YES(?, 44*a + 221)

Initial complexity problem:
1:	T:
		(?, 1)    start(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ a >= 5 /\ b = c /\ d = e /\ f = g /\ h = a ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, 0, g, h + 1) [ 2 >= a /\ b = c /\ d = e /\ f = g /\ h = a ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> lbl82(a, 0, c, d, e, 1, g, h) [ a >= 3 /\ 4 >= a /\ b = c /\ d = e /\ f = g /\ h = a ]
		(?, 1)    lbl92(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ d >= 4 /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
		(?, 1)    lbl92(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, 0, g, h + 1) [ 1 >= d /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
		(?, 1)    lbl92(a, b, c, d, e, f, g, h) -> lbl82(a, 0, c, d, e, 1, g, h) [ d >= 2 /\ 3 >= d /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
		(?, 1)    lbl82(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, f, g, h + 1) [ 2 >= h /\ 9 >= b /\ b >= 0 /\ h >= a /\ h >= 3 /\ 4 >= h /\ f = b + 1 ]
		(?, 1)    lbl82(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, f, g, h + 1) [ h >= a /\ h >= 3 /\ 4 >= h /\ f = 10 /\ b = 9 ]
		(?, 1)    lbl82(a, b, c, d, e, f, g, h) -> lbl82(a, f, c, d, e, f + 1, g, h) [ h >= 3 /\ 8 >= b /\ 9 >= b /\ b >= 0 /\ h >= a /\ 4 >= h /\ f = b + 1 ]
		(1, 1)    start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a)
	start location:	start0
	leaf cost:	0

Testing for unsatisfiable constraints removes the following transition from problem 1:
	lbl82(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, f, g, h + 1) [ 2 >= h /\ 9 >= b /\ b >= 0 /\ h >= a /\ h >= 3 /\ 4 >= h /\ f = b + 1 ]
We thus obtain the following problem:
2:	T:
		(?, 1)    start(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ a >= 5 /\ b = c /\ d = e /\ f = g /\ h = a ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, 0, g, h + 1) [ 2 >= a /\ b = c /\ d = e /\ f = g /\ h = a ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> lbl82(a, 0, c, d, e, 1, g, h) [ a >= 3 /\ 4 >= a /\ b = c /\ d = e /\ f = g /\ h = a ]
		(?, 1)    lbl92(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ d >= 4 /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
		(?, 1)    lbl92(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, 0, g, h + 1) [ 1 >= d /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
		(?, 1)    lbl92(a, b, c, d, e, f, g, h) -> lbl82(a, 0, c, d, e, 1, g, h) [ d >= 2 /\ 3 >= d /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
		(?, 1)    lbl82(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, f, g, h + 1) [ h >= a /\ h >= 3 /\ 4 >= h /\ f = 10 /\ b = 9 ]
		(?, 1)    lbl82(a, b, c, d, e, f, g, h) -> lbl82(a, f, c, d, e, f + 1, g, h) [ h >= 3 /\ 8 >= b /\ 9 >= b /\ b >= 0 /\ h >= a /\ 4 >= h /\ f = b + 1 ]
		(1, 1)    start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, 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, e, f, g, h) -> lbl92(a, b, c, h, e, 0, g, h + 1) [ 2 >= a /\ b = c /\ d = e /\ f = g /\ h = a ]
		(?, 1)    start(a, b, c, d, e, f, g, h) -> lbl82(a, 0, c, d, e, 1, g, h) [ a >= 3 /\ 4 >= a /\ b = c /\ d = e /\ f = g /\ h = a ]
		(?, 1)    lbl92(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, 0, g, h + 1) [ 1 >= d /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
		(?, 1)    lbl92(a, b, c, d, e, f, g, h) -> lbl82(a, 0, c, d, e, 1, g, h) [ d >= 2 /\ 3 >= d /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
		(?, 1)    lbl82(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, f, g, h + 1) [ h >= a /\ h >= 3 /\ 4 >= h /\ f = 10 /\ b = 9 ]
		(?, 1)    lbl82(a, b, c, d, e, f, g, h) -> lbl82(a, f, c, d, e, f + 1, g, h) [ h >= 3 /\ 8 >= b /\ 9 >= b /\ b >= 0 /\ h >= a /\ 4 >= h /\ f = b + 1 ]
		(1, 1)    start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a)
	start location:	start0
	leaf cost:	2

