YES(?, 72*a + 36*a^2 + 40) Initial complexity problem: 1: T: (?, 1) start(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, d, h) [ 0 >= a + 1 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) start(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, 0, f, d - 1, h) [ d = 0 /\ b = c /\ a = 0 /\ e = f /\ g = h ] (?, 1) start(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) lbl142(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ a >= 0 /\ g + 1 = 0 /\ e = 0 /\ d = a ] (?, 1) lbl142(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, 0, f, g - 1, h) [ a >= 1 /\ g = 0 /\ e = 1 /\ d = a ] (?, 1) lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\ e >= 0 /\ a >= e /\ g + 1 = e /\ d = a ] (?, 1) lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\ e >= 0 /\ a >= e /\ g + 1 = e /\ d = a ] (?, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\ a >= g /\ e = g /\ d = a ] (?, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] (?, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] (?, 1) lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\ g >= e + 1 /\ a >= g /\ d = a ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) 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) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\ e >= 0 /\ a >= e /\ g + 1 = e /\ d = a ] (?, 1) lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\ e >= 0 /\ a >= e /\ g + 1 = e /\ d = a ] (?, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\ a >= g /\ e = g /\ d = a ] (?, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] (?, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] (?, 1) lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\ g >= e + 1 /\ a >= g /\ d = a ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) start location: start0 leaf cost: 4 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (1, 1) start(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\ e >= 0 /\ a >= e /\ g + 1 = e /\ d = a ] (?, 1) lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\ e >= 0 /\ a >= e /\ g + 1 = e /\ d = a ] (?, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\ a >= g /\ e = g /\ d = a ] (?, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] (?, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] (?, 1) lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\ g >= e + 1 /\ a >= g /\ d = a ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) start location: start0 leaf cost: 4 A polynomial rank function with Pol(start) = 3*V_4 + 2 Pol(lbl91) = V_4 + 2*V_7 + 2 Pol(lbl131) = V_4 + 2*V_7 + 2 Pol(lbl142) = V_4 + 2*V_7 + 3 Pol(start0) = 3*V_1 + 2 orients all transitions weakly and the transitions lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\ e >= 0 /\ a >= e /\ g + 1 = e /\ d = a ] lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\ e >= 0 /\ a >= e /\ g + 1 = e /\ d = a ] lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\ a >= g /\ e = g /\ d = a ] strictly and produces the following problem: 4: T: (1, 1) start(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\ b = c /\ d = a /\ e = f /\ g = h ] (3*a + 2, 1) lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\ e >= 0 /\ a >= e /\ g + 1 = e /\ d = a ] (3*a + 2, 1) lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\ e >= 0 /\ a >= e /\ g + 1 = e /\ d = a ] (3*a + 2, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\ a >= g /\ e = g /\ d = a ] (?, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] (?, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] (?, 1) lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\ g >= e + 1 /\ a >= g /\ d = a ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) start location: start0 leaf cost: 4 A polynomial rank function with Pol(lbl91) = -2*V_5 + 2*V_7 Pol(lbl131) = -2*V_5 + 2*V_7 + 1 and size complexities S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)", 0-0) = a S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)", 0-1) = c S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)", 0-2) = c S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)", 0-3) = a S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)", 0-4) = f S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)", 0-5) = f S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)", 0-6) = h S("start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h)", 0-7) = h S("lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\\ g >= e + 1 /\\ a >= g /\\ d = a ]", 0-0) = a S("lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\\ g >= e + 1 /\\ a >= g /\\ d = a ]", 0-1) = ? S("lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\\ g >= e + 1 /\\ a >= g /\\ d = a ]", 0-2) = c S("lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\\ g >= e + 1 /\\ a >= g /\\ d = a ]", 0-3) = a S("lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\\ g >= e + 1 /\\ a >= g /\\ d = a ]", 0-4) = a S("lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\\ g >= e + 1 /\\ a >= g /\\ d = a ]", 0-5) = f S("lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\\ g >= e + 1 /\\ a >= g /\\ d = a ]", 0-6) = a S("lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\\ g >= e + 1 /\\ a >= g /\\ d = a ]", 0-7) = h S("lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-0) = a S("lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-1) = ? S("lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-2) = c S("lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-3) = a S("lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-4) = a S("lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-5) = f S("lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-6) = a S("lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-7) = h S("lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-0) = a S("lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-1) = ? S("lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-2) = c S("lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-3) = a S("lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-4) = a + 2 S("lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-5) = f S("lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-6) = a S("lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\\ g >= e /\\ e >= 1 /\\ a >= g /\\ d = a ]", 0-7) = h S("lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\\ a >= g /\\ e = g /\\ d = a ]", 0-0) = a S("lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\\ a >= g /\\ e = g /\\ d = a ]", 0-1) = ? S("lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\\ a >= g /\\ e = g /\\ d = a ]", 0-2) = c S("lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\\ a >= g /\\ e = g /\\ d = a ]", 0-3) = a S("lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\\ a >= g /\\ e = g /\\ d = a ]", 0-4) = a + 2 S("lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\\ a >= g /\\ e = g /\\ d = a ]", 0-5) = f S("lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\\ a >= g /\\ e = g /\\ d = a ]", 0-6) = a S("lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\\ a >= g /\\ e = g /\\ d = a ]", 0-7) = h S("lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-0) = a S("lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-1) = ? S("lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-2) = c S("lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-3) = a S("lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-4) = 1 S("lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-5) = f S("lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-6) = a S("lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-7) = h S("lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-0) = a S("lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-1) = ? S("lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-2) = c S("lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-3) = a S("lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-4) = 0 S("lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-5) = f S("lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-6) = a S("lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\\ e >= 0 /\\ a >= e /\\ g + 1 = e /\\ d = a ]", 0-7) = h S("start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-0) = a S("start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-1) = c S("start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-2) = c S("start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-3) = a S("start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-4) = 1 S("start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-5) = f S("start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-6) = a S("start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-7) = h S("start(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-0) = a S("start(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-1) = ? S("start(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-2) = c S("start(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-3) = a S("start(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-4) = 0 S("start(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-5) = f S("start(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-6) = a S("start(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-7) = h orients the transitions lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\ g >= e + 1 /\ a >= g /\ d = a ] lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] weakly and the transitions lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\ g >= e + 1 /\ a >= g /\ d = a ] lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] strictly and produces the following problem: 5: T: (1, 1) start(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, d, h) [ a >= 1 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, d, h) [ a >= 1 /\ b = c /\ d = a /\ e = f /\ g = h ] (3*a + 2, 1) lbl142(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, 0, f, g, h) [ e >= 2 /\ e >= 0 /\ a >= e /\ g + 1 = e /\ d = a ] (3*a + 2, 1) lbl142(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, 1, f, g, h) [ e >= 2 /\ e >= 0 /\ a >= e /\ g + 1 = e /\ d = a ] (3*a + 2, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl142(a, b, c, d, e, f, g - 1, h) [ g >= 1 /\ a >= g /\ e = g /\ d = a ] (12*a^2 + 21*a + 9, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl91(a, i, c, d, e, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] (12*a^2 + 21*a + 9, 1) lbl131(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ g >= e + 1 /\ g >= e /\ e >= 1 /\ a >= g /\ d = a ] (12*a^2 + 21*a + 9, 1) lbl91(a, b, c, d, e, f, g, h) -> lbl131(a, b, c, d, e + 1, f, g, h) [ e >= 0 /\ g >= e + 1 /\ a >= g /\ d = a ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) start location: start0 leaf cost: 4 Complexity upper bound 72*a + 36*a^2 + 40 Time: 0.526 sec (SMT: 0.484 sec)