YES(?, 2*a + 2*c + 12)

Initial complexity problem:
1:	T:
		(?, 1)    start(a, b, c, d) -> stop(a, b, c, d) [ 0 >= a + 1 /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> stop(a, b, c, d) [ 0 >= c + 1 /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> stop(a, b, c, d) [ a >= 0 /\ a + 2 >= c /\ c >= 0 /\ c + 2 >= a /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> lbl81(a, b, c, d + 1) [ a >= 0 /\ c >= a + 3 /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> lbl91(a, b + 1, c, d) [ a >= c + 3 /\ c >= 0 /\ b = c /\ d = a ]
		(?, 1)    lbl81(a, b, c, d) -> stop(a, b, c, d) [ c >= a + 3 /\ a >= 0 /\ d + 2 = c /\ b = c ]
		(?, 1)    lbl81(a, b, c, d) -> lbl81(a, b, c, d + 1) [ c >= d + 3 /\ d >= a + 1 /\ a >= 0 /\ c >= d + 2 /\ b = c ]
		(?, 1)    lbl81(a, b, c, d) -> lbl91(a, b + 1, c, d) [ d >= c + 3 /\ d >= a + 1 /\ a >= 0 /\ c >= d + 2 /\ b = c ]
		(?, 1)    lbl91(a, b, c, d) -> stop(a, b, c, d) [ a >= c + 3 /\ c >= 0 /\ b + 2 = a /\ d = a ]
		(?, 1)    lbl91(a, b, c, d) -> lbl81(a, b, c, d + 1) [ b >= a + 3 /\ a >= b + 2 /\ b >= c + 1 /\ c >= 0 /\ d = a ]
		(?, 1)    lbl91(a, b, c, d) -> lbl91(a, b + 1, c, d) [ a >= b + 3 /\ a >= b + 2 /\ b >= c + 1 /\ c >= 0 /\ d = a ]
		(1, 1)    start0(a, b, c, d) -> start(a, c, c, a)
	start location:	start0
	leaf cost:	0

Testing for unsatisfiable constraints removes the following transitions from problem 1:
	lbl81(a, b, c, d) -> lbl91(a, b + 1, c, d) [ d >= c + 3 /\ d >= a + 1 /\ a >= 0 /\ c >= d + 2 /\ b = c ]
	lbl91(a, b, c, d) -> lbl81(a, b, c, d + 1) [ b >= a + 3 /\ a >= b + 2 /\ b >= c + 1 /\ c >= 0 /\ d = a ]
We thus obtain the following problem:
2:	T:
		(?, 1)    start(a, b, c, d) -> stop(a, b, c, d) [ 0 >= a + 1 /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> stop(a, b, c, d) [ 0 >= c + 1 /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> stop(a, b, c, d) [ a >= 0 /\ a + 2 >= c /\ c >= 0 /\ c + 2 >= a /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> lbl81(a, b, c, d + 1) [ a >= 0 /\ c >= a + 3 /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> lbl91(a, b + 1, c, d) [ a >= c + 3 /\ c >= 0 /\ b = c /\ d = a ]
		(?, 1)    lbl81(a, b, c, d) -> stop(a, b, c, d) [ c >= a + 3 /\ a >= 0 /\ d + 2 = c /\ b = c ]
		(?, 1)    lbl81(a, b, c, d) -> lbl81(a, b, c, d + 1) [ c >= d + 3 /\ d >= a + 1 /\ a >= 0 /\ c >= d + 2 /\ b = c ]
		(?, 1)    lbl91(a, b, c, d) -> stop(a, b, c, d) [ a >= c + 3 /\ c >= 0 /\ b + 2 = a /\ d = a ]
		(?, 1)    lbl91(a, b, c, d) -> lbl91(a, b + 1, c, d) [ a >= b + 3 /\ a >= b + 2 /\ b >= c + 1 /\ c >= 0 /\ d = a ]
		(1, 1)    start0(a, b, c, d) -> start(a, c, c, a)
	start location:	start0
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem:
3:	T:
		(?, 1)    start(a, b, c, d) -> lbl81(a, b, c, d + 1) [ a >= 0 /\ c >= a + 3 /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> lbl91(a, b + 1, c, d) [ a >= c + 3 /\ c >= 0 /\ b = c /\ d = a ]
		(?, 1)    lbl81(a, b, c, d) -> lbl81(a, b, c, d + 1) [ c >= d + 3 /\ d >= a + 1 /\ a >= 0 /\ c >= d + 2 /\ b = c ]
		(?, 1)    lbl91(a, b, c, d) -> lbl91(a, b + 1, c, d) [ a >= b + 3 /\ a >= b + 2 /\ b >= c + 1 /\ c >= 0 /\ d = a ]
		(1, 1)    start0(a, b, c, d) -> start(a, c, c, a)
	start location:	start0
	leaf cost:	5

