MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f2(a, b, c, d) -> f1(a, b, c, d)
		(?, 1)    f1(a, b, c, d) -> f1(a + 1, b, e, d) [ e >= 1 /\ b >= a + 1 ]
		(?, 1)    f1(a, b, c, d) -> f1(a + 1, b, e, d) [ 0 >= e + 1 /\ b >= a + 1 ]
		(?, 1)    f1(a, b, c, d) -> f1(a, b, 0, d) [ b >= a + 1 ]
		(?, 1)    f1(a, b, c, d) -> f1(a + 1, a, e, d) [ e >= 1 /\ b >= f /\ a = b ]
		(?, 1)    f1(a, b, c, d) -> f1(a + 1, a, e, d) [ 0 >= e + 1 /\ b >= f /\ a = b ]
		(?, 1)    f1(a, b, c, d) -> f1(a, a, 0, d) [ b >= e /\ a = b ]
		(?, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b /\ a >= b + 1 ]
		(?, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b /\ b >= a + 1 ]
	start location:	f2
	leaf cost:	0

Testing for unsatisfiable constraints removes the following transition from problem 1:
	f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b /\ b >= a + 1 ]
We thus obtain the following problem:
2:	T:
		(1, 1)    f2(a, b, c, d) -> f1(a, b, c, d)
		(?, 1)    f1(a, b, c, d) -> f1(a + 1, b, e, d) [ e >= 1 /\ b >= a + 1 ]
		(?, 1)    f1(a, b, c, d) -> f1(a + 1, b, e, d) [ 0 >= e + 1 /\ b >= a + 1 ]
		(?, 1)    f1(a, b, c, d) -> f1(a, b, 0, d) [ b >= a + 1 ]
		(?, 1)    f1(a, b, c, d) -> f1(a + 1, a, e, d) [ e >= 1 /\ b >= f /\ a = b ]
		(?, 1)    f1(a, b, c, d) -> f1(a + 1, a, e, d) [ 0 >= e + 1 /\ b >= f /\ a = b ]
		(?, 1)    f1(a, b, c, d) -> f1(a, a, 0, d) [ b >= e /\ a = b ]
		(?, 1)    f1(a, b, c, d) -> f300(a, b, c, e) [ a >= b /\ a >= b + 1 ]
	start location:	f2
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem:
3:	T:
		(1, 1)    f2(a, b, c, d) -> f1(a, b, c, d)
		(?, 1)    f1(a, b, c, d) -> f1(a + 1, b, e, d) [ e >= 1 /\ b >= a + 1 ]
		(?, 1)    f1(a, b, c, d) -> f1(a + 1, b, e, d) [ 0 >= e + 1 /\ b >= a + 1 ]
		(?, 1)    f1(a, b, c, d) -> f1(a, b, 0, d) [ b >= a + 1 ]
		(?, 1)    f1(a, b, c, d) -> f1(a, a, 0, d) [ b >= e /\ a = b ]
	start location:	f2
	leaf cost:	3

A polynomial rank function with
	Pol(f2) = -V_1 + V_2
	Pol(f1) = -V_1 + V_2
orients all transitions weakly and the transition
	f1(a, b, c, d) -> f1(a + 1, b, e, d) [ 0 >= e + 1 /\ b >= a + 1 ]
strictly and produces the following problem:
4:	T:
		(1, 1)        f2(a, b, c, d) -> f1(a, b, c, d)
		(?, 1)        f1(a, b, c, d) -> f1(a + 1, b, e, d) [ e >= 1 /\ b >= a + 1 ]
		(a + b, 1)    f1(a, b, c, d) -> f1(a + 1, b, e, d) [ 0 >= e + 1 /\ b >= a + 1 ]
		(?, 1)        f1(a, b, c, d) -> f1(a, b, 0, d) [ b >= a + 1 ]
		(?, 1)        f1(a, b, c, d) -> f1(a, a, 0, d) [ b >= e /\ a = b ]
	start location:	f2
	leaf cost:	3

A polynomial rank function with
	Pol(f2) = -V_1 + V_2
	Pol(f1) = -V_1 + V_2
orients all transitions weakly and the transition
	f1(a, b, c, d) -> f1(a + 1, b, e, d) [ e >= 1 /\ b >= a + 1 ]
strictly and produces the following problem:
5:	T:
		(1, 1)        f2(a, b, c, d) -> f1(a, b, c, d)
		(a + b, 1)    f1(a, b, c, d) -> f1(a + 1, b, e, d) [ e >= 1 /\ b >= a + 1 ]
		(a + b, 1)    f1(a, b, c, d) -> f1(a + 1, b, e, d) [ 0 >= e + 1 /\ b >= a + 1 ]
		(?, 1)        f1(a, b, c, d) -> f1(a, b, 0, d) [ b >= a + 1 ]
		(?, 1)        f1(a, b, c, d) -> f1(a, a, 0, d) [ b >= e /\ a = b ]
	start location:	f2
	leaf cost:	3

Complexity upper bound ?

Time: 0.390 sec (SMT: 0.365 sec)