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, f2, g2, h2, i2, j2, k2) -> 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, f2, g2, h2, i2, j2, k2) [ 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, f2, g2, h2, i2, j2, k2) -> f34(a, b - 1, l2, 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, f2, g2, h2, i2, j2, k2) [ b >= 1 /\ 0 >= l2 ] (?, 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, f2, g2, h2, i2, j2, k2) -> f44(a, b - 1, l2, m2, n2, 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, f2, g2, h2, i2, j2, k2) [ 0 >= m2 /\ b >= 1 /\ l2 >= 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, f2, g2, h2, i2, j2, k2) -> 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, f2, g2, h2, i2, j2, k2) [ 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, f2, g2, h2, i2, j2, k2) -> f75(a, b, c, d, e, l2, g - 1, m2, n2, 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, f2, g2, h2, i2, j2, k2) [ g >= 1 /\ 0 >= m2 ] (?, 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, f2, g2, h2, i2, j2, k2) -> f79(l2, 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, f2, g2, h2, i2, j2, k2) [ 0 >= i ] (?, 1) f216(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, f2, g2, h2, i2, j2, k2) -> f216(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, f2, g2, h2, i2, j2, k2) (?, 1) f218(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, f2, g2, h2, i2, j2, k2) -> f221(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, f2, g2, h2, i2, j2, k2) (?, 1) f191(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, f2, g2, h2, i2, j2, k2) -> f191(a, b, c, d, e, f, g, h, i, j - 1, 1, 0, l2, 0, 0, 2, l2, 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, f2, g2, h2, i2, j2, k2) [ j >= 1 ] (?, 1) f191(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, f2, g2, h2, i2, j2, k2) -> f216(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 2, 0, l2, 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, f2, g2, h2, i2, j2, k2) [ 0 >= j /\ r = 2 ] (?, 1) f191(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, f2, g2, h2, i2, j2, k2) -> f216(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, 0, l2, 1, 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, f2, g2, h2, i2, j2, k2) [ 1 >= r /\ 0 >= j ] (?, 1) f191(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, f2, g2, h2, i2, j2, k2) -> f216(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, 0, l2, 1, 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, f2, g2, h2, i2, j2, k2) [ r >= 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, f2, g2, h2, i2, j2, k2) -> f191(a, b, c, d, e, f, g, h, i, n2, k, l, m, n, o, p, q, r, 0, t, u, 0, l2, l2, m2, n2, 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, f2, g2, h2, i2, j2, k2) [ 0 >= l2 ] (?, 1) f156(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, f2, g2, h2, i2, j2, k2) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 0, s, t, u, 0, w, x, y, z, a1, a1, a1, 0, f1, f1, a1, 0, a1, f1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ a1 >= 1 ] (?, 1) f156(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, f2, g2, h2, i2, j2, k2) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, 0, w, x, y, z, a1, a1, c1, d1, e1, f1, g1, h1, i1, j1, f1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ 0 >= a1 ] (?, 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, f2, g2, h2, i2, j2, k2) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, 0, t, u, 0, l2, l2 - 1, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, m2, n2, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ l2 >= 1 /\ 0 >= m2 ] (?, 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, f2, g2, h2, i2, j2, k2) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, 0, t, u, 0, l2, l2 - 1, y, z, a1, o2, c1, d1, e1, 0, g1, h1, i1, j1, k1, m2, n2, p2, p2, 0, 0, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ l2 >= 1 /\ m2 >= 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, f2, g2, h2, i2, j2, k2) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, 0, t, u, 0, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, l2, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ 0 >= r1 ] (?, 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, f2, g2, h2, i2, j2, k2) -> f100(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, 0, t, u, 0, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1 - 1, s1, l2, m2, n2, l2, x1, y1, z1, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ r1 >= 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, f2, g2, h2, i2, j2, k2) -> 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, f2, g2, h2, i2, j2, k2) [ 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, f2, g2, h2, i2, j2, k2) -> 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, f2, g2, h2, i2, j2, k2) [ 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, f2, g2, h2, i2, j2, k2) -> f79(l2, 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, f2, g2, h2, i2, j2, k2) [ 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, f2, g2, h2, i2, j2, k2) -> f75(a, b, c, d, e, l2, g - 1, m2, n2, 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, f2, g2, h2, i2, j2, k2) [ g >= 1 /\ m2 >= 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, f2, g2, h2, i2, j2, k2) -> f100(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, 0, t, u, 0, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, m2, s1, t1, u1, v1, w1, l2, m2, z1, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ 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, f2, g2, h2, i2, j2, k2) -> 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, c, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ 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, f2, g2, h2, i2, j2, k2) -> 