Repeatedly propagating knowledge in problem 3 produces the following problem:
4:	T:
		(1, 1)    start(a, b, c, d) -> lbl81(a, b, c, d + 1) [ a >= 0 /\ c >= a + 3 /\ b = c /\ d = a ]
		(1, 1)    start(a, b, c, d) -> lbl91(a, b + 1, c, d) [ a >= c + 3 /\ c >= 0 /\ b = c /\ d = a ]
		(?, 1)    lbl81(a, b, c, d) -> lbl81(a, b, c, d + 1) [ c >= d + 3 /\ d >= a + 1 /\ a >= 0 /\ c >= d + 2 /\ b = c ]
		(?, 1)    lbl91(a, b, c, d) -> lbl91(a, b + 1, c, d) [ a >= b + 3 /\ a >= b + 2 /\ b >= c + 1 /\ c >= 0 /\ d = a ]
		(1, 1)    start0(a, b, c, d) -> start(a, c, c, a)
	start location:	start0
	leaf cost:	5

A polynomial rank function with
	Pol(start) = 2*V_1 - V_2 + 2*V_3 - V_4 - 2
	Pol(lbl81) = V_3 - V_4 - 1
	Pol(lbl91) = 2*V_1 - V_2 - V_4 - 1
	Pol(start0) = V_1 + V_3 - 2
orients all transitions weakly and the transitions
	lbl91(a, b, c, d) -> lbl91(a, b + 1, c, d) [ a >= b + 3 /\ a >= b + 2 /\ b >= c + 1 /\ c >= 0 /\ d = a ]
	lbl81(a, b, c, d) -> lbl81(a, b, c, d + 1) [ c >= d + 3 /\ d >= a + 1 /\ a >= 0 /\ c >= d + 2 /\ b = c ]
strictly and produces the following problem:
5:	T:
		(1, 1)            start(a, b, c, d) -> lbl81(a, b, c, d + 1) [ a >= 0 /\ c >= a + 3 /\ b = c /\ d = a ]
		(1, 1)            start(a, b, c, d) -> lbl91(a, b + 1, c, d) [ a >= c + 3 /\ c >= 0 /\ b = c /\ d = a ]
		(a + c + 2, 1)    lbl81(a, b, c, d) -> lbl81(a, b, c, d + 1) [ c >= d + 3 /\ d >= a + 1 /\ a >= 0 /\ c >= d + 2 /\ b = c ]
		(a + c + 2, 1)    lbl91(a, b, c, d) -> lbl91(a, b + 1, c, d) [ a >= b + 3 /\ a >= b + 2 /\ b >= c + 1 /\ c >= 0 /\ d = a ]
		(1, 1)            start0(a, b, c, d) -> start(a, c, c, a)
	start location:	start0
	leaf cost:	5

Complexity upper bound 2*a + 2*c + 12

Time: 0.350 sec (SMT: 0.333 sec)