YES(?, 39*a + 12*a^2 + 36) Initial complexity problem: 1: T: (1, 1) evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d) (?, 1) evalperfectentryin(a, b, c, d) -> evalperfectreturnin(a, b, c, d) [ 1 >= a ] (?, 1) evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ] (?, 1) evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d) (?, 1) evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ c >= 1 ] (?, 1) evalperfectbb8in(a, b, c, d) -> evalperfectbb9in(b, b, c, d) [ 0 >= c ] (?, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ d >= c ] (?, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ c >= d + 1 ] (?, 1) evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ d = 0 ] (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ 0 >= d + 1 ] (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ d >= 1 ] (?, 1) evalperfectbb9in(a, b, c, d) -> evalperfectreturnin(a, b, c, d) [ 0 >= a + 1 ] (?, 1) evalperfectbb9in(a, b, c, d) -> evalperfectreturnin(a, b, c, d) [ a >= 1 ] (?, 1) evalperfectbb9in(a, b, c, d) -> evalperfectreturnin(a, b, c, d) [ a = 0 ] (?, 1) evalperfectreturnin(a, b, c, d) -> evalperfectstop(a, b, c, d) start location: evalperfectstart leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d) (?, 1) evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ] (?, 1) evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d) (?, 1) evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ c >= 1 ] (?, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ d >= c ] (?, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ c >= d + 1 ] (?, 1) evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ d = 0 ] (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ 0 >= d + 1 ] (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ d >= 1 ] start location: evalperfectstart leaf cost: 6 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (1, 1) evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d) (1, 1) evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ] (1, 1) evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d) (?, 1) evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ c >= 1 ] (?, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ d >= c ] (?, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ c >= d + 1 ] (?, 1) evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ d = 0 ] (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ 0 >= d + 1 ] (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ d >= 1 ] start location: evalperfectstart leaf cost: 6 A polynomial rank function with Pol(evalperfectstart) = 3*V_1 - 3 Pol(evalperfectentryin) = 3*V_1 - 3 Pol(evalperfectbb1in) = 3*V_1 - 3 Pol(evalperfectbb8in) = 3*V_3 Pol(evalperfectbb4in) = 3*V_3 - 1 Pol(evalperfectbb3in) = 3*V_3 - 1 Pol(evalperfectbb5in) = 3*V_3 - 2 orients all transitions weakly and the transition evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ c >= 1 ] strictly and produces the following problem: 4: T: (1, 1) evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d) (1, 1) evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ] (1, 1) evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d) (3*a + 3, 1) evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ c >= 1 ] (?, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ d >= c ] (?, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ c >= d + 1 ] (?, 1) evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ d = 0 ] (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ 0 >= d + 1 ] (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ d >= 1 ] start location: evalperfectstart leaf cost: 6 A polynomial rank function with Pol(evalperfectbb5in) = 1 Pol(evalperfectbb8in) = 0 Pol(evalperfectbb4in) = 2 Pol(evalperfectbb3in) = 2 and size complexities S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ d >= 1 ]", 0-0) = a S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ d >= 1 ]", 0-1) = ? S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ d >= 1 ]", 0-2) = ? S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ d >= 1 ]", 0-3) = ? S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ 0 >= d + 1 ]", 0-0) = a S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ 0 >= d + 1 ]", 0-1) = ? S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ 0 >= d + 1 ]", 0-2) = ? S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ 0 >= d + 1 ]", 0-3) = ? S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ d = 0 ]", 0-0) = a S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ d = 0 ]", 0-1) = ? S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ d = 0 ]", 0-2) = ? S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ d = 0 ]", 0-3) = 0 S("evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c)", 0-0) = a S("evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c)", 0-1) = ? S("evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c)", 0-2) = ? S("evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c)", 0-3) = ? S("evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ c >= d + 1 ]", 0-0) = a S("evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ c >= d + 1 ]", 0-1) = ? S("evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ c >= d + 1 ]", 0-2) = ? S("evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ c >= d + 1 ]", 0-3) = ? S("evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ d >= c ]", 0-0) = a S("evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ d >= c ]", 0-1) = ? S("evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ d >= c ]", 0-2) = ? S("evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ d >= c ]", 0-3) = ? S("evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ c >= 1 ]", 0-0) = a S("evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ c >= 1 ]", 0-1) = ? S("evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ c >= 1 ]", 0-2) = ? S("evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ c >= 1 ]", 0-3) = a S("evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d)", 0-0) = a S("evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d)", 0-1) = a S("evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d)", 0-2) = a + 1 S("evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d)", 0-3) = d S("evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ]", 0-0) = a