YES(?, 3*a + 3*b + 1)

Initial complexity problem:
1:	T:
		(?, 1)    eval(a, b) -> eval(a - 1, b) [ a + b >= 1 /\ a >= b + 1 ]
		(?, 1)    eval(a, b) -> eval(a - 1, b) [ 2*a >= 1 /\ b = a ]
		(?, 1)    eval(a, b) -> eval(a, b - 1) [ a + b >= 1 /\ b >= a /\ b >= a + 1 ]
		(?, 1)    eval(a, b) -> eval(a, b - 1) [ a + b >= 1 /\ b >= a /\ a >= b + 1 ]
		(1, 1)    start(a, b) -> eval(a, b)
	start location:	start
	leaf cost:	0

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

A polynomial rank function with
	Pol(eval) = V_1 + V_2
	Pol(start) = V_1 + V_2
orients all transitions weakly and the transitions
	eval(a, b) -> eval(a, b - 1) [ a + b >= 1 /\ b >= a /\ b >= a + 1 ]
	eval(a, b) -> eval(a - 1, b) [ a + b >= 1 /\ a >= b + 1 ]
	eval(a, b) -> eval(a - 1, b) [ 2*a >= 1 /\ b = a ]
strictly and produces the following problem:
3:	T:
		(a + b, 1)    eval(a, b) -> eval(a - 1, b) [ a + b >= 1 /\ a >= b + 1 ]
		(a + b, 1)    eval(a, b) -> eval(a - 1, b) [ 2*a >= 1 /\ b = a ]
		(a + b, 1)    eval(a, b) -> eval(a, b - 1) [ a + b >= 1 /\ b >= a /\ b >= a + 1 ]
		(1, 1)        start(a, b) -> eval(a, b)
	start location:	start
	leaf cost:	0

Complexity upper bound 3*a + 3*b + 1

Time: 0.220 sec (SMT: 0.210 sec)