MAYBE Initial complexity problem: 1: T: (1, 1) f0(a, b, c, d, e, f, g) -> f6(8, 0, 14, -1, e, f, g) (?, 1) f6(a, b, c, d, e, f, g) -> f12(a, b, c, d, i, f, g) [ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, d, e, f, g) -> f12(a, b, c, d, i, f, g) [ c >= b ] (?, 1) f6(a, b, c, d, e, f, g) -> f6(a, b, b - 1, i, h, f, g) [ c >= b ] (?, 1) f12(a, b, c, d, e, f, g) -> f6(a, b, e - 1, d, e, f, g) (?, 1) f12(a, b, c, d, e, f, g) -> f6(a, e + 1, c, d, e, f, g) (?, 1) f6(a, b, c, d, e, f, g) -> f20(a, b, c, d, e, d, d) [ b >= c + 1 ] start location: f0 leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [a, b, c, e]. We thus obtain the following problem: 2: T: (?, 1) f6(a, b, c, e) -> f20(a, b, c, e) [ b >= c + 1 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) (?, 1) f6(a, b, c, e) -> f6(a, b, b - 1, h) [ c >= b ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ c >= b ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ c >= b /\ a >= h + 1 ] (1, 1) f0(a, b, c, e) -> f6(8, 0, 14, e) start location: f0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem: 3: T: (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ c >= b ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ c >= b /\ a >= h + 1 ] (1, 1) f0(a, b, c, e) -> f6(8, 0, 14, e) start location: f0 leaf cost: 2 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol f12: -X_2 + X_3 >= 0 /\ -X_1 + 8 >= 0 /\ X_1 - 8 >= 0 For symbol f6: -X_1 + 8 >= 0 /\ X_1 - 8 >= 0 This yielded the following problem: 4: T: (1, 1) f0(a, b, c, e) -> f6(8, 0, 14, e) (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f6(8, 0, 14, e) with all transitions in problem 4, the following new transitions are obtained: f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 ] f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] We thus obtain the following problem: 5: T: (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 ] with all transitions in problem 5, the following new transitions are obtained: f0(a, b, c, e) -> f6(8, i + 1, 14, i) [ 0 >= 0 /\ 14 >= 0 ] f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] We thus obtain the following problem: 6: T: (1, 3) f0(a, b, c, e) -> f6(8, i + 1, 14, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f6(8, i + 1, 14, i) [ 0 >= 0 /\ 14 >= 0 ] with all transitions in problem 6, the following new transitions are obtained: f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 ] f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] We thus obtain the following problem: 7: T: (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 ] with all transitions in problem 7, the following new transitions are obtained: f0(a, b, c, e) -> f6(8, i' + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] We thus obtain the following problem: 8: T: (1, 5) f0(a, b, c, e) -> f6(8, i' + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 5) f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f6(8, i' + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] with all transitions in problem 8, the following new transitions are obtained: f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 ] f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ 8 >= h + 1 ] We thus obtain the following problem: 9: T: (1, 6) f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 ] (1, 6) f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ 8 >= h + 1 ] (1, 5) f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 ] with all transitions in problem 9, the following new transitions are obtained: f0(a, b, c, e) -> f6(8, i'' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] f0(a, b, c, e) -> f6(8, i' + 1, i'' - 1, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] We thus obtain the following problem: 10: T: (1, 7) f0(a, b, c, e) -> f6(8, i'' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] (1, 7) f0(a, b, c, e) -> f6(8, i' + 1, i'' - 1, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] (1, 6) f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ 8 >= h + 1 ] (1, 5) f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f6(8, i'' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] with all transitions in problem 10, the following new transitions are obtained: f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 ] f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ 8 >= h + 1 ] We thus obtain the following problem: 11: T: (1, 8) f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 ] (1, 8) f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ 8 >= h + 1 ] (1, 7) f0(a, b, c, e) -> f6(8, i' + 1, i'' - 1, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] (1, 6) f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ 8 >= h + 1 ] (1, 5) f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 ] with all transitions in problem 11, the following new transitions are obtained: f0(a, b, c, e) -> f6(8, i''' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 ] f0(a, b, c, e) -> f6(8, i'' + 1, i''' - 1, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 ] We thus obtain the following problem: 12: T: (1, 9) f0(a, b, c, e) -> f6(8, i''' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 ] (1, 9) f0(a, b, c, e) -> f6(8, i'' + 1, i''' - 1, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 ] (1, 8) f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ 8 >= h + 1 ] (1, 7) f0(a, b, c, e) -> f6(8, i' + 1, i'' - 1, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] (1, 