YES(?, 8*a + 813) Initial complexity problem: 1: T: (?, 1) start(a, b, c, d, e, f, g, h) -> stop(a, h - 10, c, 1, e, h, g, h) [ a >= 101 /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) start(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, 2, e, h + 11, g, h) [ 100 >= a /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) lbl161(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ 89 >= a /\ d = 1 /\ h = a /\ f = 101 /\ b = 91 ] (?, 1) lbl161(a, b, c, d, e, f, g, h) -> lbl161(a, f - 20, c, d - 1, e, f - 10, g, h) [ 0 >= 10 /\ 89 >= a /\ 0 >= 1 /\ d = 2 /\ h = a /\ f = 101 /\ b = 91 ] (?, 1) lbl161(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 0 >= 2 /\ 89 >= a /\ h = a /\ f = 101 /\ d = 1 /\ b = 91 ] (?, 1) lbl161(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 0 >= 1 /\ 89 >= a /\ h = a /\ f = 101 /\ d = 1 /\ b = 91 ] (?, 1) lbl161(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ 0 >= 10 /\ 0 >= 2 /\ 89 >= a /\ h = a /\ f = 101 /\ d = 1 /\ b = 91 ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ 1 >= d /\ d >= 2 /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl161(a, f - 20, c, d - 1, e, f - 10, g, h) [ 99 >= a /\ 89 >= a /\ f = 111 /\ d = 2 /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 3 /\ 110 >= f /\ d >= 2 /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 2 /\ 110 >= f /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ d >= 2 /\ 121 >= a + 11*d /\ 89 >= a /\ f = 111 /\ h = a /\ b = c ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d + 1, e, f + 11, g, h) [ 111 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ 11*d + a >= 112 /\ 1 >= d /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl161(a, f - 20, c, d - 1, e, f - 10, g, h) [ f = 111 /\ d = 2 /\ h = 100 /\ b = c /\ a = 100 ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 3 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 2 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ 11*d >= 22 /\ f = 111 /\ h + 11*d = 122 /\ b = c /\ a + 11*d = 122 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a) start location: start0 leaf cost: 0 Testing for unsatisfiable constraints removes the following transitions from problem 1: lbl161(a, b, c, d, e, f, g, h) -> lbl161(a, f - 20, c, d - 1, e, f - 10, g, h) [ 0 >= 10 /\ 89 >= a /\ 0 >= 1 /\ d = 2 /\ h = a /\ f = 101 /\ b = 91 ] lbl161(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 0 >= 2 /\ 89 >= a /\ h = a /\ f = 101 /\ d = 1 /\ b = 91 ] lbl161(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 0 >= 1 /\ 89 >= a /\ h = a /\ f = 101 /\ d = 1 /\ b = 91 ] lbl161(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ 0 >= 10 /\ 0 >= 2 /\ 89 >= a /\ h = a /\ f = 101 /\ d = 1 /\ b = 91 ] lbl221(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ 1 >= d /\ d >= 2 /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] lbl111(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ 11*d + a >= 112 /\ 1 >= d /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] We thus obtain the following problem: 2: T: (?, 1) start(a, b, c, d, e, f, g, h) -> stop(a, h - 10, c, 1, e, h, g, h) [ a >= 101 /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) start(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, 2, e, h + 11, g, h) [ 100 >= a /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) lbl161(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ 89 >= a /\ d = 1 /\ h = a /\ f = 101 /\ b = 91 ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl161(a, f - 20, c, d - 1, e, f - 10, g, h) [ 99 >= a /\ 89 >= a /\ f = 111 /\ d = 2 /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 3 /\ 110 >= f /\ d >= 2 /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 2 /\ 110 >= f /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ d >= 2 /\ 121 >= a + 11*d /\ 89 >= a /\ f = 111 /\ h = a /\ b = c ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d + 1, e, f + 11, g, h) [ 111 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl161(a, f - 20, c, d - 1, e, f - 10, g, h) [ f = 111 /\ d = 2 /\ h = 100 /\ b = c /\ a = 100 ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 3 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 2 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ 11*d >= 22 /\ f = 111 /\ h + 11*d = 122 /\ b = c /\ a + 11*d = 122 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a) start location: start0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem: 3: T: (?, 1) start(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, 2, e, h + 11, g, h) [ 100 >= a /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 3 /\ 110 >= f /\ d >= 2 /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 2 /\ 110 >= f /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ d >= 2 /\ 121 >= a + 11*d /\ 89 >= a /\ f = 111 /\ h = a /\ b = c ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d + 1, e, f + 11, g, h) [ 111 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 3 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 2 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ 11*d >= 22 /\ f = 111 /\ h + 11*d = 122 /\ b = c /\ a + 11*d = 122 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a) start location: start0 leaf cost: 4 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (1, 1) start(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, 