YES(?, 81*a + 72*a^2 + 30) Initial complexity problem: 1: T: (1, 1) evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c) (?, 1) evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ] (?, 1) evalrsdentryin(a, b, c) -> evalrsdreturnin(a, b, c) [ 0 >= a + 1 ] (?, 1) evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) (?, 1) evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ c >= a ] (?, 1) evalrsdbb4in(a, b, c) -> evalrsdreturnin(a, b, c) [ a >= c + 1 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ 0 >= d + 1 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ d >= 1 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) (?, 1) evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) (?, 1) evalrsdbb3in(a, b, c) -> evalrsdbb4in(a, b - 1, b - 1) (?, 1) evalrsdreturnin(a, b, c) -> evalrsdstop(a, b, c) start location: evalrsdstart leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c) (?, 1) evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ] (?, 1) evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) (?, 1) evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ c >= a ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ 0 >= d + 1 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ d >= 1 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) (?, 1) evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) (?, 1) evalrsdbb3in(a, b, c) -> evalrsdbb4in(a, b - 1, b - 1) start location: evalrsdstart leaf cost: 3 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (1, 1) evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c) (1, 1) evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ] (1, 1) evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) (?, 1) evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ c >= a ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ 0 >= d + 1 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ d >= 1 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) (?, 1) evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) (?, 1) evalrsdbb3in(a, b, c) -> evalrsdbb4in(a, b - 1, b - 1) start location: evalrsdstart leaf cost: 3 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalrsdbb1in: X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_1 >= 0 For symbol evalrsdbb2in: X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_1 >= 0 For symbol evalrsdbb3in: X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_1 >= 0 For symbol evalrsdbb4in: X_1 >= 0 For symbol evalrsdbbin: X_1 >= 0 This yielded the following problem: 4: T: (?, 1) evalrsdbb3in(a, b, c) -> evalrsdbb4in(a, b - 1, b - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] (?, 1) evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ d >= 1 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ 0 >= d + 1 ] (?, 1) evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\ c >= a ] (1, 1) evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) [ a >= 0 ] (1, 1) evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ] (1, 1) evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c) start location: evalrsdstart leaf cost: 3 By chaining the transition evalrsdbb3in(a, b, c) -> evalrsdbb4in(a, b - 1, b - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] with all transitions in problem 4, the following new transition is obtained: evalrsdbb3in(a, b, c) -> evalrsdbb1in(a, b - 1, b - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ b - 1 >= a ] We thus obtain the following problem: 5: T: (?, 2) evalrsdbb3in(a, b, c) -> evalrsdbb1in(a, b - 1, b - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ b - 1 >= a ] (?, 1) evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ d >= 1 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ 0 >= d + 1 ] (?, 1) evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\ c >= a ] (1, 1) evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) [ a >= 0 ] (1, 1) evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ] (1, 1) evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c) start location: evalrsdstart leaf cost: 3 A polynomial rank function with Pol(evalrsdbb3in) = -3*V_1 + 3*V_2 - 2 Pol(evalrsdbb1in) = -3*V_1 + 3*V_2 - 1 Pol(evalrsdbb2in) = -3*V_1 + 3*V_2 - 1 Pol(evalrsdbb4in) = -3*V_1 + 3*V_2 - 1 Pol(evalrsdbbin) = 3*V_1 - 1 Pol(evalrsdentryin) = 3*V_1 - 1 Pol(evalrsdstart) = 3*V_1 - 1 orients all transitions weakly and the transition evalrsdbb3in(a, b, c) -> evalrsdbb1in(a, b - 1, b - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ b - 1 >= a ] strictly and produces the following problem: 6: T: (3*a + 1, 2) evalrsdbb3in(a, b, c) -> evalrsdbb1in(a, b - 1, b - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ b - 1 >= a ] (?, 1) evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ d >= 1 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ 0 >= d + 1 ] (?, 1) evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\ c >= a ] (1, 1) evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) [ a >= 0 ] (1, 1) evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ] (1, 1) evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c) start location: evalrsdstart leaf cost: 3 A polynomial rank function with Pol(evalrsdbb4in) = 1 Pol(evalrsdbb1in) = 1 Pol(evalrsdbb2in) = 1 Pol(evalrsdbb3in) = 0 and size complexities S("evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c)", 0-0) = a S("evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c)", 0-1) = b S("evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c)", 0-2) = c S("evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ]", 0-0) = a S("evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ]", 0-1) = b S("evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ]", 0-2) = c S("evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) [ a >= 0 ]", 0-0) = a S("evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) [ a >= 0 ]", 0-1) = 2*a S("evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) [ a >= 0 ]", 0-2) = 2*a S("evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\\ c >= a ]", 0-0) = a S("evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\\ c >= a ]", 0-1) = 2*a S("evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\\ c >= a ]", 0-2) = 2*a + 4 S("evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ 