/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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_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: 0.076 sec (SMT: 0.057 sec) ---------------------------------------- (2) BOUNDS(1, n^1)