MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f0(a) -> f3(a)
		(?, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)    f3(a) -> f3(a - 1)
	start location:	f0
	leaf cost:	0

A polynomial rank function with
	Pol(f0) = V_1
	Pol(f3) = V_1
orients all transitions weakly and the transition
	f3(a) -> f3(a - 1) [ a >= 2 ]
strictly and produces the following problem:
2:	T:
		(1, 1)    f0(a) -> f3(a)
		(a, 1)    f3(a) -> f3(a - 1) [ a >= 2 ]
		(?, 1)    f3(a) -> f3(a - 1)
	start location:	f0
	leaf cost:	0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Complexity upper bound ?

Time: 1.798 sec (SMT: 1.707 sec)