YES(?, 27608*a + 135*a^2 + 1410294) Initial complexity problem: 1: T: (1, 1) evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d) (?, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91returnin(a, b, c, d) [ a >= 101 ] (?, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ] (?, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ] (?, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ] (?, 1) evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) (?, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ] (?, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91returnin(a, b, c, d) [ 1 >= a ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 1 >= a ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb11in(a - 1, b - 10, c, d) [ b >= 111 /\ a = 2 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 11, c, d) [ c >= 101 /\ 100 >= c ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 1, c, d) [ 100 >= c /\ c >= 101 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ] (?, 1) evalsipma91returnin(a, b, c, d) -> evalsipma91stop(a, b, c, d) start location: evalsipma91start leaf cost: 0 Testing for unsatisfiable constraints removes the following transitions from problem 1: evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 11, c, d) [ c >= 101 /\ 100 >= c ] evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 1, c, d) [ 100 >= c /\ c >= 101 ] We thus obtain the following problem: 2: T: (1, 1) evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d) (?, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91returnin(a, b, c, d) [ a >= 101 ] (?, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ] (?, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ] (?, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ] (?, 1) evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) (?, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ] (?, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91returnin(a, b, c, d) [ 1 >= a ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 1 >= a ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb11in(a - 1, b - 10, c, d) [ b >= 111 /\ a = 2 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ] (?, 1) evalsipma91returnin(a, b, c, d) -> evalsipma91stop(a, b, c, d) start location: evalsipma91start leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem: 3: T: (1, 1) evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d) (?, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ] (?, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ] (?, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ] (?, 1) evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) (?, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 1 >= a ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ] start location: evalsipma91start leaf cost: 4 Testing for reachability in the complexity graph removes the following transition from problem 3: evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 1 >= a ] We thus obtain the following problem: 4: T: (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ] (?, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ] (?, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ] (?, 1) evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) (?, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ] (?, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ] (1, 1) evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d) start location: evalsipma91start leaf cost: 4 Repeatedly propagating knowledge in problem 4 produces the following problem: 5: T: (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ] (?, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ] (?, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ] (?, 1) evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) (?, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ] (1, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ] (1, 1) evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d) start location: evalsipma91start leaf cost: 4 A polynomial rank function with Pol(evalsipma91bb8in) = -101 Pol(evalsipma91bb11in) = -101 Pol(evalsipma91bb5in) = -101 Pol(evalsipma91bb3in) = 1 Pol(evalsipma91bb2in) = 1 Pol(evalsipma91entryin) = 1 Pol(evalsipma91start) = 1 orients all transitions weakly and the transition evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ] strictly and produces the following problem: 6: T: (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ] (?, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ] (1, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ] (?, 1) evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) (?, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ] (1, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ] (1, 1) evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d) start location: evalsipma91start leaf cost: 4 A polynomial rank function with Pol(evalsipma91bb8in) = 2 Pol(evalsipma91bb11in) = 2 Pol(evalsipma91bb5in) = 2 Pol(evalsipma91bb3in) = -V_2 + 101 Pol(evalsipma91bb2in) = -V_2 + 91 and size complexities S("evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d)", 0-0) = a S("evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d)", 0-1) = b S("evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d)", 0-2) = c S("evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d)", 0-3) = d S("evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ]", 0-0) = 1 S("evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ]", 0-1) = a S("evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ]", 0-2) = c S("evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ]", 0-3) = d S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ]", 0-0) = ? S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ]", 0-1) = ? S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ]", 0-2) = c S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ]", 0-3) = d S("evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d)", 0-0) = ? S("evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d)", 0-1) = ? S("evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d)", 0-2) = c S("evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d)", 0-3) = d S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ]", 0-0) = ? S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ]", 0-1) = ? S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ]", 0-2) = c S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ]", 0-3) = d S("evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ]", 0-0) = ? S("evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ]", 0-1) = ? S("evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ]", 0-2) = ? S("evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ]", 0-3) = ? S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ]", 0-0) = ? S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ]", 0-1) = ? S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ]", 0-2) = ? S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ]", 0-3) = ? S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ]", 0-0) = ? S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ]", 0-1) = ? S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ]", 0-2) = ? S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ]", 0-3) = ? S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ]", 0-0) = ? S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ]", 0-1) = ? S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ]", 0-2) = ? S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ]", 0-3) = ? S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ]", 0-0) = ? S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ]", 0-1) = ? S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ]", 0-2) = ? S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ]", 0-3) = ? orients the transitions evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ] evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ] evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ] evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ] evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ] evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ] weakly and the transition evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ] strictly and produces the following problem: 7: T: (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ] (?, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ] (1, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ] (?, 1) evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) (a + 103, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ] (1, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ] (1, 1) evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d) start location: evalsipma91start leaf cost: 4 Repeatedly propagating knowledge in problem 7 produces the following problem: 8: T: (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ c >= 101 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ 100 >= c ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ a >= 3 ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ 110 >= b ] (?, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ a >= 2 ] (1, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ b >= 101 ] (a + 103, 1) evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) (a + 103, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ 100 >= b ] (1, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ] (1, 1) evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d) start location: evalsipma91start leaf cost: 4 Applied AI with 'oct' on problem 8 to obtain the following invariants: For symbol evalsipma91bb11in: X_2 - 101 >= 0 /\ X_1 + X_2 - 102 >= 0 /\ X_1 - 1 >= 0 For symbol evalsipma91bb2in: -X_2 + 100 >= 0 /\ X_1 - X_2 + 99 >= 0 /\ X_1 - 1 >= 0 For symbol evalsipma91bb3in: X_1 - 1 >= 0 For symbol evalsipma91bb5in: X_2 - 101 >= 0 /\ X_1 + X_2 - 103 >= 0 /\ X_1 - 2 >= 0 For symbol evalsipma91bb8in: X_1 - X_4 - 1 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 92 >= 0 /\ X_2 + X_4 - 102 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 + 1 >= 0 /\ X_2 - X_3 - 10 >= 0 /\ X_3 - 91 >= 0 /\ X_2 + X_3 - 192 >= 0 /\ -X_2 + X_3 + 10 >= 0 /\ X_1 + X_3 - 93 >= 0 /\ X_2 - 101 >= 0 /\ X_1 + X_2 - 103 >= 0 /\ X_1 - 2 >= 0 This yielded the following problem: 9: T: (1, 1) evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d) (1, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ] (a + 103, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ a - 1 >= 0 /\ 100 >= b ] (a + 103, 1) evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) [ -b + 100 >= 0 /\ a - b + 99 >= 0 /\ a - 1 >= 0 ] (1, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ a - 1 >= 0 /\ b >= 101 ] (?, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ b - 101 >= 0 /\ a + b - 102 >= 0 /\ a - 1 >= 0 /\ a >= 2 ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ 110 >= b ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ a >= 3 ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ a - d - 1 >= 0 /\ d - 1 >= 0 /\ c + d - 92 >= 0 /\ b + d - 102 >= 0 /\ a + d - 3 >= 0 /\ -a + d + 1 >= 0 /\ b - c - 10 >= 0 /\ c - 91 >= 0 /\ b + c - 192 >= 0 /\ -b + c + 10 >= 0 /\ a + c - 93 >= 0 /\ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ 100 >= c ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ a - d - 1 >= 0 /\ d - 1 >= 0 /\ c + d - 92 >= 0 /\ b + d - 102 >= 0 /\ a + d - 3 >= 0 /\ -a + d + 1 >= 0 /\ b - c - 10 >= 0 /\ c - 91 >= 0 /\ b + c - 192 >= 0 /\ -b + c + 10 >= 0 /\ a + c - 93 >= 0 /\ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ c >= 101 ] start location: evalsipma91start leaf cost: 4 A polynomial rank function with Pol(evalsipma91start) = -15*V_1 + 1488 Pol(evalsipma91entryin) = -15*V_1 + 1488 Pol(evalsipma91bb3in) = 165*V_1 - 15*V_2 + 1323 Pol(evalsipma91bb2in) = 165*V_1 - 15*V_2 + 1323 Pol(evalsipma91bb11in) = 165*V_1 - 15*V_2 + 1323 Pol(evalsipma91bb5in) = 165*V_1 - 15*V_2 + 1322 Pol(evalsipma91bb8in) = -15*V_3 + 165*V_4 + 1336 orients all transitions weakly and the transitions evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ a - d - 1 >= 0 /\ d - 1 >= 0 /\ c + d - 92 >= 0 /\ b + d - 102 >= 0 /\ a + d - 3 >= 0 /\ -a + d + 1 >= 0 /\ b - c - 10 >= 0 /\ c - 91 >= 0 /\ b + c - 192 >= 0 /\ -b + c + 10 >= 0 /\ a + c - 93 >= 0 /\ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ 100 >= c ] evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ 110 >= b ] strictly and produces the following problem: 10: T: (1, 1) evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d) (1, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ] (a + 103, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ a - 1 >= 0 /\ 100 >= b ] (a + 103, 1) evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) [ -b + 100 >= 0 /\ a - b + 99 >= 0 /\ a - 1 >= 0 ] (1, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ a - 1 >= 0 /\ b >= 101 ] (?, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ b - 101 >= 0 /\ a + b - 102 >= 0 /\ a - 1 >= 0 /\ a >= 2 ] (15*a + 1488, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ 110 >= b ] (?, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ a >= 3 ] (15*a + 1488, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ a - d - 1 >= 0 /\ d - 1 >= 0 /\ c + d - 92 >= 0 /\ b + d - 102 >= 0 /\ a + d - 3 >= 0 /\ -a + d + 1 >= 0 /\ b - c - 10 >= 0 /\ c - 91 >= 0 /\ b + c - 192 >= 0 /\ -b + c + 10 >= 0 /\ a + c - 93 >= 0 /\ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ 100 >= c ] (?, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ a - d - 1 >= 0 /\ d - 1 >= 0 /\ c + d - 92 >= 0 /\ b + d - 102 >= 