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) -> 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) [ 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) -> f34(a, b - 1, g2, 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) [ b >= 1 /\ 0 >= g2 ] (?, 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) -> f44(a, b - 1, g2, h2, i2, 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) [ 0 >= h2 /\ b >= 1 /\ g2 >= 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) -> 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) [ 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) -> f75(a, b, c, d, e, g2, g - 1, h2, i2, 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) [ g >= 1 /\ 0 >= h2 ] (?, 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) -> f79(g2, 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) [ 0 >= i ] (?, 1) f209(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) -> f209(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) (?, 1) 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, f2) -> f214(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) (?, 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, f2) -> f190(a, b, c, d, e, f, g, h, i, j - 1, 1, 2, 1, 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) [ 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, f2) -> f209(a, b, c, d, e, f, g, h, i, j, k, l, m, 2, 0, g2, 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) [ 0 >= j /\ n = 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, f2) -> f209(a, b, c, d, e, f, g, h, i, j, k, l, m, n, 0, g2, 1, 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) [ 1 >= n /\ 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, f2) -> f209(a, b, c, d, e, f, g, h, i, j, k, l, m, n, 0, g2, 1, 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) [ n >= 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) -> f190(a, b, c, d, e, f, g, h, i, i2, k, l, m, n, 0, p, q, 0, g2, g2, h2, i2, 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) [ 0 >= g2 ] (?, 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, f2) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, 0, o, p, q, 0, s, t, u, v, w, w, w, 0, b1, b1, w, 0, w, b1, 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) [ w >= 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, f2) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 0, s, t, u, v, w, w, y, z, a1, b1, c1, d1, e1, f1, b1, 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) [ 0 >= w ] (?, 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) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, 0, p, q, 0, g2, g2 - 1, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h2, i2, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2) [ g2 >= 1 /\ 0 >= h2 ] (?, 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) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, 0, p, q, 0, g2, g2 - 1, u, v, w, j2, y, z, a1, 0, c1, d1, e1, f1, g1, h2, i2, 1, 0, 0, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2) [ g2 >= 1 /\ h2 >= 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) -> f130(a, b, c, d, e, f, g, h, i, j, k, l, m, n, 0, p, q, 0, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, g2, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2) [ 0 >= m1 ] (?, 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) -> f100(a, b, c, d, e, f, g, h, i, j, k, l, m, n, 0, p, q, 0, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1 - 1, n1, g2, h2, i2, g2, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2) [ m1 >= 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) -> 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) [ 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) -> 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) [ 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) -> f79(g2, 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) [ 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) -> f75(a, b, c, d, e, g2, g - 1, h2, i2, 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) [ g >= 1 /\ h2 >= 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) -> f100(a, b, c, d, e, f, g, h, i, j, k, l, m, n, 0, p, q, 0, s, t, u, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, h2, n1, o1, p1, q1, r1, g2, h2, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2) [ 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) -> 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, c, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2) [ 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) -> 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, c, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2) [ 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) -> f44(a, b - 1, g2, h2, i2, 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) [ h2 >= 1 /\ b >= 1 /\ g2 >= 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) -> f65(a, b, c, d, e, f, h2, h, i, j, k, l, m, n, 0, p, q, 0, 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, g2, h2, x1, y1, z1, a2, b2, c2, d2, e2, f2) [ 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) -> f34(a, i2, c, d, e, f, g, h, i, j, 0, l, m, 0, 0, p, 0, 0, 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, 0, 0, g2, h2, 0, i2, d2, e2, f2) [ 0 >= h2 ] (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) -> f34(a, j2, c, d, e, f, g, h, i, j, 0, l, m, 0, 0, p, 0, 0, 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, 0, 0, g2, h2, 0, j2, 1, i2, 0) [ h2 >= 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, n, w, m1]. We thus obtain the following problem: 2: T: (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, j2, e, f, g, i, j, 0, w, m1) [ h2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, i2, e, f, g, i, j, 0, w, m1) [ 0 >= h2 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, h2, i, j, n, w, m1) [ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ h2 >= 1 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ 0 >= e ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, h2) [ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ g >= 1 /\ h2 >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ i >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ a >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ f >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, m1 - 1) [ m1 >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ 0 >= m1 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ g2 >= 1 /\ h2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ g2 >= 1 /\ 0 >= h2 ] (?, 1) f155(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ 0 >= w ] (?, 1) f155(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, 0, w, m1) [ w >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, i2, n, w, m1) [ 0 >= g2 ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ n >= 3 /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ 1 >= n /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, 2, w, m1) [ 0 >= j /\ n = 2 ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, j - 1, n, w, m1) [ j >= 1 ] (?, 1) f211(a, b, e, f, g, i, j, n, w, m1) -> f214(a, b, e, f, g, i, j, n, w, m1) (?, 1) f209(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ 0 >= i ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ g >= 1 /\ 0 >= h2 ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ 0 >= f ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ 0 >= h2 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b - 1, e, f, g, i, j, n, w, m1) [ b >= 1 /\ 0 >= g2 ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ 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, n, w, m1) -> f34(a, j2, e, f, g, i, j, 0, w, m1) [ h2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, i2, e, f, g, i, j, 0, w, m1) [ 0 >= h2 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, h2, i, j, n, w, m1) [ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ h2 >= 1 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ 0 >= e ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, h2) [ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ g >= 1 /\ h2 >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ i >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ a >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ f >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, m1 - 1) [ m1 >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ 0 >= m1 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ g2 >= 1 /\ h2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ g2 >= 1 /\ 0 >= h2 ] (?, 1) f155(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ 0 >= w ] (?, 1) f155(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, 0, w, m1) [ w >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, i2, n, w, m1) [ 0 >= g2 ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ n >= 3 /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ 1 >= n /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, 2, w, m1) [ 0 >= j /\ n = 2 ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, j - 1, n, w, m1) [ j >= 1 ] (?, 1) f209(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ 0 >= i ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ g >= 1 /\ 0 >= h2 ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ 0 >= f ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ 0 >= h2 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b - 1, e, f, g, i, j, n, w, m1) [ b >= 1 /\ 0 >= g2 ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ 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, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ 0 >= w ] f155(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, 0, w, m1) [ w >= 1 ] We thus obtain the following problem: 4: T: (?, 1) f209(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, j - 1, n, w, m1) [ j >= 1 ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, 2, w, m1) [ 0 >= j /\ n = 2 ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ 1 >= n /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ n >= 3 /\ 0 >= j ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ 0 >= f ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ f >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, i2, n, w, m1) [ 0 >= g2 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ g2 >= 1 /\ 0 >= h2 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ g2 >= 1 /\ h2 >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ 0 >= a ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ a >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ 0 >= i ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ i >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ 0 >= m1 ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, m1 - 1) [ m1 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ 0 >= e ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ e >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ g >= 1 /\ 0 >= h2 ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ g >= 1 /\ h2 >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, h2) [ 0 >= g ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b - 1, e, f, g, i, j, n, w, m1) [ b >= 1 /\ 0 >= g2 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ 0 >= h2 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ h2 >= 1 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, h2, i, j, n, w, m1) [ 0 >= b ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, i2, e, f, g, i, j, 0, w, m1) [ 0 >= h2 ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, j2, e, f, g, i, j, 0, w, m1) [ h2 >= 1 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f209) = -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, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, h2) [ 0 >= g ] f34(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, h2, i, j, n, w, m1) [ 0 >= b ] strictly and produces the following problem: 5: T: (?, 1) f209(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, j - 1, n, w, m1) [ j >= 1 ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, 2, w, m1) [ 0 >= j /\ n = 2 ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ 1 >= n /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ n >= 3 /\ 0 >= j ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ 0 >= f ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ f >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, i2, n, w, m1) [ 0 >= g2 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ g2 >= 1 /\ 0 >= h2 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ g2 >= 1 /\ h2 >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ 0 >= a ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ a >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ 0 >= i ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ i >= 1 ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ 0 >= m1 ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, m1 - 1) [ m1 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ 0 >= e ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ e >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ g >= 1 /\ 0 >= h2 ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ g >= 1 /\ h2 >= 1 ] (2, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, h2) [ 0 >= g ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b - 1, e, f, g, i, j, n, w, m1) [ b >= 1 /\ 0 >= g2 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ 0 >= h2 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ h2 >= 1 /\ b >= 1 /\ g2 >= 1 ] (2, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, h2, i, j, n, w, m1) [ 0 >= b ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, i2, e, f, g, i, j, 0, w, m1) [ 0 >= h2 ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, j2, e, f, g, i, j, 0, w, m1) [ h2 >= 1 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f209) = 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, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ 1 >= n /\ 0 >= j ] f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ n >= 3 /\ 0 >= j ] f130(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, i2, n, w, m1) [ 0 >= g2 ] f100(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ 0 >= m1 ] strictly and produces the following problem: 6: T: (?, 1) f209(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, j - 1, n, w, m1) [ j >= 1 ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, 2, w, m1) [ 0 >= j /\ n = 2 ] (3, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ 1 >= n /\ 0 >= j ] (3, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ n >= 3 /\ 0 >= j ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ 0 >= f ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ f >= 1 ] (3, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, i2, n, w, m1) [ 0 >= g2 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ g2 >= 1 /\ 0 >= h2 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ g2 >= 1 /\ h2 >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ 0 >= a ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ a >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ 0 >= i ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ i >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ 0 >= m1 ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, m1 - 1) [ m1 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ 0 >= e ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ e >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ g >= 1 /\ 0 >= h2 ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ g >= 1 /\ h2 >= 1 ] (2, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, h2) [ 0 >= g ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b - 1, e, f, g, i, j, n, w, m1) [ b >= 1 /\ 0 >= g2 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ 0 >= h2 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ h2 >= 1 /\ b >= 1 /\ g2 >= 1 ] (2, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, h2, i, j, n, w, m1) [ 0 >= b ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, i2, e, f, g, i, j, 0, w, m1) [ 0 >= h2 ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, j2, e, f, g, i, j, 0, w, m1) [ h2 >= 1 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f209) = 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, n, w, m1) -> f209(a, b, e, f, g, i, j, 2, w, m1) [ 0 >= j /\ n = 2 ] strictly and produces the following problem: 7: T: (?, 1) f209(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, j - 1, n, w, m1) [ j >= 1 ] (1, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, 2, w, m1) [ 0 >= j /\ n = 2 ] (3, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ 1 >= n /\ 0 >= j ] (3, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ n >= 3 /\ 0 >= j ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ 0 >= f ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ f >= 1 ] (3, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, i2, n, w, m1) [ 0 >= g2 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ g2 >= 1 /\ 0 >= h2 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ g2 >= 1 /\ h2 >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ 0 >= a ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ a >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ 0 >= i ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ i >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ 0 >= m1 ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, m1 - 1) [ m1 >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ 0 >= e ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ e >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ g >= 1 /\ 0 >= h2 ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ g >= 1 /\ h2 >= 1 ] (2, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, h2) [ 0 >= g ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b - 1, e, f, g, i, j, n, w, m1) [ b >= 1 /\ 0 >= g2 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ 0 >= h2 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ h2 >= 1 /\ b >= 1 /\ g2 >= 1 ] (2, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, h2, i, j, n, w, m1) [ 0 >= b ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, i2, e, f, g, i, j, 0, w, m1) [ 0 >= h2 ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, j2, e, f, g, i, j, 0, w, m1) [ h2 >= 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 f209: -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, n, w, m1) -> f34(a, j2, e, f, g, i, j, 0, w, m1) [ h2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, i2, e, f, g, i, j, 0, w, m1) [ 0 >= h2 ] (2, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, h2, i, j, n, w, m1) [ -n >= 0 /\ n >= 0 /\ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ -n >= 0 /\ n >= 0 /\ h2 >= 1 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ -n >= 0 /\ n >= 0 /\ 0 >= h2 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b - 1, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ n >= 0 /\ b >= 1 /\ 0 >= g2 ] (2, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, h2) [ -n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -b + n >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ -n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -b + n >= 0 /\ -b >= 0 /\ g >= 1 /\ h2 >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ -n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -b + n >= 0 /\ -b >= 0 /\ g >= 1 /\ 0 >= h2 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ b - n >= 0 /\ n >= 0 /\ b + n >= 0 /\ b >= 0 /\ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ b - n >= 0 /\ n >= 0 /\ b + n >= 0 /\ b >= 0 /\ 0 >= e ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, m1 - 1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ m1 >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ 0 >= m1 ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ i >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= i ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ g2 >= 1 /\ h2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ g2 >= 1 /\ 0 >= h2 ] (3, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, i2, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ 0 >= g2 ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ f >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= f ] (3, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ n >= 3 /\ 0 >= j ] (3, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ 1 >= n /\ 0 >= j ] (1, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, 2, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ 0 >= j /\ n = 2 ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, j - 1, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ j >= 1 ] (?, 1) f209(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -j - n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -j + n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -m1 - j >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 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, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ n >= 3 /\ 0 >= j ] f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, 2, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ 0 >= j /\ n = 2 ] We thus obtain the following problem: 9: T: (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, j2, e, f, g, i, j, 0, w, m1) [ h2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, i2, e, f, g, i, j, 0, w, m1) [ 0 >= h2 ] (2, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, h2, i, j, n, w, m1) [ -n >= 0 /\ n >= 0 /\ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ -n >= 0 /\ n >= 0 /\ h2 >= 1 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ -n >= 0 /\ n >= 0 /\ 0 >= h2 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b - 1, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ n >= 0 /\ b >= 1 /\ 0 >= g2 ] (2, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, h2) [ -n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -b + n >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ -n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -b + n >= 0 /\ -b >= 0 /\ g >= 1 /\ h2 >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ -n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -b + n >= 0 /\ -b >= 0 /\ g >= 1 /\ 0 >= h2 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ b - n >= 0 /\ n >= 0 /\ b + n >= 0 /\ b >= 0 /\ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ b - n >= 0 /\ n >= 0 /\ b + n >= 0 /\ b >= 0 /\ 0 >= e ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, m1 - 1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ m1 >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ 0 >= m1 ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ i >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= i ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ g2 >= 1 /\ h2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ g2 >= 1 /\ 0 >= h2 ] (3, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, i2, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ 0 >= g2 ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ f >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= f ] (3, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ 1 >= n /\ 0 >= j ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, j - 1, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ j >= 1 ] (?, 1) f209(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -j - n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -j + n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -m1 - j >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ 1 >= n /\ 0 >= j ] with all transitions in problem 9, the following new transition is obtained: f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ 1 >= n /\ 0 >= j /\ -j - n >= 0 /\ -j + n >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -m1 - j >= 0 ] We thus obtain the following problem: 10: T: (3, 2) f190(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ 1 >= n /\ 0 >= j /\ -j - n >= 0 /\ -j + n >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -m1 - j >= 0 ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, j2, e, f, g, i, j, 0, w, m1) [ h2 >= 1 ] (1, 1) f0(a, b, e, f, g, i, j, n, w, m1) -> f34(a, i2, e, f, g, i, j, 0, w, m1) [ 0 >= h2 ] (2, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, h2, i, j, n, w, m1) [ -n >= 0 /\ n >= 0 /\ 0 >= b ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ -n >= 0 /\ n >= 0 /\ h2 >= 1 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f44(a, b - 1, i2, f, g, i, j, n, w, m1) [ -n >= 0 /\ n >= 0 /\ 0 >= h2 /\ b >= 1 /\ g2 >= 1 ] (?, 1) f34(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b - 1, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ n >= 0 /\ b >= 1 /\ 0 >= g2 ] (2, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, h2) [ -n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -b + n >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ -n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -b + n >= 0 /\ -b >= 0 /\ g >= 1 /\ h2 >= 1 ] (?, 1) f65(a, b, e, f, g, i, j, n, w, m1) -> f75(a, b, e, g2, g - 1, i2, j, n, w, m1) [ -n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -b + n >= 0 /\ -b >= 0 /\ g >= 1 /\ 0 >= h2 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ b - n >= 0 /\ n >= 0 /\ b + n >= 0 /\ b >= 0 /\ e >= 1 ] (?, 1) f44(a, b, e, f, g, i, j, n, w, m1) -> f34(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ b - n >= 0 /\ n >= 0 /\ b + n >= 0 /\ b >= 0 /\ 0 >= e ] (?, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f100(a, b, e, f, g, i, j, n, w, m1 - 1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ m1 >= 1 ] (3, 1) f100(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -b >= 0 /\ 0 >= m1 ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ i >= 1 ] (?, 1) f75(a, b, e, f, g, i, j, n, w, m1) -> f79(g2, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= i ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 1) f79(a, b, e, f, g, i, j, n, w, m1) -> f81(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ g2 >= 1 /\ h2 >= 1 ] (?, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f130(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ g2 >= 1 /\ 0 >= h2 ] (3, 1) f130(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, i2, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ 0 >= g2 ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ f >= 1 ] (?, 1) f81(a, b, e, f, g, i, j, n, w, m1) -> f65(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ g - n >= 0 /\ -b - n >= 0 /\ n >= 0 /\ g + n >= 0 /\ -b + n >= 0 /\ g >= 0 /\ -b + g >= 0 /\ -b >= 0 /\ 0 >= f ] (?, 1) f190(a, b, e, f, g, i, j, n, w, m1) -> f190(a, b, e, f, g, i, j - 1, n, w, m1) [ -n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 /\ j >= 1 ] (?, 1) f209(a, b, e, f, g, i, j, n, w, m1) -> f209(a, b, e, f, g, i, j, n, w, m1) [ -n >= 0 /\ -j - n >= 0 /\ -g - n >= 0 /\ -b - n >= 0 /\ -m1 - n >= 0 /\ n >= 0 /\ -j + n >= 0 /\ -g + n >= 0 /\ -b + n >= 0 /\ -m1 + n >= 0 /\ -j >= 0 /\ -g - j >= 0 /\ -b - j >= 0 /\ -m1 - j >= 0 /\ -g >= 0 /\ -b - g >= 0 /\ -m1 - g >= 0 /\ -b >= 0 /\ -m1 - b >= 0 /\ -m1 >= 0 ] start location: f0 leaf cost: 1 Complexity upper bound ? Time: 5.092 sec (SMT: 4.104 sec)