MAYBE Initial complexity problem: 1: T: (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ 0 >= a ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ a >= 2 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ b = 0 ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ 255 >= c ] (?, 1) f25(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ c >= 0 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ 0 >= b + 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ b >= 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ 0 >= e /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 2 /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ 0 >= b + 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ b >= 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a - 1, 1, c + a - 1, d, 2, f) [ d >= f + 1 /\ b = 0 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ 1 >= e /\ f >= d + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 3 /\ f >= d + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ 0 >= b + 1 /\ f >= d + 1 /\ e = 2 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ b >= 1 /\ f >= d + 1 /\ e = 2 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a - 1, 1, c - a + 1, d, 1, f) [ f >= d + 1 /\ b = 0 /\ e = 2 ] (?, 1) f5(a, b, c, d, e, f) -> f30(1, b, c, d, e, f) [ a = 1 ] (?, 1) f16(a, b, c, d, e, f) -> f30(a, b, c, d, e, f) [ c >= 256 ] (?, 1) f25(a, b, c, d, e, f) -> f30(a, b, c, d, e, f) [ 0 >= c + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f30(a, b, c, d, e, d) [ d = f ] start location: f0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ 0 >= a ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ a >= 2 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ b = 0 ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ 255 >= c ] (?, 1) f25(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ c >= 0 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ 0 >= b + 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ b >= 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ 0 >= e /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 2 /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ 0 >= b + 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ b >= 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a - 1, 1, c + a - 1, d, 2, f) [ d >= f + 1 /\ b = 0 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ 1 >= e /\ f >= d + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 3 /\ f >= d + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ 0 >= b + 1 /\ f >= d + 1 /\ e = 2 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ b >= 1 /\ f >= d + 1 /\ e = 2 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a - 1, 1, c - a + 1, d, 1, f) [ f >= d + 1 /\ b = 0 /\ e = 2 ] start location: f0 leaf cost: 4 A polynomial rank function with Pol(f5) = -V_2 + 4 Pol(f7) = -V_2 + 4 Pol(f9) = -V_2 + 4 Pol(f16) = -V_2 + 4 Pol(f25) = -V_2 + 4 Pol(f0) = 4 orients all transitions weakly and the transitions f9(a, b, c, d, e, f) -> f25(a - 1, 1, c - a + 1, d, 1, f) [ f >= d + 1 /\ b = 0 /\ e = 2 ] f9(a, b, c, d, e, f) -> f16(a - 1, 1, c + a - 1, d, 2, f) [ d >= f + 1 /\ b = 0 /\ e = 1 ] strictly and produces the following problem: 3: T: (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ 0 >= a ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ a >= 2 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ b = 0 ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ 255 >= c ] (?, 1) f25(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ c >= 0 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ 0 >= b + 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ b >= 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ 0 >= e /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 2 /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ 0 >= b + 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ b >= 1 /\ d >= f + 1 /\ e = 1 ] (4, 1) f9(a, b, c, d, e, f) -> f16(a - 1, 1, c + a - 1, d, 2, f) [ d >= f + 1 /\ b = 0 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ 1 >= e /\ f >= d + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 3 /\ f >= d + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ 0 >= b + 1 /\ f >= d + 1 /\ e = 2 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ b >= 1 /\ f >= d + 1 /\ e = 2 ] (4, 1) f9(a, b, c, d, e, f) -> f25(a - 1, 1, c - a + 1, d, 1, f) [ f >= d + 1 /\ b = 0 /\ e = 2 ] start location: f0 leaf cost: 4 