YES(?, 49927*b + 5038821) Initial complexity problem: 1: T: (1, 1) eval0(a, b, c, d) -> eval1(b, b, 1, d) (?, 1) eval1(a, b, c, d) -> end(a, b, c, d) [ a >= 101 ] (?, 1) eval1(a, b, c, d) -> eval3(a, b, c, d) [ 100 >= a ] (?, 1) eval3(a, b, c, d) -> eval3(a + 11, b, c + 1, d) [ 100 >= a ] (?, 1) eval3(a, b, c, d) -> eval5(a, b, c, d) [ a >= 101 ] (?, 1) eval5(a, b, c, d) -> eval7(a - 10, b, c - 1, d) [ c >= 2 ] (?, 1) eval7(a, b, c, d) -> eval5(a, b, c, a - 10) [ a >= 101 /\ c = 1 ] (?, 1) eval7(a, b, c, d) -> eval9(a, b, c, d) [ 100 >= a ] (?, 1) eval7(a, b, c, d) -> eval9(a, b, c, d) [ 2 >= c ] (?, 1) eval7(a, b, c, d) -> eval9(a, b, c, d) [ c >= 0 ] (?, 1) eval9(a, b, c, d) -> eval11(a - 10, b, c - 1, d) [ a >= 101 ] (?, 1) eval9(a, b, c, d) -> eval11(a, b, c, d) [ 100 >= a ] (?, 1) eval11(a, b, c, d) -> eval5(a + 11, b, c + 1, d) start location: eval0 leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [a, b, c]. We thus obtain the following problem: 2: T: (?, 1) eval11(a, b, c) -> eval5(a + 11, b, c + 1) (?, 1) eval9(a, b, c) -> eval11(a, b, c) [ 100 >= a ] (?, 1) eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ a >= 101 ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ c >= 0 ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ 2 >= c ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ 100 >= a ] (?, 1) eval7(a, b, c) -> eval5(a, b, c) [ a >= 101 /\ c = 1 ] (?, 1) eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c >= 2 ] (?, 1) eval3(a, b, c) -> eval5(a, b, c) [ a >= 101 ] (?, 1) eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ 100 >= a ] (?, 1) eval1(a, b, c) -> eval3(a, b, c) [ 100 >= a ] (?, 1) eval1(a, b, c) -> end(a, b, c) [ a >= 101 ] (1, 1) eval0(a, b, c) -> eval1(b, b, 1) start location: eval0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem: 3: T: (?, 1) eval11(a, b, c) -> eval5(a + 11, b, c + 1) (?, 1) eval9(a, b, c) -> eval11(a, b, c) [ 100 >= a ] (?, 1) eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ a >= 101 ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ c >= 0 ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ 2 >= c ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ 100 >= a ] (?, 1) eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c >= 2 ] (?, 1) eval3(a, b, c) -> eval5(a, b, c) [ a >= 101 ] (?, 1) eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ 100 >= a ] (?, 1) eval1(a, b, c) -> eval3(a, b, c) [ 100 >= a ] (1, 1) eval0(a, b, c) -> eval1(b, b, 1) start location: eval0 leaf cost: 2 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (?, 1) eval11(a, b, c) -> eval5(a + 11, b, c + 1) (?, 1) eval9(a, b, c) -> eval11(a, b, c) [ 100 >= a ] (?, 1) eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ a >= 101 ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ c >= 0 ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ 2 >= c ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ 100 >= a ] (?, 1) eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c >= 2 ] (?, 1) eval3(a, b, c) -> eval5(a, b, c) [ a >= 101 ] (?, 1) eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ 100 >= a ] (1, 1) eval1(a, b, c) -> eval3(a, b, c) [ 100 >= a ] (1, 1) eval0(a, b, c) -> eval1(b, b, 1) start location: eval0 leaf cost: 2 A polynomial rank function with Pol(eval11) = -101 Pol(eval5) = -101 Pol(eval9) = -101 Pol(eval7) = -101 Pol(eval3) = 100 Pol(eval1) = 100 Pol(eval0) = 100 orients all transitions weakly and the transition eval3(a, b, c) -> eval5(a, b, c) [ a >= 101 ] strictly and produces the following problem: 5: T: (?, 1) eval11(a, b, c) -> eval5(a + 11, b, c + 1) (?, 1) eval9(a, b, c) -> eval11(a, b, c) [ 100 >= a ] (?, 1) eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ a >= 101 ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ c >= 0 ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ 2 >= c ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ 100 >= a ] (?, 1) eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c >= 2 ] (100, 1) eval3(a, b, c) -> eval5(a, b, c) [ a >= 101 ] (?, 1) eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ 100 >= a ] (1, 1) eval1(a, b, c) -> eval3(a, b, c) [ 100 >= a ] (1, 1) eval0(a, b, c) -> eval1(b, b, 1) start location: eval0 leaf cost: 2 A polynomial rank function with Pol(eval9) = V_2 Pol(eval11) = V_2 Pol(eval7) = V_2 Pol(eval5) = V_2 Pol(eval3) = -V_1 + 101 and size complexities S("eval0(a, b, c) -> eval1(b, b, 1)", 0-0) = b S("eval0(a, b, c) -> eval1(b, b, 1)", 0-1) = b S("eval0(a, b, c) -> eval1(b, b, 1)", 0-2) = 1 S("eval1(a, b, c) -> eval3(a, b, c) [ 100 >= a ]", 0-0) = b S("eval1(a, b, c) -> eval3(a, b, c) [ 100 >= a ]", 0-1) = b S("eval1(a, b, c) -> eval3(a, b, c) [ 100 >= a ]", 0-2) = 1 S("eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ 100 >= a ]", 0-0) = b + 111 S("eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ 100 >= a ]", 0-1) = b S("eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ 100 >= a ]", 0-2) = ? S("eval3(a, b, c) -> eval5(a, b, c) [ a >= 101 ]", 0-0) = b + 111 S("eval3(a, b, c) -> eval5(a, b, c) [ a >= 101 ]", 0-1) = b S("eval3(a, b, c) -> eval5(a, b, c) [ a >= 101 ]", 0-2) = ? S("eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c >= 2 ]", 0-0) = ? S("eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c >= 2 ]", 0-1) = b S("eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c >= 2 ]", 0-2) = ? S("eval7(a, b, c) -> eval9(a, b, c) [ 100 >= a ]", 0-0) = ? S("eval7(a, b, c) -> eval9(a, b, c) [ 100 >= a ]", 0-1) = b S("eval7(a, b, c) -> eval9(a, b, c) [ 100 >= a ]", 0-2) = ? S("eval7(a, b, c) -> eval9(a, b, c) [ 2 >= c ]", 0-0) = ? S("eval7(a, b, c) -> eval9(a, b, c) [ 2 >= c ]", 0-1) = b S("eval7(a, b, c) -> eval9(a, b, c) [ 2 >= c ]", 0-2) = ? S("eval7(a, b, c) -> eval9(a, b, c) [ c >= 0 ]", 0-0) = ? S("eval7(a, b, c) -> eval9(a, b, c) [ c >= 0 ]", 0-1) = b S("eval7(a, b, c) -> eval9(a, b, c) [ c >= 0 ]", 0-2) = ? S("eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ a >= 101 ]", 0-0) = ? S("eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ a >= 101 ]", 0-1) = b S("eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ a >= 101 ]", 0-2) = ? S("eval9(a, b, c) -> eval11(a, b, c) [ 100 >= a ]", 0-0) = ? S("eval9(a, b, c) -> eval11(a, b, c) [ 100 >= a ]", 0-1) = b S("eval9(a, b, c) -> eval11(a, b, c) [ 100 >= a ]", 0-2) = ? S("eval11(a, b, c) -> eval5(a + 11, b, c + 1)", 0-0) = ? S("eval11(a, b, c) -> eval5(a + 11, b, c + 1)", 0-1) = b S("eval11(a, b, c) -> eval5(a + 11, b, c + 1)", 0-2) = ? orients the transitions eval9(a, b, c) -> eval11(a, b, c) [ 100 >= a ] eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ a >= 101 ] eval7(a, b, c) -> eval9(a, b, c) [ 100 >= a ] eval7(a, b, c) -> eval9(a, b, c) [ 2 >= c ] eval7(a, b, c) -> eval9(a, b, c) [ c >= 0 ] eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c >= 2 ] eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ 100 >= a ] eval11(a, b, c) -> eval5(a + 11, b, c + 1) weakly and the transition eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ 100 >= a ] strictly and produces the following problem: 6: T: (?, 1) eval11(a, b, c) -> eval5(a + 11, b, c + 1) (?, 1) eval9(a, b, c) -> eval11(a, b, c) [ 100 >= a ] (?, 1) eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ a >= 101 ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ c >= 0 ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ 2 >= c ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ 100 >= a ] (?, 1) eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c >= 2 ] (100, 1) eval3(a, b, c) -> eval5(a, b, c) [ a >= 101 ] (101*b + 101, 1) eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ 100 >= a ] (1, 1) eval1(a, b, c) -> eval3(a, b, c) [ 100 >= a ] (1, 1) eval0(a, b, c) -> eval1(b, b, 1) start location: eval0 leaf cost: 2 Applied AI with 'oct' on problem 6 to obtain the following invariants: For symbol eval1: -X_3 + 1 >= 0 /\ X_3 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 + X_2 >= 0 For symbol eval11: X_3 >= 0 /\ -X_2 + X_3 + 100 >= 0 /\ X_1 + X_3 - 91 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 + 9 >= 0 /\ X_1 - 91 >= 0 For symbol eval3: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 >= 0 For symbol eval5: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ X_1 + X_3 - 102 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_1 - 101 >= 0 For symbol eval7: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ X_1 + X_3 - 92 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 + 9 >= 0 /\ X_1 - 91 >= 0 For symbol eval9: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ X_1 + X_3 - 92 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 + 9 >= 0 /\ X_1 - 91 >= 0 This yielded the following problem: 7: T: (1, 1) eval0(a, b, c) -> eval1(b, b, 1) (1, 1) eval1(a, b, c) -> eval3(a, b, c) [ -c + 1 >= 0 /\ c - 1 >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ 100 >= a ] (101*b + 101, 1) eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ -b + 100 >= 0 /\ a - b >= 0 /\ 100 >= a ] (100, 1) eval3(a, b, c) -> eval5(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ -b + 100 >= 0 /\ a - b >= 0 /\ a >= 101 ] (?, 1) eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 102 >= 0 /\ -b + 100 >= 0 /\ a - b - 1 >= 0 /\ a - 101 >= 0 /\ c >= 2 ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 100 >= a ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 2 >= c ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ c >= 0 ] (?, 1) eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ a >= 101 ] (?, 1) eval9(a, b, c) -> eval11(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 100 >= a ] (?, 1) eval11(a, b, c) -> eval5(a + 11, b, c + 1) [ c >= 0 /\ -b + c + 100 >= 0 /\ a + c - 91 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 ] start location: eval0 leaf cost: 2 A polynomial rank function with Pol(eval0) = -132*V_2 + 13072 Pol(eval1) = -132*V_1 + 1452*V_3 + 11620 Pol(eval3) = -132*V_1 + 1452*V_3 + 11620 Pol(eval5) = -132*V_1 + 1452*V_3 + 11620 Pol(eval7) = -132*V_1 + 1452*V_3 + 11751 Pol(eval9) = -132*V_1 + 1452*V_3 + 11622 Pol(eval11) = -132*V_1 + 1452*V_3 + 11621 orients all transitions weakly and the transition eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 100 >= a ] strictly and produces the following problem: 8: T: (1, 1) eval0(a, b, c) -> eval1(b, b, 1) (1, 1) eval1(a, b, c) -> eval3(a, b, c) [ -c + 1 >= 0 /\ c - 1 >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ 100 >= a ] (101*b + 101, 1) eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ -b + 100 >= 0 /\ a - b >= 0 /\ 100 >= a ] (100, 1) eval3(a, b, c) -> eval5(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ -b + 100 >= 0 /\ a - b >= 0 /\ a >= 101 ] (?, 1) eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 102 >= 0 /\ -b + 100 >= 0 /\ a - b - 1 >= 0 /\ a - 101 >= 0 /\ c >= 2 ] (132*b + 13072, 1) eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 100 >= a ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 2 >= c ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ c >= 0 ] (?, 1) eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ a >= 101 ] (?, 1) eval9(a, b, c) -> eval11(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 100 >= a ] (?, 1) eval11(a, b, c) -> eval5(a + 11, b, c + 1) [ c >= 0 /\ -b + c + 100 >= 0 /\ a + c - 91 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 ] start location: eval0 leaf cost: 2 A polynomial rank function with Pol(eval0) = -54*V_2 + 5404 Pol(eval1) = -5*V_1 - 49*V_2 + 50*V_3 + 5354 Pol(eval3) = -5*V_1 - 49*V_2 + 50*V_3 + 5354 Pol(eval5) = -5*V_1 - 49*V_2 + 50*V_3 + 5354 Pol(eval7) = -5*V_1 - 49*V_2 + 50*V_3 + 5352 Pol(eval9) = -5*V_1 - 49*V_2 + 50*V_3 + 5351 Pol(eval11) = -5*V_1 - 49*V_2 + 50*V_3 + 5350 orients all transitions weakly and the transition eval9(a, b, c) -> eval11(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 100 >= a ] strictly and produces the following problem: 9: T: (1, 1) eval0(a, b, c) -> eval1(b, b, 1) (1, 1) eval1(a, b, c) -> eval3(a, b, c) [ -c + 1 >= 0 /\ c - 1 >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ 100 >= a ] (101*b + 101, 1) eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ -b + 100 >= 0 /\ a - b >= 0 /\ 100 >= a ] (100, 1) eval3(a, b, c) -> eval5(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ -b + 100 >= 0 /\ a - b >= 0 /\ a >= 101 ] (?, 1) eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 102 >= 0 /\ -b + 100 >= 0 /\ a - b - 1 >= 0 /\ a - 101 >= 0 /\ c >= 2 ] (132*b + 13072, 1) eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 100 >= a ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 2 >= c ] (?, 1) eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ c >= 0 ] (?, 1) eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ a >= 101 ] (54*b + 5404, 1) eval9(a, b, c) -> eval11(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 100 >= a ] (?, 1) eval11(a, b, c) -> eval5(a + 11, b, c + 1) [ c >= 0 /\ -b + c + 100 >= 0 /\ a + c - 91 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 ] start location: eval0 leaf cost: 2 A polynomial rank function with Pol(eval9) = V_1 - 91 Pol(eval11) = V_1 - 82 Pol(eval7) = V_1 - 90 Pol(eval5) = V_1 - 94 and size complexities S("eval11(a, b, c) -> eval5(a + 11, b, c + 1) [ c >= 0 /\\ -b + c + 100 >= 0 /\\ a + c - 91 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 ]", 0-0) = ? S("eval11(a, b, c) -> eval5(a + 11, b, c + 1) [ c >= 0 /\\ -b + c + 100 >= 0 /\\ a + c - 91 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 ]", 0-1) = b S("eval11(a, b, c) -> eval5(a + 11, b, c + 1) [ c >= 0 /\\ -b + c + 100 >= 0 /\\ a + c - 91 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 ]", 0-2) = ? S("eval9(a, b, c) -> eval11(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ 100 >= a ]", 0-0) = 100 S("eval9(a, b, c) -> eval11(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ 100 >= a ]", 0-1) = b S("eval9(a, b, c) -> eval11(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ 100 >= a ]", 0-2) = ? S("eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ a >= 101 ]", 0-0) = ? S("eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ a >= 101 ]", 0-1) = b S("eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ a >= 101 ]", 0-2) = ? S("eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ c >= 0 ]", 0-0) = ? S("eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ c >= 0 ]", 0-1) = b S("eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ c >= 0 ]", 0-2) = ? S("eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ 2 >= c ]", 0-0) = ? S("eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ 2 >= c ]", 0-1) = b S("eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ 2 >= c ]", 0-2) = 2 S("eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ 100 >= a ]", 0-0) = 100 S("eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ 100 >= a ]", 0-1) = b S("eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 92 >= 0 /\\ -b + 100 >= 0 /\\ a - b + 9 >= 0 /\\ a - 91 >= 0 /\\ 100 >= a ]", 0-2) = ? S("eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 102 >= 0 /\\ -b + 100 >= 0 /\\ a - b - 1 >= 0 /\\ a - 101 >= 0 /\\ c >= 2 ]", 0-0) = ? S("eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 102 >= 0 /\\ -b + 100 >= 0 /\\ a - b - 1 >= 0 /\\ a - 101 >= 0 /\\ c >= 2 ]", 0-1) = b S("eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ a + c - 102 >= 0 /\\ -b + 100 >= 0 /\\ a - b - 1 >= 0 /\\ a - 101 >= 0 /\\ c >= 2 ]", 0-2) = ? S("eval3(a, b, c) -> eval5(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ -b + 100 >= 0 /\\ a - b >= 0 /\\ a >= 101 ]", 0-0) = b + 111 S("eval3(a, b, c) -> eval5(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ -b + 100 >= 0 /\\ a - b >= 0 /\\ a >= 101 ]", 0-1) = b S("eval3(a, b, c) -> eval5(a, b, c) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ -b + 100 >= 0 /\\ a - b >= 0 /\\ a >= 101 ]", 0-2) = 101*b + 105090702 S("eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ -b + 100 >= 0 /\\ a - b >= 0 /\\ 100 >= a ]", 0-0) = b + 111 S("eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ -b + 100 >= 0 /\\ a - b >= 0 /\\ 100 >= a ]", 0-1) = b S("eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ c - 1 >= 0 /\\ -b + c + 99 >= 0 /\\ -b + 100 >= 0 /\\ a - b >= 0 /\\ 100 >= a ]", 0-2) = 101*b + 1040502 S("eval1(a, b, c) -> eval3(a, b, c) [ -c + 1 >= 0 /\\ c - 1 >= 0 /\\ a - b >= 0 /\\ -a + b >= 0 /\\ 100 >= a ]", 0-0) = b S("eval1(a, b, c) -> eval3(a, b, c) [ -c + 1 >= 0 /\\ c - 1 >= 0 /\\ a - b >= 0 /\\ -a + b >= 0 /\\ 100 >= a ]", 0-1) = b S("eval1(a, b, c) -> eval3(a, b, c) [ -c + 1 >= 0 /\\ c - 1 >= 0 /\\ a - b >= 0 /\\ -a + b >= 0 /\\ 100 >= a ]", 0-2) = 1 S("eval0(a, b, c) -> eval1(b, b, 1)", 0-0) = b S("eval0(a, b, c) -> eval1(b, b, 1)", 0-1) = b S("eval0(a, b, c) -> eval1(b, b, 1)", 0-2) = 1 orients the transitions eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ a >= 101 ] eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 2 >= c ] eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ c >= 0 ] eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 102 >= 0 /\ -b + 100 >= 0 /\ a - b - 1 >= 0 /\ a - 101 >= 0 /\ c >= 2 ] eval11(a, b, c) -> eval5(a + 11, b, c + 1) [ c >= 0 /\ -b + c + 100 >= 0 /\ a + c - 91 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 ] weakly and the transitions eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ a >= 101 ] eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 2 >= c ] eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ c >= 0 ] eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 102 >= 0 /\ -b + 100 >= 0 /\ a - b - 1 >= 0 /\ a - 101 >= 0 /\ c >= 2 ] eval11(a, b, c) -> eval5(a + 11, b, c + 1) [ c >= 0 /\ -b + c + 100 >= 0 /\ a + c - 91 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 ] strictly and produces the following problem: 10: T: (1, 1) eval0(a, b, c) -> eval1(b, b, 1) (1, 1) eval1(a, b, c) -> eval3(a, b, c) [ -c + 1 >= 0 /\ c - 1 >= 0 /\ a - b >= 0 /\ -a + b >= 0 /\ 100 >= a ] (101*b + 101, 1) eval3(a, b, c) -> eval3(a + 11, b, c + 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ -b + 100 >= 0 /\ a - b >= 0 /\ 100 >= a ] (100, 1) eval3(a, b, c) -> eval5(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ -b + 100 >= 0 /\ a - b >= 0 /\ a >= 101 ] (9928*b + 1004028, 1) eval5(a, b, c) -> eval7(a - 10, b, c - 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 102 >= 0 /\ -b + 100 >= 0 /\ a - b - 1 >= 0 /\ a - 101 >= 0 /\ c >= 2 ] (132*b + 13072, 1) eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 100 >= a ] (9928*b + 1004028, 1) eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 2 >= c ] (9928*b + 1004028, 1) eval7(a, b, c) -> eval9(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ c >= 0 ] (9928*b + 1004028, 1) eval9(a, b, c) -> eval11(a - 10, b, c - 1) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ a >= 101 ] (54*b + 5404, 1) eval9(a, b, c) -> eval11(a, b, c) [ c - 1 >= 0 /\ -b + c + 99 >= 0 /\ a + c - 92 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 /\ 100 >= a ] (9928*b + 1004028, 1) eval11(a, b, c) -> eval5(a + 11, b, c + 1) [ c >= 0 /\ -b + c + 100 >= 0 /\ a + c - 91 >= 0 /\ -b + 100 >= 0 /\ a - b + 9 >= 0 /\ a - 91 >= 0 ] start location: eval0 leaf cost: 2 Complexity upper bound 49927*b + 5038821 Time: 1.045 sec (SMT: 0.984 sec)