/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 470 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb1_in(v_x, v_.01, v_.1, v_res, v_x, v_y, v_ytmp)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb2_in(v_.0, v_y, v_.0, v_res, v_x, v_y, v_ytmp)) :|: v_.0 >= v_y && v_y > 0 eval_foo_bb1_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb7_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp)) :|: v_.0 < v_y eval_foo_bb1_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb7_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp)) :|: v_y <= 0 eval_foo_bb2_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp)) :|: v_.01 < 0 eval_foo_bb2_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp)) :|: v_.01 > 0 eval_foo_bb2_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb6_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp)) :|: v_.01 >= 0 && v_.01 <= 0 eval_foo_bb3_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp)) :|: v_.01 > 0 eval_foo_bb3_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp)) :|: v_.01 <= 0 eval_foo_bb4_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb2_in(v_.0, v_.01 - 1, v_.1 - 1, v_res, v_x, v_y, v_ytmp)) :|: TRUE eval_foo_bb5_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb2_in(v_.0, v_.01 + 1, v_.1 + 1, v_res, v_x, v_y, v_ytmp)) :|: TRUE eval_foo_bb6_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_bb1_in(v_.1, v_.01, v_.1, v_res, v_x, v_y, v_ytmp)) :|: TRUE eval_foo_bb7_in(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp) -> Com_1(eval_foo_stop(v_.0, v_.01, v_.1, v_res, v_x, v_y, v_ytmp)) :|: TRUE The start-symbols are:[eval_foo_start_7] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 14*ar_1 + 8) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1)) (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1)) (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1)) (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1)) (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = 2 Pol(evalfoobb0in) = 2 Pol(evalfoobb1in) = 2 Pol(evalfoobb2in) = 2 Pol(evalfoobb7in) = 1 Pol(evalfoobb3in) = 2 Pol(evalfoobb6in) = 2 Pol(evalfoobb4in) = 2 Pol(evalfoobb5in) = 2 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1)) (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1)) (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) (Comp: 2, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = V_2 Pol(evalfoobb0in) = V_2 Pol(evalfoobb1in) = V_1 Pol(evalfoobb2in) = -V_4 + V_5 Pol(evalfoobb7in) = V_1 Pol(evalfoobb3in) = -V_4 + V_5 Pol(evalfoobb6in) = V_5 Pol(evalfoobb4in) = -V_4 + V_5 Pol(evalfoobb5in) = -V_4 + V_5 Pol(evalfoostop) = V_1 Pol(koat_start) = V_2 orients all transitions weakly and the transition evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\ ar_2 >= 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4)) (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1)) (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1)) (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) (Comp: 2, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb6in) = 1 Pol(evalfoobb1in) = 0 Pol(evalfoobb5in) = 2 Pol(evalfoobb2in) = 2 Pol(evalfoobb4in) = 2 Pol(evalfoobb3in) = 2 and size complexities S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 S("evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ? S("evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ? S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-0) = ? S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-3) = 0 S("evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-4) = ? S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1))", 0-0) = ? S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1))", 0-1) = ar_1 S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1))", 0-2) = ar_2 S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1))", 0-3) = ? S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1))", 0-4) = ? S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1))", 0-0) = ? S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1))", 0-1) = ar_1 S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1))", 0-2) = ar_2 S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1))", 0-3) = ? S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1))", 0-4) = ? S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-0) = ? S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-1) = ar_1 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-2) = ar_2 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-3) = ? S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-4) = ? S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-0) = ? S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-1) = ar_1 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-2) = ar_2 S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-3) = ? S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-4) = ? S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 = 0 ]", 0-0) = ? S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 = 0 ]", 0-1) = ar_1 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 = 0 ]", 0-2) = ar_2 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 = 0 ]", 0-3) = 0 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 = 0 ]", 0-4) = ? S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-0) = ? S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-1) = ar_1 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-2) = ar_2 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-3) = ? S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-4) = ? S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-0) = ? S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-1) = ar_1 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-2) = ar_2 S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-3) = ? S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-4) = ? S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-0) = ? S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-1) = ar_1 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-2) = ar_2 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-3) = ar_3 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-4) = ? S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]", 0-0) = ? S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ar_2 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]", 0-3) = ar_3 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ]", 0-4) = ? S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\\ ar_2 >= 1 ]", 0-0) = ? S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\\ ar_2 >= 1 ]", 0-1) = ar_1 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\\ ar_2 >= 1 ]", 0-2) = ar_2 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\\ ar_2 >= 1 ]", 0-3) = ar_2 S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\\ ar_2 >= 1 ]", 0-4) = ? S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_1 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 orients the transitions evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1)) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1)) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 ] evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 = 0 ] evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] weakly and the transitions evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 = 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4)) (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: 2*ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1)) (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1)) (Comp: 2*ar_1, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) (Comp: 2, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 5 to obtain the following invariants: For symbol evalfoobb2in: -X_4 + X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb3in: -X_4 + X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb4in: X_5 - 1 >= 0 /\ X_4 + X_5 - 2 >= 0 /\ -X_4 + X_5 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ X_1 + X_5 - 2 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb5in: -X_4 + X_5 >= 0 /\ -X_4 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalfoobb6in: X_5 >= 0 /\ X_4 + X_5 >= 0 /\ -X_4 + X_5 >= 0 /\ X_3 + X_5 - 1 >= 0 /\ X_1 + X_5 - 1 >= 0 /\ -X_4 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - 1 >= 0 This yielded the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 2*ar_1, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 0 /\ ar_3 + ar_4 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ -ar_3 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1)) [ -ar_3 + ar_4 >= 0 /\ -ar_3 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ] (Comp: 2*ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\ ar_2 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 6: evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4 + 1)) [ -ar_3 + ar_4 >= 0 /\ -ar_3 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 + 1 ] We thus obtain the following problem: 7: T: (Comp: 2*ar_1, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 0 /\ ar_3 + ar_4 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ -ar_3 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 2*ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 0 ] (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ] (Comp: 2, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoobb6in) = 3*V_5 Pol(evalfoobb1in) = 3*V_1 Pol(evalfoobb2in) = 3*V_5 Pol(evalfoobb4in) = 3*V_5 - 2 Pol(evalfoobb3in) = 3*V_5 - 1 Pol(evalfoobb7in) = 3*V_1 Pol(evalfoostop) = 3*V_1 Pol(evalfoobb0in) = 3*V_2 Pol(evalfoostart) = 3*V_2 Pol(koat_start) = 3*V_2 orients all transitions weakly and the transitions evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ] evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ] strictly and produces the following problem: 8: T: (Comp: 2*ar_1, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 0 /\ ar_3 + ar_4 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ -ar_3 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 2*ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 0 ] (Comp: 3*ar_1, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4 - 1)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 3*ar_1, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ] (Comp: 3*ar_1, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ] (Comp: 2, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ar_1, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_2, ar_0)) [ ar_0 >= ar_2 /\ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 14*ar_1 + 8 Time: 0.426 sec (SMT: 0.328 sec) ---------------------------------------- (2) BOUNDS(1, n^1)