MAYBE Initial complexity problem: 1: T: (?, 1) f38(a, b, c, d, e, f, g) -> f11(a, a, c, d, e, f, g) [ a = b ] (1, 1) f0(a, b, c, d, e, f, g) -> f11(0, 0, h, 0, 1, i, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, e, f, g) -> f34(0, h, c, d + 1, e, f, g) [ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d ] (?, 1) f11(a, b, c, d, e, f, g) -> f34(1, h, c, d + 1, e, f, g) [ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f11(a, b, c, d, e, f, g) -> f34(0, h, c, d + 1, e, f, g) [ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 ] (?, 1) f11(a, b, c, d, e, f, g) -> f34(i, j, h, 0, e + 1, f, g) [ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, e, f, g) -> f34(h, i, c - 1, d, e, f, g) [ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, e, f, g) -> f38(a, b, c, d + 1, e, f, g) [ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, e, f, g) -> f38(a, b, c, d + 1, e, f, g) [ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, e, f, g) -> f38(a, b, c, d + 1, e, f, g) [ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, e, f, g) -> f38(a, b, h, 0, e + 1, f, g) [ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, e, f, g) -> f38(a, b, c - 1, d, e, f, g) [ c >= 1 ] (?, 1) f38(a, b, c, d, e, f, g) -> f11(a, b, c, d, e, f, g - 1) [ b >= a + 1 ] (?, 1) f38(a, b, c, d, e, f, g) -> f11(a, b, c, d, e, f, g - 1) [ a >= b + 1 ] (?, 1) f11(a, b, c, d, e, f, g) -> f53(a, b, c, d, e, f, g) [ 0 >= g ] start location: f0 leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [a, b, c, d, g]. We thus obtain the following problem: 2: T: (?, 1) f11(a, b, c, d, g) -> f53(a, b, c, d, g) [ 0 >= g ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ a >= b + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ b >= a + 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ c >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 ] (?, 1) f11(a, b, c, d, g) -> f34(1, h, c, d + 1, g) [ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ a = b ] start location: f0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem: 3: T: (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ a >= b + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ b >= a + 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ c >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 ] (?, 1) f11(a, b, c, d, g) -> f34(1, h, c, d + 1, g) [ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ a = b ] start location: f0 leaf cost: 1 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol f11: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol f34: X_5 - 1 >= 0 /\ X_4 + X_5 - 1 >= 0 /\ X_3 + X_5 - 1 >= 0 /\ X_2 + X_5 - 1 >= 0 /\ -X_2 + X_5 >= 0 /\ X_1 + X_5 - 1 >= 0 /\ -X_1 + X_5 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ -X_2 + X_4 + 1 >= 0 /\ X_1 + X_4 >= 0 /\ -X_1 + X_4 + 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ -X_2 + X_3 + 1 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ -X_2 + 1 >= 0 /\ X_1 - X_2 + 1 >= 0 /\ -X_1 - X_2 + 2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 + 1 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 >= 0 For symbol f38: X_5 - 1 >= 0 /\ X_4 + X_5 - 1 >= 0 /\ X_3 + X_5 - 1 >= 0 /\ X_2 + X_5 - 1 >= 0 /\ -X_2 + X_5 >= 0 /\ X_1 + X_5 - 1 >= 0 /\ -X_1 + X_5 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 >= 0 /\ -X_2 + X_4 + 1 >= 0 /\ X_1 + X_4 >= 0 /\ -X_1 + X_4 + 