0 /\ a + d - 3 >= 0 /\ -a + d + 1 >= 0 /\ b - c - 10 >= 0 /\ c - 91 >= 0 /\ b + c - 192 >= 0 /\ -b + c + 10 >= 0 /\ a + c - 93 >= 0 /\ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ c >= 101 ] start location: evalsipma91start leaf cost: 4 A polynomial rank function with Pol(evalsipma91bb8in) = 3*V_4 - 2 Pol(evalsipma91bb11in) = 3*V_1 - 3 Pol(evalsipma91bb5in) = 3*V_1 - 4 and size complexities S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ a - d - 1 >= 0 /\\ d - 1 >= 0 /\\ c + d - 92 >= 0 /\\ b + d - 102 >= 0 /\\ a + d - 3 >= 0 /\\ -a + d + 1 >= 0 /\\ b - c - 10 >= 0 /\\ c - 91 >= 0 /\\ b + c - 192 >= 0 /\\ -b + c + 10 >= 0 /\\ a + c - 93 >= 0 /\\ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ c >= 101 ]", 0-0) = a + 104 S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ a - d - 1 >= 0 /\\ d - 1 >= 0 /\\ c + d - 92 >= 0 /\\ b + d - 102 >= 0 /\\ a + d - 3 >= 0 /\\ -a + d + 1 >= 0 /\\ b - c - 10 >= 0 /\\ c - 91 >= 0 /\\ b + c - 192 >= 0 /\\ -b + c + 10 >= 0 /\\ a + c - 93 >= 0 /\\ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ c >= 101 ]", 0-1) = a + 222 S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ a - d - 1 >= 0 /\\ d - 1 >= 0 /\\ c + d - 92 >= 0 /\\ b + d - 102 >= 0 /\\ a + d - 3 >= 0 /\\ -a + d + 1 >= 0 /\\ b - c - 10 >= 0 /\\ c - 91 >= 0 /\\ b + c - 192 >= 0 /\\ -b + c + 10 >= 0 /\\ a + c - 93 >= 0 /\\ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ c >= 101 ]", 0-2) = a + 222 S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ a - d - 1 >= 0 /\\ d - 1 >= 0 /\\ c + d - 92 >= 0 /\\ b + d - 102 >= 0 /\\ a + d - 3 >= 0 /\\ -a + d + 1 >= 0 /\\ b - c - 10 >= 0 /\\ c - 91 >= 0 /\\ b + c - 192 >= 0 /\\ -b + c + 10 >= 0 /\\ a + c - 93 >= 0 /\\ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ c >= 101 ]", 0-3) = a + 104 S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ a - d - 1 >= 0 /\\ d - 1 >= 0 /\\ c + d - 92 >= 0 /\\ b + d - 102 >= 0 /\\ a + d - 3 >= 0 /\\ -a + d + 1 >= 0 /\\ b - c - 10 >= 0 /\\ c - 91 >= 0 /\\ b + c - 192 >= 0 /\\ -b + c + 10 >= 0 /\\ a + c - 93 >= 0 /\\ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ 100 >= c ]", 0-0) = a + 104 S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ a - d - 1 >= 0 /\\ d - 1 >= 0 /\\ c + d - 92 >= 0 /\\ b + d - 102 >= 0 /\\ a + d - 3 >= 0 /\\ -a + d + 1 >= 0 /\\ b - c - 10 >= 0 /\\ c - 91 >= 0 /\\ b + c - 192 >= 0 /\\ -b + c + 10 >= 0 /\\ a + c - 93 >= 0 /\\ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ 100 >= c ]", 0-1) = 111 S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ a - d - 1 >= 0 /\\ d - 1 >= 0 /\\ c + d - 92 >= 0 /\\ b + d - 102 >= 0 /\\ a + d - 3 >= 0 /\\ -a + d + 1 >= 0 /\\ b - c - 10 >= 0 /\\ c - 91 >= 0 /\\ b + c - 192 >= 0 /\\ -b + c + 10 >= 0 /\\ a + c - 93 >= 0 /\\ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ 100 >= c ]", 0-2) = 100 S("evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ a - d - 1 >= 0 /\\ d - 1 >= 0 /\\ c + d - 92 >= 0 /\\ b + d - 102 >= 0 /\\ a + d - 3 >= 0 /\\ -a + d + 1 >= 0 /\\ b - c - 10 >= 0 /\\ c - 91 >= 0 /\\ b + c - 192 >= 0 /\\ -b + c + 10 >= 0 /\\ a + c - 93 >= 0 /\\ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ 100 >= c ]", 0-3) = a + 104 S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ a >= 3 ]", 0-0) = a + 104 S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ a >= 3 ]", 0-1) = a + 222 S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ a >= 3 ]", 0-2) = a + 222 S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ a >= 3 ]", 0-3) = a + 104 S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ 110 >= b ]", 0-0) = a + 104 S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ 110 >= b ]", 0-1) = 110 S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ 110 >= b ]", 0-2) = 100 S("evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\\ a + b - 103 >= 0 /\\ a - 2 >= 0 /\\ 110 >= b ]", 0-3) = a + 104 S("evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ b - 101 >= 0 /\\ a + b - 102 >= 0 /\\ a - 1 >= 0 /\\ a >= 2 ]", 0-0) = a + 104 S("evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ b - 101 >= 0 /\\ a + b - 102 >= 0 /\\ a - 1 >= 0 /\\ a >= 2 ]", 0-1) = a + 222 S("evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ b - 101 >= 0 /\\ a + b - 102 >= 0 /\\ a - 1 >= 0 /\\ a >= 2 ]", 0-2) = a + c + 322 S("evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ b - 101 >= 0 /\\ a + b - 102 >= 0 /\\ a - 1 >= 0 /\\ a >= 2 ]", 0-3) = a + d + 104 S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ a - 1 >= 0 /\\ b >= 101 ]", 0-0) = a + 104 