6) f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ 8 >= h + 1 ] (1, 5) f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f6(8, i''' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 ] with all transitions in problem 12, the following new transitions are obtained: f0(a, b, c, e) -> f12(8, i''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 ] f0(a, b, c, e) -> f12(8, i''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ 8 >= h + 1 ] We thus obtain the following problem: 13: T: (1, 10) f0(a, b, c, e) -> f12(8, i''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 ] (1, 10) f0(a, b, c, e) -> f12(8, i''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ 8 >= h + 1 ] (1, 9) f0(a, b, c, e) -> f6(8, i'' + 1, i''' - 1, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 ] (1, 8) f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ 8 >= h + 1 ] (1, 7) f0(a, b, c, e) -> f6(8, i' + 1, i'' - 1, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] (1, 6) f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ 8 >= h + 1 ] (1, 5) f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f12(8, i''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 ] with all transitions in problem 13, the following new transitions are obtained: f0(a, b, c, e) -> f6(8, i'''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 ] f0(a, b, c, e) -> f6(8, i''' + 1, i'''' - 1, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 ] We thus obtain the following problem: 14: T: (1, 11) f0(a, b, c, e) -> f6(8, i'''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 ] (1, 11) f0(a, b, c, e) -> f6(8, i''' + 1, i'''' - 1, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 ] (1, 10) f0(a, b, c, e) -> f12(8, i''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ 8 >= h + 1 ] (1, 9) f0(a, b, c, e) -> f6(8, i'' + 1, i''' - 1, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 ] (1, 8) f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ 8 >= h + 1 ] (1, 7) f0(a, b, c, e) -> f6(8, i' + 1, i'' - 1, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] (1, 6) f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ 8 >= h + 1 ] (1, 5) f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f6(8, i'''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 ] with all transitions in problem 14, the following new transitions are obtained: f0(a, b, c, e) -> f12(8, i'''' + 1, 14, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 ] f0(a, b, c, e) -> f12(8, i'''' + 1, 14, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ 8 >= h + 1 ] We thus obtain the following problem: 15: T: (1, 12) f0(a, b, c, e) -> f12(8, i'''' + 1, 14, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 ] (1, 12) f0(a, b, c, e) -> f12(8, i'''' + 1, 14, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ 8 >= h + 1 ] (1, 11) f0(a, b, c, e) -> f6(8, i''' + 1, i'''' - 1, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 ] (1, 10) f0(a, b, c, e) -> f12(8, i''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ 8 >= h + 1 ] (1, 9) f0(a, b, c, e) -> f6(8, i'' + 1, i''' - 1, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 ] (1, 8) f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ 8 >= h + 1 ] (1, 7) f0(a, b, c, e) -> f6(8, i' + 1, i'' - 1, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] (1, 6) f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ 8 >= h + 1 ] (1, 5) f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f12(8, i'''' + 1, 14, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 ] with all transitions in problem 15, the following new transitions are obtained: f0(a, b, c, e) -> f6(8, i''''' + 1, 14, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 ] f0(a, b, c, e) -> f6(8, i'''' + 1, i''''' - 1, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 ] We thus obtain the following problem: 16: T: (1, 13) f0(a, b, c, e) -> f6(8, i''''' + 1, 14, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 ] (1, 13) f0(a, b, c, e) -> f6(8, i'''' + 1, i''''' - 1, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 ] (1, 12) f0(a, b, c, e) -> f12(8, i'''' + 1, 14, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ 8 >= h + 1 ] (1, 11) f0(a, b, c, e) -> f6(8, i''' + 1, i'''' - 1, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 ] (1, 10) f0(a, b, c, e) -> f12(8, i''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ 8 >= h + 1 ] (1, 9) f0(a, b, c, e) -> f6(8, i'' + 1, i''' - 1, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 ] (1, 8) f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ 8 >= h + 1 ] (1, 7) f0(a, b, c, e) -> f6(8, i' + 1, i'' - 1, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] (1, 6) f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ 8 >= h + 1 ] (1, 5) f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f6(8, i''''' + 1, 14, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 ] with all transitions in problem 16, the following new transitions are obtained: f0(a, b, c, e) -> f12(8, i''''' + 1, 14, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 ] f0(a, b, c, e) -> f12(8, i''''' + 1, 14, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ 8 >= h + 1 ] We thus obtain the following problem: 17: T: (1, 14) f0(a, b, c, e) -> f12(8, i''''' + 1, 14, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 ] (1, 14) f0(a, b, c, e) -> f12(8, i''''' + 1, 14, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ 8 >= h + 1 ] (1, 13) f0(a, b, c, e) -> f6(8, i'''' + 