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ -X_2 + X_3 + 1 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ -X_2 + 1 >= 0 /\ X_1 - X_2 + 1 >= 0 /\ -X_1 - X_2 + 2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 + 1 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 >= 0 This yielded the following problem: 4: T: (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d ] (?, 1) f11(a, b, c, d, g) -> f34(1, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d ] with all transitions in problem 4, the following new transition is obtained: f11(a, b, c, d, g) -> f38(0, h, c, d + 2, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 ] We thus obtain the following problem: 5: T: (?, 2) f11(a, b, c, d, g) -> f38(0, h, c, d + 2, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(1, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f38(0, h, c, d + 2, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 ] with all transitions in problem 5, the following new transition is obtained: f11(a, b, c, d, g) -> f11(0, h, c, d + 2, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 ] We thus obtain the following problem: 6: T: (?, 3) f11(a, b, c, d, g) -> f11(0, h, c, d + 2, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(1, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f11(0, h, c, d + 2, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 ] with all transitions in problem 6, the following new transition is obtained: f11(a, b, c, d, g) -> f34(0, h', c, d + 3, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 ] We thus obtain the following problem: 7: T: (?, 4) f11(a, b, c, d, g) -> f34(0, h', c, d + 3, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(1, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f34(0, h', c, d + 3, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 ] with all transitions in problem 7, the following new transition is obtained: f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] We thus obtain the following problem: 8: T: (?, 5) f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(1, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f34(1, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 ] with all transitions in problem 8, the following new transition is obtained: f11(a, b, c, d, g) -> f38(1, h, c, d + 2, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 ] We thus obtain the following problem: 9: T: (?, 2) f11(a, b, c, d, g) -> f38(1, h, c, d + 2, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 ] (?, 5) f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f38(1, h, c, d + 2, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 ] with all transitions in problem 9, the following new transition is obtained: f11(a, b, c, d, g) -> f11(1, h, c, d + 2, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 ] We thus obtain the following problem: 10: T: (?, 3) f11(a, b, c, d, g) -> f11(1, h, c, d + 2, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 ] (?, 5) f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f11(1, h, c, d + 2, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 ] with all transitions in problem 10, the following new transition is obtained: f11(a, b, c, d, g) -> f34(i, j, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h' >= 0 /\ g - 1 >= 1 /\ d + 2 >= 3 ] We thus obtain the following problem: 11: T: (?, 