/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).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, 133 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 622 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_ex2_start(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_bb0_in(v_3, v_n, v_x_0, v_y_0)) :|: TRUE eval_ex2_bb0_in(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_0(v_3, v_n, v_x_0, v_y_0)) :|: TRUE eval_ex2_0(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_1(v_3, v_n, v_x_0, v_y_0)) :|: TRUE eval_ex2_1(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_2(v_3, v_n, v_x_0, v_y_0)) :|: TRUE eval_ex2_2(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_3(v_3, v_n, v_x_0, v_y_0)) :|: TRUE eval_ex2_3(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_4(v_3, v_n, v_x_0, v_y_0)) :|: TRUE eval_ex2_4(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_bb1_in(v_3, v_n, 1, v_y_0)) :|: TRUE eval_ex2_bb1_in(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_bb2_in(v_3, v_n, v_x_0, v_x_0)) :|: v_x_0 <= v_n eval_ex2_bb1_in(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_bb5_in(v_3, v_n, v_x_0, v_y_0)) :|: v_x_0 > v_n eval_ex2_bb2_in(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_bb3_in(v_3, v_n, v_x_0, v_y_0)) :|: v_y_0 <= v_n eval_ex2_bb2_in(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_bb4_in(v_3, v_n, v_x_0, v_y_0)) :|: v_y_0 > v_n eval_ex2_bb3_in(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_5(v_3, v_n, v_x_0, v_y_0)) :|: TRUE eval_ex2_5(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_6(v_3, v_n, v_x_0, v_y_0)) :|: TRUE eval_ex2_6(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_bb2_in(v_3, v_n, v_x_0, v_y_0 + 1)) :|: TRUE eval_ex2_bb4_in(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_9(v_x_0 + 1, v_n, v_x_0, v_y_0)) :|: TRUE eval_ex2_9(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_10(v_3, v_n, v_x_0, v_y_0)) :|: TRUE eval_ex2_10(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_bb1_in(v_3, v_n, v_3, v_y_0)) :|: TRUE eval_ex2_bb5_in(v_3, v_n, v_x_0, v_y_0) -> Com_1(eval_ex2_stop(v_3, v_n, v_x_0, v_y_0)) :|: TRUE The start-symbols are:[eval_ex2_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 293*Ar_1 + 20*Ar_1^2 + 11) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1)) (Comp: ?, Cost: 1) evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1)) (Comp: ?, Cost: 1) evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalex2start) = 2 Pol(evalex2bb0in) = 2 Pol(evalex20) = 2 Pol(evalex21) = 2 Pol(evalex22) = 2 Pol(evalex23) = 2 Pol(evalex24) = 2 Pol(evalex2bb1in) = 2 Pol(evalex2bb2in) = 2 Pol(evalex2bb5in) = 1 Pol(evalex2bb3in) = 2 Pol(evalex2bb4in) = 2 Pol(evalex25) = 2 Pol(evalex26) = 2 Pol(evalex29) = 2 Pol(evalex210) = 2 Pol(evalex2stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3)) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1)) (Comp: ?, Cost: 1) evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalex2start) = V_2 Pol(evalex2bb0in) = V_2 Pol(evalex20) = V_2 Pol(evalex21) = V_2 Pol(evalex22) = V_2 Pol(evalex23) = V_2 Pol(evalex24) = V_2 Pol(evalex2bb1in) = -V_1 + V_2 + 1 Pol(evalex2bb2in) = -V_1 + V_2 Pol(evalex2bb5in) = -V_1 + V_2 + 1 Pol(evalex2bb3in) = -V_1 + V_2 Pol(evalex2bb4in) = -V_1 + V_2 Pol(evalex25) = -V_1 + V_2 Pol(evalex26) = -V_1 + V_2 Pol(evalex29) = V_2 - V_4 + 1 Pol(evalex210) = V_2 - V_4 + 1 Pol(evalex2stop) = -V_1 + V_2 + 1 Pol(koat_start) = V_2 orients all transitions weakly and the transition evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1)) (Comp: ?, Cost: 1) evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalex2bb4in) = 3 Pol(evalex29) = 2 Pol(evalex2bb3in) = 4 Pol(evalex25) = 4 Pol(evalex2bb2in) = 4 Pol(evalex210) = 1 Pol(evalex26) = 4 Pol(evalex2bb1in) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1))", 0-0) = ? S("evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1))", 0-1) = Ar_1 S("evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1))", 0-2) = ? S("evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1))", 0-3) = ? S("evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-0) = ? S("evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-1) = Ar_1 S("evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-2) = ? S("evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-3) = ? S("evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ]", 0-0) = ? S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ]", 0-2) = ? S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ]", 0-3) = ? S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ]", 0-0) = ? S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ]", 0-1) = Ar_1 S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ]", 0-2) = ? S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ]", 0-3) = ? S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = ? S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = ? S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = ? S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ]", 0-0) = ? S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ]", 0-1) = Ar_1 S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ]", 0-2) = ? S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ]", 