S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ a - 1 >= 0 /\\ b >= 101 ]", 0-1) = a + 111 S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ a - 1 >= 0 /\\ b >= 101 ]", 0-2) = c S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ a - 1 >= 0 /\\ b >= 101 ]", 0-3) = d S("evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) [ -b + 100 >= 0 /\\ a - b + 99 >= 0 /\\ a - 1 >= 0 ]", 0-0) = a + 104 S("evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) [ -b + 100 >= 0 /\\ a - b + 99 >= 0 /\\ a - 1 >= 0 ]", 0-1) = a + 111 S("evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) [ -b + 100 >= 0 /\\ a - b + 99 >= 0 /\\ a - 1 >= 0 ]", 0-2) = c S("evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) [ -b + 100 >= 0 /\\ a - b + 99 >= 0 /\\ a - 1 >= 0 ]", 0-3) = d S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ a - 1 >= 0 /\\ 100 >= b ]", 0-0) = a + 104 S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ a - 1 >= 0 /\\ 100 >= b ]", 0-1) = a + 111 S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ a - 1 >= 0 /\\ 100 >= b ]", 0-2) = c S("evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ a - 1 >= 0 /\\ 100 >= b ]", 0-3) = d S("evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ]", 0-0) = 1 S("evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ]", 0-1) = a S("evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ]", 0-2) = c S("evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ]", 0-3) = d S("evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d)", 0-0) = a S("evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d)", 0-1) = b S("evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d)", 0-2) = c S("evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d)", 0-3) = d orients the transitions evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ a - d - 1 >= 0 /\ d - 1 >= 0 /\ c + d - 92 >= 0 /\ b + d - 102 >= 0 /\ a + d - 3 >= 0 /\ -a + d + 1 >= 0 /\ b - c - 10 >= 0 /\ c - 91 >= 0 /\ b + c - 192 >= 0 /\ -b + c + 10 >= 0 /\ a + c - 93 >= 0 /\ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ c >= 101 ] evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ a >= 3 ] evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ b - 101 >= 0 /\ a + b - 102 >= 0 /\ a - 1 >= 0 /\ a >= 2 ] weakly and the transitions evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ a - d - 1 >= 0 /\ d - 1 >= 0 /\ c + d - 92 >= 0 /\ b + d - 102 >= 0 /\ a + d - 3 >= 0 /\ -a + d + 1 >= 0 /\ b - c - 10 >= 0 /\ c - 91 >= 0 /\ b + c - 192 >= 0 /\ -b + c + 10 >= 0 /\ a + c - 93 >= 0 /\ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ c >= 101 ] evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ a >= 3 ] evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ b - 101 >= 0 /\ a + b - 102 >= 0 /\ a - 1 >= 0 /\ a >= 2 ] strictly and produces the following problem: 11: T: (1, 1) evalsipma91start(a, b, c, d) -> evalsipma91entryin(a, b, c, d) (1, 1) evalsipma91entryin(a, b, c, d) -> evalsipma91bb3in(1, a, c, d) [ 100 >= a ] (a + 103, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb2in(a, b, c, d) [ a - 1 >= 0 /\ 100 >= b ] (a + 103, 1) evalsipma91bb2in(a, b, c, d) -> evalsipma91bb3in(a + 1, b + 11, c, d) [ -b + 100 >= 0 /\ a - b + 99 >= 0 /\ a - 1 >= 0 ] (1, 1) evalsipma91bb3in(a, b, c, d) -> evalsipma91bb11in(a, b, c, d) [ a - 1 >= 0 /\ b >= 101 ] (45*a^2 + 9192*a + 469035, 1) evalsipma91bb11in(a, b, c, d) -> evalsipma91bb5in(a, b, c, d) [ b - 101 >= 0 /\ a + b - 102 >= 0 /\ a - 1 >= 0 /\ a >= 2 ] (15*a + 1488, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ 110 >= b ] (45*a^2 + 9192*a + 469035, 1) evalsipma91bb5in(a, b, c, d) -> evalsipma91bb8in(a, b, b - 10, a - 1) [ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ a >= 3 ] (15*a + 1488, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d + 1, c + 11, c, d) [ a - d - 1 >= 0 /\ d - 1 >= 0 /\ c + d - 92 >= 0 /\ b + d - 102 >= 0 /\ a + d - 3 >= 0 /\ -a + d + 1 >= 0 /\ b - c - 10 >= 0 /\ c - 91 >= 0 /\ b + c - 192 >= 0 /\ -b + c + 10 >= 0 /\ a + c - 93 >= 0 /\ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ 100 >= c ] (45*a^2 + 9192*a + 469035, 1) evalsipma91bb8in(a, b, c, d) -> evalsipma91bb11in(d, c + 1, c, d) [ a - d - 1 >= 0 /\ d - 1 >= 0 /\ c + d - 92 >= 0 /\ b + d - 102 >= 0 /\ a + d - 3 >= 0 /\ -a + d + 1 >= 0 /\ b - c - 10 >= 0 /\ c - 91 >= 0 /\ b + c - 192 >= 0 /\ -b + c + 10 >= 0 /\ a + c - 93 >= 0 /\ b - 101 >= 0 /\ a + b - 103 >= 0 /\ a - 2 >= 0 /\ c >= 101 ] start location: evalsipma91start leaf cost: 4 Complexity upper bound 27608*a + 135*a^2 + 1410294 Time: 1.092 sec (SMT: 1.026 sec)