MAYBE Initial complexity problem: 1: T: (?, 1) f6(a, b, c) -> f9(a, d, c) [ 0 >= a + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ a >= 1 ] (?, 1) f6(a, b, c) -> f17(0, b, c) [ a = 0 ] (?, 1) f17(a, b, c) -> f24(a, b, c) [ 0 >= c ] (?, 1) f17(a, b, c) -> f24(a, b, c) [ c >= 2 ] (?, 1) f17(a, b, c) -> f24(a, b, 0) [ c = 1 ] (?, 1) f9(a, b, c) -> f17(a, 0, 1) [ b = 0 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ 0 >= b + 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ b >= 1 ] (1, 1) f0(a, b, c) -> f6(d, b, 0) start location: f0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (?, 1) f6(a, b, c) -> f9(a, d, c) [ 0 >= a + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ a >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ 0 >= b + 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ b >= 1 ] (1, 1) f0(a, b, c) -> f6(d, b, 0) start location: f0 leaf cost: 5 Applied AI with 'oct' on problem 2 to obtain the following invariants: For symbol f6: -X_3 >= 0 /\ X_3 >= 0 For symbol f9: -X_3 >= 0 /\ X_3 >= 0 This yielded the following problem: 3: T: (1, 1) f0(a, b, c) -> f6(d, b, 0) (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f6(d, b, 0) with all transitions in problem 3, the following new transitions are obtained: f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ 0 >= d + 1 ] f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] We thus obtain the following problem: 4: T: (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ 0 >= d + 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ 0 >= d + 1 ] with all transitions in problem 4, the following new transitions are obtained: f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 ] f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] We thus obtain the following problem: 5: T: (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 ] with all transitions in problem 5, the following new transitions are obtained: f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 ] f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] We thus obtain the following problem: 6: T: (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 ] with all transitions in problem 6, the following new transitions are obtained: f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 ] f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] We thus obtain the following problem: 7: T: (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 ] (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 ] with all transitions in problem 7, the following new transitions are obtained: f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 ] f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ d'''' >= 1 ] We thus obtain the following problem: 8: T: (1, 6) f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 ] (1, 6) f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ d'''' >= 1 ] (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 ] with all transitions in problem 8, the following new transitions are obtained: f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 ] f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ d''''' >= 1 ] We thus obtain the following problem: 9: T: (1, 7) f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 ] (1, 7) f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ d''''' >= 1 ] (1, 6) f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ d'''' >= 1 ] (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 ] with all transitions in problem 9, the following new transitions are obtained: f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 ] f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ d'''''' >= 1 ] We thus obtain the following problem: 10: T: (1, 8) f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 ] (1, 8) f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ d'''''' >= 1 ] (1, 7) f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ d''''' >= 1 ] (1, 6) f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ d'''' >= 1 ] (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 ] with all transitions in problem 10, the following new transitions are obtained: f0(a, b, c) -> f6(d'''''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 ] f0(a, b, c) -> f6(d'''''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ d''''''' >= 1 ] We thus obtain the following problem: 11: T: (1, 9) f0(a, b, c) -> f6(d'''''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 ] (1, 9) f0(a, b, c) -> f6(d'''''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ d''''''' >= 1 ] (1, 8) f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ d'''''' >= 1 ] (1, 7) f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ d''''' >= 1 ] (1, 6) f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ d'''' >= 1 ] (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f6(d'''''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 ] with all transitions in problem 11, the following new transitions are obtained: f0(a, b, c) -> f9(d'''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 ] f0(a, b, c) -> f9(d'''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ d'''''''' >= 1 ] We thus obtain the following problem: 12: T: (1, 10) f0(a, b, c) -> f9(d'''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 ] (1, 10) f0(a, b, c) -> f9(d'''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ d'''''''' >= 1 ] (1, 9) f0(a, b, c) -> f6(d'''''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ d''''''' >= 1 ] (1, 8) f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ d'''''' >= 1 ] (1, 7) f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ d''''' >= 1 ] (1, 6) f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ d'''' >= 1 ] (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f9(d'''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 ] with all transitions in problem 12, the following new transitions are obtained: f0(a, b, c) -> f6(d'''''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 ] f0(a, b, c) -> f6(d'''''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ d''''''''' >= 1 ] We thus obtain the following problem: 13: T: (1, 11) f0(a, b, c) -> f6(d'''''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 ] (1, 11) f0(a, b, c) -> f6(d'''''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ d''''''''' >= 1 ] (1, 10) f0(a, b, c) -> f9(d'''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ d'''''''' >= 1 ] (1, 9) f0(a, b, c) -> f6(d'''''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ d''''''' >= 1 ] (1, 8) f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ d'''''' >= 1 ] (1, 7) f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ d''''' >= 1 ] (1, 6) f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ d'''' >= 1 ] (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f6(d'''''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 ] with all transitions in problem 13, the following new transitions are obtained: f0(a, b, c) -> f9(d'''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 ] f0(a, b, c) -> f9(d'''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ d'''''''''' >= 1 ] We thus obtain the following problem: 14: T: (1, 12) f0(a, b, c) -> f9(d'''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 ] (1, 12) f0(a, b, c) -> f9(d'''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ d'''''''''' >= 1 ] (1, 11) f0(a, b, c) -> f6(d'''''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ d''''''''' >= 1 ] (1, 10) f0(a, b, c) -> f9(d'''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ d'''''''' >= 1 ] (1, 9) f0(a, b, c) -> f6(d'''''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ d''''''' >= 1 ] (1, 8) f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ d'''''' >= 1 ] (1, 7) f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ d''''' >= 1 ] (1, 6) f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ d'''' >= 1 ] (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f9(d'''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 ] with all transitions in problem 14, the following new transitions are obtained: f0(a, b, c) -> f6(d'''''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 ] f0(a, b, c) -> f6(d'''''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ d''''''''''' >= 1 ] We thus obtain the following problem: 15: T: (1, 13) f0(a, b, c) -> f6(d'''''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 ] (1, 13) f0(a, b, c) -> f6(d'''''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ d''''''''''' >= 1 ] (1, 12) f0(a, b, c) -> f9(d'''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ d'''''''''' >= 1 ] (1, 11) f0(a, b, c) -> f6(d'''''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ d''''''''' >= 1 ] (1, 10) f0(a, b, c) -> f9(d'''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ d'''''''' >= 1 ] (1, 9) f0(a, b, c) -> f6(d'''''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ d''''''' >= 1 ] (1, 8) f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ d'''''' >= 1 ] (1, 7) f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ d''''' >= 1 ] (1, 6) f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ d'''' >= 1 ] (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f6(d'''''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 ] with all transitions in problem 15, the following new transitions are obtained: f0(a, b, c) -> f9(d'''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 ] f0(a, b, c) -> f9(d'''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ d'''''''''''' >= 1 ] We thus obtain the following problem: 16: T: (1, 14) f0(a, b, c) -> f9(d'''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 ] (1, 14) f0(a, b, c) -> f9(d'''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ d'''''''''''' >= 1 ] (1, 13) f0(a, b, c) -> f6(d'''''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ d''''''''''' >= 1 ] (1, 12) f0(a, b, c) -> f9(d'''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ d'''''''''' >= 1 ] (1, 