YES(?, 31) Initial complexity problem: 1: T: (1, 1) f0(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) -> f7(8, 0, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) (?, 1) f7(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) -> f7(a, b + 1, u + v, w, x + y, z, a1 + b1, c1, d1 + e1, f1, u + v + d1 + e1, u + v - d1 - e1, x + y + a1 + b1, x + y - a1 - b1, -3196, g1, h1, i1 + j1, k1 + j1, j1) [ 7 >= b ] (?, 1) f62(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) -> f62(a, b + 1, u + v, w, x + y, z, a1 + b1, c1, d1 + e1, f1, u + v + d1 + e1, u + v - d1 - e1, x + y + a1 + b1, x + y - a1 - b1, -3196, g1, h1, i1 + j1, k1 + j1, j1) [ 7 >= b ] (?, 1) f62(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) -> f118(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) [ b >= 8 ] (?, 1) f7(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) -> f62(a, 0, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) [ b >= 8 ] start location: f0 leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [b]. We thus obtain the following problem: 2: T: (?, 1) f7(b) -> f62(0) [ b >= 8 ] (?, 1) f62(b) -> f118(b) [ b >= 8 ] (?, 1) f62(b) -> f62(b + 1) [ 7 >= b ] (?, 1) f7(b) -> f7(b + 1) [ 7 >= b ] (1, 1) f0(b) -> f7(0) start location: f0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem: 3: T: (?, 1) f7(b) -> f62(0) [ b >= 8 ] (?, 1) f62(b) -> f62(b + 1) [ 7 >= b ] (?, 1) f7(b) -> f7(b + 1) [ 7 >= b ] (1, 1) f0(b) -> f7(0) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f7) = 7 Pol(f62) = 6 Pol(f0) = 7 orients all transitions weakly and the transition f7(b) -> f62(0) [ b >= 8 ] strictly and produces the following problem: 4: T: (7, 1) f7(b) -> f62(0) [ b >= 8 ] (?, 1) f62(b) -> f62(b + 1) [ 7 >= b ] (?, 1) f7(b) -> f7(b + 1) [ 7 >= b ] (1, 1) f0(b) -> f7(0) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f7) = 14 Pol(f62) = -V_1 + 14 Pol(f0) = 14 orients all transitions weakly and the transition f62(b) -> f62(b + 1) [ 7 >= b ] strictly and produces the following problem: 5: T: (7, 1) f7(b) -> f62(0) [ b >= 8 ] (14, 1) f62(b) -> f62(b + 1) [ 7 >= b ] (?, 1) f7(b) -> f7(b + 1) [ 7 >= b ] (1, 1) f0(b) -> f7(0) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f7) = -V_1 + 8 and size complexities S("f0(b) -> f7(0)", 0-0) = 0 S("f7(b) -> f7(b + 1) [ 7 >= b ]", 0-0) = 8 S("f62(b) -> f62(b + 1) [ 7 >= b ]", 0-0) = 8 S("f7(b) -> f62(0) [ b >= 8 ]", 0-0) = 0 orients the transition f7(b) -> f7(b + 1) [ 7 >= b ] weakly and the transition f7(b) -> f7(b + 1) [ 7 >= b ] strictly and produces the following problem: 6: T: (7, 1) f7(b) -> f62(0) [ b >= 8 ] (14, 1) f62(b) -> f62(b + 1) [ 7 >= b ] (8, 1) f7(b) -> f7(b + 1) [ 7 >= b ] (1, 1) f0(b) -> f7(0) start location: f0 leaf cost: 1 Complexity upper bound 31 Time: 0.152 sec (SMT: 0.142 sec)