YES(?, 20*e + 51) Initial complexity problem: 1: T: (1, 1) f0(a, b, c, d, e, f, g, h, i, j) -> f17(0, k, l, 0, e, f, g, h, i, j) (?, 1) f17(a, b, c, d, e, f, g, h, i, j) -> f17(a, b, c, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (?, 1) f27(a, b, c, d, e, f, g, h, i, j) -> f27(a, b, c, d, e, f - 1, g, h, i, j) [ f >= 0 ] (?, 1) f37(a, b, c, d, e, f, g, h, i, j) -> f37(a, b, c, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (?, 1) f45(a, b, c, d, e, f, g, h, i, j) -> f45(a + 1, b, c, d, e, f, g, h, i, j) [ e >= a + 1 ] (?, 1) f55(a, b, c, d, e, f, g, h, i, j) -> f55(a, b, c, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (?, 1) f65(a, b, c, d, e, f, g, h, i, j) -> f65(a, b, c, d, e, f, g, h, i - 1, j) [ i >= 0 ] (?, 1) f75(a, b, c, d, e, f, g, h, i, j) -> f75(a, b, c, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (?, 1) f83(a, b, c, d, e, f, g, h, i, j) -> f83(a - 1, b, c, d, e, f, g, h, i, j) [ a >= 0 ] (?, 1) f83(a, b, c, d, e, f, g, h, i, j) -> f93(a, b, c, d, e, f, g, h, i, j) [ 0 >= a + 1 ] (?, 1) f75(a, b, c, d, e, f, g, h, i, j) -> f83(e - 1, b, c, d, e, f, g, h, i, j) [ j >= e ] (?, 1) f65(a, b, c, d, e, f, g, h, i, j) -> f75(a, b, c, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (?, 1) f55(a, b, c, d, e, f, g, h, i, j) -> f65(a, b, c, d, e, f, g, h, e - 1, j) [ h >= e ] (?, 1) f45(a, b, c, d, e, f, g, h, i, j) -> f55(a, b, c, d, e, f, g, 0, i, j) [ a >= e ] (?, 1) f37(a, b, c, d, e, f, g, h, i, j) -> f45(0, b, c, d, e, f, g, h, i, j) [ g >= e ] (?, 1) f27(a, b, c, d, e, f, g, h, i, j) -> f37(a, b, c, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (?, 1) f17(a, b, c, d, e, f, g, h, i, j) -> f27(a, b, c, d, e, e - 1, g, h, i, j) [ d >= e ] start location: f0 leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [a, d, e, f, g, h, i, j]. We thus obtain the following problem: 2: T: (?, 1) f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] (?, 1) f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (?, 1) f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] (?, 1) f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] (?, 1) f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (?, 1) f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] (?, 1) f83(a, d, e, f, g, h, i, j) -> f93(a, d, e, f, g, h, i, j) [ 0 >= a + 1 ] (?, 1) f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] (?, 1) f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (?, 1) f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] (?, 1) f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] (?, 1) f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (?, 1) f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] (?, 1) f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (1, 1) f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j) start location: f0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem: 3: T: (?, 1) f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] (?, 1) f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (?, 1) f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] (?, 1) f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] (?, 1) f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (?, 1) f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] (?, 1) f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] (?, 1) f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (?, 1) f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] (?, 1) f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] (?, 1) f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (?, 1) f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] (?, 1) f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (1, 1) f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f17) = 7 Pol(f27) = 6 Pol(f37) = 5 Pol(f45) = 4 Pol(f55) = 3 Pol(f65) = 2 Pol(f75) = 1 Pol(f83) = 0 Pol(f0) = 7 orients all transitions weakly and the transitions f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] strictly and produces the following problem: 4: T: (7, 1) f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] (?, 1) f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (7, 1) f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] (7, 1) f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] (7, 1) f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] (7, 1) f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (7, 1) f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] (?, 1) f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] (?, 1) f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (?, 1) f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] (?, 1) f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] (?, 1) f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (?, 1) f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] (?, 1) f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (1, 1) f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f17) = 1 Pol(f27) = 1 Pol(f37) = -1 Pol(f45) = -1 Pol(f55) = -1 Pol(f65) = -1 Pol(f75) = -1 Pol(f83) = -1 Pol(f0) = 1 orients all transitions weakly and the transition f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] strictly and produces the following problem: 5: T: (7, 1) f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] (1, 1) f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (7, 