11) f0(a, b, c) -> f6(d'''''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ d''''''''' >= 1 ] (1, 10) f0(a, b, c) -> f9(d'''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ d'''''''' >= 1 ] (1, 9) f0(a, b, c) -> f6(d'''''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ d''''''' >= 1 ] (1, 8) f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ d'''''' >= 1 ] (1, 7) f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ d''''' >= 1 ] (1, 6) f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ d'''' >= 1 ] (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f9(d'''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 ] with all transitions in problem 16, the following new transitions are obtained: f0(a, b, c) -> f6(d'''''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 /\ 0 >= d''''''''''''' + 1 ] f0(a, b, c) -> f6(d'''''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 /\ d''''''''''''' >= 1 ] We thus obtain the following problem: 17: T: (1, 15) f0(a, b, c) -> f6(d'''''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 /\ 0 >= d''''''''''''' + 1 ] (1, 15) f0(a, b, c) -> f6(d'''''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 /\ d''''''''''''' >= 1 ] (1, 14) f0(a, b, c) -> f9(d'''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ d'''''''''''' >= 1 ] (1, 13) f0(a, b, c) -> f6(d'''''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ d''''''''''' >= 1 ] (1, 12) f0(a, b, c) -> f9(d'''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ d'''''''''' >= 1 ] (1, 11) f0(a, b, c) -> f6(d'''''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ d''''''''' >= 1 ] (1, 10) f0(a, b, c) -> f9(d'''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ d'''''''' >= 1 ] (1, 9) f0(a, b, c) -> f6(d'''''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ d''''''' >= 1 ] (1, 8) f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ d'''''' >= 1 ] (1, 7) f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ d''''' >= 1 ] (1, 6) f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ d'''' >= 1 ] (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 By chaining the transition f0(a, b, c) -> f6(d'''''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 /\ 0 >= d''''''''''''' + 1 ] with all transitions in problem 17, the following new transitions are obtained: f0(a, b, c) -> f9(d'''''''''''''', d''''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 /\ 0 >= d''''''''''''' + 1 /\ 0 >= d'''''''''''''' + 1 ] f0(a, b, c) -> f9(d'''''''''''''', d''''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 /\ 0 >= d''''''''''''' + 1 /\ d'''''''''''''' >= 1 ] We thus obtain the following problem: 18: T: (1, 16) f0(a, b, c) -> f9(d'''''''''''''', d''''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 /\ 0 >= d''''''''''''' + 1 /\ 0 >= d'''''''''''''' + 1 ] (1, 16) f0(a, b, c) -> f9(d'''''''''''''', d''''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 /\ 0 >= d''''''''''''' + 1 /\ d'''''''''''''' >= 1 ] (1, 15) f0(a, b, c) -> f6(d'''''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ 0 >= d'''''''''''' + 1 /\ d''''''''''''' >= 1 ] (1, 14) f0(a, b, c) -> f9(d'''''''''''', d''''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ 0 >= d''''''''''' + 1 /\ d'''''''''''' >= 1 ] (1, 13) f0(a, b, c) -> f6(d'''''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ 0 >= d'''''''''' + 1 /\ d''''''''''' >= 1 ] (1, 12) f0(a, b, c) -> f9(d'''''''''', d''''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ 0 >= d''''''''' + 1 /\ d'''''''''' >= 1 ] (1, 11) f0(a, b, c) -> f6(d'''''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ 0 >= d'''''''' + 1 /\ d''''''''' >= 1 ] (1, 10) f0(a, b, c) -> f9(d'''''''', d''''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ 0 >= d''''''' + 1 /\ d'''''''' >= 1 ] (1, 9) f0(a, b, c) -> f6(d'''''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ 0 >= d'''''' + 1 /\ d''''''' >= 1 ] (1, 8) f0(a, b, c) -> f9(d'''''', d''''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ 0 >= d''''' + 1 /\ d'''''' >= 1 ] (1, 7) f0(a, b, c) -> f6(d'''''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ 0 >= d'''' + 1 /\ d''''' >= 1 ] (1, 6) f0(a, b, c) -> f9(d'''', d''''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ 0 >= d''' + 1 /\ d'''' >= 1 ] (1, 5) f0(a, b, c) -> f6(d'''', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ 0 >= d'' + 1 /\ d''' >= 1 ] (1, 4) f0(a, b, c) -> f9(d'', d''', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ 0 >= d' + 1 /\ d'' >= 1 ] (1, 3) f0(a, b, c) -> f6(d'', d', 0) [ 0 >= 0 /\ 0 >= d + 1 /\ d' >= 1 ] (1, 2) f0(a, b, c) -> f9(d, d', 0) [ 0 >= 0 /\ d >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ b >= 1 ] (?, 1) f9(a, b, c) -> f6(d, b, c) [ -c >= 0 /\ c >= 0 /\ 0 >= b + 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ a >= 1 ] (?, 1) f6(a, b, c) -> f9(a, d, c) [ -c >= 0 /\ c >= 0 /\ 0 >= a + 1 ] start location: f0 leaf cost: 5 Complexity upper bound ? Time: 1.603 sec (SMT: 1.416 sec)