/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 75 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_exmini_start(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_bb0_in(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: TRUE eval_exmini_bb0_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_bb1_in(v_i, v_j, v_k, v_i, v_j, v_k)) :|: TRUE eval_exmini_bb1_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_bb2_in(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: v_.0 <= 100 && v_.01 <= v_.02 eval_exmini_bb1_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_bb3_in(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: v_.0 > 100 eval_exmini_bb1_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_bb3_in(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: v_.01 > v_.02 eval_exmini_bb2_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_bb1_in(v_.01, v_.0 + 1, v_.02 - 1, v_i, v_j, v_k)) :|: TRUE eval_exmini_bb3_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_exmini_stop(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: TRUE The start-symbols are:[eval_exmini_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 2*Ar_1 + 2*Ar_3 + 2*Ar_5 + 210) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalexministart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalexminibb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalexminibb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb1in(Ar_2, Ar_1, Ar_0 + 1, Ar_3, Ar_4 - 1, Ar_5)) (Comp: ?, Cost: 1) evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexministop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexministart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 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) evalexministart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalexminibb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalexminibb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb1in(Ar_2, Ar_1, Ar_0 + 1, Ar_3, Ar_4 - 1, Ar_5)) (Comp: ?, Cost: 1) evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexministop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexministart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalexministart) = 2 Pol(evalexminibb0in) = 2 Pol(evalexminibb1in) = 2 Pol(evalexminibb2in) = 2 Pol(evalexminibb3in) = 1 Pol(evalexministop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexministop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 + 1 ] evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 101 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalexministart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalexminibb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) (Comp: ?, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: 2, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 101 ] (Comp: 2, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalexminibb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb1in(Ar_2, Ar_1, Ar_0 + 1, Ar_3, Ar_4 - 1, Ar_5)) (Comp: 2, Cost: 1) evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexministop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexministart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalexministart) = -V_2 - V_4 + V_6 + 101 Pol(evalexminibb0in) = -V_2 - V_4 + V_6 + 101 Pol(evalexminibb1in) = -V_1 - V_3 + V_5 + 101 Pol(evalexminibb2in) = -V_1 - V_3 + V_5 + 100 Pol(evalexminibb3in) = -V_1 - V_3 + V_5 Pol(evalexministop) = -V_1 - V_3 + V_5 Pol(koat_start) = -V_2 - V_4 + V_6 + 101 orients all transitions weakly and the transition evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_0 /\ Ar_4 >= Ar_2 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalexministart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalexminibb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) (Comp: Ar_1 + Ar_3 + Ar_5 + 101, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: 2, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 101 ] (Comp: 2, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalexminibb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb1in(Ar_2, Ar_1, Ar_0 + 1, Ar_3, Ar_4 - 1, Ar_5)) (Comp: 2, Cost: 1) evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexministop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexministart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 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) evalexministart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalexminibb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_5, Ar_5)) (Comp: Ar_1 + Ar_3 + Ar_5 + 101, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_0 /\ Ar_4 >= Ar_2 ] (Comp: 2, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 101 ] (Comp: 2, Cost: 1) evalexminibb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 + 1 ] (Comp: Ar_1 + Ar_3 + Ar_5 + 101, Cost: 1) evalexminibb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexminibb1in(Ar_2, Ar_1, Ar_0 + 1, Ar_3, Ar_4 - 1, Ar_5)) (Comp: 2, Cost: 1) evalexminibb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexministop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalexministart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 2*Ar_1 + 2*Ar_3 + 2*Ar_5 + 210 Time: 0.074 sec (SMT: 0.057 sec) ---------------------------------------- (2) BOUNDS(1, n^1)