YES(?, 2*a + 2*b + 7)

Initial complexity problem:
1:	T:
		(?, 1)    eval1(a, b) -> eval2(a, b) [ a >= 1 /\ b >= 1 /\ a >= b + 1 ]
		(?, 1)    eval1(a, b) -> eval3(a, b) [ a >= 1 /\ b >= 1 /\ b >= a ]
		(?, 1)    eval2(a, b) -> eval2(a - 1, b) [ a >= 1 ]
		(?, 1)    eval2(a, b) -> eval1(a, b) [ 0 >= a ]
		(?, 1)    eval3(a, b) -> eval3(a, b - 1) [ b >= 1 ]
		(?, 1)    eval3(a, b) -> eval1(a, b) [ 0 >= b ]
		(1, 1)    start(a, b) -> eval1(a, b)
	start location:	start
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem:
2:	T:
		(?, 1)    eval1(a, b) -> eval2(a, b) [ a >= 1 /\ b >= 1 /\ a >= b + 1 ]
		(?, 1)    eval1(a, b) -> eval3(a, b) [ a >= 1 /\ b >= 1 /\ b >= a ]
		(?, 1)    eval2(a, b) -> eval2(a - 1, b) [ a >= 1 ]
		(?, 1)    eval3(a, b) -> eval3(a, b - 1) [ b >= 1 ]
		(1, 1)    start(a, b) -> eval1(a, b)
	start location:	start
	leaf cost:	2

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(1, 1)    eval1(a, b) -> eval2(a, b) [ a >= 1 /\ b >= 1 /\ a >= b + 1 ]
		(1, 1)    eval1(a, b) -> eval3(a, b) [ a >= 1 /\ b >= 1 /\ b >= a ]
		(?, 1)    eval2(a, b) -> eval2(a - 1, b) [ a >= 1 ]
		(?, 1)    eval3(a, b) -> eval3(a, b - 1) [ b >= 1 ]
		(1, 1)    start(a, b) -> eval1(a, b)
	start location:	start
	leaf cost:	2

A polynomial rank function with
	Pol(eval1) = V_1 + V_2 - 1
	Pol(eval2) = V_1
	Pol(eval3) = V_2
	Pol(start) = V_1 + V_2 - 1
orients all transitions weakly and the transitions
	eval3(a, b) -> eval3(a, b - 1) [ b >= 1 ]
	eval2(a, b) -> eval2(a - 1, b) [ a >= 1 ]
strictly and produces the following problem:
4:	T:
		(1, 1)            eval1(a, b) -> eval2(a, b) [ a >= 1 /\ b >= 1 /\ a >= b + 1 ]
		(1, 1)            eval1(a, b) -> eval3(a, b) [ a >= 1 /\ b >= 1 /\ b >= a ]
		(a + b + 1, 1)    eval2(a, b) -> eval2(a - 1, b) [ a >= 1 ]
		(a + b + 1, 1)    eval3(a, b) -> eval3(a, b - 1) [ b >= 1 ]
		(1, 1)            start(a, b) -> eval1(a, b)
	start location:	start
	leaf cost:	2

Complexity upper bound 2*a + 2*b + 7

Time: 0.177 sec (SMT: 0.168 sec)