MAYBE

Initial complexity problem:
1:	T:
		(?, 1)    f2(a, b, c) -> f2(a + 1, b, c)
		(?, 1)    f3(a, b, c) -> f3(a, b - 1, c) [ b >= 1 ]
		(?, 1)    f5(a, b, c) -> f5(a, b, 1)
		(1, 1)    f0(a, b, c) -> f2(0, b, c) [ c >= 1 ]
		(1, 1)    f0(a, b, c) -> f3(0, b, c) [ 0 >= c ]
		(?, 1)    f3(a, b, c) -> f5(0, b, c) [ 0 >= b ]
	start location:	f0
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = 0
	Pol(f3) = 1
	Pol(f5) = 0
	Pol(f0) = 1
orients all transitions weakly and the transition
	f3(a, b, c) -> f5(0, b, c) [ 0 >= b ]
strictly and produces the following problem:
2:	T:
		(?, 1)    f2(a, b, c) -> f2(a + 1, b, c)
		(?, 1)    f3(a, b, c) -> f3(a, b - 1, c) [ b >= 1 ]
		(?, 1)    f5(a, b, c) -> f5(a, b, 1)
		(1, 1)    f0(a, b, c) -> f2(0, b, c) [ c >= 1 ]
		(1, 1)    f0(a, b, c) -> f3(0, b, c) [ 0 >= c ]
		(1, 1)    f3(a, b, c) -> f5(0, b, c) [ 0 >= b ]
	start location:	f0
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = -V_1 + V_2 - V_3
	Pol(f3) = V_2
	Pol(f5) = V_1 + V_2
	Pol(f0) = V_2 - V_3
orients all transitions weakly and the transition
	f3(a, b, c) -> f3(a, b - 1, c) [ b >= 1 ]
strictly and produces the following problem:
3:	T:
		(?, 1)        f2(a, b, c) -> f2(a + 1, b, c)
		(b + c, 1)    f3(a, b, c) -> f3(a, b - 1, c) [ b >= 1 ]
		(?, 1)        f5(a, b, c) -> f5(a, b, 1)
		(1, 1)        f0(a, b, c) -> f2(0, b, c) [ c >= 1 ]
		(1, 1)        f0(a, b, c) -> f3(0, b, c) [ 0 >= c ]
		(1, 1)        f3(a, b, c) -> f5(0, b, c) [ 0 >= b ]
	start location:	f0
	leaf cost:	0

Applied AI with 'oct' on problem 3 to obtain the following invariants:
  For symbol f2: X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_1 >= 0
  For symbol f3: -X_3 >= 0 /\ X_1 - X_3 >= 0 /\ -X_1 - X_3 >= 0 /\ -X_1 >= 0 /\ X_1 >= 0
  For symbol f5: -X_2 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 >= 0 /\ -X_1 >= 0 /\ X_1 >= 0


This yielded the following problem:
4:	T:
		(1, 1)        f3(a, b, c) -> f5(0, b, c) [ -c >= 0 /\ a - c >= 0 /\ -a - c >= 0 /\ -a >= 0 /\ a >= 0 /\ 0 >= b ]
		(1, 1)        f0(a, b, c) -> f3(0, b, c) [ 0 >= c ]
		(1, 1)        f0(a, b, c) -> f2(0, b, c) [ c >= 1 ]
		(?, 1)        f5(a, b, c) -> f5(a, b, 1) [ -b >= 0 /\ a - b >= 0 /\ -a - b >= 0 /\ -a >= 0 /\ a >= 0 ]
		(b + c, 1)    f3(a, b, c) -> f3(a, b - 1, c) [ -c >= 0 /\ a - c >= 0 /\ -a - c >= 0 /\ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(?, 1)        f2(a, b, c) -> f2(a + 1, b, c) [ c - 1 >= 0 /\ a + c - 1 >= 0 /\ a >= 0 ]
	start location:	f0
	leaf cost:	0

By chaining the transition f3(a, b, c) -> f5(0, b, c) [ -c >= 0 /\ a - c >= 0 /\ -a - c >= 0 /\ -a >= 0 /\ a >= 0 /\ 0 >= b ] with all transitions in problem 4, the following new transition is obtained:
	f3(a, b, c) -> f5(0, b, 1) [ -c >= 0 /\ a - c >= 0 /\ -a - c >= 0 /\ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
5:	T:
		(1, 2)        f3(a, b, c) -> f5(0, b, 1) [ -c >= 0 /\ a - c >= 0 /\ -a - c >= 0 /\ -a >= 0 /\ a >= 0 /\ 0 >= b /\ -b >= 0 /\ 0 >= 0 ]
		(1, 1)        f0(a, b, c) -> f3(0, b, c) [ 0 >= c ]
		(1, 1)        f0(a, b, c) -> f2(0, b, c) [ c >= 1 ]
		(?, 1)        f5(a, b, c) -> f5(a, b, 1) [ -b >= 0 /\ a - b >= 0 /\ -a - b >= 0 /\ -a >= 0 /\ a >= 0 ]
		(b + c, 1)    f3(a, b, c) -> f3(a, b - 1, c) [ -c >= 0 /\ a - c >= 0 /\ -a - c >= 0 /\ -a >= 0 /\ a >= 0 /\ b >= 1 ]
		(?, 1)        f2(a, b, c) -> f2(a + 1, b, c) [ c - 1 >= 0 /\ a + c - 1 >= 0 /\ a >= 0 ]
	start location:	f0
	leaf cost:	0

Complexity upper bound ?

Time: 0.510 sec (SMT: 0.480 sec)