1) f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] (7, 1) f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] (7, 1) f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] (7, 1) f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (7, 1) f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] (?, 1) f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] (?, 1) f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (?, 1) f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] (?, 1) f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] (?, 1) f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (?, 1) f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] (?, 1) f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (1, 1) f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f17) = -V_2 + V_3 Pol(f27) = -4*V_2 + 3*V_3 + V_4 Pol(f37) = -4*V_2 + 3*V_3 + V_4 - V_5 - 2 Pol(f45) = -4*V_2 + 3*V_3 + V_4 - V_5 - 2 Pol(f55) = -4*V_2 + 3*V_3 + V_4 - V_5 - V_6 - 2 Pol(f65) = -4*V_2 + 3*V_3 + V_4 - V_5 - 2*V_6 + V_7 - 1 Pol(f75) = -4*V_2 + 3*V_3 + V_4 - V_5 - 2*V_6 + V_7 - V_8 - 2 Pol(f83) = V_1 - 4*V_2 + 2*V_3 + V_4 - V_5 - 2*V_6 + V_7 - V_8 - 1 Pol(f0) = V_3 orients all transitions weakly and the transition f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] strictly and produces the following problem: 6: T: (7, 1) f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] (1, 1) f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (7, 1) f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] (7, 1) f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] (7, 1) f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] (7, 1) f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (7, 1) f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] (?, 1) f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] (?, 1) f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (?, 1) f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] (?, 1) f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] (?, 1) f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (?, 1) f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] (e, 1) f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (1, 1) f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f17) = V_3 Pol(f27) = V_4 + 1 Pol(f37) = V_4 - V_5 - 2 Pol(f45) = 3*V_3 + V_4 - 4*V_5 - 2 Pol(f55) = 3*V_3 + V_4 - 4*V_5 - V_6 - 2 Pol(f65) = 3*V_3 + V_4 - 4*V_5 - 2*V_6 + V_7 - 1 Pol(f75) = 3*V_3 + V_4 - 4*V_5 - 2*V_6 + V_7 - V_8 - 2 Pol(f83) = V_1 + 2*V_3 + V_4 - 4*V_5 - 2*V_6 + V_7 - V_8 - 1 Pol(f0) = V_3 orients all transitions weakly and the transition f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] strictly and produces the following problem: 7: T: (7, 1) f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] (1, 1) f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (7, 1) f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] (7, 1) f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] (7, 1) f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] (7, 1) f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (7, 1) f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] (?, 1) f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] (?, 1) f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (?, 1) f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] (?, 1) f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] (?, 1) f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (e, 1) f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] (e, 1) f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (1, 1) f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f17) = 3*V_3 - 2 Pol(f27) = 3*V_3 - 2 Pol(f37) = 3*V_3 - 3*V_5 - 2 Pol(f45) = 3*V_3 - 3*V_5 - 4 Pol(f55) = 3*V_3 - 3*V_5 - V_6 - 4 Pol(f65) = 3*V_3 - 3*V_5 - 2*V_6 + V_7 - 3 Pol(f75) = 3*V_3 - 3*V_5 - 2*V_6 + V_7 - V_8 - 3 Pol(f83) = V_1 + 2*V_3 - 3*V_5 - 2*V_6 + V_7 - V_8 - 2 Pol(f0) = 3*V_3 - 2 orients all transitions weakly and the transition f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] strictly and produces the following problem: 8: T: (7, 1) f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] (1, 1) f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (7, 1) f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] (7, 1) f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] (7, 1) f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] (7, 1) f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (7, 1) f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] (?, 1) f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] (?, 1) f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (?, 1) f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] (?, 1) f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] (3*e + 2, 1) f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (e, 1) f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] (e, 1) f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (1, 1) f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f17) = 2*V_3 - 1 Pol(f27) = 2*V_3 - 1 Pol(f37) = 2*V_3 - 1 Pol(f45) = 2*V_3 - 1 Pol(f55) = 2*V_3 - 1 Pol(f65) = 2*V_3 - 1 Pol(f75) = 2*V_3 - 1 Pol(f83) = 2*V_1 + 1 Pol(f0) = 2*V_3 - 1 orients all transitions weakly and the transition