0-3) = ? S("evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3))", 0-0) = 1 S("evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1)) evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3)) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3)) evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3)) evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3)) weakly and the transitions evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1)) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3)) evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3)) strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] (Comp: 4*Ar_1, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1)) (Comp: 4*Ar_1, Cost: 1) evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalex2bb3in) = V_2 - V_3 Pol(evalex25) = V_2 - V_3 Pol(evalex2bb2in) = V_2 - V_3 + 1 Pol(evalex26) = V_2 - V_3 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 4*Ar_1 + 272 S("evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = 4*Ar_1 + 4*Ar_3 + 1024 S("evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-0) = 4*Ar_1 + 16 S("evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-3) = 4*Ar_1 + 64 S("evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 4*Ar_1 + 256 S("evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = 4*Ar_1 + 16 S("evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1))", 0-0) = 4*Ar_1 + 64 S("evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1))", 0-1) = Ar_1 S("evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1))", 0-2) = ? S("evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1))", 0-3) = 4*Ar_1 + 16 S("evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-0) = 4*Ar_1 + 16 S("evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-1) = Ar_1 S("evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-2) = ? S("evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-3) = 4*Ar_1 + 4*Ar_3 + 1024 S("evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 4*Ar_1 + 16 S("evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = 4*Ar_1 + 4*Ar_3 + 1024 S("evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 4*Ar_1 + 16 S("evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = 4*Ar_1 + 4*Ar_3 + 1024 S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ]", 0-0) = 4*Ar_1 + 16 S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ]", 0-2) = ? S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ]", 0-3) = 4*Ar_1 + 4*Ar_3 + 4096 S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ]", 0-0) = 4*Ar_1 + 16 S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ]", 0-1) = Ar_1 S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ]", 0-2) = ? S("evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ]", 0-3) = 4*Ar_1 + 4*Ar_3 + 1024 S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 4*Ar_1 + 68 S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = ? S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = 4*Ar_1 + 4*Ar_3 + 256 S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ]", 0-0) = 4*Ar_1 + 16 S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ]", 0-1) = Ar_1 S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ]", 0-2) = 4*Ar_1 + 68 S("evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ]", 0-3) = 4*Ar_1 + 4*Ar_3 + 256 S("evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3))", 0-0) = 1 S("evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3)) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3)) weakly and the transition evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 5*Ar_1^2 + 69*Ar_1, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] (Comp: 4*Ar_1, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1)) (Comp: 4*Ar_1, Cost: 1) evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (Comp: 1, Cost: 1) evalex2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex2bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex20(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex20(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex21(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex21(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex22(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex22(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex23(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex24(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalex24(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalex2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 5*Ar_1^2 + 69*Ar_1, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] (Comp: 4*Ar_1, Cost: 1) evalex2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] (Comp: 5*Ar_1^2 + 69*Ar_1, Cost: 1) evalex2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex25(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 5*Ar_1^2 + 69*Ar_1, Cost: 1) evalex25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex26(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 5*Ar_1^2 + 69*Ar_1, Cost: 1) evalex26(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalex2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex29(Ar_0, Ar_1, Ar_2, Ar_0 + 1)) (Comp: 4*Ar_1, Cost: 