S("evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ]", 0-1) = b S("evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ]", 0-2) = c S("evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ]", 0-3) = d S("evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d)", 0-0) = a S("evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d)", 0-1) = b S("evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d)", 0-2) = c S("evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d)", 0-3) = d orients the transitions evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ d = 0 ] evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ d >= 1 ] evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ 0 >= d + 1 ] evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ c >= d + 1 ] evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ d >= c ] evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) weakly and the transitions evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ d = 0 ] evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ 0 >= d + 1 ] evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ c >= d + 1 ] strictly and produces the following problem: 5: T: (1, 1) evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d) (1, 1) evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ] (1, 1) evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d) (3*a + 3, 1) evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ c >= 1 ] (?, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ d >= c ] (6*a + 6, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ c >= d + 1 ] (?, 1) evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) (6*a + 6, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ d = 0 ] (6*a + 6, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ 0 >= d + 1 ] (?, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ d >= 1 ] start location: evalperfectstart leaf cost: 6 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (1, 1) evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d) (1, 1) evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ] (1, 1) evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d) (3*a + 3, 1) evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ c >= 1 ] (?, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ d >= c ] (6*a + 6, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ c >= d + 1 ] (?, 1) evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) (6*a + 6, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ d = 0 ] (6*a + 6, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ 0 >= d + 1 ] (6*a + 6, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ d >= 1 ] start location: evalperfectstart leaf cost: 6 Applied AI with 'oct' on problem 6 to obtain the following invariants: For symbol evalperfectbb1in: X_1 - 2 >= 0 For symbol evalperfectbb3in: X_1 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalperfectbb4in: X_1 - X_4 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalperfectbb5in: X_3 - X_4 - 1 >= 0 /\ X_1 - X_4 - 2 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalperfectbb8in: X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - X_2 >= 0 /\ X_1 - 2 >= 0 This yielded the following problem: 7: T: (6*a + 6, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ c - d - 1 >= 0 /\ a - d - 2 >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ d >= 1 ] (6*a + 6, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ c - d - 1 >= 0 /\ a - d - 2 >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ 0 >= d + 1 ] (6*a + 6, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ c - d - 1 >= 0 /\ a - d - 2 >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ d = 0 ] (?, 1) evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) [ a - d >= 0 /\ d - 1 >= 0 /\ c + d - 2 >= 0 /\ -c + d >= 0 /\ a + d - 3 >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 ] (6*a + 6, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ a - d >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ c >= d + 1 ] (?, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ a - d >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ d >= c ] (3*a + 3, 1) evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ a - c - 1 >= 0 /\ c >= 0 /\ a + c - 2 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ c >= 1 ] (1, 1) evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d) [ a - 2 >= 0 ] (1, 1) evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ] (1, 1) evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d) start location: evalperfectstart leaf cost: 6 A polynomial rank function with Pol(evalperfectbb4in) = 2*V_4 Pol(evalperfectbb3in) = 2*V_4 - 1 and size complexities S("evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d)", 0-0) = a S("evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d)", 0-1) = b S("evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d)", 0-2) = c S("evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d)", 0-3) = d S("evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ]", 0-0) = a S("evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ]", 0-1) = b S("evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ]", 0-2) = c S("evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ]", 0-3) = d S("evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d) [ a - 2 >= 0 ]", 0-0) = a S("evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d) [ a - 2 >= 0 ]", 0-1) = a S("evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d) [ a - 2 >= 0 ]", 0-2) = a S("evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d) [ a - 2 >= 0 ]", 0-3) = d S("evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ a - c - 1 >= 0 /\\ c >= 0 /\\ a + c - 2 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ c >= 1 ]", 0-0) = a S("evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ a - c - 1 >= 0 /\\ c >= 0 /\\ a + c - 2 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ c >= 1 ]", 0-1) = 7*a + 6*a^2 S("evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ a - c - 1 >= 0 /\\ c >= 0 /\\ a + c - 2 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ c >= 1 ]", 0-2) = a S("evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ a - c - 1 >= 0 /\\ c >= 0 /\\ a + c - 2 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ c >= 1 ]", 0-3) = a