0 >= d + 1 ]", 0-0) = a S("evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ 0 >= d + 1 ]", 0-1) = 2*a S("evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ 0 >= d + 1 ]", 0-2) = 2*a + 4 S("evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ d >= 1 ]", 0-0) = a S("evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ d >= 1 ]", 0-1) = 2*a S("evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ d >= 1 ]", 0-2) = 2*a + 4 S("evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 ]", 0-0) = a S("evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 ]", 0-1) = 2*a S("evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 ]", 0-2) = 2*a + 8 S("evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 ]", 0-0) = a S("evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 ]", 0-1) = 2*a S("evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 ]", 0-2) = 2*a + 4 S("evalrsdbb3in(a, b, c) -> evalrsdbb1in(a, b - 1, b - 1) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ b - 1 >= a ]", 0-0) = a S("evalrsdbb3in(a, b, c) -> evalrsdbb1in(a, b - 1, b - 1) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ b - 1 >= a ]", 0-1) = 2*a S("evalrsdbb3in(a, b, c) -> evalrsdbb1in(a, b - 1, b - 1) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ b - 1 >= a ]", 0-2) = 2*a orients the transitions evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\ c >= a ] evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ d >= 1 ] evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ 0 >= d + 1 ] weakly and the transition evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] strictly and produces the following problem: 7: T: (3*a + 1, 2) evalrsdbb3in(a, b, c) -> evalrsdbb1in(a, b - 1, b - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ b - 1 >= a ] (?, 1) evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] (3*a + 2, 1) evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ d >= 1 ] (?, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ 0 >= d + 1 ] (?, 1) evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\ c >= a ] (1, 1) evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) [ a >= 0 ] (1, 1) evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ] (1, 1) evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c) start location: evalrsdstart leaf cost: 3 A polynomial rank function with Pol(evalrsdbb4in) = 3*V_3 + 3 Pol(evalrsdbb1in) = 3*V_3 + 2 Pol(evalrsdbb2in) = 3*V_3 + 1 and size complexities S("evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c)", 0-0) = a S("evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c)", 0-1) = b S("evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c)", 0-2) = c S("evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ]", 0-0) = a S("evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ]", 0-1) = b S("evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ]", 0-2) = c S("evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) [ a >= 0 ]", 0-0) = a S("evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) [ a >= 0 ]", 0-1) = 2*a S("evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) [ a >= 0 ]", 0-2) = 2*a S("evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\\ c >= a ]", 0-0) = a S("evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\\ c >= a ]", 0-1) = 2*a S("evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\\ c >= a ]", 0-2) = 2*a + 4 S("evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ 0 >= d + 1 ]", 0-0) = a S("evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ 0 >= d + 1 ]", 0-1) = 2*a S("evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ 0 >= d + 1 ]", 0-2) = 2*a + 4 S("evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ d >= 1 ]", 0-0) = a S("evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ d >= 1 ]", 0-1) = 2*a S("evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ d >= 1 ]", 0-2) = 2*a + 4 S("evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 ]", 0-0) = a S("evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 ]", 0-1) = 2*a S("evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 ]", 0-2) = 2*a + 8 S("evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 ]", 0-0) = a S("evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 ]", 0-1) = 2*a S("evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 ]", 0-2) = 2*a + 4 S("evalrsdbb3in(a, b, c) -> evalrsdbb1in(a, b - 1, b - 1) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ b - 1 >= a ]", 0-0) = a S("evalrsdbb3in(a, b, c) -> evalrsdbb1in(a, b - 1, b - 1) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ b - 1 >= a ]", 0-1) = 2*a S("evalrsdbb3in(a, b, c) -> evalrsdbb1in(a, b - 1, b - 1) [ c >= 0 /\\ a + c >= 0 /\\ -a + c >= 0 /\\ a >= 0 /\\ b - 1 >= a ]", 0-2) = 2*a orients the transitions evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\ c >= a ] evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ d >= 1 ] evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ 0 >= d + 1 ] weakly and the transitions evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\ c >= a ] evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ d >= 1 ] evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ 0 >= d + 1 ] strictly and produces the following problem: 8: T: (3*a + 1, 2) evalrsdbb3in(a, b, c) -> evalrsdbb1in(a, b - 1, b - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ b - 1 >= a ] (18*a + 18*a^2 + 5, 1) evalrsdbb2in(a, b, c) -> evalrsdbb4in(a, b, c - 1) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] (3*a + 2, 1) evalrsdbb1in(a, b, c) -> evalrsdbb3in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 ] (18*a + 18*a^2 + 5, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ d >= 1 ] (18*a + 18*a^2 + 5, 1) evalrsdbb1in(a, b, c) -> evalrsdbb2in(a, b, c) [ c >= 0 /\ a + c >= 0 /\ -a + c >= 0 /\ a >= 0 /\ 0 >= d + 1 ] (18*a + 18*a^2 + 5, 1) evalrsdbb4in(a, b, c) -> evalrsdbb1in(a, b, c) [ a >= 0 /\ c >= a ] (1, 1) evalrsdbbin(a, b, c) -> evalrsdbb4in(a, 2*a, 2*a) [ a >= 0 ] (1, 1) evalrsdentryin(a, b, c) -> evalrsdbbin(a, b, c) [ a >= 0 ] (1, 1) evalrsdstart(a, b, c) -> evalrsdentryin(a, b, c) start location: evalrsdstart leaf cost: 3 Complexity upper bound 81*a + 72*a^2 + 30 Time: 0.997 sec (SMT: 0.948 sec)