YES(?, 2*a^2 + 10*a + 15) Initial complexity problem: 1: T: (?, 1) start(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ 1 >= a /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) start(a, b, c, d, e, f, g, h) -> lbl111(a, h, c, 1, e, h - 1, g, h) [ a >= 2 /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) lbl16(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ a >= 2 /\ a >= b + 1 /\ f = 0 /\ h = a /\ d = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\ 0 >= d + 1 /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\ d >= 1 /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\ a >= f + 1 /\ a >= f /\ a >= b /\ d = 0 /\ h = a ] (?, 1) lbl82(a, b, c, d, e, f, g, h) -> lbl16(a, b, c, d, e, f, g, h) [ a >= 2 /\ a >= b /\ a >= b + 1 /\ f = 0 /\ h = a /\ d = a ] (?, 1) lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\ a >= f /\ f >= 0 /\ a >= f + 2 /\ a >= b /\ a + f >= b + 1 /\ h = a /\ d = a ] (?, 1) lbl82(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= a + 1 /\ a >= 1 /\ f >= 0 /\ a >= f + 2 /\ a >= b /\ a + f >= b + 1 /\ h = a /\ d = a ] (?, 1) lbl82(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= 1 /\ 0 >= a + 1 /\ f >= 0 /\ a >= f + 2 /\ a >= b /\ a + f >= b + 1 /\ h = a /\ d = a ] (?, 1) lbl82(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\ f >= 0 /\ 0 >= f + 2 /\ 0 >= b /\ f >= b + 1 /\ d = 0 /\ h = 0 /\ a = 0 ] (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: lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\ 0 >= d + 1 /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] lbl82(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= a + 1 /\ a >= 1 /\ f >= 0 /\ a >= f + 2 /\ a >= b /\ a + f >= b + 1 /\ h = a /\ d = a ] lbl82(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= 1 /\ 0 >= a + 1 /\ f >= 0 /\ a >= f + 2 /\ a >= b /\ a + f >= b + 1 /\ h = a /\ d = a ] lbl82(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\ f >= 0 /\ 0 >= f + 2 /\ 0 >= b /\ f >= b + 1 /\ d = 0 /\ h = 0 /\ a = 0 ] We thus obtain the following problem: 2: T: (?, 1) start(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ 1 >= a /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) start(a, b, c, d, e, f, g, h) -> lbl111(a, h, c, 1, e, h - 1, g, h) [ a >= 2 /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) lbl16(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ a >= 2 /\ a >= b + 1 /\ f = 0 /\ h = a /\ d = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\ d >= 1 /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\ a >= f + 1 /\ a >= f /\ a >= b /\ d = 0 /\ h = a ] (?, 1) lbl82(a, b, c, d, e, f, g, h) -> lbl16(a, b, c, d, e, f, g, h) [ a >= 2 /\ a >= b /\ a >= b + 1 /\ f = 0 /\ h = a /\ d = a ] (?, 1) lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\ a >= f /\ f >= 0 /\ a >= f + 2 /\ a >= b /\ a + f >= b + 1 /\ h = a /\ d = a ] (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, h, c, 1, e, h - 1, g, h) [ a >= 2 /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\ d >= 1 /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\ a >= f + 1 /\ a >= f /\ a >= b /\ d = 0 /\ h = a ] (?, 1) lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\ a >= f /\ f >= 0 /\ a >= f + 2 /\ a >= b /\ a + f >= b + 1 /\ h = a /\ d = a ] (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: 3 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, h, c, 1, e, h - 1, g, h) [ a >= 2 /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\ d >= 1 /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\ a >= f + 1 /\ a >= f /\ a >= b /\ d = 0 /\ h = a ] (?, 1) lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\ a >= f /\ f >= 0 /\ a >= f + 2 /\ a >= b /\ a + f >= b + 1 /\ h = a /\ d = a ] (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: 3 A polynomial rank function with Pol(start) = 2*V_8 - 2 Pol(lbl111) = 2*V_6 Pol(lbl82) = 2*V_6 + 1 Pol(start0) = 