YES(?, 16*a + 4)

Initial complexity problem:
1:	T:
		(?, 1)    start(a, b, c, d) -> stop1(a, b, c, d) [ a >= 0 /\ b >= 0 /\ c >= 0 /\ d = 0 ]
		(?, 1)    start(a, b, c, d) -> cont1(a, b, c, d) [ d >= 1 /\ a >= 0 /\ b >= 0 /\ c >= 0 /\ d >= 0 /\ a >= d ]
		(?, 1)    cont1(a, b, c, d) -> stop2(a, b, 1, d - 1) [ d >= 1 /\ b >= 0 /\ a >= d /\ c = 0 ]
		(?, 1)    cont1(a, b, c, d) -> a(a, b, c - 1, d) [ c >= 1 /\ d >= 1 /\ c >= 0 /\ b >= 0 /\ a >= d ]
		(?, 1)    a(a, b, c, d) -> b(a, b, e, d - 1) [ a >= d /\ b >= 0 /\ c >= 0 /\ d >= 1 ]
		(?, 1)    b(a, b, c, d) -> start(a, b, c, d) [ c >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 ]
		(?, 1)    b(a, b, c, d) -> stop3(a, b, c, d) [ 0 >= c + 1 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 ]
		(1, 1)    start0(a, b, c, d) -> start(a, b, b, a) [ a >= 0 /\ b >= 0 ]
	start location:	start0
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem:
2:	T:
		(?, 1)    start(a, b, c, d) -> cont1(a, b, c, d) [ d >= 1 /\ a >= 0 /\ b >= 0 /\ c >= 0 /\ d >= 0 /\ a >= d ]
		(?, 1)    cont1(a, b, c, d) -> a(a, b, c - 1, d) [ c >= 1 /\ d >= 1 /\ c >= 0 /\ b >= 0 /\ a >= d ]
		(?, 1)    a(a, b, c, d) -> b(a, b, e, d - 1) [ a >= d /\ b >= 0 /\ c >= 0 /\ d >= 1 ]
		(?, 1)    b(a, b, c, d) -> start(a, b, c, d) [ c >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 ]
		(1, 1)    start0(a, b, c, d) -> start(a, b, b, a) [ a >= 0 /\ b >= 0 ]
	start location:	start0
	leaf cost:	3

A polynomial rank function with
	Pol(start) = 4*V_4
	Pol(cont1) = 4*V_4 - 1
	Pol(a) = 4*V_4 - 2
	Pol(b) = 4*V_4 + 1
	Pol(start0) = 4*V_1
orients all transitions weakly and the transitions
	start(a, b, c, d) -> cont1(a, b, c, d) [ d >= 1 /\ a >= 0 /\ b >= 0 /\ c >= 0 /\ d >= 0 /\ a >= d ]
	cont1(a, b, c, d) -> a(a, b, c - 1, d) [ c >= 1 /\ d >= 1 /\ c >= 0 /\ b >= 0 /\ a >= d ]
	b(a, b, c, d) -> start(a, b, c, d) [ c >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 ]
	a(a, b, c, d) -> b(a, b, e, d - 1) [ a >= d /\ b >= 0 /\ c >= 0 /\ d >= 1 ]
strictly and produces the following problem:
3:	T:
		(4*a, 1)    start(a, b, c, d) -> cont1(a, b, c, d) [ d >= 1 /\ a >= 0 /\ b >= 0 /\ c >= 0 /\ d >= 0 /\ a >= d ]
		(4*a, 1)    cont1(a, b, c, d) -> a(a, b, c - 1, d) [ c >= 1 /\ d >= 1 /\ c >= 0 /\ b >= 0 /\ a >= d ]
		(4*a, 1)    a(a, b, c, d) -> b(a, b, e, d - 1) [ a >= d /\ b >= 0 /\ c >= 0 /\ d >= 1 ]
		(4*a, 1)    b(a, b, c, d) -> start(a, b, c, d) [ c >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 ]
		(1, 1)      start0(a, b, c, d) -> start(a, b, b, a) [ a >= 0 /\ b >= 0 ]
	start location:	start0
	leaf cost:	3

Complexity upper bound 16*a + 4

Time: 0.204 sec (SMT: 0.193 sec)