MAYBE Initial complexity problem: 1: T: (?, 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) -> f83(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) f31(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) -> f31(a, b - 1, l2, l2, 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 >= l2 /\ b >= 1 ] (?, 1) f31(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) -> f42(a, b - 1, l2, l2, m2, n2, 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 /\ l2 >= 1 /\ 0 >= m2 ] (?, 1) f83(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) -> f67(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 >= g ] (?, 1) f67(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) -> f77(a, b, c, d, e, f, l2, h - 1, m2, n2, 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) [ h >= 1 /\ 0 >= m2 ] (?, 1) f77(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(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 >= j ] (?, 1) f235(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) -> f235(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) f237(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) -> f240(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) 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, g2, h2, i2, j2, k2) -> f211(a, b, c, d, e, f, g, h, i, j, k - 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) [ k >= 1 ] (?, 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, g2, h2, i2, j2, k2) -> f235(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 0, l2, 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 >= k ] (?, 1) f144(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) -> f211(a, b, c, d, e, f, g, h, i, j, m2, l, m, n, o, p, q, 0, s, t, 0, l2, m2, 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 >= t ] (?, 1) f172(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) -> f144(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, 0, v, w, x, 0, x, x, 0, d1, d1, x, 0, x, d1, 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) [ x >= 1 ] (?, 1) f172(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) -> f144(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, 0, v, w, x, y, x, a1, b1, c1, d1, e1, f1, g1, h1, d1, 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 >= x ] (?, 1) f144(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) -> f144(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 0, s, t - 1, 0, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, l2, l2, m2, 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) [ t >= 1 /\ 0 >= l2 ] (?, 1) f144(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) -> f144(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 0, s, t - 1, 0, v, w, x, y, n2, a1, b1, c1, 0, e1, f1, g1, h1, i1, l2, l2, m2, o2, o2, 0, 0, 0, r1, s1, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ t >= 1 /\ l2 >= 1 ] (?, 1) f144(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) -> f172(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 0, s, t - 1, u, v, w, 0, y, n2, a1, b1, c1, o2, e1, f1, g1, h1, i1, l2, l2, m2, p2, p2, 0, o2, o2, 1, 0, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(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) -> f172(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 0, s, t - 1, u, v, w, 0, y, n2, a1, b1, c1, o2, e1, f1, g1, h1, i1, l2, l2, m2, p2, p2, 0, o2, o2, 1, 0, t1, u1, v1, w1, x1, y1, z1, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ o2 >= 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f104(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) -> f144(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 0, s, n2, 0, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, l2, l2, m2, n2, x1, y1, z1, a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ 0 >= l2 ] (?, 1) f104(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) -> f104(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 0, s, t, 0, v, w, x, y, z, a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, l2, l2 - 1, v1, w1, m2, n2, o2, m2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ l2 >= 1 ] (?, 1) f83(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) -> f67(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) [ g >= 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) -> f83(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) f77(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(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) [ j >= 1 ] (?, 1) f67(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) -> f77(a, b, c, d, e, f, l2, h - 1, m2, n2, 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) [ h >= 1 /\ m2 >= 1 ] (?, 1) f67(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) -> f104(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 0, s, t, 0, 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, l2, c2, d2, e2, f2, g2, h2, i2, j2, k2) [ 0 >= h ] (?, 1) f42(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) -> f31(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, d, d2, e2, f2, g2, h2, i2, j2, k2) [ 0 >= f ] (?, 1) f42(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) -> f31(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, d, d2, e2, f2, g2, h2, i2, j2, k2) [ f >= 1 ] (?, 