YES(?, 2003)

Initial complexity problem:
1:	T:
		(?, 1)    f8(a, b, c, d) -> f8(a - 1, b, c, d) [ a >= 0 ]
		(?, 1)    f19(a, b, c, d) -> f19(a, b - 1, c, d) [ b >= 0 ]
		(?, 1)    f28(a, b, c, d) -> f28(a, b, c - 1, d) [ c >= 0 ]
		(?, 1)    f28(a, b, c, d) -> f36(a, b, c, d) [ 0 >= c + 1 ]
		(?, 1)    f19(a, b, c, d) -> f28(a, b, 999, d) [ 0 >= b + 1 ]
		(1, 1)    f0(a, b, c, d) -> f19(a, 999, c, 1)
		(?, 1)    f8(a, b, c, d) -> f19(a, 999, c, d) [ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem:
2:	T:
		(?, 1)    f8(a, b, c, d) -> f8(a - 1, b, c, d) [ a >= 0 ]
		(?, 1)    f19(a, b, c, d) -> f19(a, b - 1, c, d) [ b >= 0 ]
		(?, 1)    f28(a, b, c, d) -> f28(a, b, c - 1, d) [ c >= 0 ]
		(?, 1)    f19(a, b, c, d) -> f28(a, b, 999, d) [ 0 >= b + 1 ]
		(1, 1)    f0(a, b, c, d) -> f19(a, 999, c, 1)
		(?, 1)    f8(a, b, c, d) -> f19(a, 999, c, d) [ 0 >= a + 1 ]
	start location:	f0
	leaf cost:	1

Testing for reachability in the complexity graph removes the following transitions from problem 2:
	f8(a, b, c, d) -> f8(a - 1, b, c, d) [ a >= 0 ]
	f8(a, b, c, d) -> f19(a, 999, c, d) [ 0 >= a + 1 ]
We thus obtain the following problem:
3:	T:
		(?, 1)    f28(a, b, c, d) -> f28(a, b, c - 1, d) [ c >= 0 ]
		(?, 1)    f19(a, b, c, d) -> f28(a, b, 999, d) [ 0 >= b + 1 ]
		(?, 1)    f19(a, b, c, d) -> f19(a, b - 1, c, d) [ b >= 0 ]
		(1, 1)    f0(a, b, c, d) -> f19(a, 999, c, 1)
	start location:	f0
	leaf cost:	1

A polynomial rank function with
	Pol(f28) = 0
	Pol(f19) = 1
	Pol(f0) = 1
orients all transitions weakly and the transition
	f19(a, b, c, d) -> f28(a, b, 999, d) [ 0 >= b + 1 ]
strictly and produces the following problem:
4:	T:
		(?, 1)    f28(a, b, c, d) -> f28(a, b, c - 1, d) [ c >= 0 ]
		(1, 1)    f19(a, b, c, d) -> f28(a, b, 999, d) [ 0 >= b + 1 ]
		(?, 1)    f19(a, b, c, d) -> f19(a, b - 1, c, d) [ b >= 0 ]
		(1, 1)    f0(a, b, c, d) -> f19(a, 999, c, 1)
	start location:	f0
	leaf cost:	1

A polynomial rank function with
	Pol(f28) = V_2 + V_3 - 998
	Pol(f19) = V_2 + 1
	Pol(f0) = 1000
orients all transitions weakly and the transition
	f19(a, b, c, d) -> f19(a, b - 1, c, d) [ b >= 0 ]
strictly and produces the following problem:
5:	T:
		(?, 1)       f28(a, b, c, d) -> f28(a, b, c - 1, d) [ c >= 0 ]
		(1, 1)       f19(a, b, c, d) -> f28(a, b, 999, d) [ 0 >= b + 1 ]
		(1000, 1)    f19(a, b, c, d) -> f19(a, b - 1, c, d) [ b >= 0 ]
		(1, 1)       f0(a, b, c, d) -> f19(a, 999, c, 1)
	start location:	f0
	leaf cost:	1

A polynomial rank function with
	Pol(f28) = V_3 + 1
	Pol(f19) = 1000
	Pol(f0) = 1000
orients all transitions weakly and the transition
	f28(a, b, c, d) -> f28(a, b, c - 1, d) [ c >= 0 ]
strictly and produces the following problem:
6:	T:
		(1000, 1)    f28(a, b, c, d) -> f28(a, b, c - 1, d) [ c >= 0 ]
		(1, 1)       f19(a, b, c, d) -> f28(a, b, 999, d) [ 0 >= b + 1 ]
		(1000, 1)    f19(a, b, c, d) -> f19(a, b - 1, c, d) [ b >= 0 ]
		(1, 1)       f0(a, b, c, d) -> f19(a, 999, c, 1)
	start location:	f0
	leaf cost:	1

Complexity upper bound 2003

Time: 0.213 sec (SMT: 0.202 sec)