f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] strictly and produces the following problem: 9: T: (7, 1) f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] (1, 1) f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (7, 1) f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] (7, 1) f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] (7, 1) f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] (7, 1) f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (7, 1) f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] (2*e + 1, 1) f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] (?, 1) f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (?, 1) f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] (?, 1) f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] (3*e + 2, 1) f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (e, 1) f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] (e, 1) f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (1, 1) f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f17) = 2*V_3 - 1 Pol(f27) = 2*V_3 - 1 Pol(f37) = 2*V_3 - 1 Pol(f45) = 2*V_3 - 1 Pol(f55) = 2*V_3 - 1 Pol(f65) = 2*V_3 - 1 Pol(f75) = 2*V_3 - 2*V_8 - 1 Pol(f83) = 2*V_3 - 2*V_8 - 1 Pol(f0) = 2*V_3 - 1 orients all transitions weakly and the transition f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] strictly and produces the following problem: 10: T: (7, 1) f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] (1, 1) f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (7, 1) f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] (7, 1) f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] (7, 1) f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] (7, 1) f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (7, 1) f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] (2*e + 1, 1) f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] (2*e + 1, 1) f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (?, 1) f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] (?, 1) f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] (3*e + 2, 1) f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (e, 1) f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] (e, 1) f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (1, 1) f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f17) = 2*V_3 - 1 Pol(f27) = 2*V_3 - 1 Pol(f37) = 2*V_3 - 1 Pol(f45) = 2*V_3 - 1 Pol(f55) = 2*V_3 - 1 Pol(f65) = 2*V_7 + 1 Pol(f75) = 2*V_7 + 1 Pol(f83) = 2*V_7 + 1 Pol(f0) = 2*V_3 - 1 orients all transitions weakly and the transition f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] strictly and produces the following problem: 11: T: (7, 1) f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] (1, 1) f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (7, 1) f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] (7, 1) f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] (7, 1) f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] (7, 1) f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (7, 1) f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] (2*e + 1, 1) f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] (2*e + 1, 1) f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (2*e + 1, 1) f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] (?, 1) f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] (3*e + 2, 1) f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (e, 1) f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] (e, 1) f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (1, 1) f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f17) = 2*V_3 - 1 Pol(f27) = 2*V_3 - 1 Pol(f37) = 2*V_3 - 1 Pol(f45) = 2*V_3 - 1 Pol(f55) = 2*V_3 - 2*V_6 - 1 Pol(f65) = 2*V_3 - 2*V_6 - 1 Pol(f75) = 2*V_3 - 2*V_6 - 1 Pol(f83) = 2*V_3 - 2*V_6 - 1 Pol(f0) = 2*V_3 - 1 orients all transitions weakly and the transition f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] strictly and produces the following problem: 12: T: (7, 1) f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] (1, 1) f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (7, 1) f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] (7, 1) f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] (7, 1) f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] (7, 1) f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (7, 1) f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] (2*e + 1, 1) f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] (2*e + 1, 1) f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (2*e + 1, 1) f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] (2*e + 1, 1) f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (?, 1) f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] (3*e + 2, 1) f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (e, 1) f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] (e, 1) f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (1, 1) f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j) start location: f0 leaf cost: 1 A polynomial rank function with Pol(f45) = -V_1 + V_3 and size complexities S("f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j)", 0-0) = 0 S("f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j)", 0-1) = 0 S("f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j)", 