4) f11(a, b, c, d, g) -> f34(i, j, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h' >= 0 /\ g - 1 >= 1 /\ d + 2 >= 3 ] (?, 5) f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f34(0, h, c, d + 1, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 ] with all transitions in problem 11, the following new transition is obtained: f11(a, b, c, d, g) -> f38(0, h, h', 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 ] We thus obtain the following problem: 12: T: (?, 2) f11(a, b, c, d, g) -> f38(0, h, h', 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 ] (?, 4) f11(a, b, c, d, g) -> f34(i, j, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h' >= 0 /\ g - 1 >= 1 /\ d + 2 >= 3 ] (?, 5) f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f38(0, h, h', 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 ] with all transitions in problem 12, the following new transitions are obtained: f11(a, b, c, d, g) -> f11(0, h, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 ] f11(a, b, c, d, g) -> f11(0, 0, h', 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ 0 = h ] We thus obtain the following problem: 13: T: (?, 3) f11(a, b, c, d, g) -> f11(0, h, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 ] (?, 3) f11(a, b, c, d, g) -> f11(0, 0, h', 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ 0 = h ] (?, 4) f11(a, b, c, d, g) -> f34(i, j, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h' >= 0 /\ g - 1 >= 1 /\ d + 2 >= 3 ] (?, 5) f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f11(0, h, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 ] with all transitions in problem 13, the following new transitions are obtained: f11(a, b, c, d, g) -> f38(0, h'', h''', 0, g - 2) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 ] f11(a, b, c, d, g) -> f34(h'', i, h' - 1, 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ i >= 0 /\ 1 >= i /\ h'' >= 0 /\ 1 >= h'' /\ h' >= 1 /\ g - 1 >= 1 ] We thus obtain the following problem: 14: T: (?, 8) f11(a, b, c, d, g) -> f38(0, h'', h''', 0, g - 2) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 ] (?, 4) f11(a, b, c, d, g) -> f34(h'', i, h' - 1, 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ i >= 0 /\ 1 >= i /\ h'' >= 0 /\ 1 >= h'' /\ h' >= 1 /\ g - 1 >= 1 ] (?, 3) f11(a, b, c, d, g) -> f11(0, 0, h', 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ 0 = h ] (?, 4) f11(a, b, c, d, g) -> f34(i, j, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h' >= 0 /\ g - 1 >= 1 /\ d + 2 >= 3 ] (?, 5) f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f38(0, h'', h''', 0, g - 2) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 ] with all transitions in problem 14, the following new transitions are obtained: f11(a, b, c, d, g) -> f11(0, h'', h''', 0, g - 3) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 ] f11(a, b, c, d, g) -> f11(0, 0, h''', 0, g - 2) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ 0 = h'' ] We thus obtain the following problem: 15: T: (?, 9) f11(a, b, c, d, g) -> f11(0, h'', h''', 0, g - 3) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 ] (?, 9) f11(a, b, c, d, g) -> f11(0, 0, h''', 0, g - 2) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ 0 = h'' ] (?, 4) f11(a, b, c, d, g) -> f34(h'', i, h' - 1, 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ i >= 0 /\ 1 >= i /\ h'' >= 0 /\ 1 >= h'' /\ h' >= 1 /\ g - 1 >= 1 ] (?, 3) f11(a, b, c, d, g) -> f11(0, 