4.90/2.40 WORST_CASE(Omega(n^2), O(n^2)) 4.90/2.41 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 4.90/2.41 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.90/2.41 4.90/2.41 4.90/2.41 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). 4.90/2.41 4.90/2.41 (0) CpxIntTrs 4.90/2.41 (1) Koat Proof [FINISHED, 198 ms] 4.90/2.41 (2) BOUNDS(1, n^2) 4.90/2.41 (3) Loat Proof [FINISHED, 680 ms] 4.90/2.41 (4) BOUNDS(n^2, INF) 4.90/2.41 4.90/2.41 4.90/2.41 ---------------------------------------- 4.90/2.41 4.90/2.41 (0) 4.90/2.41 Obligation: 4.90/2.41 Complexity Int TRS consisting of the following rules: 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 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 4.90/2.41 4.90/2.41 The start-symbols are:[eval_ex2_start_4] 4.90/2.41 4.90/2.41 4.90/2.41 ---------------------------------------- 4.90/2.41 4.90/2.41 (1) Koat Proof (FINISHED) 4.90/2.41 YES(?, 293*ar_1 + 20*ar_1^2 + 11) 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Initial complexity problem: 4.90/2.41 4.90/2.41 1: T: 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb0in(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex20(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex21(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex22(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex23(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex24(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex25(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex25(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex26(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex26(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex29(ar_0, ar_1, ar_2, ar_0 + 1)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex210(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex210(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(ar_3, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2stop(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 start location: koat_start 4.90/2.41 4.90/2.41 leaf cost: 0 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Repeatedly propagating knowledge in problem 1 produces the following problem: 4.90/2.41 4.90/2.41 2: T: 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb0in(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex20(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex21(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex22(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex23(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex24(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex25(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex25(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex26(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex26(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex29(ar_0, ar_1, ar_2, ar_0 + 1)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex210(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex210(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(ar_3, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2stop(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 start location: koat_start 4.90/2.41 4.90/2.41 leaf cost: 0 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 A polynomial rank function with 4.90/2.41 4.90/2.41 Pol(evalex2start) = 2 4.90/2.41 4.90/2.41 Pol(evalex2bb0in) = 2 4.90/2.41 4.90/2.41 Pol(evalex20) = 2 4.90/2.41 4.90/2.41 Pol(evalex21) = 2 4.90/2.41 4.90/2.41 Pol(evalex22) = 2 4.90/2.41 4.90/2.41 Pol(evalex23) = 2 4.90/2.41 4.90/2.41 Pol(evalex24) = 2 4.90/2.41 4.90/2.41 Pol(evalex2bb1in) = 2 4.90/2.41 4.90/2.41 Pol(evalex2bb2in) = 2 4.90/2.41 4.90/2.41 Pol(evalex2bb5in) = 1 4.90/2.41 4.90/2.41 Pol(evalex2bb3in) = 2 4.90/2.41 4.90/2.41 Pol(evalex2bb4in) = 2 4.90/2.41 4.90/2.41 Pol(evalex25) = 2 4.90/2.41 4.90/2.41 Pol(evalex26) = 2 4.90/2.41 4.90/2.41 Pol(evalex29) = 2 4.90/2.41 4.90/2.41 Pol(evalex210) = 2 4.90/2.41 4.90/2.41 Pol(evalex2stop) = 0 4.90/2.41 4.90/2.41 Pol(koat_start) = 2 4.90/2.41 4.90/2.41 orients all transitions weakly and the transitions 4.90/2.41 4.90/2.41 evalex2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2stop(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 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 ] 4.90/2.41 4.90/2.41 strictly and produces the following problem: 4.90/2.41 4.90/2.41 3: T: 