/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 86 ms] (2) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_i, v_j)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb1_in(0, v_.01, v_i, v_j)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_i, v_j)) :|: v_.0 < 100 eval_foo_bb1_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb3_in(v_.0, 5, v_i, v_j)) :|: v_.0 >= 100 eval_foo_bb2_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01, v_i, v_j)) :|: TRUE eval_foo_bb3_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_i, v_j)) :|: v_.01 < 21 eval_foo_bb3_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_i, v_j)) :|: v_.01 >= 21 eval_foo_bb4_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_bb3_in(v_.0, v_.01 + 3, v_i, v_j)) :|: TRUE eval_foo_bb5_in(v_.0, v_.01, v_i, v_j) -> Com_1(eval_foo_stop(v_.0, v_.01, v_i, v_j)) :|: TRUE The start-symbols are:[eval_foo_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 243) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(0, Ar_1)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, 5)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb4in(Ar_0, Ar_1)) [ 20 >= Ar_1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb5in(Ar_0, Ar_1)) [ Ar_1 >= 21 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1 + 3)) (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostart(Ar_0, Ar_1)) [ 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(0, Ar_1)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, 5)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb4in(Ar_0, Ar_1)) [ 20 >= Ar_1 ] (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb5in(Ar_0, Ar_1)) [ Ar_1 >= 21 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1 + 3)) (Comp: ?, Cost: 1) evalfoobb5in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = 3 Pol(evalfoobb0in) = 3 Pol(evalfoobb1in) = 3 Pol(evalfoobb2in) = 3 Pol(evalfoobb3in) = 2 Pol(evalfoobb4in) = 2 Pol(evalfoobb5in) = 1 Pol(evalfoostop) = 0 Pol(koat_start) = 3 orients all transitions weakly and the transitions evalfoobb5in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb5in(Ar_0, Ar_1)) [ Ar_1 >= 21 ] evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, 5)) [ Ar_0 >= 100 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(0, Ar_1)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ 99 >= Ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, 5)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb4in(Ar_0, Ar_1)) [ 20 >= Ar_1 ] (Comp: 3, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb5in(Ar_0, Ar_1)) [ Ar_1 >= 21 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1 + 3)) (Comp: 3, Cost: 1) evalfoobb5in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = 100 Pol(evalfoobb0in) = 100 Pol(evalfoobb1in) = -V_1 + 100 Pol(evalfoobb2in) = -V_1 + 99 Pol(evalfoobb3in) = -V_1 - V_2 + 21 Pol(evalfoobb4in) = -V_1 - V_2 + 20 Pol(evalfoobb5in) = -V_1 - V_2 Pol(evalfoostop) = -V_1 - V_2 Pol(koat_start) = 100 orients all transitions weakly and the transition evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ 99 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(0, Ar_1)) (Comp: 100, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ 99 >= Ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, 5)) [ Ar_0 >= 100 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb4in(Ar_0, Ar_1)) [ 20 >= Ar_1 ] (Comp: 3, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb5in(Ar_0, Ar_1)) [ Ar_1 >= 21 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1 + 3)) (Comp: 3, Cost: 1) evalfoobb5in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostart(Ar_0, Ar_1)) [ 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) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(0, Ar_1)) (Comp: 100, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ 99 >= Ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, 5)) [ Ar_0 >= 100 ] (Comp: 100, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_0 + 1, Ar_1)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb4in(Ar_0, Ar_1)) [ 20 >= Ar_1 ] (Comp: 3, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb5in(Ar_0, Ar_1)) [ Ar_1 >= 21 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1 + 3)) (Comp: 3, Cost: 1) evalfoobb5in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = 16 Pol(evalfoobb0in) = 16 Pol(evalfoobb1in) = 16 Pol(evalfoobb2in) = 16 Pol(evalfoobb3in) = -V_2 + 21 Pol(evalfoobb4in) = -V_2 + 18 Pol(evalfoobb5in) = -V_2 Pol(evalfoostop) = -V_2 Pol(koat_start) = 16 orients all transitions weakly and the transition evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb4in(Ar_0, Ar_1)) [ 20 >= Ar_1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(0, Ar_1)) (Comp: 100, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ 99 >= Ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, 5)) [ Ar_0 >= 100 ] (Comp: 100, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_0 + 1, Ar_1)) (Comp: 16, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb4in(Ar_0, Ar_1)) [ 20 >= Ar_1 ] (Comp: 3, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb5in(Ar_0, Ar_1)) [ Ar_1 >= 21 ] (Comp: ?, Cost: 1) evalfoobb4in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1 + 3)) (Comp: 3, Cost: 1) evalfoobb5in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1) -> Com_1(evalfoobb0in(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(0, Ar_1)) (Comp: 100, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb2in(Ar_0, Ar_1)) [ 99 >= Ar_0 ] (Comp: 3, Cost: 1) evalfoobb1in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, 5)) [ Ar_0 >= 100 ] (Comp: 100, Cost: 1) evalfoobb2in(Ar_0, Ar_1) -> Com_1(evalfoobb1in(Ar_0 + 1, Ar_1)) (Comp: 16, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb4in(Ar_0, Ar_1)) [ 20 >= Ar_1 ] (Comp: 3, Cost: 1) evalfoobb3in(Ar_0, Ar_1) -> Com_1(evalfoobb5in(Ar_0, Ar_1)) [ Ar_1 >= 21 ] (Comp: 16, Cost: 1) evalfoobb4in(Ar_0, Ar_1) -> Com_1(evalfoobb3in(Ar_0, Ar_1 + 3)) (Comp: 3, Cost: 1) evalfoobb5in(Ar_0, Ar_1) -> Com_1(evalfoostop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalfoostart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 243 Time: 0.057 sec (SMT: 0.047 sec) ---------------------------------------- (2) BOUNDS(1, 1)