2, e, h + 11, g, h) [ 100 >= a /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 3 /\ 110 >= f /\ d >= 2 /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 2 /\ 110 >= f /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ d >= 2 /\ 121 >= a + 11*d /\ 89 >= a /\ f = 111 /\ h = a /\ b = c ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d + 1, e, f + 11, g, h) [ 111 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 3 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 2 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ 11*d >= 22 /\ f = 111 /\ h + 11*d = 122 /\ b = c /\ a + 11*d = 122 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a) start location: start0 leaf cost: 4 A polynomial rank function with Pol(start) = 1 Pol(lbl111) = 1 Pol(lbl221) = 0 Pol(start0) = 1 orients all transitions weakly and the transitions lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 3 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 2 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] strictly and produces the following problem: 5: T: (1, 1) start(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, 2, e, h + 11, g, h) [ 100 >= a /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 3 /\ 110 >= f /\ d >= 2 /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 2 /\ 110 >= f /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ d >= 2 /\ 121 >= a + 11*d /\ 89 >= a /\ f = 111 /\ h = a /\ b = c ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d + 1, e, f + 11, g, h) [ 111 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (1, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 3 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (1, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 2 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ 11*d >= 22 /\ f = 111 /\ h + 11*d = 122 /\ b = c /\ a + 11*d = 122 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a) start location: start0 leaf cost: 4 A polynomial rank function with Pol(start) = 1 Pol(lbl111) = 1 Pol(lbl221) = 0 Pol(start0) = 1 orients all transitions weakly and the transition lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ 11*d >= 22 /\ f = 111 /\ h + 11*d = 122 /\ b = c /\ a + 11*d = 122 ] strictly and produces the following problem: 6: T: (1, 1) start(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, 2, e, h + 11, g, h) [ 100 >= a /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 3 /\ 110 >= f /\ d >= 2 /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 2 /\ 110 >= f /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (?, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ d >= 2 /\ 121 >= a + 11*d /\ 89 >= a /\ f = 111 /\ h = a /\ b = c ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d + 1, e, f + 11, g, h) [ 111 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (1, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 3 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (1, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 2 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (1, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ 11*d >= 22 /\ f = 111 /\ h + 11*d = 122 /\ b = c /\ a + 11*d = 122 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a) start location: start0 leaf cost: 4 A polynomial rank function with Pol(start) = -V_1 - V_8 + 201 Pol(lbl111) = -V_1 - V_6 + 212 Pol(lbl221) = 11*V_4 - V_6 + 92 Pol(start0) = -2*V_1 + 201 orients all transitions weakly and the transitions lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 3 /\ 110 >= f /\ d >= 2 /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 2 /\ 110 >= f /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ d >= 2 /\ 121 >= a + 11*d /\ 89 >= a /\ f = 111 /\ h = a /\ b = c ] lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d + 1, e, f + 11, g, h) [ 111 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] strictly and produces the following problem: 7: T: (1, 1) start(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, 2, e, h + 11, g, h) [ 100 >= a /\ b = c /\ d = e /\ f = g /\ h = a ] (2*a + 201, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 3 /\ 110 >= f /\ d >= 2 /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (2*a + 201, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ d >= 2 /\ 110 >= f /\ f >= 102 /\ 111 >= f /\ f + 10 >= a + 11*d /\ 89 >= a /\ h = a /\ b = c ] (2*a + 201, 1) lbl221(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ d >= 2 /\ 121 >= a + 11*d /\ 89 >= a /\ f = 111 /\ h = a /\ b = c ] (2*a + 201, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d + 1, e, f + 11, g, h) [ 111 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (1, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 3 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (1, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d, e, f + 1, g, h) [ 11*d + a >= 112 /\ d >= 2 /\ 121 >= 11*d + a /\ 122 >= 11*d + a /\ 11*d >= 22 /\ h = a /\ b = c /\ f + 11 = 11*d + a ] (1, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl221(a, b, c, d - 1, e, f - 9, g, h) [ d >= 3 /\ 11*d >= 22 /\ f = 111 /\ h + 11*d = 122 /\ b = c /\ a + 11*d = 122 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a) start location: start0 leaf cost: 4 Complexity upper bound 8*a + 813 Time: 0.890 sec (SMT: 0.829 sec)