Repeatedly propagating knowledge in problem 3 produces the following problem:
4:	T:
		(1, 1)    start(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, 0, g, h + 1) [ 2 >= a /\ b = c /\ d = e /\ f = g /\ h = a ]
		(1, 1)    start(a, b, c, d, e, f, g, h) -> lbl82(a, 0, c, d, e, 1, g, h) [ a >= 3 /\ 4 >= a /\ b = c /\ d = e /\ f = g /\ h = a ]
		(?, 1)    lbl92(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, 0, g, h + 1) [ 1 >= d /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
		(?, 1)    lbl92(a, b, c, d, e, f, g, h) -> lbl82(a, 0, c, d, e, 1, g, h) [ d >= 2 /\ 3 >= d /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
		(?, 1)    lbl82(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, f, g, h + 1) [ h >= a /\ h >= 3 /\ 4 >= h /\ f = 10 /\ b = 9 ]
		(?, 1)    lbl82(a, b, c, d, e, f, g, h) -> lbl82(a, f, c, d, e, f + 1, g, h) [ h >= 3 /\ 8 >= b /\ 9 >= b /\ b >= 0 /\ h >= a /\ 4 >= h /\ f = b + 1 ]
		(1, 1)    start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a)
	start location:	start0
	leaf cost:	2

A polynomial rank function with
	Pol(start) = -11*V_8 + 54
	Pol(lbl92) = -11*V_8 + 55
	Pol(lbl82) = -V_6 - 11*V_8 + 55
	Pol(start0) = -11*V_1 + 54
orients all transitions weakly and the transitions
	lbl92(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, 0, g, h + 1) [ 1 >= d /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
	lbl92(a, b, c, d, e, f, g, h) -> lbl82(a, 0, c, d, e, 1, g, h) [ d >= 2 /\ 3 >= d /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
	lbl82(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, f, g, h + 1) [ h >= a /\ h >= 3 /\ 4 >= h /\ f = 10 /\ b = 9 ]
	lbl82(a, b, c, d, e, f, g, h) -> lbl82(a, f, c, d, e, f + 1, g, h) [ h >= 3 /\ 8 >= b /\ 9 >= b /\ b >= 0 /\ h >= a /\ 4 >= h /\ f = b + 1 ]
strictly and produces the following problem:
5:	T:
		(1, 1)            start(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, 0, g, h + 1) [ 2 >= a /\ b = c /\ d = e /\ f = g /\ h = a ]
		(1, 1)            start(a, b, c, d, e, f, g, h) -> lbl82(a, 0, c, d, e, 1, g, h) [ a >= 3 /\ 4 >= a /\ b = c /\ d = e /\ f = g /\ h = a ]
		(11*a + 54, 1)    lbl92(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, 0, g, h + 1) [ 1 >= d /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
		(11*a + 54, 1)    lbl92(a, b, c, d, e, f, g, h) -> lbl82(a, 0, c, d, e, 1, g, h) [ d >= 2 /\ 3 >= d /\ d >= a /\ f + 10 >= 5*d /\ f >= 0 /\ h = d + 1 ]
		(11*a + 54, 1)    lbl82(a, b, c, d, e, f, g, h) -> lbl92(a, b, c, h, e, f, g, h + 1) [ h >= a /\ h >= 3 /\ 4 >= h /\ f = 10 /\ b = 9 ]
		(11*a + 54, 1)    lbl82(a, b, c, d, e, f, g, h) -> lbl82(a, f, c, d, e, f + 1, g, h) [ h >= 3 /\ 8 >= b /\ 9 >= b /\ b >= 0 /\ h >= a /\ 4 >= h /\ f = b + 1 ]
		(1, 1)            start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a)
	start location:	start0
	leaf cost:	2

Complexity upper bound 44*a + 221

Time: 0.714 sec (SMT: 0.679 sec)