MAYBE

Initial complexity problem:
1:	T:
		(?, 1)    f13(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f47(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) [ a >= b ]
		(?, 1)    f39(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f47(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) [ c >= 3 ]
		(?, 1)    f39(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f47(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) [ 1 >= c ]
		(?, 1)    f54(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f54(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w)
		(?, 1)    f56(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f59(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w)
		(?, 1)    f47(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f54(a, b, c, d, 0, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) [ d >= 1 ]
		(?, 1)    f47(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f54(a, b, c, d, 0, 0, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) [ 0 >= d ]
		(?, 1)    f39(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f47(a, b, 2, d, e + 1, f, h, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) [ c = 2 ]
		(?, 1)    f13(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f47(a, b, c, d, e, f, g, x, y, z, a1, e, x, x, x, p, q, r, s, t, u, v, w) [ x >= 1 /\ b >= a + 1 ]
		(?, 1)    f13(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f39(a, b, b1, d, e, f, g, x, y, z, a1, e, x, x, x, x, r, 0, b1, b1, b1, 0, w) [ b >= a + 1 /\ 0 >= x /\ b1 >= 2 ]
		(?, 1)    f13(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f39(a, b, b1, d, e, f, g, x, y, z, a1, e, x, x, x, x, r, 0, b1, b1, b1, 0, w) [ b >= a + 1 /\ 0 >= x /\ 0 >= b1 ]
		(?, 1)    f13(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f13(a + 1, b, 1, d, e, f, g, x, y, z, a1, e, x, x, x, x, r, r, 1, 1, 1, 0, w) [ 0 >= x /\ b >= a + 1 ]
		(1, 1)    f0(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f13(a, b, c, y, e, 0, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, 0) [ 0 >= y ]
		(1, 1)    f0(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> f13(a, b, c, y, e, 0, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, 0) [ y >= 1 ]
	start location:	f0
	leaf cost:	0

Slicing away variables that do not contribute to conditions from problem 1 leaves variables [a, b, c, d].
We thus obtain the following problem:
2:	T:
		(1, 1)    f0(a, b, c, d) -> f13(a, b, c, y) [ y >= 1 ]
		(1, 1)    f0(a, b, c, d) -> f13(a, b, c, y) [ 0 >= y ]
		(?, 1)    f13(a, b, c, d) -> f13(a + 1, b, 1, d) [ 0 >= x /\ b >= a + 1 ]
		(?, 1)    f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ 0 >= b1 ]
		(?, 1)    f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ b1 >= 2 ]
		(?, 1)    f13(a, b, c, d) -> f47(a, b, c, d) [ x >= 1 /\ b >= a + 1 ]
		(?, 1)    f39(a, b, c, d) -> f47(a, b, 2, d) [ c = 2 ]
		(?, 1)    f47(a, b, c, d) -> f54(a, b, c, d) [ 0 >= d ]
		(?, 1)    f47(a, b, c, d) -> f54(a, b, c, d) [ d >= 1 ]
		(?, 1)    f56(a, b, c, d) -> f59(a, b, c, d)
		(?, 1)    f54(a, b, c, d) -> f54(a, b, c, d)
		(?, 1)    f39(a, b, c, d) -> f47(a, b, c, d) [ 1 >= c ]
		(?, 1)    f39(a, b, c, d) -> f47(a, b, c, d) [ c >= 3 ]
		(?, 1)    f13(a, b, c, d) -> f47(a, b, c, d) [ a >= b ]
	start location:	f0
	leaf cost:	0

Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem:
3:	T:
		(1, 1)    f0(a, b, c, d) -> f13(a, b, c, y) [ y >= 1 ]
		(1, 1)    f0(a, b, c, d) -> f13(a, b, c, y) [ 0 >= y ]
		(?, 1)    f13(a, b, c, d) -> f13(a + 1, b, 1, d) [ 0 >= x /\ b >= a + 1 ]
		(?, 1)    f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ 0 >= b1 ]
		(?, 1)    f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ b1 >= 2 ]
		(?, 1)    f13(a, b, c, d) -> f47(a, b, c, d) [ x >= 1 /\ b >= a + 1 ]
		(?, 1)    f39(a, b, c, d) -> f47(a, b, 2, d) [ c = 2 ]
		(?, 1)    f47(a, b, c, d) -> f54(a, b, c, d) [ 0 >= d ]
		(?, 1)    f47(a, b, c, d) -> f54(a, b, c, d) [ d >= 1 ]
		(?, 1)    f54(a, b, c, d) -> f54(a, b, c, d)
		(?, 1)    f39(a, b, c, d) -> f47(a, b, c, d) [ 1 >= c ]
		(?, 1)    f39(a, b, c, d) -> f47(a, b, c, d) [ c >= 3 ]
		(?, 1)    f13(a, b, c, d) -> f47(a, b, c, d) [ a >= b ]
	start location:	f0
	leaf cost:	1

