YES(?, 2*a + 2*b + 2*c + 1)

Initial complexity problem:
1:	T:
		(?, 1)    eval(a, b, c) -> eval(a - 1, b, c) [ a + b >= c + 1 /\ c >= 0 /\ a >= 1 ]
		(?, 1)    eval(a, b, c) -> eval(a, b - 1, c) [ a + b >= c + 1 /\ c >= 0 /\ 0 >= a /\ b >= 1 ]
		(?, 1)    eval(a, b, c) -> eval(a, b, c) [ a + b >= c + 1 /\ c >= 0 /\ 0 >= a /\ 0 >= b ]
		(1, 1)    start(a, b, c) -> eval(a, b, c)
	start location:	start
	leaf cost:	0

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

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

Complexity upper bound 2*a + 2*b + 2*c + 1

Time: 0.159 sec (SMT: 0.150 sec)