MAYBE Initial complexity problem: 1: T: (?, 1) f79(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f81(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ 0 >= a ] (?, 1) f34(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f34(a, b - 1, f2, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ b >= 1 /\ 0 >= f2 ] (?, 1) f34(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f44(a, b - 1, f2, g2, h2, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ 0 >= g2 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f81(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f65(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ 0 >= f ] (?, 1) f65(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f75(a, b, c, d, e, f2, g - 1, g2, h2, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ g >= 1 /\ 0 >= g2 ] (?, 1) f75(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f79(f2, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ 0 >= i ] (?, 1) f206(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f206(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) (?, 1) f208(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f211(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) (?, 1) f190(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f190(a, b, c, d, e, f, g, h, i, j - 1, 1, 1, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ j >= 1 ] (?, 1) f190(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f206(a, b, c, d, e, f, g, h, i, j, k, l, 2, 0, f2, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ 0 >= j /\ m = 2 ] (?, 1) f190(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f206(a, b, c, d, e, f, g, h, i, j, k, l, m, 0, f2, 1, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ 1 >= m /\ 0 >= j ] (?, 1) f190(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f206(a, b, c, d, e, f, g, h, i, j, k, l, m, 0, f2, 1, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ m >= 3 /\ 0 >= j ] (?, 1) f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f190(a, b, c, d, e, f, g, h, i, h2, k, l, m, 0, o, p, 0, f2, f2, g2, h2, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ 0 >= f2 ] (?, 1) f155(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, 0, n, o, p, 0, r, s, t, u, v, v, v, 0, a1, a1, v, 0, v, a1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ v >= 1 ] (?, 1) f155(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, 0, r, s, t, u, v, v, x, y, z, a1, b1, c1, d1, e1, a1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ 0 >= v ] (?, 1) f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, 0, o, p, 0, f2, f2 - 1, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g2, h2, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ f2 >= 1 /\ 0 >= g2 ] (?, 1) f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, 0, o, p, 0, f2, f2 - 1, t, u, v, i2, x, y, z, 0, b1, c1, d1, e1, f1, g2, h2, 1, 0, 0, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ f2 >= 1 /\ g2 >= 1 ] (?, 1) f100(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, 0, o, p, 0, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, f2, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ 0 >= l1 ] (?, 1) f100(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f100(a, b, c, d, e, f, g, h, i, j, k, l, m, 0, o, p, 0, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1 - 1, m1, f2, g2, h2, f2, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ l1 >= 1 ] (?, 1) f81(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f65(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ f >= 1 ] (?, 1) f79(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f81(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ a >= 1 ] (?, 1) f75(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f79(f2, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ i >= 1 ] (?, 1) f65(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f75(a, b, c, d, e, f2, g - 1, g2, h2, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ g >= 1 /\ g2 >= 1 ] (?, 1) f65(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f100(a, b, c, d, e, f, g, h, i, j, k, l, m, 0, o, p, 0, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, g2, m1, n1, o1, p1, q1, f2, g2, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ 0 >= g ] (?, 1) f44(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f34(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, c, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ 0 >= e ] (?, 1) f44(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f34(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, c, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ e >= 1 ] (?, 1) f34(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f44(a, b - 1, f2, g2, h2, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ g2 >= 1 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f65(a, b, c, d, e, f, g2, h, i, j, k, l, m, 0, o, p, 0, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, f2, g2, w1, x1, y1, z1, a2, b2, c2, d2, e2) [ 0 >= b ] (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, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f34(a, h2, c, d, e, f, g, h, i, j, 0, l, 0, 0, o, 0, 0, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, 0, 0, f2, g2, 0, h2, c2, d2, e2) [ 0 >= g2 ] (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, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2) -> f34(a, i2, c, d, e, f, g, h, i, j, 0, l, 0, 0, o, 0, 0, r, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, 0, 0, f2, g2, 0, i2, 1, h2, 0) [ g2 >= 1 ] start location: f0 leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [a, b, e, f, g, i, j, m, v, l1]. We thus obtain the following problem: 2: T: (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, i2, e, f, g, i, j, 0, v, l1) [ g2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, h2, e, f, g, i, j, 0, v, l1) [ 0 >= g2 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g2, i, j, m, v, l1) [ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ g2 >= 1 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ 0 >= e ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, g2) [ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ g >= 1 /\ g2 >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ i >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ a >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ f >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, l1 - 1) [ l1 >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ 0 >= l1 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ f2 >= 1 /\ g2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ f2 >= 1 /\ 0 >= g2 ] (?, 1) f155(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ 0 >= v ] (?, 1) f155(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, 0, v, l1) [ v >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, h2, m, v, l1) [ 0 >= f2 ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ m >= 3 /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ 1 >= m /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, 2, v, l1) [ 0 >= j /\ m = 2 ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, j - 1, m, v, l1) [ j >= 1 ] (?, 1) f208(a, b, e, f, g, i, j, m, v, l1) -> f211(a, b, e, f, g, i, j, m, v, l1) (?, 1) f206(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ 0 >= i ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ g >= 1 /\ 0 >= g2 ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ 0 >= f ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ 0 >= g2 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b - 1, e, f, g, i, j, m, v, l1) [ b >= 1 /\ 0 >= f2 ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ 0 >= a ] 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, e, f, g, i, j, m, v, l1) -> f34(a, i2, e, f, g, i, j, 0, v, l1) [ g2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, h2, e, f, g, i, j, 0, v, l1) [ 0 >= g2 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g2, i, j, m, v, l1) [ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ g2 >= 1 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ 0 >= e ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, g2) [ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ g >= 1 /\ g2 >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ i >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ a >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ f >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, l1 - 1) [ l1 >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ 0 >= l1 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ f2 >= 1 /\ g2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ f2 >= 1 /\ 0 >= g2 ] (?, 1) f155(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ 0 >= v ] (?, 1) f155(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, 0, v, l1) [ v >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, h2, m, v, l1) [ 0 >= f2 ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ m >= 3 /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ 1 >= m /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, 2, v, l1) [ 0 >= j /\ m = 2 ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, j - 1, m, v, l1) [ j >= 1 ] (?, 1) f206(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ 0 >= i ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ g >= 1 /\ 0 >= g2 ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ 0 >= f ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ 0 >= g2 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b - 1, e, f, g, i, j, m, v, l1) [ b >= 1 /\ 0 >= f2 ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ 0 >= a ] start location: f0 leaf cost: 1 Testing for reachability in the complexity graph removes the following transitions from problem 3: f155(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ 0 >= v ] f155(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, 0, v, l1) [ v >= 1 ] We thus obtain the following problem: 4: T: (?, 1) f206(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, j - 1, m, v, l1) [ j >= 1 ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, 2, v, l1) [ 0 >= j /\ m = 2 ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ 1 >= m /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ m >= 3 /\ 0 >= j ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ 0 >= f ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ f >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, h2, m, v, l1) [ 0 >= f2 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ f2 >= 1 /\ 0 >= g2 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ f2 >= 1 /\ g2 >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ 0 >= a ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ a >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ 0 >= i ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ i >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ 0 >= l1 ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, l1 - 1) [ l1 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ 0 >= e ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ e >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ g >= 1 /\ 0 >= g2 ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ g >= 1 /\ g2 >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, g2) [ 0 >= g ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b - 1, e, f, g, i, j, m, v, l1) [ b >= 1 /\ 0 >= f2 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ 0 >= g2 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ g2 >= 1 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g2, i, j, m, v, l1) [ 0 >= b ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, h2, e, f, g, i, j, 0, v, l1) [ 0 >= g2 ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, i2, e, f, g, i, j, 0, v, l1) [ g2 >= 1 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f206) = -4 Pol(f190) = -3 Pol(f81) = 