YES(?, 3*a + 13)

Initial complexity problem:
1:	T:
		(?, 1)    start(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, 0, f, d, h) [ 0 >= a /\ b = c /\ d = a /\ e = f /\ g = h ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, 0, f, d - 1, h) [ a >= 2 /\ b = c /\ d = a /\ e = f /\ g = h ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, 0, f, d - 1, h) [ d = 1 /\ b = c /\ a = 1 /\ e = f /\ g = h ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> cut(a, 0, c, d, 1, f, d - 1, h) [ a >= 2 /\ b = c /\ d = a /\ e = f /\ g = h ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> stop(a, 0, c, d, 0, f, d - 1, h) [ d = 1 /\ b = c /\ a = 1 /\ e = f /\ g = h ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e - 1, f, g - 1, h) [ g >= 2 /\ e >= 2 /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e - 1, f, g - 1, h) [ e >= 2 /\ e >= 0 /\ a >= 2 /\ a >= e + 1 /\ g = 1 /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, 0, f, g - 1, h) [ g >= 2 /\ 1 >= e /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, 0, f, g - 1, h) [ 1 >= e /\ e >= 0 /\ a >= 2 /\ a >= e + 1 /\ g = 1 /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, e, c, d, e + 1, f, g - 1, h) [ g >= 2 /\ a >= e + 2 /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> stop(a, e, c, d, e + 1, f, g - 1, h) [ a >= e + 2 /\ e >= 0 /\ a >= 2 /\ a >= e + 1 /\ g = 1 /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, e, c, d, 0, f, g - 1, h) [ g >= 2 /\ e + 1 >= a /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> stop(a, e, c, d, 0, f, g - 1, h) [ a >= 1 /\ a >= 2 /\ g = 1 /\ e + 1 = a /\ d = a ]
		(1, 1)    start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)
	start location:	start0
	leaf cost:	0

Testing for unsatisfiable constraints removes the following transition from problem 1:
	cut(a, b, c, d, e, f, g, h) -> cut(a, e, c, d, 0, f, g - 1, h) [ g >= 2 /\ e + 1 >= a /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
We thus obtain the following problem:
2:	T:
		(?, 1)    start(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, 0, f, d, h) [ 0 >= a /\ b = c /\ d = a /\ e = f /\ g = h ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, 0, f, d - 1, h) [ a >= 2 /\ b = c /\ d = a /\ e = f /\ g = h ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, 0, f, d - 1, h) [ d = 1 /\ b = c /\ a = 1 /\ e = f /\ g = h ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> cut(a, 0, c, d, 1, f, d - 1, h) [ a >= 2 /\ b = c /\ d = a /\ e = f /\ g = h ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> stop(a, 0, c, d, 0, f, d - 1, h) [ d = 1 /\ b = c /\ a = 1 /\ e = f /\ g = h ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e - 1, f, g - 1, h) [ g >= 2 /\ e >= 2 /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e - 1, f, g - 1, h) [ e >= 2 /\ e >= 0 /\ a >= 2 /\ a >= e + 1 /\ g = 1 /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, 0, f, g - 1, h) [ g >= 2 /\ 1 >= e /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, 0, f, g - 1, h) [ 1 >= e /\ e >= 0 /\ a >= 2 /\ a >= e + 1 /\ g = 1 /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, e, c, d, e + 1, f, g - 1, h) [ g >= 2 /\ a >= e + 2 /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> stop(a, e, c, d, e + 1, f, g - 1, h) [ a >= e + 2 /\ e >= 0 /\ a >= 2 /\ a >= e + 1 /\ g = 1 /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> stop(a, e, c, d, 0, f, g - 1, h) [ a >= 1 /\ a >= 2 /\ g = 1 /\ e + 1 = a /\ d = a ]
		(1, 1)    start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)
	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, e, f, g, h) -> cut(a, b, c, d, 0, f, d - 1, h) [ a >= 2 /\ b = c /\ d = a /\ e = f /\ g = h ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> cut(a, 0, c, d, 1, f, d - 1, h) [ a >= 2 /\ b = c /\ d = a /\ e = f /\ g = h ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e - 1, f, g - 1, h) [ g >= 2 /\ e >= 2 /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, 0, f, g - 1, h) [ g >= 2 /\ 1 >= e /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, e, c, d, e + 1, f, g - 1, h) [ g >= 2 /\ a >= e + 2 /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(1, 1)    start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)
	start location:	start0
	leaf cost:	7

Repeatedly propagating knowledge in problem 3 produces the following problem:
4:	T:
		(1, 1)    start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, 0, f, d - 1, h) [ a >= 2 /\ b = c /\ d = a /\ e = f /\ g = h ]
		(1, 1)    start(a, b, c, d, e, f, g, h) -> cut(a, 0, c, d, 1, f, d - 1, h) [ a >= 2 /\ b = c /\ d = a /\ e = f /\ g = h ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e - 1, f, g - 1, h) [ g >= 2 /\ e >= 2 /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, 0, f, g - 1, h) [ g >= 2 /\ 1 >= e /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(?, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, e, c, d, e + 1, f, g - 1, h) [ g >= 2 /\ a >= e + 2 /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(1, 1)    start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)
	start location:	start0
	leaf cost:	7

A polynomial rank function with
	Pol(start) = V_4 - 1
	Pol(cut) = V_7
	Pol(start0) = V_1 - 1
orients all transitions weakly and the transitions
	cut(a, b, c, d, e, f, g, h) -> cut(a, e, c, d, e + 1, f, g - 1, h) [ g >= 2 /\ a >= e + 2 /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
	cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, 0, f, g - 1, h) [ g >= 2 /\ 1 >= e /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
	cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e - 1, f, g - 1, h) [ g >= 2 /\ e >= 2 /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
strictly and produces the following problem:
5:	T:
		(1, 1)        start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, 0, f, d - 1, h) [ a >= 2 /\ b = c /\ d = a /\ e = f /\ g = h ]
		(1, 1)        start(a, b, c, d, e, f, g, h) -> cut(a, 0, c, d, 1, f, d - 1, h) [ a >= 2 /\ b = c /\ d = a /\ e = f /\ g = h ]
		(a + 1, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e - 1, f, g - 1, h) [ g >= 2 /\ e >= 2 /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(a + 1, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, 0, f, g - 1, h) [ g >= 2 /\ 1 >= e /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(a + 1, 1)    cut(a, b, c, d, e, f, g, h) -> cut(a, e, c, d, e + 1, f, g - 1, h) [ g >= 2 /\ a >= e + 2 /\ g >= 1 /\ e >= 0 /\ a >= g + 1 /\ a >= g + e /\ d = a ]
		(1, 1)        start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)
	start location:	start0
	leaf cost:	7

Complexity upper bound 3*a + 13

Time: 0.645 sec (SMT: 0.610 sec)