0, h', 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ 0 = h ] (?, 4) f11(a, b, c, d, g) -> f34(i, j, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h' >= 0 /\ g - 1 >= 1 /\ d + 2 >= 3 ] (?, 5) f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f11(0, h'', h''', 0, g - 3) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 ] with all transitions in problem 15, the following new transitions are obtained: f11(a, b, c, d, g) -> f38(0, h''''', h'''''', 0, g - 4) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 ] f11(a, b, c, d, g) -> f34(h''''', i, h''' - 1, 0, g - 3) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ i >= 0 /\ 1 >= i /\ h''''' >= 0 /\ 1 >= h''''' /\ h''' >= 1 /\ g - 3 >= 1 ] We thus obtain the following problem: 16: T: (?, 14) f11(a, b, c, d, g) -> f38(0, h''''', h'''''', 0, g - 4) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 ] (?, 10) f11(a, b, c, d, g) -> f34(h''''', i, h''' - 1, 0, g - 3) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ i >= 0 /\ 1 >= i /\ h''''' >= 0 /\ 1 >= h''''' /\ h''' >= 1 /\ g - 3 >= 1 ] (?, 9) f11(a, b, c, d, g) -> f11(0, 0, h''', 0, g - 2) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ 0 = h'' ] (?, 4) f11(a, b, c, d, g) -> f34(h'', i, h' - 1, 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ i >= 0 /\ 1 >= i /\ h'' >= 0 /\ 1 >= h'' /\ h' >= 1 /\ g - 1 >= 1 ] (?, 3) f11(a, b, c, d, g) -> f11(0, 0, h', 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ 0 = h ] (?, 4) f11(a, b, c, d, g) -> f34(i, j, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h' >= 0 /\ g - 1 >= 1 /\ d + 2 >= 3 ] (?, 5) f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f38(0, h''''', h'''''', 0, g - 4) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 ] with all transitions in problem 16, the following new transitions are obtained: f11(a, b, c, d, g) -> f11(0, h''''', h'''''', 0, g - 5) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 ] f11(a, b, c, d, g) -> f11(0, 0, h'''''', 0, g - 4) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ 0 = h''''' ] We thus obtain the following problem: 17: T: (?, 15) f11(a, b, c, d, g) -> f11(0, h''''', h'''''', 0, g - 5) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 ] (?, 15) f11(a, b, c, d, g) -> f11(0, 0, h'''''', 0, g - 4) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ 0 = h''''' ] (?, 10) f11(a, b, c, d, g) -> f34(h''''', i, h''' - 1, 0, g - 3) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ i >= 0 /\ 1 >= i /\ h''''' >= 0 /\ 1 >= h''''' /\ h''' >= 1 /\ g - 3 >= 1 ] (?, 9) f11(a, b, c, d, g) -> f11(0, 0, h''', 0, g - 2) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ 0 = h'' ] (?, 4) f11(a, b, c, d, g) -> f34(h'', i, h' - 1, 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ i >= 0 /\ 1 >= i /\ h'' >= 0 /\ 1 >= h'' /\ h' >= 1 /\ g - 1 >= 1 ] (?, 3) f11(a, b, c, d, g) -> f11(0, 0, h', 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ 0 = h ] (?, 4) f11(a, b, c, d, g) -> f34(i, j, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h' >= 0 /\ g - 1 >= 1 /\ d + 2 >= 3 ] (?, 5) f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f11(0, h''''', h'''''', 0, g - 5) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 ] with all transitions in problem 17, the following new transitions are obtained: f11(a, b, c, d, g) -> f38(0, h'''''''', h''''''''', 0, g - 6) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 /\ h'''''''''' >= 0 /\ 1 >= h'''''''''' /\ g - 5 >= 1 /\ 0 >= h'''''' /\ g - 6 >= 0 /\ h'''''' + g - 6 >= 0 /\ h'''''''''' + g - 6 >= 0 /\ -h'''''''''' + g - 5 >= 0 /\ h'''''''''' + 1 >= 0 /\ -h'''''''''' + 2 >= 0 /\ h'''''''''' + h'''''' >= 0 /\ -h'''''''''' + h'''''' + 1 >= 0 /\ -h'''''''''' + 1 >= 0 /\ h'''''''''' >= 1 /\ h'''''' + 2 >= 0 /\ h'''''''''' + 2 >= 0 /\ -h'''''''''' + 3 >= 0 /\ h'''''''' >= 0 /\ 1 >= h'''''''' /\ g - 6 >= 1 /\ g - 7 >= 0 /\ h'''''' + g - 7 >= 0 /\ h'''''''' + g - 7 >= 0 /\ -h'''''''' + g - 6 >= 0 /\ h'''''' + 3 >= 0 /\ h'''''''' + 3 >= 0 /\ -h'''''''' + 4 >= 0 /\ h'''''''' + h'''''' >= 0 /\ -h'''''''' + h'''''' + 1 >= 0 /\ -h'''''''' + 1 >= 0 /\ -h'''''''' + 2 >= 0 /\ h'''''''' + 1 >= 0 /\ h''''''''' >= 0 ] f11(a, b, c, d, g) -> f34(h'''''''', i, h'''''' - 1, 0, g - 5) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 /\ i >= 0 /\ 1 >= i /\ h'''''''' >= 0 /\ 1 >= h'''''''' /\ h'''''' >= 1 /\ g - 5 >= 1 ] We thus obtain the following problem: 18: T: (?, 20) f11(a, b, c, d, g) -> f38(0, h'''''''', h''''''''', 0, g - 6) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 /\ h'''''''''' >= 0 /\ 1 >= h'''''''''' /\ g - 5 >= 1 /\ 0 >= h'''''' /\ g - 6 >= 0 /\ h'''''' + g - 6 >= 0 /\ h'''''''''' + g - 6 >= 0 /\ -h'''''''''' + g - 5 >= 0 /\ h'''''''''' + 1 >= 0 /\ -h'''''''''' + 2 >= 0 /\ h'''''''''' + h'''''' >= 0 /\ -h'''''''''' + h'''''' + 1 >= 0 /\ -h'''''''''' + 1 >= 0 /\ h'''''''''' >= 1 /\ h'''''' + 2 >= 0 /\ h'''''''''' + 2 >= 0 /\ -h'''''''''' + 3 >= 0 /\ h'''''''' >= 0 /\ 1 >= h'''''''' /\ g - 6 >= 1 /\ g - 7 >= 0 /\ h'''''' + g - 7 >= 0 /\ h'''''''' + g - 7 >= 0 /\ -h'''''''' + g - 6 >= 0 /\ h'''''' + 3 >= 0 /\ h'''''''' + 3 >= 0 /\ -h'''''''' + 4 >= 0 /\ h'''''''' + h'''''' >= 0 /\ -h'''''''' + h'''''' + 1 >= 0 /\ -h'''''''' + 1 >= 0 /\ -h'''''''' + 2 >= 0 /\ h'''''''' + 1 >= 0 /\ h''''''''' >= 0 ] (?, 16) f11(a, b, c, d, g) -> f34(h'''''''', i, h'''''' - 1, 0, g - 5) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 /\ i >= 0 /\ 1 >= i /\ h'''''''' >= 0 /\ 1 >= h'''''''' /\ h'''''' >= 1 /\ g - 5 >= 1 ] (?, 15) f11(a, b, c, d, g) -> f11(0, 0, h'''''', 0, g - 4) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ 0 = h''''' ] (?, 10) f11(a, b, c, d, g) -> f34(h''''', i, h''' - 1, 0, g - 3) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ i >= 0 /\ 1 >= i /\ h''''' >= 0 /\ 1 >= h''''' /\ h''' >= 1 /\ g - 3 >= 1 ] (?, 9) f11(a, b, c, d, g) -> f11(0, 0, h''', 0, g - 2) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ 0 = h'' ] (?, 4) f11(a, b, c, d, g) -> f34(h'', i, h' - 1, 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ i >= 0 /\ 1 >= i /\ h'' >= 0 /\ 1 >= h'' /\ h' >= 1 /\ g - 1 >= 1 ] (?, 3) f11(a, b, c, d, g) -> f11(0, 0, h', 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ 0 = h ] (?, 4) f11(a, b, c, d, g) -> f34(i, j, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h' >= 0 /\ g - 1 >= 1 /\ d + 2 >= 3 ] (?, 5) f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 By chaining the transition f11(a, b, c, d, g) -> f38(0, h'''''''', h''''''''', 0, g - 6) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 /\ h'''''''''' >= 0 /\ 1 >= h'''''''''' /\ g - 5 >= 1 /\ 0 >= h'''''' /\ g - 6 >= 0 /\ h'''''' + g - 6 >= 0 /\ h'''''''''' + g - 6 >= 0 /\ -h'''''''''' + g - 5 >= 0 /\ h'''''''''' + 1 >= 0 /\ -h'''''''''' + 2 >= 0 /\ h'''''''''' + h'''''' >= 