YES(?, 90*a + 69) Initial complexity problem: 1: T: (1, 1) evalEx4start(a, b, c, d) -> evalEx4entryin(a, b, c, d) (?, 1) evalEx4entryin(a, b, c, d) -> evalEx4bb4in(1, a, c, d) (?, 1) evalEx4bb4in(a, b, c, d) -> evalEx4bb2in(a, b, 0, b) [ a = 1 ] (?, 1) evalEx4bb4in(a, b, c, d) -> evalEx4returnin(a, b, c, d) [ 0 >= a ] (?, 1) evalEx4bb4in(a, b, c, d) -> evalEx4returnin(a, b, c, d) [ a >= 2 ] (?, 1) evalEx4bb2in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ 0 >= d ] (?, 1) evalEx4bb2in(a, b, c, d) -> evalEx4bb3in(a, b, c, d) [ d >= 1 ] (?, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ 0 >= e + 1 ] (?, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ e >= 1 ] (?, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) (?, 1) evalEx4bb1in(a, b, c, d) -> evalEx4bb2in(a, b, 1, d - 1) (?, 1) evalEx4returnin(a, b, c, d) -> evalEx4stop(a, b, c, d) start location: evalEx4start leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) evalEx4start(a, b, c, d) -> evalEx4entryin(a, b, c, d) (?, 1) evalEx4entryin(a, b, c, d) -> evalEx4bb4in(1, a, c, d) (?, 1) evalEx4bb4in(a, b, c, d) -> evalEx4bb2in(a, b, 0, b) [ a = 1 ] (?, 1) evalEx4bb2in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ 0 >= d ] (?, 1) evalEx4bb2in(a, b, c, d) -> evalEx4bb3in(a, b, c, d) [ d >= 1 ] (?, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ 0 >= e + 1 ] (?, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ e >= 1 ] (?, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) (?, 1) evalEx4bb1in(a, b, c, d) -> evalEx4bb2in(a, b, 1, d - 1) start location: evalEx4start leaf cost: 3 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (1, 1) evalEx4start(a, b, c, d) -> evalEx4entryin(a, b, c, d) (1, 1) evalEx4entryin(a, b, c, d) -> evalEx4bb4in(1, a, c, d) (?, 1) evalEx4bb4in(a, b, c, d) -> evalEx4bb2in(a, b, 0, b) [ a = 1 ] (?, 1) evalEx4bb2in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ 0 >= d ] (?, 1) evalEx4bb2in(a, b, c, d) -> evalEx4bb3in(a, b, c, d) [ d >= 1 ] (?, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ 0 >= e + 1 ] (?, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ e >= 1 ] (?, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) (?, 1) evalEx4bb1in(a, b, c, d) -> evalEx4bb2in(a, b, 1, d - 1) start location: evalEx4start leaf cost: 3 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalEx4bb1in: X_2 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ -X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalEx4bb2in: X_2 - X_4 >= 0 /\ X_3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalEx4bb3in: X_2 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ -X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 - 1 >= 0 This yielded the following problem: 4: T: (?, 1) evalEx4bb1in(a, b, c, d) -> evalEx4bb2in(a, b, 1, d - 1) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 ] (?, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 ] (?, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ e >= 1 ] (?, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ 0 >= e + 1 ] (?, 1) evalEx4bb2in(a, b, c, d) -> evalEx4bb3in(a, b, c, d) [ b - d >= 0 /\ c >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ d >= 1 ] (?, 1) evalEx4bb2in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\ c >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ 0 >= d ] (?, 1) evalEx4bb4in(a, b, c, d) -> evalEx4bb2in(a, b, 0, b) [ a = 1 ] (1, 1) evalEx4entryin(a, b, c, d) -> evalEx4bb4in(1, a, c, d) (1, 1) evalEx4start(a, b, c, d) -> evalEx4entryin(a, b, c, d) start location: evalEx4start leaf cost: 3 A polynomial rank function with