YES(?, 94) 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) -> f6(0, 0, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) (?, 1) f6(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) -> f6(u, b + 1, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) [ 63 >= b ] (?, 1) f14(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) -> f14(a, b, c - 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, g1, h1, i1 + j1, k1 + j1, j1) [ c >= 0 ] (?, 1) f57(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) -> f57(a, b, c - 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, g1, h1, i1 + j1, k1 + j1, j1) [ c >= 0 ] (?, 1) f57(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) -> f101(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) [ 0 >= c + 1 ] (?, 1) f14(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) -> f57(a, b, 7, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) [ 0 >= c + 1 ] (?, 1) f6(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) -> f14(a, b, 7, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) [ b >= 64 ] start location: f0 leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [b, c]. We thus obtain the following problem: 2: T: (?, 1) f6(b, c) -> f14(b, 7) [ b >= 64 ] (?, 1) f14(b, c) -> f57(b, 7) [ 0 >= c + 1 ] (?, 1) f57(b, c) -> f101(b, c) [ 0 >= c + 1 ] (?, 1) f57(b, c) -> f57(b, c - 1) [ c >= 0 ] (?, 1) f14(b, c) -> f14(b, c - 1) [ c >= 0 ] (?, 1) f6(b, c) -> f6(b + 1, c) [ 63 >= b ] (1, 1) f0(b, c) -> f6(0, c) start location: f0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem: 3: T: (?, 1) f6(b, c) -> f14(b, 7) [ b >= 64 ] (?, 1) f14(b, c) -> f57(b, 7) [ 0 >= c + 1 ] (?, 1) f57(b, c) -> f57(b, c - 1) [ c >= 0 ] (?, 1) f14(b, c) -> f14(b, c - 1) [ c >= 0 ] (?, 1) f6(b, c) -> f6(b + 1, c) [ 63 >= b ] (1, 1) f0(b, c) -> f6(0, c) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f6) = 2 Pol(f14) = 1 Pol(f57) = 0 Pol(f0) = 2 orients all transitions weakly and the transitions f6(b, c) -> f14(b, 7) [ b >= 64 ] f14(b, c) -> f57(b, 7) [ 0 >= c + 1 ] strictly and produces the following problem: 4: T: (2, 1) f6(b, c) -> f14(b, 7) [ b >= 64 ] (2, 1) f14(b, c) -> f57(b, 7) [ 0 >= c + 1 ] (?, 1) f57(b, c) -> f57(b, c - 1) [ c >= 0 ] (?, 1) f14(b, c) -> f14(b, c - 1) [ c >= 0 ] (?, 1) f6(b, c) -> f6(b + 1, c) [ 63 >= b ] (1, 1) f0(b, c) -> f6(0, c) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f6) = -V_1 + 64 Pol(f14) = -V_1 Pol(f57) = -V_1 + V_2 - 7 Pol(f0) = 64 orients all transitions weakly and the transition f6(b, c) -> f6(b + 1, c) [ 63 >= b ] strictly and produces the following problem: 5: T: (2, 1) f6(b, c) -> f14(b, 7) [ b >= 64 ] (2, 1) f14(b, c) -> f57(b, 7) [ 0 >= c + 1 ] (?, 1) f57(b, c) -> f57(b, c - 1) [ c >= 0 ] (?, 1) f14(b, c) -> f14(b, c - 1) [ c >= 0 ] (64, 1) f6(b, c) -> f6(b + 1, c) [ 63 >= b ] (1, 1) f0(b, c) -> f6(0, c) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f6) = 8 Pol(f14) = 8 Pol(f57) = V_2 + 1 Pol(f0) = 8 orients all transitions weakly and the transition f57(b, c) -> f57(b, c - 1) [ c >= 0 ] strictly and produces the following problem: 6: T: (2, 1) f6(b, c) -> f14(b, 7) [ b >= 64 ] (2, 1) f14(b, c) -> f57(b, 7) [ 0 >= c + 1 ] (8, 1) f57(b, c) -> f57(b, c - 1) [ c >= 0 ] (?, 1) f14(b, c) -> f14(b, c - 1) [ c >= 0 ] (64, 1) f6(b, c) -> f6(b + 1, c) [ 63 >= b ] (1, 1) f0(b, c) -> f6(0, c) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f14) = V_2 + 1 and size complexities S("f0(b, c) -> f6(0, c)", 0-0) = 0 S("f0(b, c) -> f6(0, c)", 0-1) = c S("f6(b, c) -> f6(b + 1, c) [ 63 >= b ]", 0-0) = 64 S("f6(b, c) -> f6(b + 1, c) [ 63 >= b ]", 0-1) = c S("f14(b, c) -> f14(b, c - 1) [ c >= 0 ]", 0-0) = 64 S("f14(b, c) -> f14(b, c - 1) [ c >= 0 ]", 0-1) = 7 S("f57(b, c) -> f57(b, c - 1) [ c >= 0 ]", 0-0) = 64 S("f57(b, c) -> f57(b, c - 1) [ c >= 0 ]", 0-1) = 7 S("f14(b, c) -> f57(b, 7) [ 0 >= c + 1 ]", 0-0) = 64 S("f14(b, c) -> f57(b, 7) [ 0 >= c + 1 ]", 0-1) = 7 S("f6(b, c) -> f14(b, 7) [ b >= 64 ]", 0-0) = 64 S("f6(b, c) -> f14(b, 7) [ b >= 64 ]", 0-1) = 7 orients the transition f14(b, c) -> f14(b, c - 1) [ c >= 0 ] weakly and the transition f14(b, c) -> f14(b, c - 1) [ c >= 0 ] strictly and produces the following problem: 7: T: (2, 1) f6(b, c) -> f14(b, 7) [ b >= 64 ] (2, 1) f14(b, c) -> f57(b, 7) [ 0 >= c + 1 ] (8, 1) f57(b, c) -> f57(b, c - 1) [ c >= 0 ] (16, 1) f14(b, c) -> f14(b, c - 1) [ c >= 0 ] (64, 1) f6(b, c) -> f6(b + 1, c) [ 63 >= b ] (1, 1) f0(b, c) -> f6(0, c) start location: f0 leaf cost: 1 Complexity upper bound 94 Time: 0.264 sec (SMT: 0.252 sec)