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, c, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ 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, f2, g2, h2, i2, j2, k2) -> f44(a, b - 1, l2, m2, n2, 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, f2, g2, h2, i2, j2, k2) [ m2 >= 1 /\ b >= 1 /\ l2 >= 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, f2, g2, h2, i2, j2, k2) -> f65(a, b, c, d, e, f, m2, h, i, j, k, l, m, n, o, p, q, r, 0, t, u, 0, 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, l2, m2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ 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, f2, g2, h2, i2, j2, k2) -> f34(a, n2, c, d, e, f, g, h, i, j, 0, l, m, n, o, p, q, 0, 0, t, 0, 0, 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, 0, 0, l2, m2, 0, n2, i2, j2, k2) [ 0 >= m2 ] (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, f2, g2, h2, i2, j2, k2) -> f34(a, p2, c, d, e, f, g, h, i, j, 0, l, m, n, o, p, q, 0, 0, t, 0, 0, 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, 0, 0, l2, m2, 0, p2, n2, o2, 0) [ m2 >= 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, r, a1, r1]. We thus obtain the following problem: 2: T: (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, p2, e, f, g, i, j, 0, a1, r1) [ m2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, n2, e, f, g, i, j, 0, a1, r1) [ 0 >= m2 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, m2, i, j, r, a1, r1) [ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ m2 >= 1 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= e ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, m2) [ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ g >= 1 /\ m2 >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ i >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ a >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ f >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, r1 - 1) [ r1 >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= r1 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ l2 >= 1 /\ m2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ l2 >= 1 /\ 0 >= m2 ] (?, 1) f156(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= a1 ] (?, 1) f156(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, 0, a1, r1) [ a1 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, n2, r, a1, r1) [ 0 >= l2 ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ r >= 3 /\ 0 >= j ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ 1 >= r /\ 0 >= j ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, 2, a1, r1) [ 0 >= j /\ r = 2 ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, j - 1, r, a1, r1) [ j >= 1 ] (?, 1) f218(a, b, e, f, g, i, j, r, a1, r1) -> f221(a, b, e, f, g, i, j, r, a1, r1) (?, 1) f216(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ 0 >= i ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ g >= 1 /\ 0 >= m2 ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= f ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ 0 >= m2 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b - 1, e, f, g, i, j, r, a1, r1) [ b >= 1 /\ 0 >= l2 ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ 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, r, a1, r1) -> f34(a, p2, e, f, g, i, j, 0, a1, r1) [ m2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, n2, e, f, g, i, j, 0, a1, r1) [ 0 >= m2 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, m2, i, j, r, a1, r1) [ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ m2 >= 1 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= e ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, m2) [ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ g >= 1 /\ m2 >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ i >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ a >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ f >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, r1 - 1) [ r1 >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= r1 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ l2 >= 1 /\ m2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ l2 >= 1 /\ 0 >= m2 ] (?, 1) f156(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= a1 ] (?, 1) f156(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, 0, a1, r1) [ a1 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, n2, r, a1, r1) [ 0 >= l2 ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ r >= 3 /\ 0 >= j ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ 1 >= r /\ 0 >= j ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, 2, a1, r1) [ 0 >= j /\ r = 2 ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, j - 1, r, a1, r1) [ j >= 1 ] (?, 1) f216(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ 0 >= i ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ g >= 1 /\ 0 >= m2 ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= f ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ 0 >= m2 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b - 1, e, f, g, i, j, r, a1, r1) [ b >= 1 /\ 0 >= l2 ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= a ] start location: f0 leaf cost: 1 Testing for reachability in the complexity graph removes the following transitions from problem 3: f156(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= a1 ] f156(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, 0, a1, r1) [ a1 >= 1 ] We thus obtain the following problem: 4: T: (?, 1) f216(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, j - 1, r, a1, r1) [ j >= 1 ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, 2, a1, r1) [ 0 >= j /\ r = 2 ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ 1 >= r /\ 0 >= j ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ r >= 3 /\ 0 >= j ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= f ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ f >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, n2, r, a1, r1) [ 0 >= l2 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ l2 >= 1 /\ 0 >= m2 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ l2 >= 1 /\ m2 >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= a ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ a >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ 0 >= i ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ i >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= r1 ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, r1 - 1) [ r1 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= e ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ e >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ g >= 1 /\ 0 >= m2 ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ g >= 1 /\ m2 >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, m2) [ 0 >= g ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b - 1, e, f, g, i, j, r, a1, r1) [ b >= 1 /\ 0 >= l2 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ 0 >= m2 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ m2 >= 1 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, m2, i, j, r, a1, r1) [ 0 >= b ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, n2, e, f, g, i, j, 0, a1, r1) [ 0 >= m2 ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, p2, e, f, g, i, j, 0, a1, r1) [ m2 >= 1 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f216) = -4 Pol(f191) = -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, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, m2) [ 0 >= g ] f34(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, m2, i, j, r, a1, r1) [ 0 >= b ] strictly and produces the following problem: 5: T: (?, 1) f216(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, j - 1, r, a1, r1) [ j >= 1 ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, 2, a1, r1) [ 0 >= j /\ r = 2 ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ 1 >= r /\ 0 >= j ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ r >= 3 /\ 0 >= j ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= f ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ f >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, n2, r, a1, r1) [ 0 >= l2 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ l2 >= 1 /\ 0 >= m2 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ l2 >= 1 /\ m2 >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= a ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ a >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ 0 >= i ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ i >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= r1 ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, r1 - 1) [ r1 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= e ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ e >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ g >= 1 /\ 0 >= m2 ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ g >= 1 /\ m2 >= 1 ] (2, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, m2) [ 0 >= g ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b - 1, e, f, g, i, j, r, a1, r1) [ b >= 1 /\ 0 >= l2 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ 0 >= m2 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ m2 >= 1 /\ b >= 1 /\ l2 >= 1 ] (2, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, m2, i, j, r, a1, r1) [ 0 >= b ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, n2, e, f, g, i, j, 0, a1, r1) [ 0 >= m2 ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, p2, e, f, g, i, j, 0, a1, r1) [ m2 >= 1 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f216) = 0 Pol(f191) = 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 f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ 1 >= r /\ 0 >= j ] f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ r >= 3 /\ 0 >= j ] f130(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, n2, r, a1, r1) [ 0 >= l2 ] f100(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= r1 ] strictly and produces the following problem: 6: T: (?, 1) f216(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, j - 1, r, a1, r1) [ j >= 1 ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, 2, a1, r1) [ 0 >= j /\ r = 2 ] (3, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ 1 >= r /\ 0 >= j ] (3, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ r >= 3 /\ 0 >= j ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= f ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ f >= 1 ] (3, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, n2, r, a1, r1) [ 0 >= l2 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ l2 >= 1 /\ 0 >= m2 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ l2 >= 1 /\ m2 >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= a ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ a >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ 0 >= i ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ i >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= r1 ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, r1 - 1) [ r1 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= e ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ e >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ g >= 1 /\ 0 >= m2 ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ g >= 1 /\ m2 >= 1 ] (2, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, m2) [ 0 >= g ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b - 1, e, f, g, i, j, r, a1, r1) [ b >= 1 /\ 0 >= l2 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ 0 >= m2 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ m2 >= 1 /\ b >= 1 /\ l2 >= 1 ] (2, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, m2, i, j, r, a1, r1) [ 0 >= b ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, n2, e, f, g, i, j, 0, a1, r1) [ 0 >= m2 ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, p2, e, f, g, i, j, 0, a1, r1) [ m2 >= 1 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f216) = 0 Pol(f191) = 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 f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, 2, a1, r1) [ 0 >= j /\ r = 2 ] strictly and produces the following problem: 7: T: (?, 1) f216(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, j - 1, r, a1, r1) [ j >= 1 ] (1, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, 2, a1, r1) [ 0 >= j /\ r = 2 ] (3, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ 1 >= r /\ 0 >= j ] (3, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ r >= 3 /\ 0 >= j ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= f ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ f >= 1 ] (3, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, n2, r, a1, r1) [ 0 >= l2 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ l2 >= 1 /\ 0 >= m2 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ l2 >= 1 /\ m2 >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= a ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ a >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ 0 >= i ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ i >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= r1 ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, r1 - 1) [ r1 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ 0 >= e ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ e >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ g >= 1 /\ 0 >= m2 ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ g >= 1 /\ m2 >= 1 ] (2, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, m2) [ 0 >= g ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b - 1, e, f, g, i, j, r, a1, r1) [ b >= 1 /\ 0 >= l2 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ 0 >= m2 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ m2 >= 1 /\ b >= 1 /\ l2 >= 1 ] (2, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, m2, i, j, r, a1, r1) [ 0 >= b ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, n2, e, f, g, i, j, 0, a1, r1) [ 0 >= m2 ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, p2, e, f, g, i, j, 0, a1, r1) [ m2 >= 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 f191: -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 f216: -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, r, a1, r1) -> f34(a, p2, e, f, g, i, j, 0, a1, r1) [ m2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, n2, e, f, g, i, j, 0, a1, r1) [ 0 >= m2 ] (2, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, m2, i, j, r, a1, r1) [ -r >= 0 /\ r >= 0 /\ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ -r >= 0 /\ r >= 0 /\ m2 >= 1 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ -r >= 0 /\ r >= 0 /\ 0 >= m2 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b - 1, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ r >= 0 /\ b >= 1 /\ 0 >= l2 ] (2, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, m2) [ -r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -b + r >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ -r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -b + r >= 0 /\ -b >= 0 /\ g >= 1 /\ m2 >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ -r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -b + r >= 0 /\ -b >= 0 /\ g >= 1 /\ 0 >= m2 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ b - r >= 0 /\ r >= 0 /\ b + r >= 0 /\ b >= 0 /\ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ b - r >= 0 /\ r >= 0 /\ b + r >= 0 /\ b >= 0 /\ 0 >= e ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, r1 - 1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ r1 >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ 0 >= r1 ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ i >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= i ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ l2 >= 1 /\ m2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ l2 >= 1 /\ 0 >= m2 ] (3, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, n2, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ 0 >= l2 ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ f >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= f ] (3, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ r >= 3 /\ 0 >= j ] (3, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ 1 >= r /\ 0 >= j ] (1, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, 2, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ 0 >= j /\ r = 2 ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, j - 1, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ j >= 1 ] (?, 1) f216(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -j - r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -j + r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -r1 - j >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 ] start location: f0 leaf cost: 1 Testing for unsatisfiable constraints removes the following transitions from problem 8: f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ r >= 3 /\ 0 >= j ] f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, 2, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ 0 >= j /\ r = 2 ] We thus obtain the following problem: 9: T: (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, p2, e, f, g, i, j, 0, a1, r1) [ m2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, n2, e, f, g, i, j, 0, a1, r1) [ 0 >= m2 ] (2, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, m2, i, j, r, a1, r1) [ -r >= 0 /\ r >= 0 /\ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ -r >= 0 /\ r >= 0 /\ m2 >= 1 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ -r >= 0 /\ r >= 0 /\ 0 >= m2 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b - 1, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ r >= 0 /\ b >= 1 /\ 0 >= l2 ] (2, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, m2) [ -r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -b + r >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ -r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -b + r >= 0 /\ -b >= 0 /\ g >= 1 /\ m2 >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ -r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -b + r >= 0 /\ -b >= 0 /\ g >= 1 /\ 0 >= m2 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ b - r >= 0 /\ r >= 0 /\ b + r >= 0 /\ b >= 0 /\ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ b - r >= 0 /\ r >= 0 /\ b + r >= 0 /\ b >= 0 /\ 0 >= e ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, r1 - 1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ r1 >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ 0 >= r1 ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ i >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= i ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ l2 >= 1 /\ m2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ l2 >= 1 /\ 0 >= m2 ] (3, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, n2, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ 0 >= l2 ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ f >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= f ] (3, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ 1 >= r /\ 0 >= j ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, j - 1, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ j >= 1 ] (?, 1) f216(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -j - r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -j + r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -r1 - j >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ 1 >= r /\ 0 >= j ] with all transitions in problem 9, the following new transition is obtained: f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ 1 >= r /\ 0 >= j /\ -j - r >= 0 /\ -j + r >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -r1 - j >= 0 ] We thus obtain the following problem: 10: T: (3, 2) f191(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ 1 >= r /\ 0 >= j /\ -j - r >= 0 /\ -j + r >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -r1 - j >= 0 ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, p2, e, f, g, i, j, 0, a1, r1) [ m2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, n2, e, f, g, i, j, 0, a1, r1) [ 0 >= m2 ] (2, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, m2, i, j, r, a1, r1) [ -r >= 0 /\ r >= 0 /\ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ -r >= 0 /\ r >= 0 /\ m2 >= 1 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f44(a, b - 1, n2, f, g, i, j, r, a1, r1) [ -r >= 0 /\ r >= 0 /\ 0 >= m2 /\ b >= 1 /\ l2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b - 1, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ r >= 0 /\ b >= 1 /\ 0 >= l2 ] (2, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, m2) [ -r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -b + r >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ -r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -b + r >= 0 /\ -b >= 0 /\ g >= 1 /\ m2 >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, r, a1, r1) -> f75(a, b, e, l2, g - 1, n2, j, r, a1, r1) [ -r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -b + r >= 0 /\ -b >= 0 /\ g >= 1 /\ 0 >= m2 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ b - r >= 0 /\ r >= 0 /\ b + r >= 0 /\ b >= 0 /\ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, r, a1, r1) -> f34(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ b - r >= 0 /\ r >= 0 /\ b + r >= 0 /\ b >= 0 /\ 0 >= e ] (?, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f100(a, b, e, f, g, i, j, r, a1, r1 - 1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ r1 >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ 0 >= r1 ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ i >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, r, a1, r1) -> f79(l2, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= i ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, r, a1, r1) -> f81(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ l2 >= 1 /\ m2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f130(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ l2 >= 1 /\ 0 >= m2 ] (3, 1) f130(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, n2, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ 0 >= l2 ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ f >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, r, a1, r1) -> f65(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ g - r >= 0 /\ -b - r >= 0 /\ r >= 0 /\ g + r >= 0 /\ -b + r >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= f ] (?, 1) f191(a, b, e, f, g, i, j, r, a1, r1) -> f191(a, b, e, f, g, i, j - 1, r, a1, r1) [ -r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 /\ j >= 1 ] (?, 1) f216(a, b, e, f, g, i, j, r, a1, r1) -> f216(a, b, e, f, g, i, j, r, a1, r1) [ -r >= 0 /\ -j - r >= 0 /\ -g - r >= 0 /\ -b - r >= 0 /\ -r1 - r >= 0 /\ r >= 0 /\ -j + r >= 0 /\ -g + r >= 0 /\ -b + r >= 0 /\ -r1 + r >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -r1 - j >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -r1 - g >= 0 /\ -b >= 0 /\ -r1 - b >= 0 /\ -r1 >= 0 ] start location: f0 leaf cost: 1 Complexity upper bound ? Time: 4.946 sec (SMT: 3.980 sec)