0 /\ -h'''''''''' + h'''''' + 1 >= 0 /\ -h'''''''''' + 1 >= 0 /\ h'''''''''' >= 1 /\ h'''''' + 2 >= 0 /\ h'''''''''' + 2 >= 0 /\ -h'''''''''' + 3 >= 0 /\ h'''''''' >= 0 /\ 1 >= h'''''''' /\ g - 6 >= 1 /\ g - 7 >= 0 /\ h'''''' + g - 7 >= 0 /\ h'''''''' + g - 7 >= 0 /\ -h'''''''' + g - 6 >= 0 /\ h'''''' + 3 >= 0 /\ h'''''''' + 3 >= 0 /\ -h'''''''' + 4 >= 0 /\ h'''''''' + h'''''' >= 0 /\ -h'''''''' + h'''''' + 1 >= 0 /\ -h'''''''' + 1 >= 0 /\ -h'''''''' + 2 >= 0 /\ h'''''''' + 1 >= 0 /\ h''''''''' >= 0 ] with all transitions in problem 18, the following new transitions are obtained: f11(a, b, c, d, g) -> f11(0, h'''''''', h''''''''', 0, g - 7) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 /\ h'''''''''' >= 0 /\ 1 >= h'''''''''' /\ g - 5 >= 1 /\ 0 >= h'''''' /\ g - 6 >= 0 /\ h'''''' + g - 6 >= 0 /\ h'''''''''' + g - 6 >= 0 /\ -h'''''''''' + g - 5 >= 0 /\ h'''''''''' + 1 >= 0 /\ -h'''''''''' + 2 >= 0 /\ h'''''''''' + h'''''' >= 0 /\ -h'''''''''' + h'''''' + 1 >= 0 /\ -h'''''''''' + 1 >= 0 /\ h'''''''''' >= 1 /\ h'''''' + 2 >= 0 /\ h'''''''''' + 2 >= 0 /\ -h'''''''''' + 3 >= 0 /\ h'''''''' >= 0 /\ 1 >= h'''''''' /\ g - 6 >= 1 /\ g - 7 >= 0 /\ h'''''' + g - 7 >= 0 /\ h'''''''' + g - 7 >= 0 /\ -h'''''''' + g - 6 >= 0 /\ h'''''' + 3 >= 0 /\ h'''''''' + 3 >= 0 /\ -h'''''''' + 4 >= 0 /\ h'''''''' + h'''''' >= 0 /\ -h'''''''' + h'''''' + 1 >= 0 /\ -h'''''''' + 1 >= 0 /\ -h'''''''' + 2 >= 0 /\ h'''''''' + 1 >= 0 /\ h''''''''' >= 0 /\ h''''''''' + g - 7 >= 0 /\ h'''''''' + h''''''''' >= 0 /\ -h'''''''' + h''''''''' + 1 >= 0 /\ h''''''''' + 1 >= 0 /\ h'''''''' >= 1 ] f11(a, b, c, d, g) -> f11(0, 0, h''''''''', 0, g - 6) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 /\ h'''''''''' >= 0 /\ 1 >= h'''''''''' /\ g - 5 >= 1 /\ 0 >= h'''''' /\ g - 6 >= 0 /\ h'''''' + g - 6 >= 0 /\ h'''''''''' + g - 6 >= 0 /\ -h'''''''''' + g - 5 >= 0 /\ h'''''''''' + 1 >= 0 /\ -h'''''''''' + 2 >= 0 /\ h'''''''''' + h'''''' >= 0 /\ -h'''''''''' + h'''''' + 1 >= 0 /\ -h'''''''''' + 1 >= 0 /\ h'''''''''' >= 1 /\ h'''''' + 2 >= 0 /\ h'''''''''' + 2 >= 0 /\ -h'''''''''' + 3 >= 0 /\ h'''''''' >= 0 /\ 1 >= h'''''''' /\ g - 6 >= 1 /\ g - 7 >= 0 /\ h'''''' + g - 7 >= 0 /\ h'''''''' + g - 7 >= 0 /\ -h'''''''' + g - 6 >= 0 /\ h'''''' + 3 >= 0 /\ h'''''''' + 3 >= 0 /\ -h'''''''' + 4 >= 0 /\ h'''''''' + h'''''' >= 0 /\ -h'''''''' + h'''''' + 1 >= 0 /\ -h'''''''' + 1 >= 0 /\ -h'''''''' + 2 >= 0 /\ h'''''''' + 1 >= 0 /\ h''''''''' >= 0 /\ h''''''''' + g - 7 >= 0 /\ h'''''''' + h''''''''' >= 0 /\ -h'''''''' + h''''''''' + 1 >= 0 /\ h''''''''' + 1 >= 0 /\ 0 = h'''''''' ] We thus obtain the following problem: 19: T: (?, 21) f11(a, b, c, d, g) -> f11(0, h'''''''', h''''''''', 0, g - 7) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 /\ h'''''''''' >= 0 /\ 1 >= h'''''''''' /\ g - 5 >= 1 /\ 0 >= h'''''' /\ g - 6 >= 0 /\ h'''''' + g - 6 >= 0 /\ h'''''''''' + g - 6 >= 0 /\ -h'''''''''' + g - 5 >= 0 /\ h'''''''''' + 1 >= 0 /\ -h'''''''''' + 2 >= 0 /\ h'''''''''' + h'''''' >= 0 /\ -h'''''''''' + h'''''' + 1 >= 0 /\ -h'''''''''' + 1 >= 0 /\ h'''''''''' >= 1 /\ h'''''' + 2 >= 0 /\ h'''''''''' + 2 >= 0 /\ -h'''''''''' + 3 >= 0 /\ h'''''''' >= 0 /\ 1 >= h'''''''' /\ g - 6 >= 1 /\ g - 7 >= 0 /\ h'''''' + g - 7 >= 0 /\ h'''''''' + g - 7 >= 0 /\ -h'''''''' + g - 6 >= 0 /\ h'''''' + 3 >= 0 /\ h'''''''' + 3 >= 0 /\ -h'''''''' + 4 >= 0 /\ h'''''''' + h'''''' >= 0 /\ -h'''''''' + h'''''' + 1 >= 0 /\ -h'''''''' + 1 >= 0 /\ -h'''''''' + 2 >= 0 /\ h'''''''' + 1 >= 0 /\ h''''''''' >= 0 /\ h''''''''' + g - 7 >= 0 /\ h'''''''' + h''''''''' >= 0 /\ -h'''''''' + h''''''''' + 1 >= 0 /\ h''''''''' + 1 >= 0 /\ h'''''''' >= 1 ] (?, 21) f11(a, b, c, d, g) -> f11(0, 0, h''''''''', 0, g - 6) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 /\ h'''''''''' >= 0 /\ 1 >= h'''''''''' /\ g - 5 >= 1 /\ 0 >= h'''''' /\ g - 6 >= 0 /\ h'''''' + g - 6 >= 0 /\ h'''''''''' + g - 6 >= 0 /\ -h'''''''''' + g - 5 >= 0 /\ h'''''''''' + 1 >= 0 /\ -h'''''''''' + 2 >= 0 /\ h'''''''''' + h'''''' >= 0 /\ -h'''''''''' + h'''''' + 1 >= 0 /\ -h'''''''''' + 1 >= 0 /\ h'''''''''' >= 1 /\ h'''''' + 2 >= 0 /\ h'''''''''' + 2 >= 0 /\ -h'''''''''' + 3 >= 0 /\ h'''''''' >= 0 /\ 1 >= h'''''''' /\ g - 6 >= 1 /\ g - 7 >= 0 /\ h'''''' + g - 7 >= 0 /\ h'''''''' + g - 7 >= 0 /\ -h'''''''' + g - 6 >= 0 /\ h'''''' + 3 >= 0 /\ h'''''''' + 3 >= 0 /\ -h'''''''' + 4 >= 0 /\ h'''''''' + h'''''' >= 0 /\ -h'''''''' + h'''''' + 1 >= 0 /\ -h'''''''' + 1 >= 0 /\ -h'''''''' + 2 >= 0 /\ h'''''''' + 1 >= 0 /\ h''''''''' >= 0 /\ h''''''''' + g - 7 >= 0 /\ h'''''''' + h''''''''' >= 0 /\ -h'''''''' + h''''''''' + 1 >= 0 /\ h''''''''' + 1 >= 0 /\ 0 = h'''''''' ] (?, 16) f11(a, b, c, d, g) -> f34(h'''''''', i, h'''''' - 1, 0, g - 5) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ h''''' >= 1 /\ i >= 0 /\ 1 >= i /\ h'''''''' >= 0 /\ 1 >= h'''''''' /\ h'''''' >= 1 /\ g - 5 >= 1 ] (?, 15) f11(a, b, c, d, g) -> f11(0, 0, h'''''', 0, g - 4) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ h''''''' >= 0 /\ 1 >= h''''''' /\ g - 3 >= 1 /\ 0 >= h''' /\ g - 4 >= 0 /\ h''' + g - 4 >= 0 /\ h''''''' + g - 4 >= 0 /\ -h''''''' + g - 3 >= 0 /\ h''''''' + 1 >= 0 /\ -h''''''' + 2 >= 0 /\ h''''''' + h''' >= 0 /\ -h''''''' + h''' + 1 >= 0 /\ -h''''''' + 1 >= 0 /\ h''''''' >= 1 /\ h''' + 2 >= 0 /\ h''''''' + 2 >= 0 /\ -h''''''' + 3 >= 0 /\ h''''' >= 0 /\ 1 >= h''''' /\ g - 4 >= 1 /\ g - 5 >= 0 /\ h''' + g - 5 >= 0 /\ h''''' + g - 5 >= 0 /\ -h''''' + g - 4 >= 0 /\ h''' + 3 >= 0 /\ h''''' + 3 >= 0 /\ -h''''' + 4 >= 0 /\ h''''' + h''' >= 0 /\ -h''''' + h''' + 1 >= 0 /\ -h''''' + 1 >= 0 /\ -h''''' + 2 >= 0 /\ h''''' + 1 >= 0 /\ h'''''' >= 0 /\ h'''''' + g - 5 >= 0 /\ h''''' + h'''''' >= 0 /\ -h''''' + h'''''' + 1 >= 0 /\ h'''''' + 1 >= 0 /\ 0 = h''''' ] (?, 10) f11(a, b, c, d, g) -> f34(h''''', i, h''' - 1, 0, g - 3) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ h'' >= 1 /\ i >= 0 /\ 1 >= i /\ h''''' >= 0 /\ 1 >= h''''' /\ h''' >= 1 /\ g - 3 >= 1 ] (?, 9) f11(a, b, c, d, g) -> f11(0, 0, h''', 0, g - 2) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ h'''' >= 0 /\ 1 >= h'''' /\ g - 1 >= 1 /\ 0 >= h' /\ g - 2 >= 0 /\ h' + g - 2 >= 0 /\ h'''' + g - 2 >= 0 /\ -h'''' + g - 1 >= 0 /\ h'''' + 1 >= 0 /\ -h'''' + 2 >= 0 /\ 2 >= 0 /\ h'''' + h' >= 0 /\ -h'''' + h' + 1 >= 0 /\ -h'''' + 1 >= 0 /\ h'''' >= 1 /\ 1 = 1 /\ h' + 2 >= 0 /\ h'''' + 2 >= 0 /\ -h'''' + 3 >= 0 /\ 3 >= 0 /\ h'' >= 0 /\ 1 >= h'' /\ g - 2 >= 1 /\ 2 = 2 /\ g - 3 >= 0 /\ h' + g - 3 >= 0 /\ h'' + g - 3 >= 0 /\ -h'' + g - 2 >= 0 /\ h' + 3 >= 0 /\ h'' + 3 >= 0 /\ -h'' + 4 >= 0 /\ 4 >= 0 /\ h'' + h' >= 0 /\ -h'' + h' + 1 >= 0 /\ -h'' + 1 >= 0 /\ -h'' + 2 >= 0 /\ h'' + 1 >= 0 /\ h''' >= 0 /\ 3 >= 3 /\ h''' + g - 3 >= 0 /\ h'' + h''' >= 0 /\ -h'' + h''' + 1 >= 0 /\ h''' + 1 >= 0 /\ 0 = h'' ] (?, 