1 Pol(f65) = 1 Pol(f130) = -2 Pol(f79) = 1 Pol(f75) = 1 Pol(f100) = -1 Pol(f44) = 2 Pol(f34) = 2 Pol(f0) = 2 orients all transitions weakly and the transitions f65(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, g2) [ 0 >= g ] f34(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g2, i, j, m, v, l1) [ 0 >= b ] strictly and produces the following problem: 5: T: (?, 1) f206(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, j - 1, m, v, l1) [ j >= 1 ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, 2, v, l1) [ 0 >= j /\ m = 2 ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ 1 >= m /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ m >= 3 /\ 0 >= j ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ 0 >= f ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ f >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, h2, m, v, l1) [ 0 >= f2 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ f2 >= 1 /\ 0 >= g2 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ f2 >= 1 /\ g2 >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ 0 >= a ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ a >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ 0 >= i ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ i >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ 0 >= l1 ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, l1 - 1) [ l1 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ 0 >= e ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ e >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ g >= 1 /\ 0 >= g2 ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ g >= 1 /\ g2 >= 1 ] (2, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, g2) [ 0 >= g ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b - 1, e, f, g, i, j, m, v, l1) [ b >= 1 /\ 0 >= f2 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ 0 >= g2 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ g2 >= 1 /\ b >= 1 /\ f2 >= 1 ] (2, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g2, i, j, m, v, l1) [ 0 >= b ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, h2, e, f, g, i, j, 0, v, l1) [ 0 >= g2 ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, i2, e, f, g, i, j, 0, v, l1) [ g2 >= 1 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f206) = 0 Pol(f190) = 1 Pol(f81) = 3 Pol(f65) = 3 Pol(f130) = 2 Pol(f79) = 3 Pol(f75) = 3 Pol(f100) = 3 Pol(f44) = 3 Pol(f34) = 3 Pol(f0) = 3 orients all transitions weakly and the transitions f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ 1 >= m /\ 0 >= j ] f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ m >= 3 /\ 0 >= j ] f130(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, h2, m, v, l1) [ 0 >= f2 ] f100(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ 0 >= l1 ] strictly and produces the following problem: 6: T: (?, 1) f206(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, j - 1, m, v, l1) [ j >= 1 ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, 2, v, l1) [ 0 >= j /\ m = 2 ] (3, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ 1 >= m /\ 0 >= j ] (3, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ m >= 3 /\ 0 >= j ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ 0 >= f ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ f >= 1 ] (3, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, h2, m, v, l1) [ 0 >= f2 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ f2 >= 1 /\ 0 >= g2 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ f2 >= 1 /\ g2 >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ 0 >= a ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ a >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ 0 >= i ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ i >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ 0 >= l1 ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, l1 - 1) [ l1 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ 0 >= e ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ e >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ g >= 1 /\ 0 >= g2 ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ g >= 1 /\ g2 >= 1 ] (2, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, g2) [ 0 >= g ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b - 1, e, f, g, i, j, m, v, l1) [ b >= 1 /\ 0 >= f2 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ 0 >= g2 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ g2 >= 1 /\ b >= 1 /\ f2 >= 1 ] (2, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g2, i, j, m, v, l1) [ 0 >= b ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, h2, e, f, g, i, j, 0, v, l1) [ 0 >= g2 ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, i2, e, f, g, i, j, 0, v, l1) [ g2 >= 1 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f206) = 0 Pol(f190) = 1 Pol(f81) = 1 Pol(f65) = 1 Pol(f130) = 1 Pol(f79) = 1 Pol(f75) = 1 Pol(f100) = 1 Pol(f44) = 1 Pol(f34) = 1 Pol(f0) = 1 orients all transitions weakly and the transition f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, 2, v, l1) [ 0 >= j /\ m = 2 ] strictly and produces the following problem: 7: T: (?, 1) f206(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, j - 1, m, v, l1) [ j >= 1 ] (1, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, 2, v, l1) [ 0 >= j /\ m = 2 ] (3, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ 1 >= m /\ 0 >= j ] (3, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ m >= 3 /\ 0 >= j ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ 0 >= f ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ f >= 1 ] (3, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, h2, m, v, l1) [ 0 >= f2 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ f2 >= 1 /\ 0 >= g2 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ f2 >= 1 /\ g2 >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ 0 >= a ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ a >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ 0 >= i ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ i >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ 0 >= l1 ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, l1 - 1) [ l1 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ 0 >= e ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ e >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ g >= 1 /\ 0 >= g2 ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ g >= 1 /\ g2 >= 1 ] (2, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, g2) [ 0 >= g ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b - 1, e, f, g, i, j, m, v, l1) [ b >= 1 /\ 0 >= f2 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ 0 >= g2 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ g2 >= 1 /\ b >= 1 /\ f2 >= 1 ] (2, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g2, i, j, m, v, l1) [ 0 >= b ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, h2, e, f, g, i, j, 0, v, l1) [ 0 >= g2 ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, i2, e, f, g, i, j, 0, v, l1) [ g2 >= 1 ] start location: f0 leaf cost: 1 Applied AI with 'oct' on problem 7 to obtain the following invariants: For symbol f100: -X_8 >= 0 /\ -X_5 - X_8 >= 0 /\ -X_2 - X_8 >= 0 /\ X_8 >= 0 /\ -X_5 + X_8 >= 0 /\ -X_2 + X_8 >= 0 /\ -X_5 >= 0 /\ -X_2 - X_5 >= 0 /\ -X_2 >= 0 For symbol f130: -X_8 >= 0 /\ -X_5 - X_8 >= 0 /\ -X_2 - X_8 >= 0 /\ -X_10 - X_8 >= 0 /\ X_8 >= 0 /\ -X_5 + X_8 >= 0 /\ -X_2 + X_8 >= 0 /\ -X_10 + X_8 >= 0 /\ -X_5 >= 0 /\ -X_2 - X_5 >= 0 /\ -X_10 - X_5 >= 0 /\ -X_2 >= 0 /\ -X_10 - X_2 >= 0 /\ -X_10 >= 0 For symbol f190: -X_8 >= 0 /\ -X_5 - X_8 >= 0 /\ -X_2 - X_8 >= 0 /\ -X_10 - X_8 >= 0 /\ X_8 >= 0 /\ -X_5 + X_8 >= 0 /\ -X_2 + X_8 >= 0 /\ -X_10 + X_8 >= 0 /\ -X_5 >= 0 /\ -X_2 - X_5 >= 0 /\ -X_10 - X_5 >= 0 /\ -X_2 >= 0 /\ -X_10 - X_2 >= 0 /\ -X_10 >= 0 For symbol f206: -X_8 >= 0 /\ -X_7 - X_8 >= 0 /\ -X_5 - X_8 >= 0 /\ -X_2 - X_8 >= 0 /\ -X_10 - X_8 >= 0 /\ X_8 >= 0 /\ -X_7 + X_8 >= 0 /\ -X_5 + X_8 >= 0 /\ -X_2 + X_8 >= 0 /\ -X_10 + X_8 >= 0 /\ -X_7 >= 0 /\ -X_5 - X_7 >= 0 /\ -X_2 - X_7 >= 0 /\ -X_10 - X_7 >= 0 /\ -X_5 >= 0 /\ -X_2 - X_5 >= 0 /\ -X_10 - X_5 >= 0 /\ -X_2 >= 0 /\ -X_10 - X_2 >= 0 /\ -X_10 >= 0 For symbol f34: -X_8 >= 0 /\ X_8 >= 0 For symbol f44: -X_8 >= 0 /\ X_2 - X_8 >= 0 /\ X_8 >= 0 /\ X_2 + X_8 >= 0 /\ X_2 >= 0 For symbol f65: -X_8 >= 0 /\ -X_2 - X_8 >= 0 /\ X_8 >= 0 /\ -X_2 + X_8 >= 0 /\ -X_2 >= 0 For symbol f75: -X_8 >= 0 /\ X_5 - X_8 >= 0 /\ -X_2 - X_8 >= 0 /\ X_8 >= 0 /\ X_5 + X_8 >= 0 /\ -X_2 + X_8 >= 0 /\ X_5 >= 0 /\ -X_2 + X_5 >= 0 /\ -X_2 >= 0 For symbol f79: -X_8 >= 0 /\ X_5 - X_8 >= 0 /\ -X_2 - X_8 >= 0 /\ X_8 >= 0 /\ X_5 + X_8 >= 0 /\ -X_2 + X_8 >= 0 /\ X_5 >= 0 /\ -X_2 + X_5 >= 0 /\ -X_2 >= 0 For symbol f81: -X_8 >= 0 /\ X_5 - X_8 >= 0 /\ -X_2 - X_8 >= 0 /\ X_8 >= 0 /\ X_5 + X_8 >= 0 /\ -X_2 + X_8 >= 0 /\ X_5 >= 0 /\ -X_2 + X_5 >= 0 /\ -X_2 >= 0 This yielded the following problem: 8: T: (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, i2, e, f, g, i, j, 0, v, l1) [ g2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, h2, e, f, g, i, j, 0, v, l1) [ 0 >= g2 ] (2, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g2, i, j, m, v, l1) [ -m >= 0 /\ m >= 0 /\ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ -m >= 0 /\ m >= 0 /\ g2 >= 1 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ -m >= 0 /\ m >= 0 /\ 0 >= g2 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b - 1, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ m >= 0 /\ b >= 1 /\ 0 >= f2 ] (2, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, g2) [ -m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -b + m >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ -m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -b + m >= 0 /\ -b >= 0 /\ g >= 1 /\ g2 >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ -m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -b + m >= 0 /\ -b >= 0 /\ g >= 1 /\ 0 >= g2 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ b - m >= 0 /\ m >= 0 /\ b + m >= 0 /\ b >= 0 /\ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ b - m >= 0 /\ m >= 0 /\ b + m >= 0 /\ b >= 0 /\ 0 >= e ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, l1 - 1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ l1 >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ 0 >= l1 ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ i >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= i ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ f2 >= 1 /\ g2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ f2 >= 1 /\ 0 >= g2 ] (3, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, h2, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ 0 >= f2 ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ f >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= f ] (3, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ m >= 3 /\ 0 >= j ] (3, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ 1 >= m /\ 0 >= j ] (1, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, 2, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ 0 >= j /\ m = 2 ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, j - 1, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ j >= 1 ] (?, 1) f206(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -j - m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -j + m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -l1 - j >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 ] start location: f0 leaf cost: 1 Testing for unsatisfiable constraints removes the following transitions from problem 8: f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ m >= 3 /\ 0 >= j ] f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, 2, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ 0 >= j /\ m = 2 ] We thus obtain the following problem: 9: T: (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, i2, e, f, g, i, j, 