1) f31(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) -> f42(a, b - 1, l2, l2, m2, n2, 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 /\ l2 >= 1 /\ m2 >= 1 ] (?, 1) f31(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) -> f67(a, b, c, d, e, f, g, m2, i, j, k, l, m, n, o, p, q, 0, s, t, 0, 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, l2, m2, 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) -> f31(a, m2, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 0, s, t, 0, v, w, x, 0, 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, l2, 0, m2, i2, j2, k2) [ 0 >= l2 ] (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) -> f31(a, o2, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, 0, s, t, 0, v, w, x, 0, 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, l2, 0, o2, m2, n2, 0) [ l2 >= 1 ] start location: f0 leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [a, b, f, g, h, j, k, t, x]. We thus obtain the following problem: 2: T: (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, o2, f, g, h, j, k, t, x) [ l2 >= 1 ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, m2, f, g, h, j, k, t, x) [ 0 >= l2 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, m2, j, k, t, x) [ 0 >= b ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ m2 >= 1 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ f >= 1 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ 0 >= f ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ 0 >= h ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ h >= 1 /\ m2 >= 1 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ j >= 1 ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ a >= 1 ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ g >= 1 ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ l2 >= 1 ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, n2, x) [ 0 >= l2 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ o2 >= 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ t >= 1 /\ 0 >= l2 ] (?, 1) f172(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t, x) [ 0 >= x ] (?, 1) f172(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t, x) [ x >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, m2, t, x) [ 0 >= t ] (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ 0 >= k ] (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, k - 1, t, x) [ k >= 1 ] (?, 1) f237(a, b, f, g, h, j, k, t, x) -> f240(a, b, f, g, h, j, k, t, x) (?, 1) f235(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ 0 >= j ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ h >= 1 /\ 0 >= m2 ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ 0 >= g ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ 0 >= m2 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f31(a, b - 1, f, g, h, j, k, t, x) [ 0 >= l2 /\ b >= 1 ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ 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, f, g, h, j, k, t, x) -> f31(a, o2, f, g, h, j, k, t, x) [ l2 >= 1 ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, m2, f, g, h, j, k, t, x) [ 0 >= l2 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, m2, j, k, t, x) [ 0 >= b ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ m2 >= 1 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ f >= 1 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ 0 >= f ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ 0 >= h ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ h >= 1 /\ m2 >= 1 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ j >= 1 ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ a >= 1 ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ g >= 1 ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ l2 >= 1 ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, n2, x) [ 0 >= l2 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ o2 >= 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ t >= 1 /\ 0 >= l2 ] (?, 1) f172(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t, x) [ 0 >= x ] (?, 1) f172(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t, x) [ x >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, m2, t, x) [ 0 >= t ] (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ 0 >= k ] (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, k - 1, t, x) [ k >= 1 ] (?, 1) f235(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ 0 >= j ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ h >= 1 /\ 0 >= m2 ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ 0 >= g ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ 0 >= m2 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f31(a, b - 1, f, g, h, j, k, t, x) [ 0 >= l2 /\ b >= 1 ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ 0 >= a ] start location: f0 leaf cost: 1 Testing for reachability in the complexity graph removes the following transition from problem 3: f172(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t, x) [ x >= 1 ] We thus obtain the following problem: 4: T: (?, 1) f235(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, k - 1, t, x) [ k >= 1 ] (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ 0 >= k ] (?, 1) f172(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t, x) [ 0 >= x ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ 0 >= g ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ g >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, m2, t, x) [ 0 >= t ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ t >= 1 /\ 0 >= l2 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ o2 >= 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ 0 >= a ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ a >= 1 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ 0 >= j ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ j >= 1 ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, n2, x) [ 0 >= l2 ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ l2 >= 1 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ 0 >= f ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ f >= 1 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ h >= 1 /\ 0 >= m2 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ h >= 1 /\ m2 >= 1 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ 0 >= h ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f31(a, b - 1, f, g, h, j, k, t, x) [ 0 >= l2 /\ b >= 1 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ 0 >= m2 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ m2 >= 1 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, m2, j, k, t, x) [ 0 >= b ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, m2, f, g, h, j, k, t, x) [ 0 >= l2 ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, o2, f, g, h, j, k, t, x) [ l2 >= 1 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f235) = -5 Pol(f211) = -4 Pol(f172) = -3 Pol(f144) = -3 Pol(f83) = 1 Pol(f67) = 1 Pol(f81) = 1 Pol(f77) = 1 Pol(f104) = -1 Pol(f42) = 2 Pol(f31) = 2 Pol(f0) = 2 orients all transitions weakly and the transitions f67(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ 0 >= h ] f31(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, m2, j, k, t, x) [ 0 >= b ] strictly and produces the following problem: 5: T: (?, 1) f235(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, k - 1, t, x) [ k >= 1 ] (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ 0 >= k ] (?, 1) f172(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t, x) [ 0 >= x ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ 0 >= g ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ g >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, m2, t, x) [ 0 >= t ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ t >= 1 /\ 0 >= l2 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ o2 >= 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ 0 >= a ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ a >= 1 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ 0 >= j ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ j >= 1 ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, n2, x) [ 0 >= l2 ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ l2 >= 1 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ 0 >= f ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ f >= 1 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ h >= 1 /\ 0 >= m2 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ h >= 1 /\ m2 >= 1 ] (2, 1) f67(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ 0 >= h ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f31(a, b - 1, f, g, h, j, k, t, x) [ 0 >= l2 /\ b >= 1 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ 0 >= m2 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ m2 >= 1 ] (2, 1) f31(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, m2, j, k, t, x) [ 0 >= b ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, m2, f, g, h, j, k, t, x) [ 0 >= l2 ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, o2, f, g, h, j, k, t, x) [ l2 >= 1 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f235) = 0 Pol(f211) = 1 Pol(f172) = 2 Pol(f144) = 2 Pol(f83) = 3 Pol(f67) = 3 Pol(f81) = 3 Pol(f77) = 3 Pol(f104) = 3 Pol(f42) = 3 Pol(f31) = 3 Pol(f0) = 3 orients all transitions weakly and the transitions f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ 0 >= k ] f144(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, m2, t, x) [ 0 >= t ] f104(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, n2, x) [ 0 >= l2 ] strictly and produces the following problem: 6: T: (?, 1) f235(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, k - 1, t, x) [ k >= 1 ] (3, 1) f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ 0 >= k ] (?, 1) f172(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t, x) [ 0 >= x ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ 0 >= g ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ g >= 1 ] (3, 1) f144(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, m2, t, x) [ 0 >= t ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ t >= 1 /\ 0 >= l2 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ o2 >= 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ 0 >= a ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ a >= 1 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ 0 >= j ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ j >= 1 ] (3, 1) f104(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, n2, x) [ 0 >= l2 ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ l2 >= 1 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ 0 >= f ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ f >= 1 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ h >= 1 /\ 0 >= m2 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ h >= 1 /\ m2 >= 1 ] (2, 1) f67(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ 0 >= h ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f31(a, b - 1, f, g, h, j, k, t, x) [ 0 >= l2 /\ b >= 1 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ 0 >= m2 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ m2 >= 1 ] (2, 1) f31(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, m2, j, k, t, x) [ 0 >= b ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, m2, f, g, h, j, k, t, x) [ 0 >= l2 ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, o2, f, g, h, j, k, t, x) [ l2 >= 1 ] start location: f0 leaf cost: 1 Applied AI with 'oct' on problem 6 to obtain the following invariants: For symbol f104: -X_5 >= 0 /\ -X_2 - X_5 >= 0 /\ -X_2 >= 0 For symbol f144: -X_5 >= 0 /\ -X_2 - X_5 >= 0 /\ -X_2 >= 0 For symbol f172: -X_9 >= 0 /\ X_8 - X_9 >= 0 /\ -X_5 - X_9 >= 0 /\ -X_2 - X_9 >= 0 /\ X_9 >= 0 /\ X_8 + X_9 >= 0 /\ -X_5 + X_9 >= 0 /\ -X_2 + X_9 >= 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 f211: -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 f235: -X_8 >= 0 /\ -X_7 - X_8 >= 0 /\ -X_5 - X_8 >= 0 /\ -X_2 - X_8 >= 0 /\ -X_7 >= 0 /\ -X_5 - X_7 >= 0 /\ -X_2 - X_7 >= 0 /\ -X_5 >= 0 /\ -X_2 - X_5 >= 0 /\ -X_2 >= 0 For symbol f42: X_2 >= 0 For symbol f67: -X_2 >= 0 For symbol f77: X_5 >= 0 /\ -X_2 + X_5 >= 0 /\ -X_2 >= 0 For symbol f81: X_5 >= 0 /\ -X_2 + X_5 >= 0 /\ -X_2 >= 0 For symbol f83: X_5 >= 0 /\ -X_2 + X_5 >= 0 /\ -X_2 >= 0 This yielded the following problem: 7: T: (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, o2, f, g, h, j, k, t, x) [ l2 >= 1 ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, m2, f, g, h, j, k, t, x) [ 0 >= l2 ] (2, 1) f31(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, m2, j, k, t, x) [ 0 >= b ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ m2 >= 1 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ 0 >= m2 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f31(a, b - 1, f, g, h, j, k, t, x) [ 0 >= l2 /\ b >= 1 ] (2, 1) f67(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ -b >= 0 /\ 0 >= h ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ -b >= 0 /\ h >= 1 /\ m2 >= 1 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ -b >= 0 /\ h >= 1 /\ 0 >= m2 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ b >= 0 /\ f >= 1 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ b >= 0 /\ 0 >= f ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ l2 >= 1 ] (3, 1) f104(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, n2, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= l2 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ j >= 1 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= j ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ o2 >= 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ t >= 1 /\ 0 >= l2 ] (3, 1) f144(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, m2, t, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= t ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ g >= 1 ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f172(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t, x) [ -x >= 0 /\ t - x >= 0 /\ -h - x >= 0 /\ -b - x >= 0 /\ x >= 0 /\ t + x >= 0 /\ -h + x >= 0 /\ -b + x >= 0 /\ t >= 0 /\ -h + t >= 0 /\ -b + t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= x ] (3, 1) f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ -t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= k ] (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, k - 1, t, x) [ -t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ k >= 1 ] (?, 1) f235(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ -t >= 0 /\ -k - t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -k >= 0 /\ -h - k >= 0 /\ -b - k >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ o2 >= 1 /\ t >= 1 /\ l2 >= 1 ] with all transitions in problem 7, the following new transition is obtained: f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ o2 >= 1 /\ t >= 1 /\ l2 >= 1 /\ 0 >= 0 /\ t - 1 >= 0 /\ -h + t - 1 >= 0 /\ -b + t - 1 >= 0 ] We thus obtain the following problem: 8: T: (?, 2) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ o2 >= 1 /\ t >= 1 /\ l2 >= 1 /\ 0 >= 0 /\ t - 1 >= 0 /\ -h + t - 1 >= 0 /\ -b + t - 1 >= 0 ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, o2, f, g, h, j, k, t, x) [ l2 >= 1 ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, m2, f, g, h, j, k, t, x) [ 0 >= l2 ] (2, 1) f31(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, m2, j, k, t, x) [ 0 >= b ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ m2 >= 1 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ 0 >= m2 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f31(a, b - 1, f, g, h, j, k, t, x) [ 0 >= l2 /\ b >= 1 ] (2, 1) f67(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ -b >= 0 /\ 0 >= h ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ -b >= 0 /\ h >= 1 /\ m2 >= 1 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ -b >= 0 /\ h >= 1 /\ 0 >= m2 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ b >= 0 /\ f >= 1 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ b >= 0 /\ 0 >= f ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ l2 >= 1 ] (3, 1) f104(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, n2, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= l2 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ j >= 1 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= j ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ t >= 1 /\ 0 >= l2 ] (3, 1) f144(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, m2, t, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= t ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ g >= 1 ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f172(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t, x) [ -x >= 0 /\ t - x >= 0 /\ -h - x >= 0 /\ -b - x >= 0 /\ x >= 0 /\ t + x >= 0 /\ -h + x >= 0 /\ -b + x >= 0 /\ t >= 0 /\ -h + t >= 0 /\ -b + t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= x ] (3, 1) f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ -t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= k ] (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, k - 1, t, x) [ -t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ k >= 1 ] (?, 1) f235(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ -t >= 0 /\ -k - t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -k >= 0 /\ -h - k >= 0 /\ -b - k >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f144(a, b, f, g, h, j, k, t, x) -> f172(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 ] with all transitions in problem 8, the following new transition is obtained: f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 /\ 0 >= 0 /\ t - 1 >= 0 /\ -h + t - 1 >= 0 /\ -b + t - 1 >= 0 ] We thus obtain the following problem: 9: T: (?, 2) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 /\ 0 >= 0 /\ t - 1 >= 0 /\ -h + t - 1 >= 0 /\ -b + t - 1 >= 0 ] (?, 2) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ o2 >= 1 /\ t >= 1 /\ l2 >= 1 /\ 0 >= 0 /\ t - 1 >= 0 /\ -h + t - 1 >= 0 /\ -b + t - 1 >= 0 ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, o2, f, g, h, j, k, t, x) [ l2 >= 1 ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, m2, f, g, h, j, k, t, x) [ 0 >= l2 ] (2, 1) f31(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, m2, j, k, t, x) [ 0 >= b ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ m2 >= 1 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ 0 >= m2 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f31(a, b - 1, f, g, h, j, k, t, x) [ 0 >= l2 /\ b >= 1 ] (2, 1) f67(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ -b >= 0 /\ 0 >= h ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ -b >= 0 /\ h >= 1 /\ m2 >= 1 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ -b >= 0 /\ h >= 1 /\ 0 >= m2 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ b >= 0 /\ f >= 1 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ b >= 0 /\ 0 >= f ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ l2 >= 1 ] (3, 1) f104(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, n2, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= l2 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ j >= 1 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= j ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ t >= 1 /\ 0 >= l2 ] (3, 1) f144(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, m2, t, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= t ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ g >= 1 ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f172(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t, x) [ -x >= 0 /\ t - x >= 0 /\ -h - x >= 0 /\ -b - x >= 0 /\ x >= 0 /\ t + x >= 0 /\ -h + x >= 0 /\ -b + x >= 0 /\ t >= 0 /\ -h + t >= 0 /\ -b + t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= x ] (3, 1) f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ -t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= k ] (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, k - 1, t, x) [ -t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ k >= 1 ] (?, 1) f235(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ -t >= 0 /\ -k - t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -k >= 0 /\ -h - k >= 0 /\ -b - k >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 ] start location: f0 leaf cost: 1 Testing for reachability in the complexity graph removes the following transition from problem 9: f172(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t, x) [ -x >= 0 /\ t - x >= 0 /\ -h - x >= 0 /\ -b - x >= 0 /\ x >= 0 /\ t + x >= 0 /\ -h + x >= 0 /\ -b + x >= 0 /\ t >= 0 /\ -h + t >= 0 /\ -b + t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= x ] We thus obtain the following problem: 10: T: (?, 1) f235(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ -t >= 0 /\ -k - t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -k >= 0 /\ -h - k >= 0 /\ -b - k >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 ] (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, k - 1, t, x) [ -t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ k >= 1 ] (3, 1) f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ -t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= k ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ g >= 1 ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 2) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 /\ 0 >= 0 /\ t - 1 >= 0 /\ -h + t - 1 >= 0 /\ -b + t - 1 >= 0 ] (?, 2) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ o2 >= 1 /\ t >= 1 /\ l2 >= 1 /\ 0 >= 0 /\ t - 1 >= 0 /\ -h + t - 1 >= 0 /\ -b + t - 1 >= 0 ] (3, 1) f144(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, m2, t, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= t ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ t >= 1 /\ 0 >= l2 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= j ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ j >= 1 ] (3, 1) f104(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, n2, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= l2 ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ l2 >= 1 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ b >= 0 /\ 0 >= f ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ b >= 0 /\ f >= 1 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ -b >= 0 /\ h >= 1 /\ 0 >= m2 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ -b >= 0 /\ h >= 1 /\ m2 >= 1 ] (2, 1) f67(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ -b >= 0 /\ 0 >= h ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f31(a, b - 1, f, g, h, j, k, t, x) [ 0 >= l2 /\ b >= 1 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ 0 >= m2 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ m2 >= 1 ] (2, 1) f31(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, m2, j, k, t, x) [ 0 >= b ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, m2, f, g, h, j, k, t, x) [ 0 >= l2 ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, o2, f, g, h, j, k, t, x) [ l2 >= 1 ] start location: f0 leaf cost: 1 By chaining the transition f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ -t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= k ] with all transitions in problem 10, the following new transition is obtained: f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ -t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= k /\ -k - t >= 0 /\ -k >= 0 /\ -h - k >= 0 /\ -b - k >= 0 ] We thus obtain the following problem: 11: T: (3, 2) f211(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ -t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= k /\ -k - t >= 0 /\ -k >= 0 /\ -h - k >= 0 /\ -b - k >= 0 ] (?, 1) f235(a, b, f, g, h, j, k, t, x) -> f235(a, b, f, g, h, j, k, t, x) [ -t >= 0 /\ -k - t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -k >= 0 /\ -h - k >= 0 /\ -b - k >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 ] (?, 1) f211(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, k - 1, t, x) [ -t >= 0 /\ -h - t >= 0 /\ -b - t >= 0 /\ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ k >= 1 ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= g ] (?, 1) f83(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ g >= 1 ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= a ] (?, 1) f81(a, b, f, g, h, j, k, t, x) -> f83(a, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ a >= 1 ] (?, 2) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= o2 + 1 /\ t >= 1 /\ l2 >= 1 /\ 0 >= 0 /\ t - 1 >= 0 /\ -h + t - 1 >= 0 /\ -b + t - 1 >= 0 ] (?, 2) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, 0) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ o2 >= 1 /\ t >= 1 /\ l2 >= 1 /\ 0 >= 0 /\ t - 1 >= 0 /\ -h + t - 1 >= 0 /\ -b + t - 1 >= 0 ] (3, 1) f144(a, b, f, g, h, j, k, t, x) -> f211(a, b, f, g, h, j, m2, t, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= t ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ t >= 1 /\ 0 >= l2 ] (?, 1) f144(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, t - 1, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ t >= 1 /\ l2 >= 1 ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ 0 >= j ] (?, 1) f77(a, b, f, g, h, j, k, t, x) -> f81(l2, b, f, g, h, j, k, t, x) [ h >= 0 /\ -b + h >= 0 /\ -b >= 0 /\ j >= 1 ] (3, 1) f104(a, b, f, g, h, j, k, t, x) -> f144(a, b, f, g, h, j, k, n2, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ 0 >= l2 ] (?, 1) f104(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ -h >= 0 /\ -b - h >= 0 /\ -b >= 0 /\ l2 >= 1 ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ b >= 0 /\ 0 >= f ] (?, 1) f42(a, b, f, g, h, j, k, t, x) -> f31(a, b, f, g, h, j, k, t, x) [ b >= 0 /\ f >= 1 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ -b >= 0 /\ h >= 1 /\ 0 >= m2 ] (?, 1) f67(a, b, f, g, h, j, k, t, x) -> f77(a, b, f, l2, h - 1, n2, k, t, x) [ -b >= 0 /\ h >= 1 /\ m2 >= 1 ] (2, 1) f67(a, b, f, g, h, j, k, t, x) -> f104(a, b, f, g, h, j, k, t, x) [ -b >= 0 /\ 0 >= h ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f31(a, b - 1, f, g, h, j, k, t, x) [ 0 >= l2 /\ b >= 1 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ 0 >= m2 ] (?, 1) f31(a, b, f, g, h, j, k, t, x) -> f42(a, b - 1, n2, g, h, j, k, t, x) [ b >= 1 /\ l2 >= 1 /\ m2 >= 1 ] (2, 1) f31(a, b, f, g, h, j, k, t, x) -> f67(a, b, f, g, m2, j, k, t, x) [ 0 >= b ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, m2, f, g, h, j, k, t, x) [ 0 >= l2 ] (1, 1) f0(a, b, f, g, h, j, k, t, x) -> f31(a, o2, f, g, h, j, k, t, x) [ l2 >= 1 ] start location: f0 leaf cost: 1 Complexity upper bound ? Time: 5.447 sec (SMT: 4.331 sec)