1) evalex29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex210(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalex210(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2bb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalex2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalex2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 293*Ar_1 + 20*Ar_1^2 + 11 Time: 0.148 sec (SMT: 0.105 sec) ---------------------------------------- (2) BOUNDS(1, n^2) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalex2start 0: evalex2start -> evalex2bb0in : [], cost: 1 1: evalex2bb0in -> evalex20 : [], cost: 1 2: evalex20 -> evalex21 : [], cost: 1 3: evalex21 -> evalex22 : [], cost: 1 4: evalex22 -> evalex23 : [], cost: 1 5: evalex23 -> evalex24 : [], cost: 1 6: evalex24 -> evalex2bb1in : A'=1, [], cost: 1 7: evalex2bb1in -> evalex2bb2in : C'=A, [ B>=A ], cost: 1 8: evalex2bb1in -> evalex2bb5in : [ A>=1+B ], cost: 1 9: evalex2bb2in -> evalex2bb3in : [ B>=C ], cost: 1 10: evalex2bb2in -> evalex2bb4in : [ C>=1+B ], cost: 1 11: evalex2bb3in -> evalex25 : [], cost: 1 12: evalex25 -> evalex26 : [], cost: 1 13: evalex26 -> evalex2bb2in : C'=1+C, [], cost: 1 14: evalex2bb4in -> evalex29 : D'=1+A, [], cost: 1 15: evalex29 -> evalex210 : [], cost: 1 16: evalex210 -> evalex2bb1in : A'=D, [], cost: 1 17: evalex2bb5in -> evalex2stop : [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: evalex2start -> evalex2bb0in : [], cost: 1 Removed unreachable and leaf rules: Start location: evalex2start 0: evalex2start -> evalex2bb0in : [], cost: 1 1: evalex2bb0in -> evalex20 : [], cost: 1 2: evalex20 -> evalex21 : [], cost: 1 3: evalex21 -> evalex22 : [], cost: 1 4: evalex22 -> evalex23 : [], cost: 1 5: evalex23 -> evalex24 : [], cost: 1 6: evalex24 -> evalex2bb1in : A'=1, [], cost: 1 7: evalex2bb1in -> evalex2bb2in : C'=A, [ B>=A ], cost: 1 9: evalex2bb2in -> evalex2bb3in : [ B>=C ], cost: 1 10: evalex2bb2in -> evalex2bb4in : [ C>=1+B ], cost: 1 11: evalex2bb3in -> evalex25 : [], cost: 1 12: evalex25 -> evalex26 : [], cost: 1 13: evalex26 -> evalex2bb2in : C'=1+C, [], cost: 1 14: evalex2bb4in -> evalex29 : D'=1+A, [], cost: 1 15: evalex29 -> evalex210 : [], cost: 1 16: evalex210 -> evalex2bb1in : A'=D, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalex2start 23: evalex2start -> evalex2bb1in : A'=1, [], cost: 7 7: evalex2bb1in -> evalex2bb2in : C'=A, [ B>=A ], cost: 1 28: evalex2bb2in -> evalex2bb2in : C'=1+C, [ B>=C ], cost: 4 29: evalex2bb2in -> evalex2bb1in : A'=1+A, D'=1+A, [ C>=1+B ], cost: 4 Accelerating simple loops of location 8. Accelerating the following rules: 28: evalex2bb2in -> evalex2bb2in : C'=1+C, [ B>=C ], cost: 4 Accelerated rule 28 with metering function 1-C+B, yielding the new rule 30. Removing the simple loops: 28. Accelerated all simple loops using metering functions (where possible): Start location: evalex2start 23: evalex2start -> evalex2bb1in : A'=1, [], cost: 7 7: evalex2bb1in -> evalex2bb2in : C'=A, [ B>=A ], cost: 1 29: evalex2bb2in -> evalex2bb1in : A'=1+A, D'=1+A, [ C>=1+B ], cost: 4 30: evalex2bb2in -> evalex2bb2in : C'=1+B, [ B>=C ], cost: 4-4*C+4*B Chained accelerated rules (with incoming rules): Start location: evalex2start 23: evalex2start -> evalex2bb1in : A'=1, [], cost: 7 7: evalex2bb1in -> evalex2bb2in : C'=A, [ B>=A ], cost: 1 31: evalex2bb1in -> evalex2bb2in : C'=1+B, [ B>=A ], cost: 5-4*A+4*B 29: evalex2bb2in -> evalex2bb1in : A'=1+A, D'=1+A, [ C>=1+B ], cost: 4 Eliminated locations (on tree-shaped paths): Start location: evalex2start 23: evalex2start -> evalex2bb1in : A'=1, [], cost: 7 32: evalex2bb1in -> evalex2bb1in : A'=1+A, C'=1+B, D'=1+A, [ B>=A ], cost: 9-4*A+4*B Accelerating simple loops of location 7. Accelerating the following rules: 32: evalex2bb1in -> evalex2bb1in : A'=1+A, C'=1+B, D'=1+A, [ B>=A ], cost: 9-4*A+4*B Accelerated rule 32 with metering function 1-A+B, yielding the new rule 33. Removing the simple loops: 32. Accelerated all simple loops using metering functions (where possible): Start location: evalex2start 23: evalex2start -> evalex2bb1in : A'=1, [], cost: 7 33: evalex2bb1in -> evalex2bb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=A ], cost: 11-11*A-4*(-1+A-B)*B-2*(-1+A-B)^2+11*B+4*(-1+A-B)*A Chained accelerated rules (with incoming rules): Start location: evalex2start 23: evalex2start -> evalex2bb1in : A'=1, [], cost: 7 34: evalex2start -> evalex2bb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=1 ], cost: 7+7*B+2*B^2 Removed unreachable locations (and leaf rules with constant cost): Start location: evalex2start 34: evalex2start -> evalex2bb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=1 ], cost: 7+7*B+2*B^2 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalex2start 34: evalex2start -> evalex2bb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=1 ], cost: 7+7*B+2*B^2 Computing asymptotic complexity for rule 34 Solved the limit problem by the following transformations: Created initial limit problem: 7+7*B+2*B^2 (+), B (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {B==n} resulting limit problem: [solved] Solution: B / n Resulting cost 7+2*n^2+7*n 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: 7+2*n^2+7*n Rule cost: 7+7*B+2*B^2 Rule guard: [ B>=1 ] WORST_CASE(Omega(n^2),?) ---------------------------------------- (4) BOUNDS(n^2, INF)