YES(?, 10)

Initial complexity problem:
1:	T:
		(1, 1)    f0(a) -> f4(b)
		(?, 1)    f4(a) -> f4(a + 1) [ 3 >= a /\ a >= 1 ]
		(?, 1)    f4(a) -> f4(1) [ 0 >= a /\ 3 >= a ]
		(?, 1)    f4(a) -> f12(a) [ a >= 4 ]
	start location:	f0
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem:
2:	T:
		(1, 1)    f0(a) -> f4(b)
		(?, 1)    f4(a) -> f4(a + 1) [ 3 >= a /\ a >= 1 ]
		(?, 1)    f4(a) -> f4(1) [ 0 >= a /\ 3 >= a ]
	start location:	f0
	leaf cost:	1

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(1, 1)    f0(a) -> f4(b)
		(?, 1)    f4(a) -> f4(a + 1) [ 3 >= a /\ a >= 1 ]
		(1, 1)    f4(a) -> f4(1) [ 0 >= a /\ 3 >= a ]
	start location:	f0
	leaf cost:	1

By chaining the transition f4(a) -> f4(1) [ 0 >= a /\ 3 >= a ] with all transitions in problem 3, the following new transition is obtained:
	f4(a) -> f4(2) [ 0 >= a /\ 3 >= a /\ 3 >= 1 /\ 1 >= 1 ]
We thus obtain the following problem:
4:	T:
		(1, 2)    f4(a) -> f4(2) [ 0 >= a /\ 3 >= a /\ 3 >= 1 /\ 1 >= 1 ]
		(1, 1)    f0(a) -> f4(b)
		(?, 1)    f4(a) -> f4(a + 1) [ 3 >= a /\ a >= 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f4(a) -> f4(2) [ 0 >= a /\ 3 >= a /\ 3 >= 1 /\ 1 >= 1 ] with all transitions in problem 4, the following new transition is obtained:
	f4(a) -> f4(3) [ 0 >= a /\ 3 >= a /\ 3 >= 1 /\ 1 >= 1 /\ 3 >= 2 /\ 2 >= 1 ]
We thus obtain the following problem:
5:	T:
		(1, 3)    f4(a) -> f4(3) [ 0 >= a /\ 3 >= a /\ 3 >= 1 /\ 1 >= 1 /\ 3 >= 2 /\ 2 >= 1 ]
		(1, 1)    f0(a) -> f4(b)
		(?, 1)    f4(a) -> f4(a + 1) [ 3 >= a /\ a >= 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f4(a) -> f4(3) [ 0 >= a /\ 3 >= a /\ 3 >= 1 /\ 1 >= 1 /\ 3 >= 2 /\ 2 >= 1 ] with all transitions in problem 5, the following new transition is obtained:
	f4(a) -> f4(4) [ 0 >= a /\ 3 >= a /\ 3 >= 1 /\ 1 >= 1 /\ 3 >= 2 /\ 2 >= 1 /\ 3 >= 3 ]
We thus obtain the following problem:
6:	T:
		(1, 4)    f4(a) -> f4(4) [ 0 >= a /\ 3 >= a /\ 3 >= 1 /\ 1 >= 1 /\ 3 >= 2 /\ 2 >= 1 /\ 3 >= 3 ]
		(1, 1)    f0(a) -> f4(b)
		(?, 1)    f4(a) -> f4(a + 1) [ 3 >= a /\ a >= 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f0(a) -> f4(b) with all transitions in problem 6, the following new transitions are obtained:
	f0(a) -> f4(4) [ 0 >= b /\ 3 >= b /\ 3 >= 1 /\ 1 >= 1 /\ 3 >= 2 /\ 2 >= 1 /\ 3 >= 3 ]
	f0(a) -> f4(b + 1) [ 3 >= b /\ b >= 1 ]
We thus obtain the following problem:
7:	T:
		(1, 5)    f0(a) -> f4(4) [ 0 >= b /\ 3 >= b /\ 3 >= 1 /\ 1 >= 1 /\ 3 >= 2 /\ 2 >= 1 /\ 3 >= 3 ]
		(1, 2)    f0(a) -> f4(b + 1) [ 3 >= b /\ b >= 1 ]
		(1, 4)    f4(a) -> f4(4) [ 0 >= a /\ 3 >= a /\ 3 >= 1 /\ 1 >= 1 /\ 3 >= 2 /\ 2 >= 1 /\ 3 >= 3 ]
		(?, 1)    f4(a) -> f4(a + 1) [ 3 >= a /\ a >= 1 ]
	start location:	f0
	leaf cost:	1

Testing for reachability in the complexity graph removes the following transition from problem 7:
	f4(a) -> f4(4) [ 0 >= a /\ 3 >= a /\ 3 >= 1 /\ 1 >= 1 /\ 3 >= 2 /\ 2 >= 1 /\ 3 >= 3 ]
We thus obtain the following problem:
8:	T:
		(?, 1)    f4(a) -> f4(a + 1) [ 3 >= a /\ a >= 1 ]
		(1, 2)    f0(a) -> f4(b + 1) [ 3 >= b /\ b >= 1 ]
		(1, 5)    f0(a) -> f4(4) [ 0 >= b /\ 3 >= b /\ 3 >= 1 /\ 1 >= 1 /\ 3 >= 2 /\ 2 >= 1 /\ 3 >= 3 ]
	start location:	f0
	leaf cost:	1

A polynomial rank function with
	Pol(f4) = -V_1 + 4
	Pol(f0) = 2
orients all transitions weakly and the transition
	f4(a) -> f4(a + 1) [ 3 >= a /\ a >= 1 ]
strictly and produces the following problem:
9:	T:
		(2, 1)    f4(a) -> f4(a + 1) [ 3 >= a /\ a >= 1 ]
		(1, 2)    f0(a) -> f4(b + 1) [ 3 >= b /\ b >= 1 ]
		(1, 5)    f0(a) -> f4(4) [ 0 >= b /\ 3 >= b /\ 3 >= 1 /\ 1 >= 1 /\ 3 >= 2 /\ 2 >= 1 /\ 3 >= 3 ]
	start location:	f0
	leaf cost:	1

Complexity upper bound 10

Time: 0.294 sec (SMT: 0.275 sec)