A polynomial rank function with
	Pol(f0) = 3
	Pol(f13) = 3
	Pol(f39) = 2
	Pol(f47) = 1
	Pol(f54) = 0
orients all transitions weakly and the transitions
	f47(a, b, c, d) -> f54(a, b, c, d) [ d >= 1 ]
	f47(a, b, c, d) -> f54(a, b, c, d) [ 0 >= d ]
	f39(a, b, c, d) -> f47(a, b, 2, d) [ c = 2 ]
	f39(a, b, c, d) -> f47(a, b, c, d) [ 1 >= c ]
	f39(a, b, c, d) -> f47(a, b, c, d) [ c >= 3 ]
	f13(a, b, c, d) -> f47(a, b, c, d) [ x >= 1 /\ b >= a + 1 ]
	f13(a, b, c, d) -> f47(a, b, c, d) [ a >= b ]
	f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ b1 >= 2 ]
	f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ 0 >= b1 ]
strictly and produces the following problem:
4:	T:
		(1, 1)    f0(a, b, c, d) -> f13(a, b, c, y) [ y >= 1 ]
		(1, 1)    f0(a, b, c, d) -> f13(a, b, c, y) [ 0 >= y ]
		(?, 1)    f13(a, b, c, d) -> f13(a + 1, b, 1, d) [ 0 >= x /\ b >= a + 1 ]
		(3, 1)    f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ 0 >= b1 ]
		(3, 1)    f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ b1 >= 2 ]
		(3, 1)    f13(a, b, c, d) -> f47(a, b, c, d) [ x >= 1 /\ b >= a + 1 ]
		(3, 1)    f39(a, b, c, d) -> f47(a, b, 2, d) [ c = 2 ]
		(3, 1)    f47(a, b, c, d) -> f54(a, b, c, d) [ 0 >= d ]
		(3, 1)    f47(a, b, c, d) -> f54(a, b, c, d) [ d >= 1 ]
		(?, 1)    f54(a, b, c, d) -> f54(a, b, c, d)
		(3, 1)    f39(a, b, c, d) -> f47(a, b, c, d) [ 1 >= c ]
		(3, 1)    f39(a, b, c, d) -> f47(a, b, c, d) [ c >= 3 ]
		(3, 1)    f13(a, b, c, d) -> f47(a, b, c, d) [ a >= b ]
	start location:	f0
	leaf cost:	1

A polynomial rank function with
	Pol(f0) = -V_1 + V_2
	Pol(f13) = -V_1 + V_2
	Pol(f39) = -V_1 + V_2
	Pol(f47) = -V_1 + V_2
	Pol(f54) = -V_1 + V_2
orients all transitions weakly and the transition
	f13(a, b, c, d) -> f13(a + 1, b, 1, d) [ 0 >= x /\ b >= a + 1 ]
strictly and produces the following problem:
5:	T:
		(1, 1)        f0(a, b, c, d) -> f13(a, b, c, y) [ y >= 1 ]
		(1, 1)        f0(a, b, c, d) -> f13(a, b, c, y) [ 0 >= y ]
		(a + b, 1)    f13(a, b, c, d) -> f13(a + 1, b, 1, d) [ 0 >= x /\ b >= a + 1 ]
		(3, 1)        f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ 0 >= b1 ]
		(3, 1)        f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ b1 >= 2 ]
		(3, 1)        f13(a, b, c, d) -> f47(a, b, c, d) [ x >= 1 /\ b >= a + 1 ]
		(3, 1)        f39(a, b, c, d) -> f47(a, b, 2, d) [ c = 2 ]
		(3, 1)        f47(a, b, c, d) -> f54(a, b, c, d) [ 0 >= d ]
		(3, 1)        f47(a, b, c, d) -> f54(a, b, c, d) [ d >= 1 ]
		(?, 1)        f54(a, b, c, d) -> f54(a, b, c, d)
		(3, 1)        f39(a, b, c, d) -> f47(a, b, c, d) [ 1 >= c ]
		(3, 1)        f39(a, b, c, d) -> f47(a, b, c, d) [ c >= 3 ]
		(3, 1)        f13(a, b, c, d) -> f47(a, b, c, d) [ a >= b ]
	start location:	f0
	leaf cost:	1

