/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 518 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 810 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_start_start(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb0_in(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE eval_start_bb0_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_0(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE eval_start_0(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_1(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE eval_start_1(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_2(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE eval_start_2(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb1_in(v_x, v_3, v_x, v_y, v_z_0)) :|: v_y >= 0 eval_start_2(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb6_in(v__0, v_3, v_x, v_y, v_z_0)) :|: v_y < 0 eval_start_bb1_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb2_in(v__0, v_3, v_x, v_y, v_z_0)) :|: v__0 > v_y eval_start_bb1_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb5_in(v__0, v_3, v_x, v_y, v_z_0)) :|: v__0 <= v_y eval_start_bb2_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb3_in(v__0, v__0 - v_y - 1, v_x, v_y, v_y)) :|: TRUE eval_start_bb3_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb4_in(v__0, v_3, v_x, v_y, v_z_0)) :|: v_z_0 > 0 eval_start_bb3_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb1_in(v_3, v_3, v_x, v_y, v_z_0)) :|: v_z_0 <= 0 eval_start_bb4_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_bb3_in(v__0, v_3, v_x, v_y, v_z_0 - 1)) :|: TRUE eval_start_bb5_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_stop(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE eval_start_bb6_in(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_8(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE eval_start_8(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_9(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE eval_start_9(v__0, v_3, v_x, v_y, v_z_0) -> Com_1(eval_start_stop(v__0, v_3, v_x, v_y, v_z_0)) :|: TRUE The start-symbols are:[eval_start_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 10*ar_0 + 40*ar_2 + 18) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ] (Comp: ?, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ] (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) (Comp: ?, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ] (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ] (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) (Comp: ?, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalstartstart) = 2 Pol(evalstartbb0in) = 2 Pol(evalstart0) = 2 Pol(evalstart1) = 2 Pol(evalstart2) = 2 Pol(evalstartbb1in) = 2 Pol(evalstartbb6in) = 0 Pol(evalstartbb2in) = 2 Pol(evalstartbb5in) = 1 Pol(evalstartbb3in) = 2 Pol(evalstartbb4in) = 2 Pol(evalstartstop) = 0 Pol(evalstart8) = 0 Pol(evalstart9) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ] (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ] (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) (Comp: 2, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalstart8: -X_1 - 1 >= 0 For symbol evalstart9: -X_1 - 1 >= 0 For symbol evalstartbb1in: -X_2 + X_3 >= 0 /\ X_1 >= 0 For symbol evalstartbb2in: X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalstartbb3in: X_3 - X_5 - 1 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 >= 0 /\ X_5 >= 0 /\ X_3 + X_5 - 1 >= 0 /\ X_2 + X_5 - 1 >= 0 /\ X_1 + X_5 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalstartbb4in: X_3 - X_5 - 1 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 >= 0 /\ X_5 - 1 >= 0 /\ X_3 + X_5 - 3 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 2 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 >= 0 /\ X_3 - 2 >= 0 /\ X_2 + X_3 - 4 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalstartbb5in: -X_2 + X_3 >= 0 /\ X_1 - X_2 >= 0 /\ X_1 >= 0 For symbol evalstartbb6in: -X_1 - 1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ] (Comp: 1, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ] (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ] (Comp: ?, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 3 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 2 >= 0 /\ ar_1 + ar_2 - 4 