YES(?, 123984*a + 360*a^2 + 530498) Initial complexity problem: 1: T: (1, 1) evalwcet2start(a, b) -> evalwcet2entryin(a, b) (?, 1) evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b) (?, 1) evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ] (?, 1) evalwcet2bb5in(a, b) -> evalwcet2returnin(a, b) [ a >= 5 ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ] (?, 1) evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1) (?, 1) evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b) (?, 1) evalwcet2returnin(a, b) -> evalwcet2stop(a, b) start location: evalwcet2start leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) evalwcet2start(a, b) -> evalwcet2entryin(a, b) (?, 1) evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b) (?, 1) evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ] (?, 1) evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1) (?, 1) evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b) start location: evalwcet2start leaf cost: 2 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (1, 1) evalwcet2start(a, b) -> evalwcet2entryin(a, b) (1, 1) evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b) (?, 1) evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ] (?, 1) evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1) (?, 1) evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b) start location: evalwcet2start leaf cost: 2 A polynomial rank function with Pol(evalwcet2start) = -3*V_1 + 8 Pol(evalwcet2entryin) = -3*V_1 + 8 Pol(evalwcet2bb5in) = -3*V_1 + 8 Pol(evalwcet2bb2in) = -3*V_1 + 7 Pol(evalwcet2bb1in) = -3*V_1 + 7 Pol(evalwcet2bb4in) = -3*V_1 + 6 orients all transitions weakly and the transition evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ] strictly and produces the following problem: 4: T: (1, 1) evalwcet2start(a, b) -> evalwcet2entryin(a, b) (1, 1) evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b) (?, 1) evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] (3*a + 8, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ] (?, 1) evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1) (?, 1) evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b) start location: evalwcet2start leaf cost: 2 A polynomial rank function with Pol(evalwcet2start) = -3*V_1 + 13 Pol(evalwcet2entryin) = -3*V_1 + 13 Pol(evalwcet2bb5in) = -3*V_1 + 13 Pol(evalwcet2bb2in) = -3*V_1 + 12 Pol(evalwcet2bb1in) = -3*V_1 + 12 Pol(evalwcet2bb4in) = -3*V_1 + 11 orients all transitions weakly and the transition evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ] strictly and produces the following problem: 5: T: (1, 1) evalwcet2start(a, b) -> evalwcet2entryin(a, b) (1, 1) evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b) (3*a + 13, 1) evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] (3*a + 8, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ] (?, 1) evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1) (?, 1) evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b) start location: evalwcet2start leaf cost: 2 A polynomial rank function with Pol(evalwcet2bb4in) = 1 Pol(evalwcet2bb5in) = 0 Pol(evalwcet2bb2in) = 2 Pol(evalwcet2bb1in) = 2 and size complexities S("evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b)", 0-0) = ? S("evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b)", 0-1) = ? S("evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1)", 0-0) = ? S("evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1)", 0-1) = ? S("evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ]", 0-0) = ? S("evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ]", 0-1) = ? S("evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ]", 0-0) = ? S("evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ]", 0-1) = ? S("evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\\ 9 >= b ]", 0-0) = ? S("evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\\ 9 >= b ]", 0-1) = ? S("evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ]", 0-0) = ? S("evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ]", 0-1) = 0 S("evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b)", 0-0) = a S("evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b)", 0-1) = b S("evalwcet2start(a, b) -> evalwcet2entryin(a, b)", 0-0) = a S("evalwcet2start(a, b) -> evalwcet2entryin(a, b)", 0-1) = b orients the transitions evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ] evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1) weakly and the transition evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b) strictly and produces the following problem: 6: T: (1, 1) evalwcet2start(a, b) -> evalwcet2entryin(a, b) (1, 1) evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b) (3*a + 13, 1) evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] (3*a + 8, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ] (?, 1) evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1) (9*a + 34, 1) evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b) start location: evalwcet2start leaf cost: 2 A polynomial rank