YES(?, 4*a + 4*c + 18)

Initial complexity problem:
1:	T:
		(?, 1)    start(a, b, c, d) -> stop(a, b, c, d) [ 0 >= a /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> lbl6(a, b, c, d) [ a >= 1 /\ 0 >= c /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> cut(a, b, c, d) [ a >= 1 /\ d = a /\ b = a /\ c = a ]
		(?, 1)    start(a, b, c, d) -> lbl101(a, b - d, c, d) [ a >= 1 /\ c >= a + 1 /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> lbl111(a, b, c, d - b) [ a >= c + 1 /\ c >= 1 /\ b = c /\ d = a ]
		(?, 1)    lbl6(a, b, c, d) -> stop(a, b, c, d) [ a >= 1 /\ 0 >= c /\ d = a /\ b = c ]
		(?, 1)    lbl101(a, b, c, d) -> cut(a, b, c, d) [ a >= b /\ b >= 1 /\ c >= 2*b /\ d = b ]
		(?, 1)    lbl101(a, b, c, d) -> lbl101(a, b - d, c, d) [ b >= d + 1 /\ a >= d /\ b >= 1 /\ d >= 1 /\ c >= d + b ]
		(?, 1)    lbl101(a, b, c, d) -> lbl111(a, b, c, d - b) [ d >= b + 1 /\ a >= d /\ b >= 1 /\ d >= 1 /\ c >= d + b ]
		(?, 1)    lbl111(a, b, c, d) -> cut(a, b, c, d) [ c >= b /\ b >= 1 /\ a >= 2*b /\ d = b ]
		(?, 1)    lbl111(a, b, c, d) -> lbl101(a, b - d, c, d) [ b >= d + 1 /\ c >= b /\ b >= 1 /\ d >= 1 /\ a >= d + b ]
		(?, 1)    lbl111(a, b, c, d) -> lbl111(a, b, c, d - b) [ d >= b + 1 /\ c >= b /\ b >= 1 /\ d >= 1 /\ a >= d + b ]
		(?, 1)    cut(a, b, c, d) -> stop(a, b, c, d) [ a >= b /\ b >= 1 /\ c >= b /\ d = b ]
		(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 1 produces the following problem:
2:	T:
		(?, 1)    start(a, b, c, d) -> lbl101(a, b - d, c, d) [ a >= 1 /\ c >= a + 1 /\ b = c /\ d = a ]
		(?, 1)    start(a, b, c, d) -> lbl111(a, b, c, d - b) [ a >= c + 1 /\ c >= 1 /\ b = c /\ d = a ]
		(?, 1)    lbl101(a, b, c, d) -> lbl101(a, b - d, c, d) [ b >= d + 1 /\ a >= d /\ b >= 1 /\ d >= 1 /\ c >= d + b ]
		(?, 1)    lbl101(a, b, c, d) -> lbl111(a, b, c, d - b) [ d >= b + 1 /\ a >= d /\ b >= 1 /\ d >= 1 /\ c >= d + b ]
		(?, 1)    lbl111(a, b, c, d) -> lbl101(a, b - d, c, d) [ b >= d + 1 /\ c >= b /\ b >= 1 /\ d >= 1 /\ a >= d + b ]
		(?, 1)    lbl111(a, b, c, d) -> lbl111(a, b, c, d - b) [ d >= b + 1 /\ c >= b /\ b >= 1 /\ d >= 1 /\ a >= d + b ]
		(1, 1)    start0(a, b, c, d) -> start(a, c, c, a)
	start location:	start0
	leaf cost:	7

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(1, 1)    start(a, b, c, d) -> lbl101(a, b - d, c, d) [ a >= 1 /\ c >= a + 1 /\ b = c /\ d = a ]
		(1, 1)    start(a, b, c, d) -> lbl111(a, b, c, d - b) [ a >= c + 1 /\ c >= 1 /\ b = c /\ d = a ]
		(?, 1)    lbl101(a, b, c, d) -> lbl101(a, b - d, c, d) [ b >= d + 1 /\ a >= d /\ b >= 1 /\ d >= 1 /\ c >= d + b ]
		(?, 1)    lbl101(a, b, c, d) -> lbl111(a, b, c, d - b) [ d >= b + 1 /\ a >= d /\ b >= 1 /\ d >= 1 /\ c >= d + b ]
		(?, 1)    lbl111(a, b, c, d) -> lbl101(a, b - d, c, d) [ b >= d + 1 /\ c >= b /\ b >= 1 /\ d >= 1 /\ a >= d + b ]
		(?, 1)    lbl111(a, b, c, d) -> lbl111(a, b, c, d - b) [ d >= b + 1 /\ c >= b /\ b >= 1 /\ d >= 1 /\ a >= d + b ]
		(1, 1)    start0(a, b, c, d) -> start(a, c, c, a)
	start location:	start0
	leaf cost:	7

A polynomial rank function with
	Pol(start) = V_2 + V_4 - 2
	Pol(lbl101) = V_2 + 2*V_4 - 2
	Pol(lbl111) = 2*V_2 + V_4 - 2
	Pol(start0) = V_1 + V_3 - 2
orients all transitions weakly and the transitions
	lbl111(a, b, c, d) -> lbl111(a, b, c, d - b) [ d >= b + 1 /\ c >= b /\ b >= 1 /\ d >= 1 /\ a >= d + b ]
	lbl111(a, b, c, d) -> lbl101(a, b - d, c, d) [ b >= d + 1 /\ c >= b /\ b >= 1 /\ d >= 1 /\ a >= d + b ]
	lbl101(a, b, c, d) -> lbl111(a, b, c, d - b) [ d >= b + 1 /\ a >= d /\ b >= 1 /\ d >= 1 /\ c >= d + b ]
	lbl101(a, b, c, d) -> lbl101(a, b - d, c, d) [ b >= d + 1 /\ a >= d /\ b >= 1 /\ d >= 1 /\ c >= d + b ]
strictly and produces the following problem:
4:	T:
		(1, 1)            start(a, b, c, d) -> lbl101(a, b - d, c, d) [ a >= 1 /\ c >= a + 1 /\ b = c /\ d = a ]
		(1, 1)            start(a, b, c, d) -> lbl111(a, b, c, d - b) [ a >= c + 1 /\ c >= 1 /\ b = c /\ d = a ]
		(a + c + 2, 1)    lbl101(a, b, c, d) -> lbl101(a, b - d, c, d) [ b >= d + 1 /\ a >= d /\ b >= 1 /\ d >= 1 /\ c >= d + b ]
		(a + c + 2, 1)    lbl101(a, b, c, d) -> lbl111(a, b, c, d - b) [ d >= b + 1 /\ a >= d /\ b >= 1 /\ d >= 1 /\ c >= d + b ]
		(a + c + 2, 1)    lbl111(a, b, c, d) -> lbl101(a, b - d, c, d) [ b >= d + 1 /\ c >= b /\ b >= 1 /\ d >= 1 /\ a >= d + b ]
		(a + c + 2, 1)    lbl111(a, b, c, d) -> lbl111(a, b, c, d - b) [ d >= b + 1 /\ c >= b /\ b >= 1 /\ d >= 1 /\ a >= d + b ]
		(1, 1)            start0(a, b, c, d) -> start(a, c, c, a)
	start location:	start0
	leaf cost:	7

Complexity upper bound 4*a + 4*c + 18

Time: 0.448 sec (SMT: 0.427 sec)