - 1 ] with all transitions in problem 4, the following new transition is obtained:
	f300(a) -> f3(a - 3) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 ]
We thus obtain the following problem:
5:	T:
		(1, 4)          f300(a) -> f3(a - 3) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 3) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 ] with all transitions in problem 5, the following new transition is obtained:
	f300(a) -> f3(a - 4) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 ]
We thus obtain the following problem:
6:	T:
		(1, 5)          f300(a) -> f3(a - 4) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 4) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 ] with all transitions in problem 6, the following new transition is obtained:
	f300(a) -> f3(a - 5) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 ]
We thus obtain the following problem:
7:	T:
		(1, 6)          f300(a) -> f3(a - 5) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 5) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 ] with all transitions in problem 7, the following new transition is obtained:
	f300(a) -> f3(a - 6) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 ]
We thus obtain the following problem:
8:	T:
		(1, 7)          f300(a) -> f3(a - 6) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 6) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 ] with all transitions in problem 8, the following new transition is obtained:
	f300(a) -> f3(a - 7) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 ]
We thus obtain the following problem:
9:	T:
		(1, 8)          f300(a) -> f3(a - 7) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 7) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 ] with all transitions in problem 9, the following new transition is obtained:
	f300(a) -> f3(a - 8) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 ]
We thus obtain the following problem:
10:	T:
		(1, 9)          f300(a) -> f3(a - 8) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 8) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 ] with all transitions in problem 10, the following new transition is obtained:
	f300(a) -> f3(a - 9) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 ]
We thus obtain the following problem:
11:	T:
		(1, 10)         f300(a) -> f3(a - 9) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 9) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 ] with all transitions in problem 11, the following new transition is obtained:
	f300(a) -> f3(a - 10) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 ]
We thus obtain the following problem:
12:	T:
		(1, 11)         f300(a) -> f3(a - 10) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 10) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 ] with all transitions in problem 12, the following new transition is obtained:
	f300(a) -> f3(a - 11) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 ]
We thus obtain the following problem:
13:	T:
		(1, 12)         f300(a) -> f3(a - 11) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 11) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 ] with all transitions in problem 13, the following new transition is obtained:
	f300(a) -> f3(a - 12) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 /\ 1 >= a - 11 ]
We thus obtain the following problem:
14:	T:
		(1, 13)         f300(a) -> f3(a - 12) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 /\ 1 >= a - 11 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 12) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 /\ 1 >= a - 11 ] with all transitions in problem 14, the following new transition is obtained:
	f300(a) -> f3(a - 13) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 /\ 1 >= a - 11 /\ 1 >= a - 12 ]
We thus obtain the following problem:
15:	T:
		(1, 14)         f300(a) -> f3(a - 13) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 /\ 1 >= a - 11 /\ 1 >= a - 12 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 13) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 /\ 1 >= a - 11 /\ 1 >= a - 12 ] with all transitions in problem 15, the following new transition is obtained:
	f300(a) -> f3(a - 14) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 /\ 1 >= a - 11 /\ 1 >= a - 12 /\ 1 >= a - 13 ]
We thus obtain the following problem:
16:	T:
		(1, 15)         f300(a) -> f3(a - 14) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 /\ 1 >= a - 11 /\ 1 >= a - 12 /\ 1 >= a - 13 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

By chaining the transition f300(a) -> f3(a - 14) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 /\ 1 >= a - 11 /\ 1 >= a - 12 /\ 1 >= a - 13 ] with all transitions in problem 16, the following new transition is obtained:
	f300(a) -> f3(a - 15) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 /\ 1 >= a - 11 /\ 1 >= a - 12 /\ 1 >= a - 13 /\ 1 >= a - 14 ]
We thus obtain the following problem:
17:	T:
		(1, 16)         f300(a) -> f3(a - 15) [ 1 >= a /\ 1 >= a - 1 /\ 1 >= a - 2 /\ 1 >= a - 3 /\ 1 >= a - 4 /\ 1 >= a - 5 /\ 1 >= a - 6 /\ 1 >= a - 7 /\ 1 >= a - 8 /\ 1 >= a - 9 /\ 1 >= a - 10 /\ 1 >= a - 11 /\ 1 >= a - 12 /\ 1 >= a - 13 /\ 1 >= a - 14 ]
		(1, 2)          f300(a) -> f3(a - 1) [ a >= 2 ]
		(2*a + 3, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)          f3(a) -> f3(a - 1) [ 1 >= a ]
	start location:	f300
	leaf cost:	0

Complexity upper bound ?

Time: 0.884 sec (SMT: 0.829 sec)