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_4 >= 1 ] (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] (Comp: 2, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ] (Comp: ?, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ] (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ] (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalstartbb4in) = 4*V_2 + 4*V_4 + 2*V_5 Pol(evalstartbb3in) = 4*V_2 + 4*V_4 + 2*V_5 + 1 Pol(evalstartbb1in) = -2*V_1 + 8*V_2 - 1 Pol(evalstartbb2in) = -2*V_1 + 8*V_2 - 2 and size complexities S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]", 0-0) = ar_0 S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]", 0-1) = ar_2 S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]", 0-2) = ar_2 S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]", 0-3) = ar_3 S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ]", 0-4) = ar_4 S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0 S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1 S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2 S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-3) = ar_3 S("evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ]", 0-4) = ar_4 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ar_2 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = ar_2 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-3) = ar_2 + ar_3 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-4) = ar_4 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-0) = ar_0 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-1) = ar_2 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-2) = ar_2 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-3) = ar_2 + ar_3 S("evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-4) = ar_4 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_0 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_2 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = ar_2 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-3) = ar_2 S("evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-4) = ar_0 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_4 >= 1 ]", 0-0) = ar_0 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_4 >= 1 ]", 0-1) = ar_2 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_4 >= 1 ]", 0-2) = ar_2 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_4 >= 1 ]", 0-3) = ar_2 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_4 >= 1 ]", 0-4) = ar_0 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_4 ]", 0-0) = ar_0 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_4 ]", 0-1) = ar_2 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_4 ]", 0-2) = ar_2 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_4 ]", 0-3) = ar_2 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 >= 0 /\\ ar_2 + ar_4 - 1 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_4 ]", 0-4) = 0 S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 3 >= 0 /\\ ar_1 + ar_4 - 3 >= 0 /\\ ar_0 + ar_4 - 2 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 2 >= 0 /\\ ar_1 + ar_2 - 4 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0 S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 3 >= 0 /\\ ar_1 + ar_4 - 3 >= 0 /\\ ar_0 + ar_4 - 2 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 2 >= 0 /\\ ar_1 + ar_2 - 4 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_2 S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 3 >= 0 /\\ ar_1 + ar_4 - 3 >= 0 /\\ ar_0 + ar_4 - 2 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 2 >= 0 /\\ ar_1 + ar_2 - 4 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_2 S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 3 >= 0 /\\ ar_1 + ar_4 - 3 >= 0 /\\ ar_0 + ar_4 - 2 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 2 >= 0 /\\ ar_1 + ar_2 - 4 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_2 S("evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\\ ar_1 - ar_4 - 1 >= 0 /\\ ar_0 - ar_4 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 3 >= 0 /\\ ar_1 + ar_4 - 3 >= 0 /\\ ar_0 + ar_4 - 2 >= 0 /\\ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 >= 0 /\\ ar_2 - 2 >= 0 /\\ ar_1 + ar_2 - 4 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-4) = ar_0 S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_0 