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

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

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

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

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

Complexity upper bound 2*a + b + 2

Time: 0.296 sec (SMT: 0.285 sec)