function with Pol(evalwcet2bb2in) = 1 Pol(evalwcet2bb4in) = 0 Pol(evalwcet2bb1in) = 1 and size complexities S("evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b)", 0-0) = 10*a + 3400 S("evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b)", 0-1) = ? S("evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1)", 0-0) = 10*a + 3400 S("evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1)", 0-1) = ? S("evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ]", 0-0) = 10*a + 3400 S("evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ]", 0-1) = ? S("evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ]", 0-0) = 10*a + 3400 S("evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ]", 0-1) = ? S("evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\\ 9 >= b ]", 0-0) = 10*a + 3400 S("evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\\ 9 >= b ]", 0-1) = ? S("evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ]", 0-0) = 10*a + 3400 S("evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ]", 0-1) = 0 S("evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b)", 0-0) = a S("evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b)", 0-1) = b S("evalwcet2start(a, b) -> evalwcet2entryin(a, b)", 0-0) = a S("evalwcet2start(a, b) -> evalwcet2entryin(a, b)", 0-1) = b orients the transitions evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ] evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1) weakly and the transition evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ] strictly and produces the following problem: 7: T: (1, 1) evalwcet2start(a, b) -> evalwcet2entryin(a, b) (1, 1) evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b) (3*a + 13, 1) evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ] (?, 1) evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] (3*a + 8, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ] (3*a + 13, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ] (?, 1) evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1) (9*a + 34, 1) evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b) start location: evalwcet2start leaf cost: 2 A polynomial rank function with Pol(evalwcet2bb2in) = 6*V_1 - 2*V_2 + 1 Pol(evalwcet2bb1in) = 6*V_1 - 2*V_2 and size complexities S("evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b)", 0-0) = 10*a + 3400 S("evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b)", 0-1) = ? S("evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1)", 0-0) = 10*a + 3400 S("evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1)", 0-1) = ? S("evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ]", 0-0) = 10*a + 3400 S("evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ]", 0-1) = ? S("evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ]", 0-0) = 10*a + 3400 S("evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ]", 0-1) = ? S("evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\\ 9 >= b ]", 0-0) = 10*a + 3400 S("evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\\ 9 >= b ]", 0-1) = ? S("evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ]", 0-0) = 10*a + 3400 S("evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ]", 0-1) = 0 S("evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b)", 0-0) = a S("evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b)", 0-1) = b S("evalwcet2start(a, b) -> evalwcet2entryin(a, b)", 0-0) = a S("evalwcet2start(a, b) -> evalwcet2entryin(a, b)", 0-1) = b orients the transitions evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1) weakly and the transition evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] strictly and produces the following problem: 8: T: (1, 1) evalwcet2start(a, b) -> evalwcet2entryin(a, b) (1, 1) evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b) (3*a + 13, 1) evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ] (180*a^2 + 61983*a + 265213, 1) evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] (3*a + 8, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ] (3*a + 13, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ] (?, 1) evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1) (9*a + 34, 1) evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b) start location: evalwcet2start leaf cost: 2 Repeatedly propagating knowledge in problem 8 produces the following problem: 9: T: (1, 1) evalwcet2start(a, b) -> evalwcet2entryin(a, b) (1, 1) evalwcet2entryin(a, b) -> evalwcet2bb5in(a, b) (3*a + 13, 1) evalwcet2bb5in(a, b) -> evalwcet2bb2in(a, 0) [ 4 >= a ] (180*a^2 + 61983*a + 265213, 1) evalwcet2bb2in(a, b) -> evalwcet2bb1in(a, b) [ a >= 3 /\ 9 >= b ] (3*a + 8, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ 2 >= a ] (3*a + 13, 1) evalwcet2bb2in(a, b) -> evalwcet2bb4in(a, b) [ b >= 10 ] (180*a^2 + 61983*a + 265213, 1) evalwcet2bb1in(a, b) -> evalwcet2bb2in(a, b + 1) (9*a + 34, 1) evalwcet2bb4in(a, b) -> evalwcet2bb5in(a + 1, b) start location: evalwcet2start leaf cost: 2 Complexity upper bound 123984*a + 360*a^2 + 530498 Time: 0.198 sec (SMT: 0.185 sec)