YES(?, 12*b + 8*b^2 + 5)

Initial complexity problem:
1:	T:
		(1, 1)    f0(a, b, c, d) -> f4(0, b, c, d)
		(?, 1)    f4(a, b, c, d) -> f7(a, b, a + 1, d) [ b >= a + 1 ]
		(?, 1)    f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b >= c + 1 ]
		(?, 1)    f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\ 0 >= e + 1 ]
		(?, 1)    f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\ e >= 1 ]
		(?, 1)    f7(a, b, c, d) -> f4(a + 1, b, c, d) [ c >= b ]
		(?, 1)    f4(a, b, c, d) -> f19(a, b, c, d) [ a >= b ]
	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, b, c, d) -> f4(0, b, c, d)
		(?, 1)    f4(a, b, c, d) -> f7(a, b, a + 1, d) [ b >= a + 1 ]
		(?, 1)    f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b >= c + 1 ]
		(?, 1)    f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\ 0 >= e + 1 ]
		(?, 1)    f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\ e >= 1 ]
		(?, 1)    f7(a, b, c, d) -> f4(a + 1, b, c, d) [ c >= b ]
	start location:	f0
	leaf cost:	1

A polynomial rank function with
	Pol(f0) = 2*V_2 - 1
	Pol(f4) = -2*V_1 + 2*V_2 - 1
	Pol(f7) = -2*V_1 + 2*V_2 - 2
orients all transitions weakly and the transition
	f4(a, b, c, d) -> f7(a, b, a + 1, d) [ b >= a + 1 ]
strictly and produces the following problem:
3:	T:
		(1, 1)          f0(a, b, c, d) -> f4(0, b, c, d)
		(2*b + 1, 1)    f4(a, b, c, d) -> f7(a, b, a + 1, d) [ b >= a + 1 ]
		(?, 1)          f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b >= c + 1 ]
		(?, 1)          f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\ 0 >= e + 1 ]
		(?, 1)          f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\ e >= 1 ]
		(?, 1)          f7(a, b, c, d) -> f4(a + 1, b, c, d) [ c >= b ]
	start location:	f0
	leaf cost:	1

A polynomial rank function with
	Pol(f7) = 1
	Pol(f4) = 0
and size complexities
	S("f7(a, b, c, d) -> f4(a + 1, b, c, d) [ c >= b ]", 0-0) = ?
	S("f7(a, b, c, d) -> f4(a + 1, b, c, d) [ c >= b ]", 0-1) = ?
	S("f7(a, b, c, d) -> f4(a + 1, b, c, d) [ c >= b ]", 0-2) = ?
	S("f7(a, b, c, d) -> f4(a + 1, b, c, d) [ c >= b ]", 0-3) = ?
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\\ e >= 1 ]", 0-0) = ?
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\\ e >= 1 ]", 0-1) = ?
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\\ e >= 1 ]", 0-2) = ?
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\\ e >= 1 ]", 0-3) = ?
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\\ 0 >= e + 1 ]", 0-0) = ?
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\\ 0 >= e + 1 ]", 0-1) = ?
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\\ 0 >= e + 1 ]", 0-2) = ?
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\\ 0 >= e + 1 ]", 0-3) = ?
	S("f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b >= c + 1 ]", 0-0) = ?
	S("f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b >= c + 1 ]", 0-1) = ?
	S("f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b >= c + 1 ]", 0-2) = ?
	S("f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b >= c + 1 ]", 0-3) = 0
	S("f4(a, b, c, d) -> f7(a, b, a + 1, d) [ b >= a + 1 ]", 0-0) = ?
	S("f4(a, b, c, d) -> f7(a, b, a + 1, d) [ b >= a + 1 ]", 0-1) = ?
	S("f4(a, b, c, d) -> f7(a, b, a + 1, d) [ b >= a + 1 ]", 0-2) = ?
	S("f4(a, b, c, d) -> f7(a, b, a + 1, d) [ b >= a + 1 ]", 0-3) = ?
	S("f0(a, b, c, d) -> f4(0, b, c, d)", 0-0) = 0
	S("f0(a, b, c, d) -> f4(0, b, c, d)", 0-1) = b
	S("f0(a, b, c, d) -> f4(0, b, c, d)", 0-2) = c
	S("f0(a, b, c, d) -> f4(0, b, c, d)", 0-3) = d
orients the transitions
	f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b >= c + 1 ]
	f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\ e >= 1 ]
	f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\ 0 >= e + 1 ]
	f7(a, b, c, d) -> f4(a + 1, b, c, d) [ c >= b ]
weakly and the transition
	f7(a, b, c, d) -> f4(a + 1, b, c, d) [ c >= b ]
strictly and produces the following problem:
4:	T:
		(1, 1)          f0(a, b, c, d) -> f4(0, b, c, d)
		(2*b + 1, 1)    f4(a, b, c, d) -> f7(a, b, a + 1, d) [ b >= a + 1 ]
		(?, 1)          f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b >= c + 1 ]
		(?, 1)          f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\ 0 >= e + 1 ]
		(?, 1)          f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b >= c + 1 /\ e >= 1 ]
		(2*b + 1, 1)    f7(a, b, c, d) -> f4(a + 1, b, c, d) [ c >= b ]
	start location:	f0
	leaf cost:	1

Applied AI with 'oct' on problem 4 to obtain the following invariants:
  For symbol f4: X_1 >= 0
  For symbol f7: X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0


