MAYBE Initial complexity problem: 1: T: (?, 1) start(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ 0 >= a + 1 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (?, 1) cut(a, b, c, d, e, f, g, h) -> stop(a, b, c, d, e, f, g, h) [ a >= 0 /\ d + 1 = 0 /\ g = h ] (?, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\ b >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (?, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (?, 1) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\ d >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (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) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (?, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\ b >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (?, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (?, 1) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\ d >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (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: 2 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (?, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\ b >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (?, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (?, 1) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\ d >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (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: 2 A polynomial rank function with Pol(start) = 7*V_4 + V_7 - V_8 + 1 Pol(lbl42) = 7*V_4 + V_7 - V_8 + 1 Pol(cut) = 7*V_4 + V_7 - V_8 + 2 Pol(lbl72) = 7*V_4 + V_7 - V_8 + 3 Pol(start0) = 7*V_1 + 1 orients all transitions weakly and the transitions lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\ d >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\ b >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] strictly and produces the following problem: 4: T: (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\ b >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\ d >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (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: 2 A polynomial rank function with Pol(lbl72) = 1 Pol(cut) = 0 Pol(lbl42) = -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("cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-0) = a S("cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-1) = ? S("cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-2) = c S("cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-3) = a + 5 S("cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-4) = ? S("cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-5) = f S("cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-6) = h S("cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-7) = h S("cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-0) = a S("cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-1) = ? S("cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-2) = c S("cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-3) = a + 5 S("cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-4) = ? S("cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-5) = f S("cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-6) = h S("cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-7) = h S("cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\\ b >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-0) = a S("cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\\ b >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-1) = ? S("cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\\ b >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-2) = c S("cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\\ b >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-3) = a + 5 S("cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\\ b >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-4) = ? S("cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\\ b >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-5) = f S("cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\\ b >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-6) = h S("cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\\ b >= 0 /\\ d + 1 >= 0 /\\ a >= d + 1 /\\ g = h ]", 0-7) = h S("lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-0) = a S("lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-1) = ? S("lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-2) = c S("lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-3) = a + 5 S("lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-4) = ? S("lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-5) = f S("lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-6) = h S("lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-7) = h S("lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-0) = a S("lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-1) = ? S("lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-2) = c S("lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-3) = a + 5 S("lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-4) = ? S("lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-5) = f S("lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-6) = h S("lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-7) = h S("lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-0) = a S("lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-1) = ? S("lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-2) = c S("lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-3) = a + 5 S("lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-4) = ? S("lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-5) = f S("lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-6) = h S("lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\\ b + 1 >= 0 /\\ d >= 0 /\\ a >= d /\\ g = h ]", 0-7) = h S("lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\\ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-0) = a