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol f16: X_4 - X_6 - 1 >= 0 /\ -X_5 + 2 >= 0 /\ X_2 - X_5 + 2 >= 0 /\ -X_1 - X_5 + 6 >= 0 /\ X_5 - 2 >= 0 /\ X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 + 2 >= 0 /\ -X_1 - X_2 + 4 >= 0 /\ X_2 >= 0 /\ -X_1 + X_2 + 4 >= 0 /\ -X_1 + 4 >= 0 For symbol f25: -X_4 + X_6 - 1 >= 0 /\ -X_5 + 1 >= 0 /\ X_2 - X_5 + 1 >= 0 /\ -X_1 - X_5 + 5 >= 0 /\ X_5 - 1 >= 0 /\ X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 + 3 >= 0 /\ -X_1 - X_2 + 4 >= 0 /\ X_2 >= 0 /\ -X_1 + X_2 + 4 >= 0 /\ -X_1 + 4 >= 0 For symbol f5: X_5 >= 0 /\ X_2 + X_5 >= 0 /\ -X_1 + X_5 + 4 >= 0 /\ -X_1 - X_2 + 4 >= 0 /\ X_2 >= 0 /\ -X_1 + X_2 + 4 >= 0 /\ -X_1 + 4 >= 0 For symbol f7: X_5 >= 0 /\ X_2 + X_5 >= 0 /\ -X_1 + X_5 + 4 >= 0 /\ -X_1 - X_2 + 4 >= 0 /\ X_2 >= 0 /\ -X_1 + X_2 + 4 >= 0 /\ -X_1 + 4 >= 0 For symbol f9: X_5 >= 0 /\ X_2 + X_5 >= 0 /\ -X_1 + X_5 + 4 >= 0 /\ -X_1 - X_2 + 4 >= 0 /\ X_2 >= 0 /\ -X_1 + X_2 + 4 >= 0 /\ -X_1 + 4 >= 0 This yielded the following problem: 4: T: (4, 1) f9(a, b, c, d, e, f) -> f25(a - 1, 1, c - a + 1, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= b + 1 /\ f >= d + 1 /\ e = 2 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 ] (4, 1) f9(a, b, c, d, e, f) -> f16(a - 1, 1, c + a - 1, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= b + 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= b + 1 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) (?, 1) f25(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ -d + f - 1 >= 0 /\ -e + 1 >= 0 /\ b - e + 1 >= 0 /\ -a - e + 5 >= 0 /\ e - 1 >= 0 /\ b + e - 1 >= 0 /\ -a + e + 3 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ c >= 0 ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ d - f - 1 >= 0 /\ -e + 2 >= 0 /\ b - e + 2 >= 0 /\ -a - e + 6 >= 0 /\ e - 2 >= 0 /\ b + e - 2 >= 0 /\ -a + e + 2 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 255 >= c ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] start location: f0 leaf cost: 4 Testing for unsatisfiable constraints removes the following transitions from problem 4: f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= b + 1 /\ f >= d + 1 /\ e = 2 ] f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= b + 1 /\ d >= f + 1 /\ e = 1 ] f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= b + 1 ] We thus obtain the following problem: 5: T: (4, 1) f9(a, b, c, d, e, f) -> f25(a - 1, 1, c - a + 1, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 ] (4, 1) f9(a, b, c, d, e, f) -> f16(a - 1, 1, c + a - 1, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) (?, 1) f25(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ -d + f - 1 >= 0 /\ -e + 1 >= 0 /\ b - e + 1 >= 0 /\ -a - e + 5 >= 0 /\ e - 1 >= 0 /\ b + e - 1 >= 0 /\ -a + e + 3 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ c >= 0 ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ d - f - 1 >= 0 /\ -e + 2 >= 0 /\ b - e + 2 >= 0 /\ -a - e + 6 >= 0 /\ e - 2 >= 0 /\ b + e - 2 >= 0 /\ -a + e + 2 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 255 >= c ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] start location: f0 leaf cost: 4 By chaining the transition f9(a, b, c, d, e, f) -> f25(a - 1, 1, c - a + 1, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 ] with all transitions in problem 5, the following new transition is obtained: f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] We thus obtain the following problem: 6: T: (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 ] (4, 1) f9(a, b, c, d, e, f) -> f16(a - 1, 1, c + a - 1, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) (?, 1) f25(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ -d + f - 1 >= 0 /\ -e + 1 >= 0 /\ b - e + 1 >= 0 /\ -a - e + 5 >= 0 /\ e - 1 >= 0 /\ b + e - 1 >= 0 /\ -a + e + 3 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ c >= 0 ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ d - f - 1 >= 0 /\ -e + 2 >= 0 /\ b - e + 2 >= 0 /\ -a - e + 6 >= 0 /\ e - 2 >= 0 /\ b + e - 2 >= 0 /\ -a + e + 2 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 255 >= c ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] start location: f0 leaf cost: 4 By chaining the transition f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 ] with all transitions in problem 6, the following new transition is obtained: f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] We thus obtain the following problem: 7: T: (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 ] (4, 1) f9(a, b, c, d, e, f) -> f16(a - 1, 1, c + a - 1, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) (?, 1) f25(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ -d + f - 1 >= 0 /\ -e + 1 >= 0 /\ b - e + 1 >= 0 /\ -a - e + 5 >= 0 /\ e - 1 >= 0 /\ b + e - 1 >= 0 /\ -a + e + 3 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ c >= 0 ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ d - f - 1 >= 0 /\ -e + 2 >= 0 /\ b - e + 2 >= 0 /\ -a - e + 6 >= 0 /\ e - 2 >= 0 /\ b + e - 2 >= 0 /\ -a + e + 2 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 255 >= c ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] start location: f0 leaf cost: 4 By chaining the transition f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 ] with all transitions in problem 7, the following new transition is obtained: f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] We thus obtain the following problem: 8: T: (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 1) f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 ] (4, 1) f9(a, b, c, d, e, f) -> f16(a - 1, 1, c + a - 1, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) (?, 1) f25(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ -d + f - 1 >= 0 /\ -e + 1 >= 0 /\ b - e + 1 >= 0 /\ -a - e + 5 >= 0 /\ e - 1 >= 0 /\ b + e - 1 >= 0 /\ -a + e + 3 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ c >= 0 ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ d - f - 1 >= 0 /\ -e + 2 >= 0 /\ b - e + 2 >= 0 /\ -a - e + 6 >= 0 /\ e - 2 >= 0 /\ b + e - 2 >= 0 /\ -a + e + 2 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 255 >= c ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] start location: f0 leaf cost: 4 By chaining the transition f9(a, b, c, d, e, f) -> f25(a, b, c - a, d, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 ] with all transitions in problem 8, the following new transition is obtained: f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] We thus obtain the following problem: 9: T: (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (4, 1) f9(a, b, c, d, e, f) -> f16(a - 1, 1, c + a - 1, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) (?, 1) f25(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ -d + f - 1 >= 0 /\ -e + 1 >= 0 /\ b - e + 1 >= 0 /\ -a - e + 5 >= 0 /\ e - 1 >= 0 /\ b + e - 1 >= 0 /\ -a + e + 3 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ c >= 0 ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ d - f - 1 >= 0 /\ -e + 2 >= 0 /\ b - e + 2 >= 0 /\ -a - e + 6 >= 0 /\ e - 2 >= 0 /\ b + e - 2 >= 0 /\ -a + e + 2 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 255 >= c ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] start location: f0 leaf cost: 4 Testing for reachability in the complexity graph removes the following transition from problem 9: f25(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ -d + f - 1 >= 0 /\ -e + 1 >= 0 /\ b - e + 1 >= 0 /\ -a - e + 5 >= 0 /\ e - 1 >= 0 /\ b + e - 1 >= 0 /\ -a + e + 3 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ c >= 0 ] We thus obtain the following problem: 10: T: (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ d - f - 1 >= 0 /\ -e + 2 >= 0 /\ b - e + 2 >= 0 /\ -a - e + 6 >= 0 /\ e - 2 >= 0 /\ b + e - 2 >= 0 /\ -a + e + 2 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 255 >= c ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (4, 1) f9(a, b, c, d, e, f) -> f16(a - 1, 1, c + a - 1, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) start location: f0 leaf cost: 4 By chaining the transition f9(a, b, c, d, e, f) -> f16(a - 1, 1, c + a - 1, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 ] with all transitions in problem 10, the following new transition is obtained: f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] We thus obtain the following problem: 11: T: (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ d - f - 1 >= 0 /\ -e + 2 >= 0 /\ b - e + 2 >= 0 /\ -a - e + 6 >= 0 /\ e - 2 >= 0 /\ b + e - 2 >= 0 /\ -a + e + 2 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 255 >= c ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) start location: f0 leaf cost: 4 By chaining the transition f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 ] with all transitions in problem 11, the following new transition is obtained: f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] We thus obtain the following problem: 12: T: (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ d - f - 1 >= 0 /\ -e + 2 >= 0 /\ b - e + 2 >= 0 /\ -a - e + 6 >= 0 /\ e - 2 >= 0 /\ b + e - 2 >= 0 /\ -a + e + 2 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 255 >= c ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) start location: f0 leaf cost: 4 By chaining the transition f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 ] with all transitions in problem 12, the following new transition is obtained: f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] We thus obtain the following problem: 13: T: (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ d - f - 1 >= 0 /\ -e + 2 >= 0 /\ b - e + 2 >= 0 /\ -a - e + 6 >= 0 /\ e - 2 >= 0 /\ b + e - 2 >= 0 /\ -a + e + 2 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 255 >= c ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) start location: f0 leaf cost: 4 By chaining the transition f9(a, b, c, d, e, f) -> f16(a, b, c + a, d, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 ] with all transitions in problem 13, the following new transition is obtained: f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] We thus obtain the following problem: 14: T: (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (?, 1) f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ d - f - 1 >= 0 /\ -e + 2 >= 0 /\ b - e + 2 >= 0 /\ -a - e + 6 >= 0 /\ e - 2 >= 0 /\ b + e - 2 >= 0 /\ -a + e + 2 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 255 >= c ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) start location: f0 leaf cost: 4 Testing for reachability in the complexity graph removes the following transition from problem 14: f16(a, b, c, d, e, f) -> f5(a, b, c, g, e, f) [ d - f - 1 >= 0 /\ -e + 2 >= 0 /\ b - e + 2 >= 0 /\ -a - e + 6 >= 0 /\ e - 2 >= 0 /\ b + e - 2 >= 0 /\ -a + e + 2 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 255 >= c ] We thus obtain the following problem: 15: T: (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] (1, 1) f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) start location: f0 leaf cost: 4 By chaining the transition f0(a, b, c, d, e, f) -> f5(4, 0, c, g, 0, f) with all transitions in problem 15, the following new transition is obtained: f0(a, b, c, d, e, f) -> f7(4, 0, c, g, 0, f) [ 0 >= 0 /\ 4 >= 2 ] We thus obtain the following problem: 16: T: (1, 2) f0(a, b, c, d, e, f) -> f7(4, 0, c, g, 0, f) [ 0 >= 0 /\ 4 >= 2 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] start location: f0 leaf cost: 4 By chaining the transition f0(a, b, c, d, e, f) -> f7(4, 0, c, g, 0, f) [ 0 >= 0 /\ 4 >= 2 ] with all transitions in problem 16, the following new transition is obtained: f0(a, b, c, d, e, f) -> f9(4, 0, c, g, 0, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 ] We thus obtain the following problem: 17: T: (1, 3) f0(a, b, c, d, e, f) -> f9(4, 0, c, g, 0, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] start location: f0 leaf cost: 4 By chaining the transition f0(a, b, c, d, e, f) -> f9(4, 0, c, g, 0, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 ] with all transitions in problem 17, the following new transitions are obtained: f0(a, b, c, d, e, f) -> f5(4, 0, c + 4, g', 2, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ g >= f + 1 /\ g - f - 1 >= 0 /\ 255 >= c + 4 ] f0(a, b, c, d, e, f) -> f5(4, 0, c - 4, g', 1, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ 1 >= 0 /\ f >= g + 1 /\ -g + f - 1 >= 0 /\ c - 4 >= 0 ] We thus obtain the following problem: 18: T: (1, 5) f0(a, b, c, d, e, f) -> f5(4, 0, c + 4, g', 2, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ g >= f + 1 /\ g - f - 1 >= 0 /\ 255 >= c + 4 ] (1, 5) f0(a, b, c, d, e, f) -> f5(4, 0, c - 4, g', 1, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ 1 >= 0 /\ f >= g + 1 /\ -g + f - 1 >= 0 /\ c - 4 >= 0 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] start location: f0 leaf cost: 4 By chaining the transition f0(a, b, c, d, e, f) -> f5(4, 0, c + 4, g', 2, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ g >= f + 1 /\ g - f - 1 >= 0 /\ 255 >= c + 4 ] with all transitions in problem 18, the following new transition is obtained: f0(a, b, c, d, e, f) -> f7(4, 0, c + 4, g', 2, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ g >= f + 1 /\ g - f - 1 >= 0 /\ 255 >= c + 4 /\ 2 >= 0 ] We thus obtain the following problem: 19: T: (1, 6) f0(a, b, c, d, e, f) -> f7(4, 0, c + 4, g', 2, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ g >= f + 1 /\ g - f - 1 >= 0 /\ 255 >= c + 4 /\ 2 >= 0 ] (1, 5) f0(a, b, c, d, e, f) -> f5(4, 0, c - 4, g', 1, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ 1 >= 0 /\ f >= g + 1 /\ -g + f - 1 >= 0 /\ c - 4 >= 0 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] start location: f0 leaf cost: 4 By chaining the transition f0(a, b, c, d, e, f) -> f7(4, 0, c + 4, g', 2, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ g >= f + 1 /\ g - f - 1 >= 0 /\ 255 >= c + 4 /\ 2 >= 0 ] with all transitions in problem 19, the following new transition is obtained: f0(a, b, c, d, e, f) -> f9(4, 0, c + 4, g', 2, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ g >= f + 1 /\ g - f - 1 >= 0 /\ 255 >= c + 4 /\ 2 >= 0 ] We thus obtain the following problem: 20: T: (1, 7) f0(a, b, c, d, e, f) -> f9(4, 0, c + 4, g', 2, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ g >= f + 1 /\ g - f - 1 >= 0 /\ 255 >= c + 4 /\ 2 >= 0 ] (1, 5) f0(a, b, c, d, e, f) -> f5(4, 0, c - 4, g', 1, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ 1 >= 0 /\ f >= g + 1 /\ -g + f - 1 >= 0 /\ c - 4 >= 0 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] start location: f0 leaf cost: 4 By chaining the transition f0(a, b, c, d, e, f) -> f5(4, 0, c - 4, g', 1, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ 1 >= 0 /\ f >= g + 1 /\ -g + f - 1 >= 0 /\ c - 4 >= 0 ] with all transitions in problem 20, the following new transition is obtained: f0(a, b, c, d, e, f) -> f7(4, 0, c - 4, g', 1, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ 1 >= 0 /\ f >= g + 1 /\ -g + f - 1 >= 0 /\ c - 4 >= 0 ] We thus obtain the following problem: 21: T: (1, 6) f0(a, b, c, d, e, f) -> f7(4, 0, c - 4, g', 1, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ 1 >= 0 /\ f >= g + 1 /\ -g + f - 1 >= 0 /\ c - 4 >= 0 ] (1, 7) f0(a, b, c, d, e, f) -> f9(4, 0, c + 4, g', 2, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ g >= f + 1 /\ g - f - 1 >= 0 /\ 255 >= c + 4 /\ 2 >= 0 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] start location: f0 leaf cost: 4 By chaining the transition f0(a, b, c, d, e, f) -> f7(4, 0, c - 4, g', 1, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ 1 >= 0 /\ f >= g + 1 /\ -g + f - 1 >= 0 /\ c - 4 >= 0 ] with all transitions in problem 21, the following new transition is obtained: f0(a, b, c, d, e, f) -> f9(4, 0, c - 4, g', 1, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ 1 >= 0 /\ f >= g + 1 /\ -g + f - 1 >= 0 /\ c - 4 >= 0 ] We thus obtain the following problem: 22: T: (1, 7) f0(a, b, c, d, e, f) -> f9(4, 0, c - 4, g', 1, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ 1 >= 0 /\ f >= g + 1 /\ -g + f - 1 >= 0 /\ c - 4 >= 0 ] (1, 7) f0(a, b, c, d, e, f) -> f9(4, 0, c + 4, g', 2, f) [ 0 >= 0 /\ 4 >= 2 /\ 0 = 0 /\ g >= f + 1 /\ g - f - 1 >= 0 /\ 255 >= c + 4 /\ 2 >= 0 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= a ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c + a - 1, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ d >= f + 1 /\ b = 0 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ 255 >= c + a - 1 ] (4, 2) f9(a, b, c, d, e, f) -> f5(a - 1, 1, c - a + 1, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ f >= d + 1 /\ b = 0 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ -a + 5 >= 0 /\ -a + 6 >= 0 /\ c - a + 1 >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ d >= f + 1 /\ e = 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 2 /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c + a, g, 2, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 0 >= e /\ d >= f + 1 /\ d - f - 1 >= 0 /\ 0 >= 0 /\ 255 >= c + a ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ 1 >= e /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ e >= 3 /\ f >= d + 1 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 2) f9(a, b, c, d, e, f) -> f5(a, b, c - a, g, 1, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 /\ f >= d + 1 /\ e = 2 /\ -d + f - 1 >= 0 /\ 0 >= 0 /\ c - a >= 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a, 0, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b = 0 ] (?, 1) f7(a, b, c, d, e, f) -> f9(a - 1, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ b >= 1 ] (?, 1) f5(a, b, c, d, e, f) -> f7(a, b, c, d, e, f) [ e >= 0 /\ b + e >= 0 /\ -a + e + 4 >= 0 /\ -a - b + 4 >= 0 /\ b >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a >= 2 ] start location: f0 leaf cost: 4 Complexity upper bound ? Time: 6.242 sec (SMT: 5.437 sec)