/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^2)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 85 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_jama_ex7_start(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb0_in(v_i.0, v_j.0, v_m, v_n)) :|: TRUE eval_jama_ex7_bb0_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb1_in(v_n, v_j.0, v_m, v_n)) :|: TRUE eval_jama_ex7_bb1_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb2_in(v_i.0, v_m, v_m, v_n)) :|: v_i.0 >= 1 eval_jama_ex7_bb1_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb5_in(v_i.0, v_j.0, v_m, v_n)) :|: v_i.0 < 1 eval_jama_ex7_bb2_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb3_in(v_i.0, v_j.0, v_m, v_n)) :|: v_j.0 >= 1 eval_jama_ex7_bb2_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb4_in(v_i.0, v_j.0, v_m, v_n)) :|: v_j.0 < 1 eval_jama_ex7_bb3_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb2_in(v_i.0, v_j.0 - 1, v_m, v_n)) :|: TRUE eval_jama_ex7_bb4_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_bb1_in(v_i.0 - 1, v_j.0, v_m, v_n)) :|: TRUE eval_jama_ex7_bb5_in(v_i.0, v_j.0, v_m, v_n) -> Com_1(eval_jama_ex7_stop(v_i.0, v_j.0, v_m, v_n)) :|: TRUE The start-symbols are:[eval_jama_ex7_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 5*Ar_1 + 2*Ar_1*Ar_3 + 2*Ar_3 + 11) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) (Comp: ?, Cost: 1) evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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) evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) (Comp: ?, Cost: 1) evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaljamaex7start) = 2 Pol(evaljamaex7bb0in) = 2 Pol(evaljamaex7bb1in) = 2 Pol(evaljamaex7bb2in) = 2 Pol(evaljamaex7bb5in) = 1 Pol(evaljamaex7bb3in) = 2 Pol(evaljamaex7bb4in) = 2 Pol(evaljamaex7stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3)) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) (Comp: ?, Cost: 1) evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaljamaex7start) = V_2 + 1 Pol(evaljamaex7bb0in) = V_2 + 1 Pol(evaljamaex7bb1in) = V_1 + 1 Pol(evaljamaex7bb2in) = V_1 Pol(evaljamaex7bb5in) = V_1 Pol(evaljamaex7bb3in) = V_1 Pol(evaljamaex7bb4in) = V_1 Pol(evaljamaex7stop) = V_1 Pol(koat_start) = V_2 + 1 orients all transitions weakly and the transition evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + 1, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) (Comp: ?, Cost: 1) evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaljamaex7bb4in) = 1 Pol(evaljamaex7bb1in) = 0 Pol(evaljamaex7bb3in) = 2 Pol(evaljamaex7bb2in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3))", 0-0) = ? S("evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3))", 0-1) = Ar_1 S("evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3))", 0-2) = ? S("evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3))", 0-3) = Ar_3 S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-0) = ? S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-1) = Ar_1 S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-2) = ? S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-3) = Ar_3 S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-0) = ? S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-1) = Ar_1 S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-2) = ? S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-3) = Ar_3 S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-0) = ? S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-1) = Ar_1 S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-2) = ? S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-3) = Ar_3 S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ]", 0-0) = ? S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ]", 0-1) = Ar_1 S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ]", 0-2) = Ar_3 S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ]", 0-3) = Ar_3 S("evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_1 S("evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] weakly and the transitions evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + 1, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: 2*Ar_1 + 2, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) (Comp: 2*Ar_1 + 2, Cost: 1) evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaljamaex7bb3in) = V_3 - 1 Pol(evaljamaex7bb2in) = V_3 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 3*Ar_1 + 162 S("evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3))", 0-0) = 3*Ar_1 + 18 S("evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3))", 0-0) = 3*Ar_1 + 18 S("evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3))", 0-1) = Ar_1 S("evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3))", 0-2) = ? S("evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3))", 0-3) = Ar_3 S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-0) = 3*Ar_1 + 18 S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-1) = Ar_1 S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-2) = ? S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-3) = Ar_3 S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-0) = 3*Ar_1 + 18 S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-1) = Ar_1 S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-2) = ? S("evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-3) = Ar_3 S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-0) = 3*Ar_1 + 54 S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-1) = Ar_1 S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-2) = ? S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-3) = Ar_3 S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ]", 0-0) = 3*Ar_1 + 18 S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ]", 0-1) = Ar_1 S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ]", 0-2) = Ar_3 S("evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ]", 0-3) = Ar_3 S("evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_1 S("evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] weakly and the transition evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + 1, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: Ar_1*Ar_3 + Ar_3, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: 2*Ar_1 + 2, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) (Comp: 2*Ar_1 + 2, Cost: 1) evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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) evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evaljamaex7bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + 1, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evaljamaex7bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: Ar_1*Ar_3 + Ar_3, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: 2*Ar_1 + 2, Cost: 1) evaljamaex7bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: Ar_1*Ar_3 + Ar_3, Cost: 1) evaljamaex7bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb2in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) (Comp: 2*Ar_1 + 2, Cost: 1) evaljamaex7bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7bb1in(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evaljamaex7bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evaljamaex7start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 5*Ar_1 + 2*Ar_1*Ar_3 + 2*Ar_3 + 11 Time: 0.079 sec (SMT: 0.061 sec) ---------------------------------------- (2) BOUNDS(1, n^2)