4) f11(a, b, c, d, g) -> f34(h'', i, h' - 1, 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ h >= 1 /\ i >= 0 /\ 1 >= i /\ h'' >= 0 /\ 1 >= h'' /\ h' >= 1 /\ g - 1 >= 1 ] (?, 3) f11(a, b, c, d, g) -> f11(0, 0, h', 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 2 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h' >= 0 /\ d + 1 >= 3 /\ h' + g - 1 >= 0 /\ h + h' >= 0 /\ -h + h' + 1 >= 0 /\ h' + 1 >= 0 /\ 0 = h ] (?, 4) f11(a, b, c, d, g) -> f34(i, j, h', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ d = 1 /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 0 >= 0 /\ 1 >= 0 /\ 0 >= h /\ d + 1 = 2 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ 1 >= h + 1 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h' >= 0 /\ g - 1 >= 1 /\ d + 2 >= 3 ] (?, 5) f11(a, b, c, d, g) -> f38(0, h', h'', 0, g - 1) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ h >= 0 /\ 1 >= h /\ g >= 1 /\ 0 >= c /\ 0 >= d /\ g - 1 >= 0 /\ d + g >= 0 /\ c + g - 1 >= 0 /\ h + g - 1 >= 0 /\ -h + g >= 0 /\ g >= 0 /\ d + 1 >= 0 /\ c + d + 1 >= 0 /\ h + d + 1 >= 0 /\ -h + d + 2 >= 0 /\ d + 2 >= 0 /\ h + c >= 0 /\ -h + c + 1 >= 0 /\ c + 1 >= 0 /\ -h + 1 >= 0 /\ -h + 2 >= 0 /\ h + 1 >= 0 /\ 1 >= 0 /\ 0 >= 0 /\ h >= 1 /\ d + 1 = 1 /\ d + g + 1 >= 0 /\ c + d + 2 >= 0 /\ h + d + 2 >= 0 /\ -h + d + 3 >= 0 /\ d + 3 >= 0 /\ h' >= 0 /\ 1 >= h' /\ g - 1 >= 1 /\ d + 2 = 2 /\ g - 2 >= 0 /\ c + g - 2 >= 0 /\ h' + g - 2 >= 0 /\ -h' + g - 1 >= 0 /\ c + d + 3 >= 0 /\ h' + d + 3 >= 0 /\ -h' + d + 4 >= 0 /\ d + 4 >= 0 /\ h' + c >= 0 /\ -h' + c + 1 >= 0 /\ -h' + 1 >= 0 /\ -h' + 2 >= 0 /\ h' + 1 >= 0 /\ h'' >= 0 /\ d + 3 >= 3 ] (?, 1) f38(a, b, c, d, g) -> f11(a, a, c, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a = b ] (1, 1) f0(a, b, c, d, g) -> f11(0, 0, h, 0, i) [ h >= 0 /\ i >= 1 ] (?, 1) f11(a, b, c, d, g) -> f34(i, j, h, 0, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ j >= 0 /\ 1 >= j /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ g >= 1 /\ 0 >= c /\ d >= 3 ] (?, 1) f11(a, b, c, d, g) -> f34(h, i, c - 1, d, g) [ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ a + d >= 0 /\ c >= 0 /\ b + c >= 0 /\ a + c >= 0 /\ b >= 0 /\ a + b >= 0 /\ a >= 0 /\ i >= 0 /\ 1 >= i /\ h >= 0 /\ 1 >= h /\ c >= 1 /\ g >= 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ 0 >= d ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= 1 /\ 0 >= c /\ d = 1 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c, d + 1, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ 0 >= b /\ 0 >= c /\ d = 2 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, h, 0, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ h >= 0 /\ 0 >= c /\ d >= 3 ] (?, 1) f34(a, b, c, d, g) -> f38(a, b, c - 1, d, g) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ c >= 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ b >= a + 1 ] (?, 1) f38(a, b, c, d, g) -> f11(a, b, c, d, g - 1) [ g - 1 >= 0 /\ d + g - 1 >= 0 /\ c + g - 1 >= 0 /\ b + g - 1 >= 0 /\ -b + g >= 0 /\ a + g - 1 >= 0 /\ -a + g >= 0 /\ d >= 0 /\ c + d >= 0 /\ b + d >= 0 /\ -b + d + 1 >= 0 /\ a + d >= 0 /\ -a + d + 1 >= 0 /\ c >= 0 /\ b + c >= 0 /\ -b + c + 1 >= 0 /\ a + c >= 0 /\ -a + c + 1 >= 0 /\ -b + 1 >= 0 /\ a - b + 1 >= 0 /\ -a - b + 2 >= 0 /\ b >= 0 /\ a + b >= 0 /\ -a + b + 1 >= 0 /\ -a + 1 >= 0 /\ a >= 0 /\ a >= b + 1 ] start location: f0 leaf cost: 1 Complexity upper bound ? Time: 14.921 sec (SMT: 8.883 sec)