MAYBE Initial complexity problem: 1: T: (1, 1) f0(a) -> f1(100) (?, 1) f1(a) -> f1(a - 1) [ a >= 302 ] (?, 1) f1(a) -> f1(a - 1) [ 300 >= a ] start location: f0 leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 1: f1(a) -> f1(a - 1) [ a >= 302 ] We thus obtain the following problem: 2: T: (?, 1) f1(a) -> f1(a - 1) [ 300 >= a ] (1, 1) f0(a) -> f1(100) start location: f0 leaf cost: 0 Applied AI with 'oct' on problem 2 to obtain the following invariants: For symbol f1: -X_1 + 100 >= 0 This yielded the following problem: 3: T: (1, 1) f0(a) -> f1(100) (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(100) with all transitions in problem 3, the following new transition is obtained: f0(a) -> f1(99) [ 0 >= 0 /\ 300 >= 100 ] We thus obtain the following problem: 4: T: (1, 2) f0(a) -> f1(99) [ 0 >= 0 /\ 300 >= 100 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(99) [ 0 >= 0 /\ 300 >= 100 ] with all transitions in problem 4, the following new transition is obtained: f0(a) -> f1(98) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 ] We thus obtain the following problem: 5: T: (1, 3) f0(a) -> f1(98) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(98) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 ] with all transitions in problem 5, the following new transition is obtained: f0(a) -> f1(97) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 ] We thus obtain the following problem: 6: T: (1, 4) f0(a) -> f1(97) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(97) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 ] with all transitions in problem 6, the following new transition is obtained: f0(a) -> f1(96) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 ] We thus obtain the following problem: 7: T: (1, 5) f0(a) -> f1(96) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(96) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 ] with all transitions in problem 7, the following new transition is obtained: f0(a) -> f1(95) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 ] We thus obtain the following problem: 8: T: (1, 6) f0(a) -> f1(95) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(95) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 ] with all transitions in problem 8, the following new transition is obtained: f0(a) -> f1(94) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 ] We thus obtain the following problem: 9: T: (1, 7) f0(a) -> f1(94) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(94) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 ] with all transitions in problem 9, the following new transition is obtained: f0(a) -> f1(93) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 ] We thus obtain the following problem: 10: T: (1, 8) f0(a) -> f1(93) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(93) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 ] with all transitions in problem 10, the following new transition is obtained: f0(a) -> f1(92) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 ] We thus obtain the following problem: 11: T: (1, 9) f0(a) -> f1(92) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(92) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 ] with all transitions in problem 11, the following new transition is obtained: f0(a) -> f1(91) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 ] We thus obtain the following problem: 12: T: (1, 10) f0(a) -> f1(91) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(91) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 ] with all transitions in problem 12, the following new transition is obtained: f0(a) -> f1(90) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 ] We thus obtain the following problem: 13: T: (1, 11) f0(a) -> f1(90) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(90) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 ] with all transitions in problem 13, the following new transition is obtained: f0(a) -> f1(89) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 ] We thus obtain the following problem: 14: T: (1, 12) f0(a) -> f1(89) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(89) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 ] with all transitions in problem 14, the following new transition is obtained: f0(a) -> f1(88) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 /\ 11 >= 0 /\ 300 >= 89 ] We thus obtain the following problem: 15: T: (1, 13) f0(a) -> f1(88) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 /\ 11 >= 0 /\ 300 >= 89 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(88) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 /\ 11 >= 0 /\ 300 >= 89 ] with all transitions in problem 15, the following new transition is obtained: f0(a) -> f1(87) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 /\ 11 >= 0 /\ 300 >= 89 /\ 12 >= 0 /\ 300 >= 88 ] We thus obtain the following problem: 16: T: (1, 14) f0(a) -> f1(87) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 /\ 11 >= 0 /\ 300 >= 89 /\ 12 >= 0 /\ 300 >= 88 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(87) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 /\ 11 >= 0 /\ 300 >= 89 /\ 12 >= 0 /\ 300 >= 88 ] with all transitions in problem 16, the following new transition is obtained: f0(a) -> f1(86) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 /\ 11 >= 0 /\ 300 >= 89 /\ 12 >= 0 /\ 300 >= 88 /\ 13 >= 0 /\ 300 >= 87 ] We thus obtain the following problem: 17: T: (1, 15) f0(a) -> f1(86) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 /\ 11 >= 0 /\ 300 >= 89 /\ 12 >= 0 /\ 300 >= 88 /\ 13 >= 0 /\ 300 >= 87 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 By chaining the transition f0(a) -> f1(86) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 /\ 11 >= 0 /\ 300 >= 89 /\ 12 >= 0 /\ 300 >= 88 /\ 13 >= 0 /\ 300 >= 87 ] with all transitions in problem 17, the following new transition is obtained: f0(a) -> f1(85) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 /\ 11 >= 0 /\ 300 >= 89 /\ 12 >= 0 /\ 300 >= 88 /\ 13 >= 0 /\ 300 >= 87 /\ 14 >= 0 /\ 300 >= 86 ] We thus obtain the following problem: 18: T: (1, 16) f0(a) -> f1(85) [ 0 >= 0 /\ 300 >= 100 /\ 1 >= 0 /\ 300 >= 99 /\ 2 >= 0 /\ 300 >= 98 /\ 3 >= 0 /\ 300 >= 97 /\ 4 >= 0 /\ 300 >= 96 /\ 5 >= 0 /\ 300 >= 95 /\ 6 >= 0 /\ 300 >= 94 /\ 7 >= 0 /\ 300 >= 93 /\ 8 >= 0 /\ 300 >= 92 /\ 9 >= 0 /\ 300 >= 91 /\ 10 >= 0 /\ 300 >= 90 /\ 11 >= 0 /\ 300 >= 89 /\ 12 >= 0 /\ 300 >= 88 /\ 13 >= 0 /\ 300 >= 87 /\ 14 >= 0 /\ 300 >= 86 ] (?, 1) f1(a) -> f1(a - 1) [ -a + 100 >= 0 /\ 300 >= a ] start location: f0 leaf cost: 0 Complexity upper bound ? Time: 0.582 sec (SMT: 0.534 sec)