Applied AI with 'oct' on problem 5 to obtain the following invariants:
  For symbol f39: -X_1 + X_2 - 1 >= 0


This yielded the following problem:
6:	T:
		(3, 1)        f13(a, b, c, d) -> f47(a, b, c, d) [ a >= b ]
		(3, 1)        f39(a, b, c, d) -> f47(a, b, c, d) [ -a + b - 1 >= 0 /\ c >= 3 ]
		(3, 1)        f39(a, b, c, d) -> f47(a, b, c, d) [ -a + b - 1 >= 0 /\ 1 >= c ]
		(?, 1)        f54(a, b, c, d) -> f54(a, b, c, d)
		(3, 1)        f47(a, b, c, d) -> f54(a, b, c, d) [ d >= 1 ]
		(3, 1)        f47(a, b, c, d) -> f54(a, b, c, d) [ 0 >= d ]
		(3, 1)        f39(a, b, c, d) -> f47(a, b, 2, d) [ -a + b - 1 >= 0 /\ c = 2 ]
		(3, 1)        f13(a, b, c, d) -> f47(a, b, c, d) [ x >= 1 /\ b >= a + 1 ]
		(3, 1)        f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ b1 >= 2 ]
		(3, 1)        f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ 0 >= b1 ]
		(a + b, 1)    f13(a, b, c, d) -> f13(a + 1, b, 1, d) [ 0 >= x /\ b >= a + 1 ]
		(1, 1)        f0(a, b, c, d) -> f13(a, b, c, y) [ 0 >= y ]
		(1, 1)        f0(a, b, c, d) -> f13(a, b, c, y) [ y >= 1 ]
	start location:	f0
	leaf cost:	1

By chaining the transition f13(a, b, c, d) -> f47(a, b, c, d) [ a >= b ] with all transitions in problem 6, the following new transitions are obtained:
	f13(a, b, c, d) -> f54(a, b, c, d) [ a >= b /\ 0 >= d ]
	f13(a, b, c, d) -> f54(a, b, c, d) [ a >= b /\ d >= 1 ]
We thus obtain the following problem:
7:	T:
		(3, 2)        f13(a, b, c, d) -> f54(a, b, c, d) [ a >= b /\ 0 >= d ]
		(3, 2)        f13(a, b, c, d) -> f54(a, b, c, d) [ a >= b /\ d >= 1 ]
		(3, 1)        f39(a, b, c, d) -> f47(a, b, c, d) [ -a + b - 1 >= 0 /\ c >= 3 ]
		(3, 1)        f39(a, b, c, d) -> f47(a, b, c, d) [ -a + b - 1 >= 0 /\ 1 >= c ]
		(?, 1)        f54(a, b, c, d) -> f54(a, b, c, d)
		(3, 1)        f47(a, b, c, d) -> f54(a, b, c, d) [ d >= 1 ]
		(3, 1)        f47(a, b, c, d) -> f54(a, b, c, d) [ 0 >= d ]
		(3, 1)        f39(a, b, c, d) -> f47(a, b, 2, d) [ -a + b - 1 >= 0 /\ c = 2 ]
		(3, 1)        f13(a, b, c, d) -> f47(a, b, c, d) [ x >= 1 /\ b >= a + 1 ]
		(3, 1)        f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ b1 >= 2 ]
		(3, 1)        f13(a, b, c, d) -> f39(a, b, b1, d) [ b >= a + 1 /\ 0 >= x /\ 0 >= b1 ]
		(a + b, 1)    f13(a, b, c, d) -> f13(a + 1, b, 1, d) [ 0 >= x /\ b >= a + 1 ]
		(1, 1)        f0(a, b, c, d) -> f13(a, b, c, y) [ 0 >= y ]
		(1, 1)        f0(a, b, c, d) -> f13(a, b, c, y) [ y >= 1 ]
	start location:	f0
	leaf cost:	1

Complexity upper bound ?

Time: 0.958 sec (SMT: 0.883 sec)