Pol(evalEx4bb1in) = 3*V_1 + 6*V_4 - 2 Pol(evalEx4bb2in) = 3*V_1 + 3*V_3 + 6*V_4 Pol(evalEx4bb3in) = 3*V_1 + 3*V_3 + 6*V_4 - 1 Pol(evalEx4bb4in) = 3*V_1 + 6*V_2 + 1 Pol(evalEx4entryin) = 6*V_1 + 4 Pol(evalEx4start) = 6*V_1 + 4 orients all transitions weakly and the transitions evalEx4bb3in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 ] evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ e >= 1 ] evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ 0 >= e + 1 ] evalEx4bb2in(a, b, c, d) -> evalEx4bb3in(a, b, c, d) [ b - d >= 0 /\ c >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ d >= 1 ] evalEx4bb1in(a, b, c, d) -> evalEx4bb2in(a, b, 1, d - 1) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 ] strictly and produces the following problem: 5: T: (6*a + 4, 1) evalEx4bb1in(a, b, c, d) -> evalEx4bb2in(a, b, 1, d - 1) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 ] (6*a + 4, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 ] (6*a + 4, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ e >= 1 ] (6*a + 4, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ 0 >= e + 1 ] (6*a + 4, 1) evalEx4bb2in(a, b, c, d) -> evalEx4bb3in(a, b, c, d) [ b - d >= 0 /\ c >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ d >= 1 ] (?, 1) evalEx4bb2in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\ c >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ 0 >= d ] (?, 1) evalEx4bb4in(a, b, c, d) -> evalEx4bb2in(a, b, 0, b) [ a = 1 ] (1, 1) evalEx4entryin(a, b, c, d) -> evalEx4bb4in(1, a, c, d) (1, 1) evalEx4start(a, b, c, d) -> evalEx4entryin(a, b, c, d) start location: evalEx4start leaf cost: 3 A polynomial rank function with Pol(evalEx4bb4in) = 2*V_1 Pol(evalEx4bb2in) = 2*V_3 + 1 and size complexities S("evalEx4start(a, b, c, d) -> evalEx4entryin(a, b, c, d)", 0-0) = a S("evalEx4start(a, b, c, d) -> evalEx4entryin(a, b, c, d)", 0-1) = b S("evalEx4start(a, b, c, d) -> evalEx4entryin(a, b, c, d)", 0-2) = c S("evalEx4start(a, b, c, d) -> evalEx4entryin(a, b, c, d)", 0-3) = d S("evalEx4entryin(a, b, c, d) -> evalEx4bb4in(1, a, c, d)", 0-0) = 1 S("evalEx4entryin(a, b, c, d) -> evalEx4bb4in(1, a, c, d)", 0-1) = a S("evalEx4entryin(a, b, c, d) -> evalEx4bb4in(1, a, c, d)", 0-2) = c S("evalEx4entryin(a, b, c, d) -> evalEx4bb4in(1, a, c, d)", 0-3) = d S("evalEx4bb4in(a, b, c, d) -> evalEx4bb2in(a, b, 0, b) [ a = 1 ]", 0-0) = 1 S("evalEx4bb4in(a, b, c, d) -> evalEx4bb2in(a, b, 0, b) [ a = 1 ]", 0-1) = a S("evalEx4bb4in(a, b, c, d) -> evalEx4bb2in(a, b, 0, b) [ a = 1 ]", 0-2) = 0 S("evalEx4bb4in(a, b, c, d) -> evalEx4bb2in(a, b, 0, b) [ a = 1 ]", 0-3) = a S("evalEx4bb2in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\\ c >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ 0 >= d ]", 0-0) = 1 S("evalEx4bb2in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\\ c >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ 0 >= d ]", 0-1) = a S("evalEx4bb2in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\\ c >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ 0 >= d ]", 0-2) = 1 S("evalEx4bb2in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\\ c >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ 0 >= d ]", 0-3) = a S("evalEx4bb2in(a, b, c, d) -> evalEx4bb3in(a, b, c, d) [ b - d >= 0 /\\ c >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ d >= 1 ]", 0-0) = 1 S("evalEx4bb2in(a, b, c, d) -> evalEx4bb3in(a, b, c, d) [ b - d >= 0 /\\ c >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ d >= 1 ]", 0-1) = a S("evalEx4bb2in(a, b, c, d) -> evalEx4bb3in(a, b, c, d) [ b - d >= 0 /\\ c >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ d >= 1 ]", 0-2) = 1 S("evalEx4bb2in(a, b, c, d) -> evalEx4bb3in(a, b, c, d) [ b - d >= 0 /\\ c >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ d >= 1 ]", 0-3) = a S("evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ 0 >= e + 1 ]", 0-0) = 1 S("evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ 0 >= e + 1 ]", 0-1) = a S("evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ 0 >= e + 1 ]", 0-2) = 1 S("evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ 0 >= e + 1 ]", 0-3) = a S("evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ e >= 1 ]", 0-0) = 1 S("evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ e >= 1 ]", 0-1) = a S("evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ e >= 1 ]", 0-2) = 1 S("evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 /\\ e >= 1 ]", 0-3) = a S("evalEx4bb3in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 ]", 0-0) = 1 S("evalEx4bb3in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 ]", 0-1) = a S("evalEx4bb3in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 ]", 0-2) = 1 S("evalEx4bb3in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 ]", 0-3) = a S("evalEx4bb1in(a, b, c, d) -> evalEx4bb2in(a, b, 1, d - 1) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 ]", 0-0) = 1 S("evalEx4bb1in(a, b, c, d) -> evalEx4bb2in(a, b, 1, d - 1) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 ]", 0-1) = a S("evalEx4bb1in(a, b, c, d) -> evalEx4bb2in(a, b, 1, d - 1) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 ]", 0-2) = 1 S("evalEx4bb1in(a, b, c, d) -> evalEx4bb2in(a, b, 1, d - 1) [ b - d >= 0 /\\ d - 1 >= 0 /\\ c + d - 1 >= 0 /\\ b + d - 2 >= 0 /\\ a + d - 2 >= 0 /\\ -a + d >= 0 /\\ c >= 0 /\\ b + c - 1 >= 0 /\\ a + c - 1 >= 0 /\\ -a + c + 1 >= 0 /\\ b - 1 >= 0 /\\ a + b - 2 >= 0 /\\ -a + b >= 0 /\\ -a + 1 >= 0 /\\ a - 1 >= 0 ]", 0-3) = a orients the transitions evalEx4bb4in(a, b, c, d) -> evalEx4bb2in(a, b, 0, b) [ a = 1 ] evalEx4bb2in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\ c >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ 0 >= d ] weakly and the transitions evalEx4bb4in(a, b, c, d) -> evalEx4bb2in(a, b, 0, b) [ a = 1 ] evalEx4bb2in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\ c >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ 0 >= d ] strictly and produces the following problem: 6: T: (6*a + 4, 1) evalEx4bb1in(a, b, c, d) -> evalEx4bb2in(a, b, 1, d - 1) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 ] (6*a + 4, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 ] (6*a + 4, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ e >= 1 ] (6*a + 4, 1) evalEx4bb3in(a, b, c, d) -> evalEx4bb1in(a, b, c, d) [ b - d >= 0 /\ d - 1 >= 0 /\ c + d - 1 >= 0 /\ b + d - 2 >= 0 /\ a + d - 2 >= 0 /\ -a + d >= 0 /\ c >= 0 /\ b + c - 1 >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ b - 1 >= 0 /\ a + b - 2 >= 0 /\ -a + b >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ 0 >= e + 1 ] (6*a + 4, 1) evalEx4bb2in(a, b, c, d) -> evalEx4bb3in(a, b, c, d) [ b - d >= 0 /\ c >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ d >= 1 ] (30*a + 22, 1) evalEx4bb2in(a, b, c, d) -> evalEx4bb4in(c, d, c, d) [ b - d >= 0 /\ c >= 0 /\ a + c - 1 >= 0 /\ -a + c + 1 >= 0 /\ -a + 1 >= 0 /\ a - 1 >= 0 /\ 0 >= d ] (30*a + 22, 1) evalEx4bb4in(a, b, c, d) -> evalEx4bb2in(a, b, 0, b) [ a = 1 ] (1, 1) evalEx4entryin(a, b, c, d) -> evalEx4bb4in(1, a, c, d) (1, 1) evalEx4start(a, b, c, d) -> evalEx4entryin(a, b, c, d) start location: evalEx4start leaf cost: 3 Complexity upper bound 90*a + 69 Time: 0.722 sec (SMT: 0.671 sec)