/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 75 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_speed_pldi10_ex4_start(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb0_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n)) :|: TRUE eval_speed_pldi10_ex4_bb0_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb1_in(v_n, v_.1, 1, v_flag.1, v_n)) :|: TRUE eval_speed_pldi10_ex4_bb1_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb2_in(v_.0, v_.0, v_flag.0, 0, v_n)) :|: v_flag.0 > 0 eval_speed_pldi10_ex4_bb1_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb4_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n)) :|: v_flag.0 <= 0 eval_speed_pldi10_ex4_bb2_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb3_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n)) :|: v_.1 > 0 eval_speed_pldi10_ex4_bb2_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb1_in(v_.1, v_.1, v_flag.1, v_flag.1, v_n)) :|: v_.1 <= 0 eval_speed_pldi10_ex4_bb3_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_bb2_in(v_.0, v_.1 - 1, v_flag.0, 1, v_n)) :|: TRUE eval_speed_pldi10_ex4_bb4_in(v_.0, v_.1, v_flag.0, v_flag.1, v_n) -> Com_1(eval_speed_pldi10_ex4_stop(v_.0, v_.1, v_flag.0, v_flag.1, v_n)) :|: TRUE The start-symbols are:[eval_speed_pldi10_ex4_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 5*ar_1 + 8) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1)) (Comp: ?, Cost: 1) evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(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(evalspeedpldi10ex4start(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) evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1)) (Comp: ?, Cost: 1) evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(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(evalspeedpldi10ex4start(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(evalspeedpldi10ex4start) = 2 Pol(evalspeedpldi10ex4bb0in) = 2 Pol(evalspeedpldi10ex4bb1in) = 2 Pol(evalspeedpldi10ex4bb2in) = 2 Pol(evalspeedpldi10ex4bb4in) = 1 Pol(evalspeedpldi10ex4bb3in) = 2 Pol(evalspeedpldi10ex4stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4)) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(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) evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1)) (Comp: 2, Cost: 1) evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(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(evalspeedpldi10ex4start(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(evalspeedpldi10ex4start) = V_2 Pol(evalspeedpldi10ex4bb0in) = V_2 Pol(evalspeedpldi10ex4bb1in) = V_1 Pol(evalspeedpldi10ex4bb2in) = V_4 Pol(evalspeedpldi10ex4bb4in) = V_1 Pol(evalspeedpldi10ex4bb3in) = V_4 - 1 Pol(evalspeedpldi10ex4stop) = V_1 Pol(koat_start) = V_2 orients all transitions weakly and the transition evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: ar_1, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1)) (Comp: 2, Cost: 1) evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(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(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 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) evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: ar_1, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ] (Comp: ar_1, Cost: 1) evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1)) (Comp: 2, Cost: 1) evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(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(evalspeedpldi10ex4start(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(evalspeedpldi10ex4bb2in) = V_5 Pol(evalspeedpldi10ex4bb1in) = V_3 and size complexities S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4start(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(evalspeedpldi10ex4start(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(evalspeedpldi10ex4start(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(evalspeedpldi10ex4start(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(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 S("evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = 2*ar_1 S("evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = 1 S("evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = 2*ar_1 S("evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = 1 S("evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-0) = 2*ar_1 S("evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-1) = ar_1 S("evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-2) = 1 S("evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-3) = 2*ar_1 S("evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1))", 0-4) = 1 S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-0) = 2*ar_1 S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-1) = ar_1 S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-2) = 1 S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-3) = 2*ar_1 S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ]", 0-4) = 1 S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-0) = 2*ar_1 S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-1) = ar_1 S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-2) = 1 S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-3) = 2*ar_1 S("evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ]", 0-4) = 1 S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-0) = 2*ar_1 S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-1) = ar_1 S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-2) = 1 S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-3) = 2*ar_1 S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ]", 0-4) = 1 S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-0) = 2*ar_1 S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-1) = ar_1 S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-2) = 1 S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-3) = 2*ar_1 S("evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ]", 0-4) = 0 S("evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-0) = ar_1 S("evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-1) = ar_1 S("evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-2) = 1 S("evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-3) = ar_3 S("evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4))", 0-4) = ar_4 S("evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 orients the transitions evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ] evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ] weakly and the transition evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4)) (Comp: ar_1 + 1, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: ar_1, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ] (Comp: ar_1, Cost: 1) evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1)) (Comp: 2, Cost: 1) evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(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(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 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) evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalspeedpldi10ex4bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_1, ar_1, 1, ar_3, ar_4)) (Comp: ar_1 + 1, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_0, 0)) [ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalspeedpldi10ex4bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 ] (Comp: ar_1, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] (Comp: 2*ar_1 + 1, Cost: 1) evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb1in(ar_3, ar_1, ar_4, ar_3, ar_4)) [ 0 >= ar_3 ] (Comp: ar_1, Cost: 1) evalspeedpldi10ex4bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4bb2in(ar_0, ar_1, ar_2, ar_3 - 1, 1)) (Comp: 2, Cost: 1) evalspeedpldi10ex4bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpldi10ex4stop(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(evalspeedpldi10ex4start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 5*ar_1 + 8 Time: 0.089 sec (SMT: 0.073 sec) ---------------------------------------- (2) BOUNDS(1, n^1)