MAYBE

Initial complexity problem:
1:	T:
		(1, 1)    f2(a, b, c, d) -> f300(a, b, c, d)
		(?, 1)    f300(a, b, c, d) -> f300(b - 1, b - 1, e, d) [ a >= 1 /\ b >= 1 /\ e >= 1 /\ b + a >= 1 ]
		(?, 1)    f300(a, b, c, d) -> f300(b - 1, b - 1, e, d) [ a >= 1 /\ b >= 1 /\ 0 >= e + 1 /\ b + a >= 1 ]
		(?, 1)    f300(a, b, c, d) -> f300(a - 1, a - 2, 0, d) [ a >= 1 /\ b + a >= 1 /\ b >= 1 ]
		(?, 1)    f300(a, b, c, d) -> f1(a, b, c, e) [ a >= 1 /\ 0 >= b + a /\ b >= 1 ]
		(?, 1)    f300(a, b, c, d) -> f1(a, b, c, e) [ b >= 1 /\ 0 >= a ]
		(?, 1)    f300(a, b, c, d) -> f1(a, b, c, e) [ 0 >= b ]
	start location:	f2
	leaf cost:	0

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

Complexity upper bound ?

Time: 0.517 sec (SMT: 0.492 sec)