0, v, l1) [ g2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, h2, e, f, g, i, j, 0, v, l1) [ 0 >= g2 ] (2, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g2, i, j, m, v, l1) [ -m >= 0 /\ m >= 0 /\ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ -m >= 0 /\ m >= 0 /\ g2 >= 1 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ -m >= 0 /\ m >= 0 /\ 0 >= g2 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b - 1, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ m >= 0 /\ b >= 1 /\ 0 >= f2 ] (2, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, g2) [ -m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -b + m >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ -m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -b + m >= 0 /\ -b >= 0 /\ g >= 1 /\ g2 >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ -m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -b + m >= 0 /\ -b >= 0 /\ g >= 1 /\ 0 >= g2 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ b - m >= 0 /\ m >= 0 /\ b + m >= 0 /\ b >= 0 /\ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ b - m >= 0 /\ m >= 0 /\ b + m >= 0 /\ b >= 0 /\ 0 >= e ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, l1 - 1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ l1 >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ 0 >= l1 ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ i >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= i ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ f2 >= 1 /\ g2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ f2 >= 1 /\ 0 >= g2 ] (3, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, h2, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ 0 >= f2 ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ f >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= f ] (3, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ 1 >= m /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, j - 1, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ j >= 1 ] (?, 1) f206(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -j - m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -j + m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -l1 - j >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ 1 >= m /\ 0 >= j ] with all transitions in problem 9, the following new transition is obtained: f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ 1 >= m /\ 0 >= j /\ -j - m >= 0 /\ -j + m >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -l1 - j >= 0 ] We thus obtain the following problem: 10: T: (3, 2) f190(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ 1 >= m /\ 0 >= j /\ -j - m >= 0 /\ -j + m >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -l1 - j >= 0 ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, i2, e, f, g, i, j, 0, v, l1) [ g2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, m, v, l1) -> f34(a, h2, e, f, g, i, j, 0, v, l1) [ 0 >= g2 ] (2, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g2, i, j, m, v, l1) [ -m >= 0 /\ m >= 0 /\ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ -m >= 0 /\ m >= 0 /\ g2 >= 1 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f44(a, b - 1, h2, f, g, i, j, m, v, l1) [ -m >= 0 /\ m >= 0 /\ 0 >= g2 /\ b >= 1 /\ f2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b - 1, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ m >= 0 /\ b >= 1 /\ 0 >= f2 ] (2, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, g2) [ -m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -b + m >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ -m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -b + m >= 0 /\ -b >= 0 /\ g >= 1 /\ g2 >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, m, v, l1) -> f75(a, b, e, f2, g - 1, h2, j, m, v, l1) [ -m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -b + m >= 0 /\ -b >= 0 /\ g >= 1 /\ 0 >= g2 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ b - m >= 0 /\ m >= 0 /\ b + m >= 0 /\ b >= 0 /\ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, m, v, l1) -> f34(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ b - m >= 0 /\ m >= 0 /\ b + m >= 0 /\ b >= 0 /\ 0 >= e ] (?, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f100(a, b, e, f, g, i, j, m, v, l1 - 1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ l1 >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ 0 >= l1 ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ i >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, m, v, l1) -> f79(f2, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= i ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, m, v, l1) -> f81(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ f2 >= 1 /\ g2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f130(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ f2 >= 1 /\ 0 >= g2 ] (3, 1) f130(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, h2, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ 0 >= f2 ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ f >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, m, v, l1) -> f65(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ g - m >= 0 /\ -b - m >= 0 /\ m >= 0 /\ g + m >= 0 /\ -b + m >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= f ] (?, 1) f190(a, b, e, f, g, i, j, m, v, l1) -> f190(a, b, e, f, g, i, j - 1, m, v, l1) [ -m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 /\ j >= 1 ] (?, 1) f206(a, b, e, f, g, i, j, m, v, l1) -> f206(a, b, e, f, g, i, j, m, v, l1) [ -m >= 0 /\ -j - m >= 0 /\ -g - m >= 0 /\ -b - m >= 0 /\ -l1 - m >= 0 /\ m >= 0 /\ -j + m >= 0 /\ -g + m >= 0 /\ -b + m >= 0 /\ -l1 + m >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -l1 - j >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -l1 - g >= 0 /\ -b >= 0 /\ -l1 - b >= 0 /\ -l1 >= 0 ] start location: f0 leaf cost: 1 Complexity upper bound ? Time: 4.975 sec (SMT: 4.016 sec)