YES(?, 3*a^2 + 22*a + 28) Initial complexity problem: 1: T: (?, 1) start(a, b, c, d, e, f, g, h, i, j) -> stop(a, b, c, d, e, f, g, h, 1, j) [ 1 >= a /\ b = c /\ d = e /\ f = a /\ g = h /\ i = j ] (?, 1) start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\ b = c /\ d = e /\ f = a /\ g = h /\ i = j ] (?, 1) lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] (?, 1) lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] (?, 1) lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\ a >= i + 1 /\ f = a ] (?, 1) lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\ a >= i + 1 /\ f = a ] (?, 1) lbl13(a, b, c, d, e, f, g, h, i, j) -> stop(a, b, c, d, e, f, g, h, i, j) [ g + a >= 2 /\ g + 1 >= 0 /\ a >= g + 2 /\ f = a /\ i = a /\ d + 1 = a ] (?, 1) lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\ g + d >= 1 /\ g + 1 >= 0 /\ a >= d + 1 /\ d >= g + 1 /\ f = a /\ i = d + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j) start location: start0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (?, 1) start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\ b = c /\ d = e /\ f = a /\ g = h /\ i = j ] (?, 1) lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] (?, 1) lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] (?, 1) lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\ a >= i + 1 /\ f = a ] (?, 1) lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\ a >= i + 1 /\ f = a ] (?, 1) lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\ g + d >= 1 /\ g + 1 >= 0 /\ a >= d + 1 /\ d >= g + 1 /\ f = a /\ i = d + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j) start location: start0 leaf cost: 2 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (1, 1) start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\ b = c /\ d = e /\ f = a /\ g = h /\ i = j ] (?, 1) lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] (?, 1) lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] (?, 1) lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\ a >= i + 1 /\ f = a ] (?, 1) lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\ a >= i + 1 /\ f = a ] (?, 1) lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\ g + d >= 1 /\ g + 1 >= 0 /\ a >= d + 1 /\ d >= g + 1 /\ f = a /\ i = d + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j) start location: start0 leaf cost: 2 A polynomial rank function with Pol(start) = 3*V_1 - 4 Pol(lbl31) = 3*V_1 - 3*V_9 - 1 Pol(lbl43) = 3*V_1 - 3*V_9 - 2 Pol(lbl13) = 3*V_1 - 3*V_4 - 3 Pol(start0) = 3*V_1 - 4 orients all transitions weakly and the transitions lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\ a >= i + 1 /\ f = a ] lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\ a >= i + 1 /\ f = a ] lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\ g + d >= 1 /\ g + 1 >= 0 /\ a >= d + 1 /\ d >= g + 1 /\ f = a /\ i = d + 1 ] strictly and produces the following problem: 4: T: (1, 1) start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\ b = c /\ d = e /\ f = a /\ g = h /\ i = j ] (?, 1) lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] (3*a + 4, 1) lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] (3*a + 4, 1) lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\ a >= i + 1 /\ f = a ] (3*a + 4, 1) lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\ a >= i + 1 /\ f = a ] (3*a + 4, 1) lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\ g + d >= 1 /\ g + 1 >= 0 /\ a >= d + 1 /\ d >= g + 1 /\ f = a /\ i = d + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j) start location: start0 leaf cost: 2 A polynomial rank function with Pol(lbl43) = V_7 + 1 and size complexities S("start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j)", 0-0) = a S("start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j)", 0-1) = c S("start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j)", 0-2) = c S("start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j)", 0-3) = e S("start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j)", 0-4) = e S("start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j)", 0-5) = a S("start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j)", 0-6) = h S("start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j)", 0-7) = h S("start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j)", 0-8) = j S("start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j)", 0-9) = j S("lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\\ g + d >= 1 /\\ g + 1 >= 0 /\\ a >= d + 1 /\\ d >= g + 1 /\\ f = a /\\ i = d + 1 ]", 0-0) = a S("lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\\ g + d >= 1 /\\ g + 1 >= 0 /\\ a >= d + 1 /\\ d >= g + 1 /\\ f = a /\\ i = d + 1 ]", 0-1) = ? S("lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\\ g + d >= 1 /\\ g + 1 >= 0 /\\ a >= d + 1 /\\ d >= g + 1 /\\ f = a /\\ i = d + 1 ]", 0-2) = c S("lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\\ g + d >= 1 /\\ g + 1 >= 0 /\\ a >= d + 1 /\\ d >= g + 1 /\\ f = a /\\ i = d + 1 ]", 0-3) = a + 1 S("lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\\ g + d >= 1 /\\ g + 1 >= 0 /\\ a >= d + 1 /\\ d >= g + 1 /\\ f = a /\\ i = d + 1 ]", 0-4) = e S("lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\\ g + d >= 1 /\\ g + 1 >= 0 /\\ a >= d + 1 /\\ d >= g + 1 /\\ f = a /\\ i = d + 1 ]", 0-5) = a S("lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\\ g + d >= 1 /\\ g + 1 >= 0 /\\ a >= d + 1 /\\ d >= g + 1 /\\ f = a /\\ i = d + 1 ]", 0-6) = a + 2 S("lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\\ g + d >= 1 /\\ g + 1 >= 0 /\\ a >= d + 1 /\\ d >= g + 1 /\\ f = a /\\ i = d + 1 ]", 0-7) = h S("lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\\ g + d >= 1 /\\ g + 1 >= 0 /\\ a >= d + 1 /\\ d >= g + 1 /\\ f = a /\\ i = d + 1 ]", 0-8) = a