/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 130 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 732 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_speedNestedMultipleDep_start(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_bb0_in(v_1, v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedNestedMultipleDep_bb0_in(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_0(v_1, v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedNestedMultipleDep_0(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_1(v_1, v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedNestedMultipleDep_1(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_2(v_1, v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedNestedMultipleDep_2(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_3(v_1, v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedNestedMultipleDep_3(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_4(v_1, v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedNestedMultipleDep_4(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_5(v_1, v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedNestedMultipleDep_5(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_6(v_1, v_m, v_n, v_x_0, v_y_0)) :|: TRUE eval_speedNestedMultipleDep_6(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, 0, v_y_0)) :|: TRUE eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_bb2_in(v_1, v_m, v_n, v_x_0, v_y_0)) :|: v_x_0 < v_n eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_bb5_in(v_1, v_m, v_n, v_x_0, v_y_0)) :|: v_x_0 >= v_n eval_speedNestedMultipleDep_bb2_in(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_bb3_in(v_x_0 + 1, v_m, v_n, v_x_0, 0)) :|: TRUE eval_speedNestedMultipleDep_bb3_in(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_bb4_in(v_1, v_m, v_n, v_x_0, v_y_0)) :|: v_y_0 < v_m eval_speedNestedMultipleDep_bb3_in(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_bb1_in(v_1, v_m, v_n, v_1, v_y_0)) :|: v_y_0 >= v_m eval_speedNestedMultipleDep_bb4_in(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_bb3_in(v_1, v_m, v_n, v_x_0, v_y_0 + 1)) :|: TRUE eval_speedNestedMultipleDep_bb5_in(v_1, v_m, v_n, v_x_0, v_y_0) -> Com_1(eval_speedNestedMultipleDep_stop(v_1, v_m, v_n, v_x_0, v_y_0)) :|: TRUE The start-symbols are:[eval_speedNestedMultipleDep_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 3*Ar_1 + 2*Ar_1*Ar_4 + 13) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(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) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart) = 2 Pol(evalspeedNestedMultipleDepbb0in) = 2 Pol(evalspeedNestedMultipleDep0) = 2 Pol(evalspeedNestedMultipleDep1) = 2 Pol(evalspeedNestedMultipleDep2) = 2 Pol(evalspeedNestedMultipleDep3) = 2 Pol(evalspeedNestedMultipleDep4) = 2 Pol(evalspeedNestedMultipleDep5) = 2 Pol(evalspeedNestedMultipleDep6) = 2 Pol(evalspeedNestedMultipleDepbb1in) = 2 Pol(evalspeedNestedMultipleDepbb2in) = 2 Pol(evalspeedNestedMultipleDepbb5in) = 1 Pol(evalspeedNestedMultipleDepbb3in) = 2 Pol(evalspeedNestedMultipleDepbb4in) = 2 Pol(evalspeedNestedMultipleDepstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart) = V_2 Pol(evalspeedNestedMultipleDepbb0in) = V_2 Pol(evalspeedNestedMultipleDep0) = V_2 Pol(evalspeedNestedMultipleDep1) = V_2 Pol(evalspeedNestedMultipleDep2) = V_2 Pol(evalspeedNestedMultipleDep3) = V_2 Pol(evalspeedNestedMultipleDep4) = V_2 Pol(evalspeedNestedMultipleDep5) = V_2 Pol(evalspeedNestedMultipleDep6) = V_2 Pol(evalspeedNestedMultipleDepbb1in) = -V_1 + V_2 Pol(evalspeedNestedMultipleDepbb2in) = -V_1 + V_2 - 1 Pol(evalspeedNestedMultipleDepbb5in) = -V_1 + V_2 Pol(evalspeedNestedMultipleDepbb3in) = V_2 - V_3 Pol(evalspeedNestedMultipleDepbb4in) = V_2 - V_3 Pol(evalspeedNestedMultipleDepstop) = -V_1 + V_2 Pol(koat_start) = V_2 orients all transitions weakly and the transition evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(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) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepbb4in) = 1 Pol(evalspeedNestedMultipleDepbb3in) = 1 Pol(evalspeedNestedMultipleDepbb1in) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_1 + Ar_2 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-3) = 0 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-2) = Ar_1 + Ar_2 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = Ar_1 + Ar_2 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 0 S("evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] weakly and the transition evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepbb4in) = -V_4 + V_5 - 1 Pol(evalspeedNestedMultipleDepbb3in) = -V_4 + V_5 