/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 76 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp) -> Com_1(eval_foo_bb1_in(v_x, v_.01, v_res, v_restmp, v_x, v_xtmp)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp) -> Com_1(eval_foo_bb2_in(v_.0, v_.0, v_res, v_restmp, v_x, v_xtmp)) :|: v_.0 > 1 eval_foo_bb1_in(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp)) :|: v_.0 <= 1 eval_foo_bb2_in(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp)) :|: v_.01 > 1 eval_foo_bb2_in(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp)) :|: v_.01 <= 1 eval_foo_bb3_in(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp) -> Com_1(eval_foo_bb2_in(v_.0, v_.01 - 2, v_res, v_restmp, v_x, v_xtmp)) :|: TRUE eval_foo_bb4_in(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp) -> Com_1(eval_foo_bb1_in(v_.01, v_.01, v_res, v_restmp, v_x, v_xtmp)) :|: TRUE eval_foo_bb5_in(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp) -> Com_1(eval_foo_stop(v_.0, v_.01, v_res, v_restmp, v_x, v_xtmp)) :|: TRUE The start-symbols are:[eval_foo_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 10*Ar_1 + 6) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_0)) [ Ar_0 >= 2 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2)) [ 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 2 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2)) [ 1 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2 - 2)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2)) [ 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_0)) [ Ar_0 >= 2 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2)) [ 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 2 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2)) [ 1 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2 - 2)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2)) [ 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(evalfoobb5in) = 1 Pol(evalfoobb3in) = 2 Pol(evalfoobb4in) = 2 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2)) evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2)) [ 1 >= Ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_0)) [ Ar_0 >= 2 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2)) [ 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 2 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2)) [ 1 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2 - 2)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = 2*V_2 Pol(evalfoobb0in) = 2*V_2 Pol(evalfoobb1in) = 2*V_1 Pol(evalfoobb2in) = V_3 + 1 Pol(evalfoobb5in) = 2*V_1 Pol(evalfoobb3in) = V_3 Pol(evalfoobb4in) = 2*V_3 Pol(evalfoostop) = 2*V_1 Pol(koat_start) = 2*V_2 orients all transitions weakly and the transitions evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 2 ] evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_0)) [ Ar_0 >= 2 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_2)) (Comp: 2*Ar_1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_0)) [ Ar_0 >= 2 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2)) [ 1 >= Ar_0 ] (Comp: 2*Ar_1, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 2 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2)) [ 1 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2 - 2)) (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_2)) (Comp: 2*Ar_1, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_0)) [ Ar_0 >= 2 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb5in(Ar_0, Ar_1, Ar_2)) [ 1 >= Ar_0 ] (Comp: 2*Ar_1, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 2 ] (Comp: 2*Ar_1, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb4in(Ar_0, Ar_1, Ar_2)) [ 1 >= Ar_2 ] (Comp: 2*Ar_1, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2 - 2)) (Comp: 2*Ar_1, Cost: 1) evalfoobb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoobb1in(Ar_2, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evalfoobb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 10*Ar_1 + 6 Time: 0.051 sec (SMT: 0.041 sec) ---------------------------------------- (2) BOUNDS(1, n^1)