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb0in(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex20(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex21(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex22(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex23(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex24(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex25(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex25(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex26(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex26(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex29(ar_0, ar_1, ar_2, ar_0 + 1)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex210(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex210(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(ar_3, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 2, Cost: 1) evalex2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2stop(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 start location: koat_start 4.90/2.41 4.90/2.41 leaf cost: 0 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 A polynomial rank function with 4.90/2.41 4.90/2.41 Pol(evalex2start) = V_2 4.90/2.41 4.90/2.41 Pol(evalex2bb0in) = V_2 4.90/2.41 4.90/2.41 Pol(evalex20) = V_2 4.90/2.41 4.90/2.41 Pol(evalex21) = V_2 4.90/2.41 4.90/2.41 Pol(evalex22) = V_2 4.90/2.41 4.90/2.41 Pol(evalex23) = V_2 4.90/2.41 4.90/2.41 Pol(evalex24) = V_2 4.90/2.41 4.90/2.41 Pol(evalex2bb1in) = -V_1 + V_2 + 1 4.90/2.41 4.90/2.41 Pol(evalex2bb2in) = -V_1 + V_2 4.90/2.41 4.90/2.41 Pol(evalex2bb5in) = -V_1 + V_2 4.90/2.41 4.90/2.41 Pol(evalex2bb3in) = -V_1 + V_2 4.90/2.41 4.90/2.41 Pol(evalex2bb4in) = -V_1 + V_2 4.90/2.41 4.90/2.41 Pol(evalex25) = -V_1 + V_2 4.90/2.41 4.90/2.41 Pol(evalex26) = -V_1 + V_2 4.90/2.41 4.90/2.41 Pol(evalex29) = V_2 - V_4 + 1 4.90/2.41 4.90/2.41 Pol(evalex210) = V_2 - V_4 + 1 4.90/2.41 4.90/2.41 Pol(evalex2stop) = -V_1 + V_2 4.90/2.41 4.90/2.41 Pol(koat_start) = V_2 4.90/2.41 4.90/2.41 orients all transitions weakly and the transition 4.90/2.41 4.90/2.41 evalex2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_1 >= ar_0 ] 4.90/2.41 4.90/2.41 strictly and produces the following problem: 4.90/2.41 4.90/2.41 4: T: 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb0in(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex20(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex21(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex22(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex23(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex24(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex25(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex25(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex26(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex26(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex29(ar_0, ar_1, ar_2, ar_0 + 1)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex210(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex210(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(ar_3, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 2, Cost: 1) evalex2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2stop(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 start location: koat_start 4.90/2.41 4.90/2.41 leaf cost: 0 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 A polynomial rank function with 4.90/2.41 4.90/2.41 Pol(evalex2bb4in) = 3 4.90/2.41 4.90/2.41 Pol(evalex29) = 2 4.90/2.41 4.90/2.41 Pol(evalex2bb3in) = 4 4.90/2.41 4.90/2.41 Pol(evalex25) = 4 4.90/2.41 4.90/2.41 Pol(evalex2bb2in) = 4 4.90/2.41 4.90/2.41 Pol(evalex210) = 1 4.90/2.41 4.90/2.41 Pol(evalex26) = 4 4.90/2.41 4.90/2.41 Pol(evalex2bb1in) = 0 4.90/2.41 4.90/2.41 and size complexities 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 4.90/2.41 4.90/2.41 S("evalex2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? 4.90/2.41 4.90/2.41 S("evalex210(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-0) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex210(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ? 4.90/2.41 4.90/2.41 S("evalex210(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-3) = ? 4.90/2.41 4.90/2.41 S("evalex29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex210(ar_0, ar_1, ar_2, ar_3))", 0-0) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex210(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 4.90/2.41 4.90/2.41 S("evalex29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex210(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? 