S("evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ a - d >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ d >= c ]", 0-0) = a S("evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ a - d >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ d >= c ]", 0-1) = 7*a + 6*a^2 S("evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ a - d >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ d >= c ]", 0-2) = a S("evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ a - d >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ d >= c ]", 0-3) = a S("evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ a - d >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ c >= d + 1 ]", 0-0) = a S("evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ a - d >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ c >= d + 1 ]", 0-1) = 7*a + 6*a^2 S("evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ a - d >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ c >= d + 1 ]", 0-2) = a S("evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ a - d >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ c >= d + 1 ]", 0-3) = a S("evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) [ a - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 2 >= 0 /\\ -c + d >= 0 /\\ a + d - 3 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 ]", 0-0) = a S("evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) [ a - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 2 >= 0 /\\ -c + d >= 0 /\\ a + d - 3 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 ]", 0-1) = 7*a + 6*a^2 S("evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) [ a - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 2 >= 0 /\\ -c + d >= 0 /\\ a + d - 3 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 ]", 0-2) = a S("evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) [ a - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 2 >= 0 /\\ -c + d >= 0 /\\ a + d - 3 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 ]", 0-3) = a S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ c - d - 1 >= 0 /\\ a - d - 2 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ d = 0 ]", 0-0) = a S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ c - d - 1 >= 0 /\\ a - d - 2 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ d = 0 ]", 0-1) = 7*a + 6*a^2 S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ c - d - 1 >= 0 /\\ a - d - 2 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ d = 0 ]", 0-2) = a S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ c - d - 1 >= 0 /\\ a - d - 2 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ d = 0 ]", 0-3) = 0 S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ c - d - 1 >= 0 /\\ a - d - 2 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ 0 >= d + 1 ]", 0-0) = a S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ c - d - 1 >= 0 /\\ a - d - 2 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ 0 >= d + 1 ]", 0-1) = 7*a + 6*a^2 S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ c - d - 1 >= 0 /\\ a - d - 2 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ 0 >= d + 1 ]", 0-2) = a S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ c - d - 1 >= 0 /\\ a - d - 2 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ 0 >= d + 1 ]", 0-3) = a S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ c - d - 1 >= 0 /\\ a - d - 2 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ d >= 1 ]", 0-0) = a S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ c - d - 1 >= 0 /\\ a - d - 2 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ d >= 1 ]", 0-1) = 7*a + 6*a^2 S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ c - d - 1 >= 0 /\\ a - d - 2 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ d >= 1 ]", 0-2) = a S("evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ c - d - 1 >= 0 /\\ a - d - 2 >= 0 /\\ a - c - 1 >= 0 /\\ c - 1 >= 0 /\\ a + c - 3 >= 0 /\\ a - b >= 0 /\\ a - 2 >= 0 /\\ d >= 1 ]", 0-3) = a orients the transitions evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ a - d >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ d >= c ] evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) [ a - d >= 0 /\ d - 1 >= 0 /\ c + d - 2 >= 0 /\ -c + d >= 0 /\ a + d - 3 >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 ] weakly and the transitions evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ a - d >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ d >= c ] evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) [ a - d >= 0 /\ d - 1 >= 0 /\ c + d - 2 >= 0 /\ -c + d >= 0 /\ a + d - 3 >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 ] strictly and produces the following problem: 8: T: (6*a + 6, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ c - d - 1 >= 0 /\ a - d - 2 >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ d >= 1 ] (6*a + 6, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b, c - 1, d) [ c - d - 1 >= 0 /\ a - d - 2 >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ 0 >= d + 1 ] (6*a + 6, 1) evalperfectbb5in(a, b, c, d) -> evalperfectbb8in(a, b - c, c - 1, d) [ c - d - 1 >= 0 /\ a - d - 2 >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ d = 0 ] (6*a^2 + 6*a, 1) evalperfectbb3in(a, b, c, d) -> evalperfectbb4in(a, b, c, d - c) [ a - d >= 0 /\ d - 1 >= 0 /\ c + d - 2 >= 0 /\ -c + d >= 0 /\ a + d - 3 >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 ] (6*a + 6, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb5in(a, b, c, d) [ a - d >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ c >= d + 1 ] (6*a^2 + 6*a, 1) evalperfectbb4in(a, b, c, d) -> evalperfectbb3in(a, b, c, d) [ a - d >= 0 /\ a - c - 1 >= 0 /\ c - 1 >= 0 /\ a + c - 3 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ d >= c ] (3*a + 3, 1) evalperfectbb8in(a, b, c, d) -> evalperfectbb4in(a, b, c, a) [ a - c - 1 >= 0 /\ c >= 0 /\ a + c - 2 >= 0 /\ a - b >= 0 /\ a - 2 >= 0 /\ c >= 1 ] (1, 1) evalperfectbb1in(a, b, c, d) -> evalperfectbb8in(a, a, a - 1, d) [ a - 2 >= 0 ] (1, 1) evalperfectentryin(a, b, c, d) -> evalperfectbb1in(a, b, c, d) [ a >= 2 ] (1, 1) evalperfectstart(a, b, c, d) -> evalperfectentryin(a, b, c, d) start location: evalperfectstart leaf cost: 6 Complexity upper bound 39*a + 12*a^2 + 36 Time: 1.035 sec (SMT: 0.976 sec)