This yielded the following problem:
5:	T:
		(2*b + 1, 1)    f7(a, b, c, d) -> f4(a + 1, b, c, d) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ c >= b ]
		(?, 1)          f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 /\ e >= 1 ]
		(?, 1)          f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 /\ 0 >= e + 1 ]
		(?, 1)          f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 ]
		(2*b + 1, 1)    f4(a, b, c, d) -> f7(a, b, a + 1, d) [ a >= 0 /\ b >= a + 1 ]
		(1, 1)          f0(a, b, c, d) -> f4(0, b, c, d)
	start location:	f0
	leaf cost:	1

A polynomial rank function with
	Pol(f7) = V_2
	Pol(f4) = V_2
	Pol(f0) = V_2
orients all transitions weakly and the transitions
	f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 /\ e >= 1 ]
	f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 /\ 0 >= e + 1 ]
strictly and produces the following problem:
6:	T:
		(2*b + 1, 1)    f7(a, b, c, d) -> f4(a + 1, b, c, d) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ c >= b ]
		(b, 1)          f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 /\ e >= 1 ]
		(b, 1)          f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 /\ 0 >= e + 1 ]
		(?, 1)          f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 ]
		(2*b + 1, 1)    f4(a, b, c, d) -> f7(a, b, a + 1, d) [ a >= 0 /\ b >= a + 1 ]
		(1, 1)          f0(a, b, c, d) -> f4(0, b, c, d)
	start location:	f0
	leaf cost:	1

A polynomial rank function with
	Pol(f7) = V_2 - V_3 + 1
and size complexities
	S("f0(a, b, c, d) -> f4(0, b, c, d)", 0-0) = 0
	S("f0(a, b, c, d) -> f4(0, b, c, d)", 0-1) = b
	S("f0(a, b, c, d) -> f4(0, b, c, d)", 0-2) = c
	S("f0(a, b, c, d) -> f4(0, b, c, d)", 0-3) = d
	S("f4(a, b, c, d) -> f7(a, b, a + 1, d) [ a >= 0 /\\ b >= a + 1 ]", 0-0) = b
	S("f4(a, b, c, d) -> f7(a, b, a + 1, d) [ a >= 0 /\\ b >= a + 1 ]", 0-1) = b
	S("f4(a, b, c, d) -> f7(a, b, a + 1, d) [ a >= 0 /\\ b >= a + 1 ]", 0-2) = b
	S("f4(a, b, c, d) -> f7(a, b, a + 1, d) [ a >= 0 /\\ b >= a + 1 ]", 0-3) = ?
	S("f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ b >= c + 1 ]", 0-0) = b
	S("f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ b >= c + 1 ]", 0-1) = b
	S("f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ b >= c + 1 ]", 0-2) = b
	S("f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ b >= c + 1 ]", 0-3) = 0
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ b >= c + 1 /\\ 0 >= e + 1 ]", 0-0) = b
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ b >= c + 1 /\\ 0 >= e + 1 ]", 0-1) = b
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ b >= c + 1 /\\ 0 >= e + 1 ]", 0-2) = b
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ b >= c + 1 /\\ 0 >= e + 1 ]", 0-3) = ?
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ b >= c + 1 /\\ e >= 1 ]", 0-0) = b
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ b >= c + 1 /\\ e >= 1 ]", 0-1) = b
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ b >= c + 1 /\\ e >= 1 ]", 0-2) = b
	S("f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ b >= c + 1 /\\ e >= 1 ]", 0-3) = ?
	S("f7(a, b, c, d) -> f4(a + 1, b, c, d) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ c >= b ]", 0-0) = b
	S("f7(a, b, c, d) -> f4(a + 1, b, c, d) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ c >= b ]", 0-1) = b
	S("f7(a, b, c, d) -> f4(a + 1, b, c, d) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ c >= b ]", 0-2) = b
	S("f7(a, b, c, d) -> f4(a + 1, b, c, d) [ b - c >= 0 /\\ c - 1 >= 0 /\\ b + c - 2 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c - 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 1 >= 0 /\\ -a + b - 1 >= 0 /\\ a >= 0 /\\ c >= b ]", 0-3) = ?
orients the transition
	f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 ]
weakly and the transition
	f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 ]
strictly and produces the following problem:
7:	T:
		(2*b + 1, 1)            f7(a, b, c, d) -> f4(a + 1, b, c, d) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ c >= b ]
		(b, 1)                  f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 /\ e >= 1 ]
		(b, 1)                  f7(a, b, c, d) -> f7(a, b - 1, c, e) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 /\ 0 >= e + 1 ]
		(8*b^2 + 6*b + 1, 1)    f7(a, b, c, d) -> f7(a, b, c + 1, 0) [ b - c >= 0 /\ c - 1 >= 0 /\ b + c - 2 >= 0 /\ a + c - 1 >= 0 /\ -a + c - 1 >= 0 /\ b - 1 >= 0 /\ a + b - 1 >= 0 /\ -a + b - 1 >= 0 /\ a >= 0 /\ b >= c + 1 ]
		(2*b + 1, 1)            f4(a, b, c, d) -> f7(a, b, a + 1, d) [ a >= 0 /\ b >= a + 1 ]
		(1, 1)                  f0(a, b, c, d) -> f4(0, b, c, d)
	start location:	f0
	leaf cost:	1

Complexity upper bound 12*b + 8*b^2 + 5

Time: 0.615 sec (SMT: 0.576 sec)