4.90/2.41 4.90/2.41 S("evalex2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex29(ar_0, ar_1, ar_2, ar_0 + 1))", 0-0) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex29(ar_0, ar_1, ar_2, ar_0 + 1))", 0-2) = ? 4.90/2.41 4.90/2.41 S("evalex2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex29(ar_0, ar_1, ar_2, ar_0 + 1))", 0-3) = ? 4.90/2.41 4.90/2.41 S("evalex26(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex26(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ? 4.90/2.41 4.90/2.41 S("evalex26(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = ? 4.90/2.41 4.90/2.41 S("evalex25(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex26(ar_0, ar_1, ar_2, ar_3))", 0-0) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex25(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex26(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 4.90/2.41 4.90/2.41 S("evalex25(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex26(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? 4.90/2.41 4.90/2.41 S("evalex2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex25(ar_0, ar_1, ar_2, ar_3))", 0-0) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex25(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 4.90/2.41 4.90/2.41 S("evalex2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex25(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 S("evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3))", 0-0) = 1 4.90/2.41 4.90/2.41 S("evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.90/2.41 4.90/2.41 S("evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.90/2.41 4.90/2.41 S("evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 orients the transitions 4.90/2.41 4.90/2.41 evalex2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex29(ar_0, ar_1, ar_2, ar_0 + 1)) 4.90/2.41 4.90/2.41 evalex2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex25(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 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 ] 4.90/2.41 4.90/2.41 evalex2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.90/2.41 4.90/2.41 evalex29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex210(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 evalex26(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.90/2.41 4.90/2.41 evalex25(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex26(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 evalex210(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(ar_3, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 weakly and the transitions 4.90/2.41 4.90/2.41 evalex2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex29(ar_0, ar_1, ar_2, ar_0 + 1)) 4.90/2.41 4.90/2.41 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 ] 4.90/2.41 4.90/2.41 evalex29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex210(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 evalex210(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(ar_3, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 strictly and produces the following problem: 4.90/2.41 4.90/2.41 5: T: 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb0in(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex20(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex21(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex22(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex23(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex24(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex25(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex25(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex26(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex26(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.90/2.41 4.90/2.41 (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)) 4.90/2.41 4.90/2.41 (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)) 4.90/2.41 4.90/2.41 (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)) 4.90/2.41 4.90/2.41 (Comp: 2, Cost: 1) evalex2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2stop(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 start location: koat_start 4.90/2.41 4.90/2.41 leaf cost: 0 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 A polynomial rank function with 4.90/2.41 4.90/2.41 Pol(evalex2bb3in) = V_2 - V_3 4.90/2.41 4.90/2.41 Pol(evalex25) = V_2 - V_3 4.90/2.41 4.90/2.41 Pol(evalex2bb2in) = V_2 - V_3 + 1 4.90/2.41 4.90/2.41 Pol(evalex26) = V_2 - V_3 4.90/2.41 4.90/2.41 and size complexities 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex210(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(ar_3, ar_1, ar_2, ar_3))", 0-2) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex210(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex29(ar_0, ar_1, ar_2, ar_0 + 1))", 0-2) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex26(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex25(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex26(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex25(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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) = ? 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 S("evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3))", 0-0) = 1 4.90/2.41 4.90/2.41 S("evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3))", 0-1) = ar_1 4.90/2.41 4.90/2.41 S("evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3))", 0-2) = ar_2 4.90/2.41 4.90/2.41 S("evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3))", 0-3) = ar_3 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 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 4.90/2.41 4.90/2.41 orients the transitions 4.90/2.41 4.90/2.41 evalex2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex25(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 evalex2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.90/2.41 4.90/2.41 evalex26(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.90/2.41 4.90/2.41 evalex25(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex26(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 weakly and the transition 4.90/2.41 4.90/2.41 evalex2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ] 4.90/2.41 4.90/2.41 strictly and produces the following problem: 4.90/2.41 4.90/2.41 6: T: 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb0in(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex20(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex21(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex22(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex23(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex24(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex25(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex25(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex26(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: ?, Cost: 1) evalex26(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) 4.90/2.41 4.90/2.41 (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)) 4.90/2.41 4.90/2.41 (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)) 4.90/2.41 4.90/2.41 (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)) 4.90/2.41 4.90/2.41 (Comp: 2, Cost: 1) evalex2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2stop(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 start location: koat_start 4.90/2.41 4.90/2.41 leaf cost: 0 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Repeatedly propagating knowledge in problem 6 produces the following problem: 4.90/2.41 4.90/2.41 7: T: 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb0in(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex2bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex20(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex20(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex21(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex21(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex22(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex22(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex23(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex23(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex24(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (Comp: 1, Cost: 1) evalex24(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2bb1in(1, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 (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)) 4.90/2.41 4.90/2.41 (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)) 4.90/2.41 4.90/2.41 (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)) 4.90/2.41 4.90/2.41 (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)) 4.90/2.41 4.90/2.41 (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)) 4.90/2.41 4.90/2.41 (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)) 4.90/2.41 4.90/2.41 (Comp: 2, Cost: 1) evalex2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalex2stop(ar_0, ar_1, ar_2, ar_3)) 4.90/2.41 4.90/2.41 (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 ] 4.90/2.41 4.90/2.41 start location: koat_start 4.90/2.41 4.90/2.41 leaf cost: 0 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Complexity upper bound 293*ar_1 + 20*ar_1^2 + 11 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Time: 0.198 sec (SMT: 0.150 sec) 4.90/2.41 4.90/2.41 4.90/2.41 ---------------------------------------- 4.90/2.41 4.90/2.41 (2) 4.90/2.41 BOUNDS(1, n^2) 4.90/2.41 4.90/2.41 ---------------------------------------- 4.90/2.41 4.90/2.41 (3) Loat Proof (FINISHED) 4.90/2.41 4.90/2.41 4.90/2.41 ### Pre-processing the ITS problem ### 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Initial linear ITS problem 4.90/2.41 4.90/2.41 Start location: evalex2start 4.90/2.41 4.90/2.41 0: evalex2start -> evalex2bb0in : [], cost: 1 4.90/2.41 4.90/2.41 1: evalex2bb0in -> evalex20 : [], cost: 1 4.90/2.41 4.90/2.41 2: evalex20 -> evalex21 : [], cost: 1 4.90/2.41 4.90/2.41 3: evalex21 -> evalex22 : [], cost: 1 4.90/2.41 4.90/2.41 4: evalex22 -> evalex23 : [], cost: 1 4.90/2.41 4.90/2.41 5: evalex23 -> evalex24 : [], cost: 1 4.90/2.41 4.90/2.41 6: evalex24 -> evalex2bb1in : A'=1, [], cost: 1 4.90/2.41 4.90/2.41 7: evalex2bb1in -> evalex2bb2in : C'=A, [ B>=A ], cost: 1 4.90/2.41 4.90/2.41 8: evalex2bb1in -> evalex2bb5in : [ A>=1+B ], cost: 1 4.90/2.41 4.90/2.41 9: evalex2bb2in -> evalex2bb3in : [ B>=C ], cost: 1 4.90/2.41 4.90/2.41 10: evalex2bb2in -> evalex2bb4in : [ C>=1+B ], cost: 1 4.90/2.41 4.90/2.41 11: evalex2bb3in -> evalex25 : [], cost: 1 4.90/2.41 4.90/2.41 12: evalex25 -> evalex26 : [], cost: 1 4.90/2.41 4.90/2.41 13: evalex26 -> evalex2bb2in : C'=1+C, [], cost: 1 4.90/2.41 4.90/2.41 14: evalex2bb4in -> evalex29 : D'=1+A, [], cost: 1 4.90/2.41 4.90/2.41 15: evalex29 -> evalex210 : [], cost: 1 4.90/2.41 4.90/2.41 16: evalex210 -> evalex2bb1in : A'=D, [], cost: 1 4.90/2.41 4.90/2.41 17: evalex2bb5in -> evalex2stop : [], cost: 1 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Removed unreachable and leaf rules: 4.90/2.41 4.90/2.41 Start location: evalex2start 4.90/2.41 4.90/2.41 0: evalex2start -> evalex2bb0in : [], cost: 1 4.90/2.41 4.90/2.41 1: evalex2bb0in -> evalex20 : [], cost: 1 4.90/2.41 4.90/2.41 2: evalex20 -> evalex21 : [], cost: 1 4.90/2.41 4.90/2.41 3: evalex21 -> evalex22 : [], cost: 1 4.90/2.41 4.90/2.41 4: evalex22 -> evalex23 : [], cost: 1 4.90/2.41 4.90/2.41 5: evalex23 -> evalex24 : [], cost: 1 4.90/2.41 4.90/2.41 6: evalex24 -> evalex2bb1in : A'=1, [], cost: 1 4.90/2.41 4.90/2.41 7: evalex2bb1in -> evalex2bb2in : C'=A, [ B>=A ], cost: 1 4.90/2.41 4.90/2.41 9: evalex2bb2in -> evalex2bb3in : [ B>=C ], cost: 1 4.90/2.41 4.90/2.41 10: evalex2bb2in -> evalex2bb4in : [ C>=1+B ], cost: 1 4.90/2.41 4.90/2.41 11: evalex2bb3in -> evalex25 : [], cost: 1 4.90/2.41 4.90/2.41 12: evalex25 -> evalex26 : [], cost: 1 4.90/2.41 4.90/2.41 13: evalex26 -> evalex2bb2in : C'=1+C, [], cost: 1 4.90/2.41 4.90/2.41 14: evalex2bb4in -> evalex29 : D'=1+A, [], cost: 1 4.90/2.41 4.90/2.41 15: evalex29 -> evalex210 : [], cost: 1 4.90/2.41 4.90/2.41 16: evalex210 -> evalex2bb1in : A'=D, [], cost: 1 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 ### Simplification by acceleration and chaining ### 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Eliminated locations (on linear paths): 4.90/2.41 4.90/2.41 Start location: evalex2start 4.90/2.41 4.90/2.41 23: evalex2start -> evalex2bb1in : A'=1, [], cost: 7 4.90/2.41 4.90/2.41 7: evalex2bb1in -> evalex2bb2in : C'=A, [ B>=A ], cost: 1 4.90/2.41 4.90/2.41 28: evalex2bb2in -> evalex2bb2in : C'=1+C, [ B>=C ], cost: 4 4.90/2.41 4.90/2.41 29: evalex2bb2in -> evalex2bb1in : A'=1+A, D'=1+A, [ C>=1+B ], cost: 4 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Accelerating simple loops of location 8. 4.90/2.41 4.90/2.41 Accelerating the following rules: 4.90/2.41 4.90/2.41 28: evalex2bb2in -> evalex2bb2in : C'=1+C, [ B>=C ], cost: 4 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Accelerated rule 28 with metering function 1-C+B, yielding the new rule 30. 4.90/2.41 4.90/2.41 Removing the simple loops: 28. 