0-2) = e S("f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j)", 0-3) = f S("f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j)", 0-4) = g S("f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j)", 0-5) = h S("f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j)", 0-6) = i S("f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j)", 0-7) = j S("f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ]", 0-0) = 0 S("f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ]", 0-1) = e S("f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ]", 0-2) = e S("f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ]", 0-3) = f S("f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ]", 0-4) = g S("f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ]", 0-5) = h S("f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ]", 0-6) = i S("f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ]", 0-7) = j S("f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ]", 0-0) = 0 S("f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ]", 0-1) = e S("f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ]", 0-2) = e S("f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ]", 0-3) = e + 2 S("f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ]", 0-4) = g S("f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ]", 0-5) = h S("f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ]", 0-6) = i S("f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ]", 0-7) = j S("f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ]", 0-0) = 0 S("f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ]", 0-1) = e S("f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ]", 0-2) = e S("f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ]", 0-3) = e + 2 S("f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ]", 0-4) = 3*e + 18 S("f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ]", 0-5) = h S("f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ]", 0-6) = i S("f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ]", 0-7) = j S("f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ]", 0-0) = ? S("f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ]", 0-1) = e S("f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ]", 0-2) = e S("f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ]", 0-3) = e + 2 S("f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ]", 0-4) = 3*e + 162 S("f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ]", 0-5) = h S("f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ]", 0-6) = i S("f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ]", 0-7) = j S("f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ]", 0-0) = ? S("f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ]", 0-1) = e S("f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ]", 0-2) = e S("f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ]", 0-3) = e + 2 S("f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ]", 0-4) = 3*e + 1458 S("f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ]", 0-5) = 2*e + 4 S("f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ]", 0-6) = i S("f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ]", 0-7) = j S("f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ]", 0-0) = ? S("f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ]", 0-1) = e S("f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ]", 0-2) = e S("f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ]", 0-3) = e + 2 S("f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ]", 0-4) = 3*e + 13122 S("f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ]", 0-5) = 2*e + 16 S("f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ]", 0-6) = e + 2 S("f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ]", 0-7) = j S("f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ]", 0-0) = ? S("f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ]", 0-1) = e S("f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ]", 0-2) = e S("f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ]", 0-3) = e + 2 S("f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ]", 0-4) = 3*e + 118098 S("f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ]", 0-5) = 2*e + 64 S("f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ]", 0-6) = e + 2 S("f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ]", 0-7) = 2*e + 4 S("f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ]", 0-0) = e + 2 S("f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ]", 0-1) = e S("f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ]", 0-2) = e S("f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ]", 0-3) = e + 2 S("f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ]", 0-4) = 3*e + 1062882 S("f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ]", 0-5) = 2*e + 256 S("f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ]", 0-6) = e + 2 S("f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ]", 0-7) = 2*e + 16 S("f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ]", 0-0) = e + 1 S("f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ]", 0-1) = e S("f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ]", 0-2) = e S("f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ]", 0-3) = e + 2 S("f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ]", 0-4) = 