2*V_1 - 2 orients all transitions weakly and the transitions lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\ a >= f /\ f >= 0 /\ a >= f + 2 /\ a >= b /\ a + f >= b + 1 /\ h = a /\ d = a ] lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\ a >= f + 1 /\ a >= f /\ a >= b /\ d = 0 /\ h = a ] lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\ d >= 1 /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] strictly and produces the following problem: 5: T: (1, 1) start(a, b, c, d, e, f, g, h) -> lbl111(a, h, c, 1, e, h - 1, g, h) [ a >= 2 /\ b = c /\ d = e /\ f = g /\ h = a ] (?, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (2*a + 2, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\ d >= 1 /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (2*a + 2, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\ a >= f + 1 /\ a >= f /\ a >= b /\ d = 0 /\ h = a ] (2*a + 2, 1) lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\ a >= f /\ f >= 0 /\ a >= f + 2 /\ a >= b /\ a + f >= b + 1 /\ h = a /\ d = a ] (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: 3 A polynomial rank function with Pol(lbl111) = V_4 + 1 and size complexities S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a)", 0-0) = a S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a)", 0-1) = c S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a)", 0-2) = c S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a)", 0-3) = e S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a)", 0-4) = e S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a)", 0-5) = g S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a)", 0-6) = g S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, e, e, g, g, a)", 0-7) = a S("lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\\ a >= f /\\ f >= 0 /\\ a >= f + 2 /\\ a >= b /\\ a + f >= b + 1 /\\ h = a /\\ d = a ]", 0-0) = a S("lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\\ a >= f /\\ f >= 0 /\\ a >= f + 2 /\\ a >= b /\\ a + f >= b + 1 /\\ h = a /\\ d = a ]", 0-1) = 3*a + 2*a^2 S("lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\\ a >= f /\\ f >= 0 /\\ a >= f + 2 /\\ a >= b /\\ a + f >= b + 1 /\\ h = a /\\ d = a ]", 0-2) = c S("lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\\ a >= f /\\ f >= 0 /\\ a >= f + 2 /\\ a >= b /\\ a + f >= b + 1 /\\ h = a /\\ d = a ]", 0-3) = a S("lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\\ a >= f /\\ f >= 0 /\\ a >= f + 2 /\\ a >= b /\\ a + f >= b + 1 /\\ h = a /\\ d = a ]", 0-4) = e S("lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\\ a >= f /\\ f >= 0 /\\ a >= f + 2 /\\ a >= b /\\ a + f >= b + 1 /\\ h = a /\\ d = a ]", 0-5) = a S("lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\\ a >= f /\\ f >= 0 /\\ a >= f + 2 /\\ a >= b /\\ a + f >= b + 1 /\\ h = a /\\ d = a ]", 0-6) = g S("lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\\ a >= f /\\ f >= 0 /\\ a >= f + 2 /\\ a >= b /\\ a + f >= b + 1 /\\ h = a /\\ d = a ]", 0-7) = a S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\\ a >= f + 1 /\\ a >= f /\\ a >= b /\\ d = 0 /\\ h = a ]", 0-0) = a S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\\ a >= f + 1 /\\ a >= f /\\ a >= b /\\ d = 0 /\\ h = a ]", 0-1) = 3*a + 2*a^2 S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\\ a >= f + 1 /\\ a >= f /\\ a >= b /\\ d = 0 /\\ h = a ]", 0-2) = c S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\\ a >= f + 1 /\\ a >= f /\\ a >= b /\\ d = 0 /\\ h = a ]", 0-3) = a S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\\ a >= f + 1 /\\ a >= f /\\ a >= b /\\ d = 0 /\\ h = a ]", 0-4) = e S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\\ a >= f + 1 /\\ a >= f /\\ a >= b /\\ d = 0 /\\ h = a ]", 0-5) = a S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\\ a >= f + 1 /\\ a >= f /\\ a >= b /\\ d = 0 /\\ h = a ]", 0-6) = g