S("lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\\ g + d >= 1 /\\ g + 1 >= 0 /\\ a >= d + 1 /\\ d >= g + 1 /\\ f = a /\\ i = d + 1 ]", 0-9) = j S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-0) = a S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-1) = ? S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-2) = c S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-3) = a + 1 S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-4) = e S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-5) = a S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-6) = a + 1 S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-7) = h S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-8) = a S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-9) = j S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-0) = a S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-1) = ? S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-2) = c S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-3) = a + e + 1 S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-4) = e S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-5) = a S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-6) = a + 1 S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-7) = h S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-8) = a + 1 S("lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\\ a >= i + 1 /\\ f = a ]", 0-9) = j S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-0) = a S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-1) = ? S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-2) = c S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-3) = a + 1 S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-4) = e S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-5) = a S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-6) = a + 2 S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-7) = h S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-8) = a S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-9) = j S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\\ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-0) = a S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\\ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-1) = ? S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\\ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-2) = c S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\\ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-3) = a + e + 1 S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\\ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-4) = e S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\\ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-5) = a S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\\ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-6) = a + 2 S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\\ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-7) = h S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\\ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-8) = a + 1 S("lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\\ i >= g + 2 /\\ g + 1 >= 0 /\\ a >= i + 1 /\\ f = a ]", 0-9) = j S("start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\\ b = c /\\ d = e /\\ f = a /\\ g = h /\\ i = j ]", 0-0) = a S("start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\\ b = c /\\ d = e /\\ f = a /\\ g = h /\\ i = j ]", 0-1) = ? S("start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\\ b = c /\\ d = e /\\ f = a /\\ g = h /\\ i = j ]", 0-2) = c S("start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\\ b = c /\\ d = e /\\ f = a /\\ g = h /\\ i = j ]", 0-3) = e S("start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\\ b = c /\\ d = e /\\ f = a /\\ g = h /\\ i = j ]", 0-4) = e S("start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\\ b = c /\\ d = e /\\ f = a /\\ g = h /\\ i = j ]", 0-5) = a S("start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\\ b = c /\\ d = e /\\ f = a /\\ g = h /\\ i = j ]", 0-6) = h S("start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\\ b = c /\\ d = e /\\ f = a /\\ g = h /\\ i = j ]", 0-7) = h S("start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\\ b = c /\\ d = e /\\ f = a /\\ g = h /\\ i = j ]", 0-8) = 1 S("start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\\ b = c /\\ d = e /\\ f = a /\\ g = h /\\ i = j ]", 0-9) = j orients the transition lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] weakly and the transition lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] strictly and produces the following problem: 5: T: (1, 1) start(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, 1, j) [ a >= 2 /\ b = c /\ d = e /\ f = a /\ g = h /\ i = j ] (3*a^2 + 10*a + 8, 1) lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, g - 1, h, i, j) [ g >= 0 /\ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] (3*a + 4, 1) lbl43(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, g, h, i + 1, j) [ i >= g + 2 /\ g + 1 >= 0 /\ a >= i + 1 /\ f = a ] (3*a + 4, 1) lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl43(a, b, c, d, e, f, i - 2, h, i, j) [ i >= 1 /\ a >= i + 1 /\ f = a ] (3*a + 4, 1) lbl31(a, b, c, d, e, f, g, h, i, j) -> lbl13(a, b, c, i, e, f, i - 1, h, i + 1, j) [ i >= 1 /\ a >= i + 1 /\ f = a ] (3*a + 4, 1) lbl13(a, b, c, d, e, f, g, h, i, j) -> lbl31(a, k, c, d, e, f, g, h, i, j) [ a >= d + 2 /\ g + d >= 1 /\ g + 1 >= 0 /\ a >= d + 1 /\ d >= g + 1 /\ f = a /\ i = d + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h, i, j) -> start(a, c, c, e, e, a, h, h, j, j) start location: start0 leaf cost: 2 Complexity upper bound 3*a^2 + 22*a + 28 Time: 0.536 sec (SMT: 0.497 sec)