1, i''''' - 1, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 ] (1, 12) f0(a, b, c, e) -> f12(8, i'''' + 1, 14, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ 8 >= h + 1 ] (1, 11) f0(a, b, c, e) -> f6(8, i''' + 1, i'''' - 1, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 ] (1, 10) f0(a, b, c, e) -> f12(8, i''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ 8 >= h + 1 ] (1, 9) f0(a, b, c, e) -> f6(8, i'' + 1, i''' - 1, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 ] (1, 8) f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ 8 >= h + 1 ] (1, 7) f0(a, b, c, e) -> f6(8, i' + 1, i'' - 1, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] (1, 6) f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ 8 >= h + 1 ] (1, 5) f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f12(8, i''''' + 1, 14, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 ] with all transitions in problem 17, the following new transitions are obtained: f0(a, b, c, e) -> f6(8, i'''''' + 1, 14, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ -i''''' + 13 >= 0 ] f0(a, b, c, e) -> f6(8, i''''' + 1, i'''''' - 1, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ -i''''' + 13 >= 0 ] We thus obtain the following problem: 18: T: (1, 15) f0(a, b, c, e) -> f6(8, i'''''' + 1, 14, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ -i''''' + 13 >= 0 ] (1, 15) f0(a, b, c, e) -> f6(8, i''''' + 1, i'''''' - 1, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ -i''''' + 13 >= 0 ] (1, 14) f0(a, b, c, e) -> f12(8, i''''' + 1, 14, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ 8 >= h + 1 ] (1, 13) f0(a, b, c, e) -> f6(8, i'''' + 1, i''''' - 1, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 ] (1, 12) f0(a, b, c, e) -> f12(8, i'''' + 1, 14, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ 8 >= h + 1 ] (1, 11) f0(a, b, c, e) -> f6(8, i''' + 1, i'''' - 1, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 ] (1, 10) f0(a, b, c, e) -> f12(8, i''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ 8 >= h + 1 ] (1, 9) f0(a, b, c, e) -> f6(8, i'' + 1, i''' - 1, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 ] (1, 8) f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ 8 >= h + 1 ] (1, 7) f0(a, b, c, e) -> f6(8, i' + 1, i'' - 1, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] (1, 6) f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ 8 >= h + 1 ] (1, 5) f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 By chaining the transition f0(a, b, c, e) -> f6(8, i'''''' + 1, 14, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ -i''''' + 13 >= 0 ] with all transitions in problem 18, the following new transitions are obtained: f0(a, b, c, e) -> f12(8, i'''''' + 1, 14, i''''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ -i''''' + 13 >= 0 /\ 14 >= i'''''' + 1 ] f0(a, b, c, e) -> f12(8, i'''''' + 1, 14, i''''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ -i''''' + 13 >= 0 /\ 14 >= i'''''' + 1 /\ 8 >= h + 1 ] We thus obtain the following problem: 19: T: (1, 16) f0(a, b, c, e) -> f12(8, i'''''' + 1, 14, i''''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ -i''''' + 13 >= 0 /\ 14 >= i'''''' + 1 ] (1, 16) f0(a, b, c, e) -> f12(8, i'''''' + 1, 14, i''''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ -i''''' + 13 >= 0 /\ 14 >= i'''''' + 1 /\ 8 >= h + 1 ] (1, 15) f0(a, b, c, e) -> f6(8, i''''' + 1, i'''''' - 1, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ -i''''' + 13 >= 0 ] (1, 14) f0(a, b, c, e) -> f12(8, i''''' + 1, 14, i'''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 /\ 14 >= i''''' + 1 /\ 8 >= h + 1 ] (1, 13) f0(a, b, c, e) -> f6(8, i'''' + 1, i''''' - 1, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ -i'''' + 13 >= 0 ] (1, 12) f0(a, b, c, e) -> f12(8, i'''' + 1, 14, i''''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 /\ 14 >= i'''' + 1 /\ 8 >= h + 1 ] (1, 11) f0(a, b, c, e) -> f6(8, i''' + 1, i'''' - 1, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ -i''' + 13 >= 0 ] (1, 10) f0(a, b, c, e) -> f12(8, i''' + 1, 14, i'''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 /\ 14 >= i''' + 1 /\ 8 >= h + 1 ] (1, 9) f0(a, b, c, e) -> f6(8, i'' + 1, i''' - 1, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ -i'' + 13 >= 0 ] (1, 8) f0(a, b, c, e) -> f12(8, i'' + 1, 14, i''') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 /\ 14 >= i'' + 1 /\ 8 >= h + 1 ] (1, 7) f0(a, b, c, e) -> f6(8, i' + 1, i'' - 1, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ -i' + 13 >= 0 ] (1, 6) f0(a, b, c, e) -> f12(8, i' + 1, 14, i'') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 /\ 14 >= i' + 1 /\ 8 >= h + 1 ] (1, 5) f0(a, b, c, e) -> f6(8, i + 1, i' - 1, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ -i + 13 >= 0 ] (1, 4) f0(a, b, c, e) -> f12(8, i + 1, 14, i') [ 0 >= 0 /\ 14 >= 0 /\ 14 >= i + 1 /\ 8 >= h + 1 ] (1, 3) f0(a, b, c, e) -> f6(8, 0, i - 1, i) [ 0 >= 0 /\ 14 >= 0 ] (1, 2) f0(a, b, c, e) -> f12(8, 0, 14, i) [ 0 >= 0 /\ 14 >= 0 /\ 8 >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b /\ a >= h + 1 ] (?, 1) f6(a, b, c, e) -> f12(a, b, c, i) [ -a + 8 >= 0 /\ a - 8 >= 0 /\ c >= b ] (?, 1) f12(a, b, c, e) -> f6(a, b, e - 1, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] (?, 1) f12(a, b, c, e) -> f6(a, e + 1, c, e) [ -b + c >= 0 /\ -a + 8 >= 0 /\ a - 8 >= 0 ] start location: f0 leaf cost: 2 Complexity upper bound ? Time: 2.021 sec (SMT: 1.800 sec)