S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\\ a >= f + 1 /\\ a >= f /\\ a >= b /\\ d = 0 /\\ h = a ]", 0-7) = a S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\\ d >= 1 /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-0) = a S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\\ d >= 1 /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-1) = 3*a + 2*a^2 S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\\ d >= 1 /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-2) = c S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\\ d >= 1 /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-3) = a S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\\ d >= 1 /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-4) = e S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\\ d >= 1 /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-5) = a S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\\ d >= 1 /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-6) = g S("lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\\ d >= 1 /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-7) = a S("lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-0) = a S("lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-1) = 3*a + 2*a^2 S("lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-2) = c S("lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-3) = a + 1 S("lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-4) = e S("lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-5) = a S("lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-6) = g S("lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\\ a >= f + 1 /\\ a >= f + d /\\ a >= b /\\ f >= 1 /\\ d >= 0 /\\ h = a ]", 0-7) = a S("start(a, b, c, d, e, f, g, h) -> lbl111(a, h, c, 1, e, h - 1, g, h) [ a >= 2 /\\ b = c /\\ d = e /\\ f = g /\\ h = a ]", 0-0) = a S("start(a, b, c, d, e, f, g, h) -> lbl111(a, h, c, 1, e, h - 1, g, h) [ a >= 2 /\\ b = c /\\ d = e /\\ f = g /\\ h = a ]", 0-1) = a S("start(a, b, c, d, e, f, g, h) -> lbl111(a, h, c, 1, e, h - 1, g, h) [ a >= 2 /\\ b = c /\\ d = e /\\ f = g /\\ h = a ]", 0-2) = c S("start(a, b, c, d, e, f, g, h) -> lbl111(a, h, c, 1, e, h - 1, g, h) [ a >= 2 /\\ b = c /\\ d = e /\\ f = g /\\ h = a ]", 0-3) = 1 S("start(a, b, c, d, e, f, g, h) -> lbl111(a, h, c, 1, e, h - 1, g, h) [ a >= 2 /\\ b = c /\\ d = e /\\ f = g /\\ h = a ]", 0-4) = e S("start(a, b, c, d, e, f, g, h) -> lbl111(a, h, c, 1, e, h - 1, g, h) [ a >= 2 /\\ b = c /\\ d = e /\\ f = g /\\ h = a ]", 0-5) = a S("start(a, b, c, d, e, f, g, h) -> lbl111(a, h, c, 1, e, h - 1, g, h) [ a >= 2 /\\ b = c /\\ d = e /\\ f = g /\\ h = a ]", 0-6) = g S("start(a, b, c, d, e, f, g, h) -> lbl111(a, h, c, 1, e, h - 1, g, h) [ a >= 2 /\\ b = c /\\ d = e /\\ f = g /\\ h = a ]", 0-7) = a orients the transition lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] weakly and the transition lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] strictly and produces the following problem: 6: T: (1, 1) start(a, b, c, d, e, f, g, h) -> lbl111(a, h, c, 1, e, h - 1, g, h) [ a >= 2 /\ b = c /\ d = e /\ f = g /\ h = a ] (2*a^2 + 4*a + 4, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ d >= f /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (2*a + 2, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b, c, h, e, f - 1, g, h) [ f >= d + 1 /\ d >= 1 /\ a >= f + 1 /\ a >= f + d /\ a >= b /\ f >= 1 /\ d >= 0 /\ h = a ] (2*a + 2, 1) lbl111(a, b, c, d, e, f, g, h) -> lbl82(a, b - f, c, h, e, f - 1, g, h) [ f >= 1 /\ a >= f + 1 /\ a >= f /\ a >= b /\ d = 0 /\ h = a ] (2*a + 2, 1) lbl82(a, b, c, d, e, f, g, h) -> lbl111(a, b, c, d - f, e, f, g, h) [ f >= 1 /\ a >= f /\ f >= 0 /\ a >= f + 2 /\ a >= b /\ a + f >= b + 1 /\ h = a /\ d = a ] (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: 3 Complexity upper bound 2*a^2 + 10*a + 15 Time: 0.651 sec (SMT: 0.611 sec)