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(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(evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_1 + Ar_2 S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-2) = Ar_1 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-3) = 0 S("evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-2) = Ar_1 + Ar_2 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = Ar_1 + Ar_2 S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-4) = Ar_4 S("evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 0 S("evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] weakly and the transition evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: Ar_1*Ar_4, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 7 produces the following problem: 8: T: (Comp: 1, Cost: 1) evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDepbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedNestedMultipleDep6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: Ar_1*Ar_4, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: Ar_1, Cost: 1) evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: Ar_1*Ar_4, Cost: 1) evalspeedNestedMultipleDepbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2, Cost: 1) evalspeedNestedMultipleDepbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedNestedMultipleDepstop(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(evalspeedNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 3*Ar_1 + 2*Ar_1*Ar_4 + 13 Time: 0.180 sec (SMT: 0.124 sec) ---------------------------------------- (2) BOUNDS(1, n^2) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalspeedNestedMultipleDepstart 0: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb0in : [], cost: 1 1: evalspeedNestedMultipleDepbb0in -> evalspeedNestedMultipleDep0 : [], cost: 1 2: evalspeedNestedMultipleDep0 -> evalspeedNestedMultipleDep1 : [], cost: 1 3: evalspeedNestedMultipleDep1 -> evalspeedNestedMultipleDep2 : [], cost: 1 4: evalspeedNestedMultipleDep2 -> evalspeedNestedMultipleDep3 : [], cost: 1 5: evalspeedNestedMultipleDep3 -> evalspeedNestedMultipleDep4 : [], cost: 1 6: evalspeedNestedMultipleDep4 -> evalspeedNestedMultipleDep5 : [], cost: 1 7: evalspeedNestedMultipleDep5 -> evalspeedNestedMultipleDep6 : [], cost: 1 8: evalspeedNestedMultipleDep6 -> evalspeedNestedMultipleDepbb1in : A'=0, [], cost: 1 9: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb2in : [ B>=1+A ], cost: 1 10: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb5in : [ A>=B ], cost: 1 11: evalspeedNestedMultipleDepbb2in -> evalspeedNestedMultipleDepbb3in : C'=1+A, D'=0, [], cost: 1 12: evalspeedNestedMultipleDepbb3in -> evalspeedNestedMultipleDepbb4in : [ E>=1+D ], cost: 1 13: evalspeedNestedMultipleDepbb3in -> evalspeedNestedMultipleDepbb1in : A'=C, [ D>=E ], cost: 1 14: evalspeedNestedMultipleDepbb4in -> evalspeedNestedMultipleDepbb3in : D'=1+D, [], cost: 1 15: evalspeedNestedMultipleDepbb5in -> evalspeedNestedMultipleDepstop : [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb0in : [], cost: 1 Removed unreachable and leaf rules: Start location: evalspeedNestedMultipleDepstart 0: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb0in : [], cost: 1 1: evalspeedNestedMultipleDepbb0in -> evalspeedNestedMultipleDep0 : [], cost: 1 2: evalspeedNestedMultipleDep0 -> evalspeedNestedMultipleDep1 : [], cost: 1 3: evalspeedNestedMultipleDep1 -> evalspeedNestedMultipleDep2 : [], cost: 1 4: evalspeedNestedMultipleDep2 -> evalspeedNestedMultipleDep3 : [], cost: 1 5: evalspeedNestedMultipleDep3 -> evalspeedNestedMultipleDep4 : [], cost: 1 6: evalspeedNestedMultipleDep4 -> evalspeedNestedMultipleDep5 : [], cost: 1 7: evalspeedNestedMultipleDep5 -> evalspeedNestedMultipleDep6 : [], cost: 1 8: evalspeedNestedMultipleDep6 -> evalspeedNestedMultipleDepbb1in : A'=0, [], cost: 1 9: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb2in : [ B>=1+A ], cost: 1 11: evalspeedNestedMultipleDepbb2in -> evalspeedNestedMultipleDepbb3in : C'=1+A, D'=0, [], cost: 1 12: evalspeedNestedMultipleDepbb3in -> evalspeedNestedMultipleDepbb4in : [ E>=1+D ], cost: 1 13: evalspeedNestedMultipleDepbb3in -> evalspeedNestedMultipleDepbb1in : A'=C, [ D>=E ], cost: 1 14: evalspeedNestedMultipleDepbb4in -> evalspeedNestedMultipleDepbb3in : D'=1+D, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalspeedNestedMultipleDepstart 23: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb1in : A'=0, [], cost: 9 24: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb3in : C'=1+A, D'=0, [ B>=1+A ], cost: 2 13: evalspeedNestedMultipleDepbb3in -> evalspeedNestedMultipleDepbb1in : A'=C, [ D>=E ], cost: 1 25: evalspeedNestedMultipleDepbb3in -> evalspeedNestedMultipleDepbb3in : D'=1+D, [ E>=1+D ], cost: 2 Accelerating simple loops of location 11. Accelerating the following rules: 25: evalspeedNestedMultipleDepbb3in -> evalspeedNestedMultipleDepbb3in : D'=1+D, [ E>=1+D ], cost: 2 Accelerated rule 25 with metering function -D+E, yielding the new rule 26. Removing the simple loops: 25. Accelerated all simple loops using metering functions (where possible): Start location: evalspeedNestedMultipleDepstart 23: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb1in : A'=0, [], cost: 9 24: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb3in : C'=1+A, D'=0, [ B>=1+A ], cost: 2 13: evalspeedNestedMultipleDepbb3in -> evalspeedNestedMultipleDepbb1in : A'=C, [ D>=E ], cost: 1 26: evalspeedNestedMultipleDepbb3in -> evalspeedNestedMultipleDepbb3in : D'=E, [ E>=1+D ], cost: -2*D+2*E Chained accelerated rules (with incoming rules): Start location: evalspeedNestedMultipleDepstart 23: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb1in : A'=0, [], cost: 9 24: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb3in : C'=1+A, D'=0, [ B>=1+A ], cost: 2 27: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb3in : C'=1+A, D'=E, [ B>=1+A && E>=1 ], cost: 2+2*E 13: evalspeedNestedMultipleDepbb3in -> evalspeedNestedMultipleDepbb1in : A'=C, [ D>=E ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalspeedNestedMultipleDepstart 23: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb1in : A'=0, [], cost: 9 28: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb1in : A'=1+A, C'=1+A, D'=0, [ B>=1+A && 0>=E ], cost: 3 29: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb1in : A'=1+A, C'=1+A, D'=E, [ B>=1+A && E>=1 ], cost: 3+2*E Accelerating simple loops of location 9. Accelerating the following rules: 28: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb1in : A'=1+A, C'=1+A, D'=0, [ B>=1+A && 0>=E ], cost: 3 29: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb1in : A'=1+A, C'=1+A, D'=E, [ B>=1+A && E>=1 ], cost: 3+2*E Accelerated rule 28 with metering function -A+B, yielding the new rule 30. Accelerated rule 29 with metering function -A+B, yielding the new rule 31. Removing the simple loops: 28 29. Accelerated all simple loops using metering functions (where possible): Start location: evalspeedNestedMultipleDepstart 23: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb1in : A'=0, [], cost: 9 30: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb1in : A'=B, C'=B, D'=0, [ B>=1+A && 0>=E ], cost: -3*A+3*B 31: evalspeedNestedMultipleDepbb1in -> evalspeedNestedMultipleDepbb1in : A'=B, C'=B, D'=E, [ B>=1+A && E>=1 ], cost: -2*(A-B)*E-3*A+3*B Chained accelerated rules (with incoming rules): Start location: evalspeedNestedMultipleDepstart 23: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb1in : A'=0, [], cost: 9 32: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb1in : A'=B, C'=B, D'=0, [ B>=1 && 0>=E ], cost: 9+3*B 33: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb1in : A'=B, C'=B, D'=E, [ B>=1 && E>=1 ], cost: 9+2*E*B+3*B Removed unreachable locations (and leaf rules with constant cost): Start location: evalspeedNestedMultipleDepstart 32: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb1in : A'=B, C'=B, D'=0, [ B>=1 && 0>=E ], cost: 9+3*B 33: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb1in : A'=B, C'=B, D'=E, [ B>=1 && E>=1 ], cost: 9+2*E*B+3*B ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalspeedNestedMultipleDepstart 32: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb1in : A'=B, C'=B, D'=0, [ B>=1 && 0>=E ], cost: 9+3*B 33: evalspeedNestedMultipleDepstart -> evalspeedNestedMultipleDepbb1in : A'=B, C'=B, D'=E, [ B>=1 && E>=1 ], cost: 9+2*E*B+3*B Computing asymptotic complexity for rule 32 Solved the limit problem by the following transformations: Created initial limit problem: 9+3*B (+), 1-E (+/+!), B (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {E==-n,B==n} resulting limit problem: [solved] Solution: E / -n B / n Resulting cost 9+3*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Computing asymptotic complexity for rule 33 Solved the limit problem by the following transformations: Created initial limit problem: E (+/+!), 9+2*E*B+3*B (+), B (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {E==n,B==n} resulting limit problem: [solved] Solution: E / n B / n Resulting cost 9+3*n+2*n^2 has complexity: Poly(n^2) Found new complexity Poly(n^2). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^2) Cpx degree: 2 Solved cost: 9+3*n+2*n^2 Rule cost: 9+2*E*B+3*B Rule guard: [ B>=1 && E>=1 ] WORST_CASE(Omega(n^2),?) ---------------------------------------- (4) BOUNDS(n^2, INF)