3*e + 354294 S("f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ]", 0-5) = 2*e + 128 S("f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ]", 0-6) = e + 2 S("f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ]", 0-7) = 2*e + 8 S("f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ]", 0-0) = ? S("f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ]", 0-1) = e S("f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ]", 0-2) = e S("f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ]", 0-3) = e + 2 S("f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ]", 0-4) = 3*e + 39366 S("f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ]", 0-5) = 2*e + 32 S("f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ]", 0-6) = e + 2 S("f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ]", 0-7) = 0 S("f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ]", 0-0) = ? S("f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ]", 0-1) = e S("f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ]", 0-2) = e S("f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ]", 0-3) = e + 2 S("f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ]", 0-4) = 3*e + 4374 S("f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ]", 0-5) = 2*e + 8 S("f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ]", 0-6) = e + 1 S("f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ]", 0-7) = j S("f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ]", 0-0) = ? S("f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ]", 0-1) = e S("f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ]", 0-2) = e S("f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ]", 0-3) = e + 2 S("f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ]", 0-4) = 3*e + 486 S("f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ]", 0-5) = 0 S("f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ]", 0-6) = i S("f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ]", 0-7) = j S("f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ]", 0-0) = 0 S("f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ]", 0-1) = e S("f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ]", 0-2) = e S("f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ]", 0-3) = e + 2 S("f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ]", 0-4) = 3*e + 54 S("f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ]", 0-5) = h S("f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ]", 0-6) = i S("f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ]", 0-7) = j S("f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ]", 0-0) = 0 S("f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ]", 0-1) = e S("f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ]", 0-2) = e S("f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ]", 0-3) = e + 2 S("f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ]", 0-4) = 0 S("f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ]", 0-5) = h S("f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ]", 0-6) = i S("f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ]", 0-7) = j S("f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ]", 0-0) = 0 S("f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ]", 0-1) = e S("f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ]", 0-2) = e S("f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ]", 0-3) = e + 1 S("f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ]", 0-4) = g S("f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ]", 0-5) = h S("f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ]", 0-6) = i S("f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ]", 0-7) = j orients the transition f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] weakly and the transition f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] strictly and produces the following problem: 13: T: (7, 1) f17(a, d, e, f, g, h, i, j) -> f27(a, d, e, e - 1, g, h, i, j) [ d >= e ] (1, 1) f27(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, 0, h, i, j) [ 0 >= f + 1 ] (7, 1) f37(a, d, e, f, g, h, i, j) -> f45(0, d, e, f, g, h, i, j) [ g >= e ] (7, 1) f45(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, 0, i, j) [ a >= e ] (7, 1) f55(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, e - 1, j) [ h >= e ] (7, 1) f65(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, 0) [ 0 >= i + 1 ] (7, 1) f75(a, d, e, f, g, h, i, j) -> f83(e - 1, d, e, f, g, h, i, j) [ j >= e ] (2*e + 1, 1) f83(a, d, e, f, g, h, i, j) -> f83(a - 1, d, e, f, g, h, i, j) [ a >= 0 ] (2*e + 1, 1) f75(a, d, e, f, g, h, i, j) -> f75(a, d, e, f, g, h, i, j + 1) [ e >= j + 1 ] (2*e + 1, 1) f65(a, d, e, f, g, h, i, j) -> f65(a, d, e, f, g, h, i - 1, j) [ i >= 0 ] (2*e + 1, 1) f55(a, d, e, f, g, h, i, j) -> f55(a, d, e, f, g, h + 1, i, j) [ e >= h + 1 ] (7*e, 1) f45(a, d, e, f, g, h, i, j) -> f45(a + 1, d, e, f, g, h, i, j) [ e >= a + 1 ] (3*e + 2, 1) f37(a, d, e, f, g, h, i, j) -> f37(a, d, e, f, g + 1, h, i, j) [ e >= g + 1 ] (e, 1) f27(a, d, e, f, g, h, i, j) -> f27(a, d, e, f - 1, g, h, i, j) [ f >= 0 ] (e, 1) f17(a, d, e, f, g, h, i, j) -> f17(a, d + 1, e, f, g, h, i, j) [ e >= d + 1 ] (1, 1) f0(a, d, e, f, g, h, i, j) -> f17(0, 0, e, f, g, h, i, j) start location: f0 leaf cost: 1 Complexity upper bound 20*e + 51 Time: 1.112 sec (SMT: 0.946 sec)