YES(?, d + 2)

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

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

A polynomial rank function with
	Pol(sqrt) = V_4
	Pol(f) = -V_3 + V_4 + 1
orients all transitions weakly and the transition
	f(a, b, c, d) -> f(a + 1, b + 2, c + b + 2, d) [ d >= c /\ b >= 0 ]
strictly and produces the following problem:
3:	T:
		(1, 1)    sqrt(a, b, c, d) -> f(0, 1, 1, d)
		(d, 1)    f(a, b, c, d) -> f(a + 1, b + 2, c + b + 2, d) [ d >= c /\ b >= 0 ]
	start location:	sqrt
	leaf cost:	1

Complexity upper bound d + 2

Time: 0.138 sec (SMT: 0.133 sec)