S("lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\\ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-1) = ? S("lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\\ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-2) = c S("lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\\ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-3) = a + 5 S("lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\\ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-4) = ? S("lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\\ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-5) = f S("lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\\ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-6) = h S("lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\\ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-7) = h S("lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-0) = a S("lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-1) = ? S("lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-2) = c S("lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-3) = a + 5 S("lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-4) = ? S("lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-5) = f S("lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-6) = h S("lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\\ d + 1 >= 0 /\\ h + 1 >= b /\\ e + 1 = b /\\ g = h ]", 0-7) = h S("start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\\ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-0) = a S("start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\\ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-1) = c + 1 S("start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\\ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-2) = c S("start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\\ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-3) = a + 1 S("start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\\ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-4) = c S("start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\\ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-5) = f S("start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\\ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-6) = h S("start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\\ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-7) = h S("start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-0) = a S("start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-1) = c S("start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-2) = c S("start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-3) = a + 1 S("start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-4) = f S("start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-5) = f S("start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-6) = h S("start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-7) = h S("start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\\ c >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-0) = a S("start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\\ c >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-1) = c + 1 S("start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\\ c >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-2) = c S("start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\\ c >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-3) = a S("start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\\ c >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-4) = f S("start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\\ c >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-5) = f S("start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\\ c >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-6) = h S("start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\\ c >= 0 /\\ b = c /\\ d = a /\\ e = f /\\ g = h ]", 0-7) = h orients the transitions lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] weakly and the transition lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] strictly and produces the following problem: 5: T: (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ h >= b /\ a >= d + 1 /\ d + 1 >= 0 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ b >= 0 /\ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\ b + 1 >= 0 /\ d >= 0 /\ a >= d /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ d >= 0 /\ b >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ d >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ h >= b /\ d >= 0 /\ d + 1 >= 0 /\ a >= d + 1 /\ g = h ] (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: 2 Applied AI with 'oct' on problem 5 to obtain the following invariants: For symbol cut: X_7 - X_8 >= 0 /\ -X_7 + X_8 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_4 + 1 >= 0 /\ X_1 + X_4 + 1 >= 0 /\ X_1 >= 0 For symbol lbl42: X_7 - X_8 >= 0 /\ -X_7 + X_8 >= 0 /\ X_1 - X_4 >= 0 /\ X_4 >= 0 /\ X_2 + X_4 + 1 >= 0 /\ X_1 + X_4 >= 0 /\ X_2 + 1 >= 0 /\ X_1 + X_2 + 1 >= 0 /\ X_1 >= 0 For symbol lbl72: X_7 - X_8 >= 0 /\ -X_7 + X_8 >= 0 /\ -X_5 + X_8 >= 0 /\ -X_2 + X_8 + 1 >= 0 /\ -X_5 + X_7 >= 0 /\ -X_2 + X_7 + 1 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ -X_2 + X_5 + 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_4 + 1 >= 0 /\ X_1 + X_4 + 1 >= 0 /\ X_1 >= 0 For symbol start: X_7 - X_8 >= 0 /\ -X_7 + X_8 >= 0 /\ X_5 - X_6 >= 0 /\ -X_5 + X_6 >= 0 /\ X_1 - X_4 >= 0 /\ -X_1 + X_4 >= 0 /\ X_2 - X_3 >= 0 /\ -X_2 + X_3 >= 0 This yielded the following problem: 6: T: (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h ] with all transitions in problem 6, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] We thus obtain the following problem: 7: T: (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] with all transitions in problem 7, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] We thus obtain the following problem: 8: T: (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] with all transitions in problem 8, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] We thus obtain the following problem: 9: T: (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] with all transitions in problem 9, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] We thus obtain the following problem: 10: T: (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] with all transitions in problem 10, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] We thus obtain the following problem: 11: T: (7*a + 1, 6) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] (7*a + 1, 6) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] with all transitions in problem 11, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] We thus obtain the following problem: 12: T: (7*a + 1, 7) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] (7*a + 1, 7) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] (7*a + 1, 6) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] with all transitions in problem 12, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 8, c, d - 1, b + 7, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] We thus obtain the following problem: 13: T: (7*a + 1, 8) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] (7*a + 1, 8) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 8, c, d - 1, b + 7, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] (7*a + 1, 7) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] (7*a + 1, 6) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 8, c, d - 1, b + 7, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] with all transitions in problem 13, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 8, c, d - 1, b + 7, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 9, c, d - 1, b + 8, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 ] We thus obtain the following problem: 14: T: (7*a + 1, 9) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 8, c, d - 1, b + 7, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 ] (7*a + 1, 9) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 9, c, d - 1, b + 8, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 ] (7*a + 1, 8) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] (7*a + 1, 7) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] (7*a + 1, 6) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 9, c, d - 1, b + 8, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 ] with all transitions in problem 14, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 9, c, d - 1, b + 8, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 10, c, d - 1, b + 9, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 ] We thus obtain the following problem: 15: T: (7*a + 1, 10) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 9, c, d - 1, b + 8, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 ] (7*a + 1, 10) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 10, c, d - 1, b + 9, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 ] (7*a + 1, 9) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 8, c, d - 1, b + 7, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 ] (7*a + 1, 8) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] (7*a + 1, 7) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] (7*a + 1, 6) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 10, c, d - 1, b + 9, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 ] with all transitions in problem 15, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 10, c, d - 1, b + 9, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 11, c, d - 1, b + 10, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 ] We thus obtain the following problem: 16: T: (7*a + 1, 11) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 10, c, d - 1, b + 9, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 ] (7*a + 1, 11) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 11, c, d - 1, b + 10, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 ] (7*a + 1, 10) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 9, c, d - 1, b + 8, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 ] (7*a + 1, 9) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 8, c, d - 1, b + 7, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 ] (7*a + 1, 8) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] (7*a + 1, 7) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] (7*a + 1, 6) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 11, c, d - 1, b + 10, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 ] with all transitions in problem 16, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 11, c, d - 1, b + 10, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 12, c, d - 1, b + 11, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 ] We thus obtain the following problem: 17: T: (7*a + 1, 12) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 11, c, d - 1, b + 10, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 ] (7*a + 1, 12) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 12, c, d - 1, b + 11, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 ] (7*a + 1, 11) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 10, c, d - 1, b + 9, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 ] (7*a + 1, 10) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 9, c, d - 1, b + 8, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 ] (7*a + 1, 9) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 8, c, d - 1, b + 7, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 ] (7*a + 1, 8) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] (7*a + 1, 7) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] (7*a + 1, 6) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 12, c, d - 1, b + 11, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 ] with all transitions in problem 17, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 12, c, d - 1, b + 11, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 13, c, d - 1, b + 12, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 ] We thus obtain the following problem: 18: T: (7*a + 1, 13) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 12, c, d - 1, b + 11, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 ] (7*a + 1, 13) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 13, c, d - 1, b + 12, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 ] (7*a + 1, 12) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 11, c, d - 1, b + 10, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 ] (7*a + 1, 11) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 10, c, d - 1, b + 9, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 ] (7*a + 1, 10) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 9, c, d - 1, b + 8, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 ] (7*a + 1, 9) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 8, c, d - 1, b + 7, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 ] (7*a + 1, 8) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] (7*a + 1, 7) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] (7*a + 1, 6) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 13, c, d - 1, b + 12, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 ] with all transitions in problem 18, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 13, c, d - 1, b + 12, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 14, c, d - 1, b + 13, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 ] We thus obtain the following problem: 19: T: (7*a + 1, 14) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 13, c, d - 1, b + 12, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 ] (7*a + 1, 14) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 14, c, d - 1, b + 13, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 ] (7*a + 1, 13) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 12, c, d - 1, b + 11, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 ] (7*a + 1, 12) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 11, c, d - 1, b + 10, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 ] (7*a + 1, 11) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 10, c, d - 1, b + 9, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 ] (7*a + 1, 10) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 9, c, d - 1, b + 8, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 ] (7*a + 1, 9) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 8, c, d - 1, b + 7, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 ] (7*a + 1, 8) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] (7*a + 1, 7) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] (7*a + 1, 6) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 14, c, d - 1, b + 13, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 ] with all transitions in problem 19, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 14, c, d - 1, b + 13, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 /\ -b + h - 13 >= 0 /\ -b + g - 13 >= 0 /\ h + 1 >= b + 14 /\ b + 14 = b + 14 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 15, c, d - 1, b + 14, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 /\ -b + h - 13 >= 0 /\ -b + g - 13 >= 0 /\ h >= b + 14 /\ h + 1 >= b + 14 /\ b + 14 = b + 14 ] We thus obtain the following problem: 20: T: (7*a + 1, 15) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 14, c, d - 1, b + 13, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 /\ -b + h - 13 >= 0 /\ -b + g - 13 >= 0 /\ h + 1 >= b + 14 /\ b + 14 = b + 14 ] (7*a + 1, 15) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 15, c, d - 1, b + 14, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 /\ -b + h - 13 >= 0 /\ -b + g - 13 >= 0 /\ h >= b + 14 /\ h + 1 >= b + 14 /\ b + 14 = b + 14 ] (7*a + 1, 14) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 13, c, d - 1, b + 12, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 ] (7*a + 1, 13) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 12, c, d - 1, b + 11, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 ] (7*a + 1, 12) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 11, c, d - 1, b + 10, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 ] (7*a + 1, 11) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 10, c, d - 1, b + 9, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 ] (7*a + 1, 10) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 9, c, d - 1, b + 8, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 ] (7*a + 1, 9) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 8, c, d - 1, b + 7, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 ] (7*a + 1, 8) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] (7*a + 1, 7) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] (7*a + 1, 6) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 By chaining the transition cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 15, c, d - 1, b + 14, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 /\ -b + h - 13 >= 0 /\ -b + g - 13 >= 0 /\ h >= b + 14 /\ h + 1 >= b + 14 /\ b + 14 = b + 14 ] with all transitions in problem 20, the following new transitions are obtained: cut(a, b, c, d, e, f, g, h) -> cut(a, b + 15, c, d - 1, b + 14, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 /\ -b + h - 13 >= 0 /\ -b + g - 13 >= 0 /\ h >= b + 14 /\ h + 1 >= b + 14 /\ b + 14 = b + 14 /\ -b + h - 14 >= 0 /\ -b + g - 14 >= 0 /\ h + 1 >= b + 15 /\ b + 15 = b + 15 ] cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 16, c, d - 1, b + 15, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 /\ -b + h - 13 >= 0 /\ -b + g - 13 >= 0 /\ h >= b + 14 /\ h + 1 >= b + 14 /\ b + 14 = b + 14 /\ -b + h - 14 >= 0 /\ -b + g - 14 >= 0 /\ h >= b + 15 /\ h + 1 >= b + 15 /\ b + 15 = b + 15 ] We thus obtain the following problem: 21: T: (7*a + 1, 16) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 15, c, d - 1, b + 14, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 /\ -b + h - 13 >= 0 /\ -b + g - 13 >= 0 /\ h >= b + 14 /\ h + 1 >= b + 14 /\ b + 14 = b + 14 /\ -b + h - 14 >= 0 /\ -b + g - 14 >= 0 /\ h + 1 >= b + 15 /\ b + 15 = b + 15 ] (7*a + 1, 16) cut(a, b, c, d, e, f, g, h) -> lbl72(a, b + 16, c, d - 1, b + 15, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 /\ -b + h - 13 >= 0 /\ -b + g - 13 >= 0 /\ h >= b + 14 /\ h + 1 >= b + 14 /\ b + 14 = b + 14 /\ -b + h - 14 >= 0 /\ -b + g - 14 >= 0 /\ h >= b + 15 /\ h + 1 >= b + 15 /\ b + 15 = b + 15 ] (7*a + 1, 15) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 14, c, d - 1, b + 13, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h >= b + 13 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 /\ -b + h - 13 >= 0 /\ -b + g - 13 >= 0 /\ h + 1 >= b + 14 /\ b + 14 = b + 14 ] (7*a + 1, 14) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 13, c, d - 1, b + 12, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h >= b + 12 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 /\ -b + h - 12 >= 0 /\ -b + g - 12 >= 0 /\ h + 1 >= b + 13 /\ b + 13 = b + 13 ] (7*a + 1, 13) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 12, c, d - 1, b + 11, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h >= b + 11 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 /\ -b + h - 11 >= 0 /\ -b + g - 11 >= 0 /\ h + 1 >= b + 12 /\ b + 12 = b + 12 ] (7*a + 1, 12) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 11, c, d - 1, b + 10, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h >= b + 10 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 /\ -b + h - 10 >= 0 /\ -b + g - 10 >= 0 /\ h + 1 >= b + 11 /\ b + 11 = b + 11 ] (7*a + 1, 11) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 10, c, d - 1, b + 9, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h >= b + 9 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 /\ -b + h - 9 >= 0 /\ -b + g - 9 >= 0 /\ h + 1 >= b + 10 /\ b + 10 = b + 10 ] (7*a + 1, 10) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 9, c, d - 1, b + 8, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h >= b + 8 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 /\ -b + h - 8 >= 0 /\ -b + g - 8 >= 0 /\ h + 1 >= b + 9 /\ b + 9 = b + 9 ] (7*a + 1, 9) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 8, c, d - 1, b + 7, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h >= b + 7 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 /\ -b + h - 7 >= 0 /\ -b + g - 7 >= 0 /\ h + 1 >= b + 8 /\ b + 8 = b + 8 ] (7*a + 1, 8) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 7, c, d - 1, b + 6, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h >= b + 6 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 /\ -b + h - 6 >= 0 /\ -b + g - 6 >= 0 /\ h + 1 >= b + 7 /\ b + 7 = b + 7 ] (7*a + 1, 7) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 6, c, d - 1, b + 5, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h >= b + 5 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 /\ -b + h - 5 >= 0 /\ -b + g - 5 >= 0 /\ h + 1 >= b + 6 /\ b + 6 = b + 6 ] (7*a + 1, 6) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 5, c, d - 1, b + 4, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h >= b + 4 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 /\ -b + h - 4 >= 0 /\ -b + g - 4 >= 0 /\ h + 1 >= b + 5 /\ b + 5 = b + 5 ] (7*a + 1, 5) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 4, c, d - 1, b + 3, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h >= b + 3 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 /\ -b + h - 3 >= 0 /\ -b + g - 3 >= 0 /\ h + 1 >= b + 4 /\ b + 4 = b + 4 ] (7*a + 1, 4) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 3, c, d - 1, b + 2, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h >= b + 2 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 /\ -b + h - 2 >= 0 /\ -b + g - 2 >= 0 /\ h + 1 >= b + 3 /\ b + 3 = b + 3 ] (7*a + 1, 3) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 2, c, d - 1, b + 1, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ h >= b + 1 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 /\ -b + h - 1 >= 0 /\ -b + g - 1 >= 0 /\ h + 1 >= b + 2 /\ b + 2 = b + 2 ] (7*a + 1, 2) cut(a, b, c, d, e, f, g, h) -> cut(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ d >= 0 /\ a >= d + 1 /\ g = h /\ -b + h >= 0 /\ -b + g >= 0 /\ 0 >= 0 /\ a - d >= 0 /\ a + d >= 0 /\ a >= d /\ h + 1 >= b + 1 /\ b + 1 = b + 1 ] (1, 1) start0(a, b, c, d, e, f, g, h) -> start(a, c, c, a, f, f, h, h) (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) cut(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ d >= 0 /\ b >= 0 /\ a >= d + 1 /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d /\ g = h ] (7*a + 1, 1) lbl42(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ a >= d /\ g = h ] (?, 1) lbl42(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ a - d >= 0 /\ d >= 0 /\ b + d + 1 >= 0 /\ a + d >= 0 /\ b + 1 >= 0 /\ a + b + 1 >= 0 /\ a >= 0 /\ b >= 0 /\ a >= d /\ g = h ] (?, 1) lbl72(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ h >= b /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (21*a + 5, 1) lbl72(a, b, c, d, e, f, g, h) -> cut(a, b, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ -e + h >= 0 /\ -b + h + 1 >= 0 /\ -e + g >= 0 /\ -b + g + 1 >= 0 /\ b - e - 1 >= 0 /\ -b + e + 1 >= 0 /\ a - d - 1 >= 0 /\ d + 1 >= 0 /\ a + d + 1 >= 0 /\ a >= 0 /\ a >= d + 1 /\ h + 1 >= b /\ e + 1 = b /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl72(a, b + 1, c, d - 1, b, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ h >= c /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> cut(a, b, c, d - 1, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] (1, 1) start(a, b, c, d, e, f, g, h) -> lbl42(a, b - 1, c, d, e, f, g, h) [ g - h >= 0 /\ -g + h >= 0 /\ e - f >= 0 /\ -e + f >= 0 /\ a - d >= 0 /\ -a + d >= 0 /\ b - c >= 0 /\ -b + c >= 0 /\ a >= 0 /\ c >= 0 /\ b = c /\ d = a /\ e = f /\ g = h ] start location: start0 leaf cost: 2 Complexity upper bound ? Time: 29.195 sec (SMT: 24.083 sec)