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Accelerated all simple loops using metering functions (where possible): 4.90/2.41 4.90/2.41 Start location: evalex2start 4.90/2.41 4.90/2.41 23: evalex2start -> evalex2bb1in : A'=1, [], cost: 7 4.90/2.41 4.90/2.41 7: evalex2bb1in -> evalex2bb2in : C'=A, [ B>=A ], cost: 1 4.90/2.41 4.90/2.41 29: evalex2bb2in -> evalex2bb1in : A'=1+A, D'=1+A, [ C>=1+B ], cost: 4 4.90/2.41 4.90/2.41 30: evalex2bb2in -> evalex2bb2in : C'=1+B, [ B>=C ], cost: 4-4*C+4*B 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Chained accelerated rules (with incoming rules): 4.90/2.41 4.90/2.41 Start location: evalex2start 4.90/2.41 4.90/2.41 23: evalex2start -> evalex2bb1in : A'=1, [], cost: 7 4.90/2.41 4.90/2.41 7: evalex2bb1in -> evalex2bb2in : C'=A, [ B>=A ], cost: 1 4.90/2.41 4.90/2.41 31: evalex2bb1in -> evalex2bb2in : C'=1+B, [ B>=A ], cost: 5-4*A+4*B 4.90/2.41 4.90/2.41 29: evalex2bb2in -> evalex2bb1in : A'=1+A, D'=1+A, [ C>=1+B ], cost: 4 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Eliminated locations (on tree-shaped paths): 4.90/2.41 4.90/2.41 Start location: evalex2start 4.90/2.41 4.90/2.41 23: evalex2start -> evalex2bb1in : A'=1, [], cost: 7 4.90/2.41 4.90/2.41 32: evalex2bb1in -> evalex2bb1in : A'=1+A, C'=1+B, D'=1+A, [ B>=A ], cost: 9-4*A+4*B 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Accelerating simple loops of location 7. 4.90/2.41 4.90/2.41 Accelerating the following rules: 4.90/2.41 4.90/2.41 32: evalex2bb1in -> evalex2bb1in : A'=1+A, C'=1+B, D'=1+A, [ B>=A ], cost: 9-4*A+4*B 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Accelerated rule 32 with metering function 1-A+B, yielding the new rule 33. 4.90/2.41 4.90/2.41 Removing the simple loops: 32. 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Accelerated all simple loops using metering functions (where possible): 4.90/2.41 4.90/2.41 Start location: evalex2start 4.90/2.41 4.90/2.41 23: evalex2start -> evalex2bb1in : A'=1, [], cost: 7 4.90/2.41 4.90/2.41 33: evalex2bb1in -> evalex2bb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=A ], cost: 11+4*(-1+A-B)*A-11*A-4*(-1+A-B)*B-2*(-1+A-B)^2+11*B 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Chained accelerated rules (with incoming rules): 4.90/2.41 4.90/2.41 Start location: evalex2start 4.90/2.41 4.90/2.41 23: evalex2start -> evalex2bb1in : A'=1, [], cost: 7 4.90/2.41 4.90/2.41 34: evalex2start -> evalex2bb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=1 ], cost: 7+2*B^2+7*B 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Removed unreachable locations (and leaf rules with constant cost): 4.90/2.41 4.90/2.41 Start location: evalex2start 4.90/2.41 4.90/2.41 34: evalex2start -> evalex2bb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=1 ], cost: 7+2*B^2+7*B 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 ### Computing asymptotic complexity ### 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Fully simplified ITS problem 4.90/2.41 4.90/2.41 Start location: evalex2start 4.90/2.41 4.90/2.41 34: evalex2start -> evalex2bb1in : A'=1+B, C'=1+B, D'=1+B, [ B>=1 ], cost: 7+2*B^2+7*B 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Computing asymptotic complexity for rule 34 4.90/2.41 4.90/2.41 Solved the limit problem by the following transformations: 4.90/2.41 4.90/2.41 Created initial limit problem: 4.90/2.41 4.90/2.41 7+2*B^2+7*B (+), B (+/+!) [not solved] 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 removing all constraints (solved by SMT) 4.90/2.41 4.90/2.41 resulting limit problem: [solved] 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 applying transformation rule (C) using substitution {B==n} 4.90/2.41 4.90/2.41 resulting limit problem: 4.90/2.41 4.90/2.41 [solved] 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Solution: 4.90/2.41 4.90/2.41 B / n 4.90/2.41 4.90/2.41 Resulting cost 7+7*n+2*n^2 has complexity: Poly(n^2) 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Found new complexity Poly(n^2). 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 Obtained the following overall complexity (w.r.t. the length of the input n): 4.90/2.41 4.90/2.41 Complexity: Poly(n^2) 4.90/2.41 4.90/2.41 Cpx degree: 2 4.90/2.41 4.90/2.41 Solved cost: 7+7*n+2*n^2 4.90/2.41 4.90/2.41 Rule cost: 7+2*B^2+7*B 4.90/2.41 4.90/2.41 Rule guard: [ B>=1 ] 4.90/2.41 4.90/2.41 4.90/2.41 4.90/2.41 WORST_CASE(Omega(n^2),?) 4.90/2.41 4.90/2.41 4.90/2.41 ---------------------------------------- 4.90/2.41 4.90/2.41 (4) 4.90/2.41 BOUNDS(n^2, INF) 4.90/2.45 EOF