S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_2 S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = ar_2 S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-3) = ar_2 + ar_3 S("evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-4) = ar_4 S("evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-0) = ar_0 S("evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-1) = ar_1 S("evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-2) = ar_2 S("evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-3) = ar_3 S("evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-4) = ar_4 S("evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-0) = ar_0 S("evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-1) = ar_1 S("evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-2) = ar_2 S("evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-3) = ar_3 S("evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-4) = ar_4 S("evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-0) = ar_0 S("evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-1) = ar_1 S("evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-2) = ar_2 S("evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-3) = ar_3 S("evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ]", 0-4) = ar_4 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 orients the transitions evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 3 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 2 >= 0 /\ ar_1 + ar_2 - 4 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_4 >= 1 ] evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_4 ] evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ] weakly and the transitions evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 3 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 2 >= 0 /\ ar_1 + ar_2 - 4 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_4 >= 1 ] evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_4 ] evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ] (Comp: 1, Cost: 1) evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ] (Comp: 1, Cost: 1) evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ] (Comp: 2*ar_0 + 8*ar_2 + 1, Cost: 1) evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 3 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 2 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 2 >= 0 /\ ar_1 + ar_2 - 4 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 2*ar_0 + 8*ar_2 + 1, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_4 ] (Comp: 2*ar_0 + 8*ar_2 + 1, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ ar_1 - ar_4 - 1 >= 0 /\ ar_0 - ar_4 >= 0 /\ ar_4 >= 0 /\ ar_2 + ar_4 - 1 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_4 >= 1 ] (Comp: 2*ar_0 + 8*ar_2 + 1, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2, ar_1 - ar_0 - 1, ar_0)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] (Comp: 2, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ] (Comp: 2*ar_0 + 8*ar_2 + 1, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ] (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] (Comp: 1, Cost: 1) evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb1in(ar_0, ar_2, ar_2, ar_3, ar_4)) [ ar_0 >= 0 ] (Comp: 1, Cost: 1) evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalstartstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) start location: koat_start leaf cost: 0 Complexity upper bound 10*ar_0 + 40*ar_2 + 18 Time: 0.482 sec (SMT: 0.364 sec) ---------------------------------------- (2) BOUNDS(1, n^1) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalstartstart 0: evalstartstart -> evalstartbb0in : [], cost: 1 1: evalstartbb0in -> evalstart0 : [], cost: 1 2: evalstart0 -> evalstart1 : [], cost: 1 3: evalstart1 -> evalstart2 : [], cost: 1 4: evalstart2 -> evalstartbb1in : B'=C, [ A>=0 ], cost: 1 5: evalstart2 -> evalstartbb6in : [ 0>=1+A ], cost: 1 6: evalstartbb1in -> evalstartbb2in : [ B>=1+A ], cost: 1 7: evalstartbb1in -> evalstartbb5in : [ A>=B ], cost: 1 8: evalstartbb2in -> evalstartbb3in : D'=-1-A+B, E'=A, [], cost: 1 9: evalstartbb3in -> evalstartbb4in : [ E>=1 ], cost: 1 10: evalstartbb3in -> evalstartbb1in : B'=D, [ 0>=E ], cost: 1 11: evalstartbb4in -> evalstartbb3in : E'=-1+E, [], cost: 1 12: evalstartbb5in -> evalstartstop : [], cost: 1 13: evalstartbb6in -> evalstart8 : [], cost: 1 14: evalstart8 -> evalstart9 : [], cost: 1 15: evalstart9 -> evalstartstop : [], cost: 1 Removed unreachable and leaf rules: Start location: evalstartstart 0: evalstartstart -> evalstartbb0in : [], cost: 1 1: evalstartbb0in -> evalstart0 : [], cost: 1 2: evalstart0 -> evalstart1 : [], cost: 1 3: evalstart1 -> evalstart2 : [], cost: 1 4: evalstart2 -> evalstartbb1in : B'=C, [ A>=0 ], cost: 1 6: evalstartbb1in -> evalstartbb2in : [ B>=1+A ], cost: 1 8: evalstartbb2in -> evalstartbb3in : D'=-1-A+B, E'=A, [], cost: 1 9: evalstartbb3in -> evalstartbb4in : [ E>=1 ], cost: 1 10: evalstartbb3in -> evalstartbb1in : B'=D, [ 0>=E ], cost: 1 11: evalstartbb4in -> evalstartbb3in : E'=-1+E, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalstartstart 19: evalstartstart -> evalstartbb1in : B'=C, [ A>=0 ], cost: 5 20: evalstartbb1in -> evalstartbb3in : D'=-1-A+B, E'=A, [ B>=1+A ], cost: 2 10: evalstartbb3in -> evalstartbb1in : B'=D, [ 0>=E ], cost: 1 21: evalstartbb3in -> evalstartbb3in : E'=-1+E, [ E>=1 ], cost: 2 Accelerating simple loops of location 7. Accelerating the following rules: 21: evalstartbb3in -> evalstartbb3in : E'=-1+E, [ E>=1 ], cost: 2 Accelerated rule 21 with metering function E, yielding the new rule 22. Removing the simple loops: 21. Accelerated all simple loops using metering functions (where possible): Start location: evalstartstart 19: evalstartstart -> evalstartbb1in : B'=C, [ A>=0 ], cost: 5 20: evalstartbb1in -> evalstartbb3in : D'=-1-A+B, E'=A, [ B>=1+A ], cost: 2 10: evalstartbb3in -> evalstartbb1in : B'=D, [ 0>=E ], cost: 1 22: evalstartbb3in -> evalstartbb3in : E'=0, [ E>=1 ], cost: 2*E Chained accelerated rules (with incoming rules): Start location: evalstartstart 19: evalstartstart -> evalstartbb1in : B'=C, [ A>=0 ], cost: 5 20: evalstartbb1in -> evalstartbb3in : D'=-1-A+B, E'=A, [ B>=1+A ], cost: 2 23: evalstartbb1in -> evalstartbb3in : D'=-1-A+B, E'=0, [ B>=1+A && A>=1 ], cost: 2+2*A 10: evalstartbb3in -> evalstartbb1in : B'=D, [ 0>=E ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalstartstart 19: evalstartstart -> evalstartbb1in : B'=C, [ A>=0 ], cost: 5 24: evalstartbb1in -> evalstartbb1in : B'=-1-A+B, D'=-1-A+B, E'=A, [ B>=1+A && 0>=A ], cost: 3 25: evalstartbb1in -> evalstartbb1in : B'=-1-A+B, D'=-1-A+B, E'=0, [ B>=1+A && A>=1 ], cost: 3+2*A Accelerating simple loops of location 5. Accelerating the following rules: 24: evalstartbb1in -> evalstartbb1in : B'=-1-A+B, D'=-1-A+B, E'=A, [ B>=1+A && 0>=A ], cost: 3 25: evalstartbb1in -> evalstartbb1in : B'=-1-A+B, D'=-1-A+B, E'=0, [ B>=1+A && A>=1 ], cost: 3+2*A Accelerated rule 24 with metering function -A+B, yielding the new rule 26. Accelerated rule 25 with backward acceleration, yielding the new rule 27. Removing the simple loops: 24 25. Accelerated all simple loops using metering functions (where possible): Start location: evalstartstart 19: evalstartstart -> evalstartbb1in : B'=C, [ A>=0 ], cost: 5 26: evalstartbb1in -> evalstartbb1in : B'=A+A*(A-B), D'=A+A*(A-B), E'=A, [ B>=1+A && 0>=A ], cost: -3*A+3*B 27: evalstartbb1in -> evalstartbb1in : B'=-A*k-k+B, D'=-A*k-k+B, E'=0, [ B>=1+A && A>=1 && k>0 && 1-k-(-1+k)*A+B>=1+A ], cost: 2*A*k+3*k Chained accelerated rules (with incoming rules): Start location: evalstartstart 19: evalstartstart -> evalstartbb1in : B'=C, [ A>=0 ], cost: 5 28: evalstartstart -> evalstartbb1in : B'=-A*(C-A)+A, D'=-A*(C-A)+A, E'=A, [ -A==0 && C>=1+A ], cost: 5+3*C-3*A 29: evalstartstart -> evalstartbb1in : B'=C-A*k-k, D'=C-A*k-k, E'=0, [ C>=1+A && A>=1 && k>0 && 1+C-k-(-1+k)*A>=1+A ], cost: 5+2*A*k+3*k Removed unreachable locations (and leaf rules with constant cost): Start location: evalstartstart 28: evalstartstart -> evalstartbb1in : B'=-A*(C-A)+A, D'=-A*(C-A)+A, E'=A, [ -A==0 && C>=1+A ], cost: 5+3*C-3*A 29: evalstartstart -> evalstartbb1in : B'=C-A*k-k, D'=C-A*k-k, E'=0, [ C>=1+A && A>=1 && k>0 && 1+C-k-(-1+k)*A>=1+A ], cost: 5+2*A*k+3*k ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalstartstart 28: evalstartstart -> evalstartbb1in : B'=-A*(C-A)+A, D'=-A*(C-A)+A, E'=A, [ -A==0 && C>=1+A ], cost: 5+3*C-3*A 29: evalstartstart -> evalstartbb1in : B'=C-A*k-k, D'=C-A*k-k, E'=0, [ C>=1+A && A>=1 && k>0 && 1+C-k-(-1+k)*A>=1+A ], cost: 5+2*A*k+3*k Computing asymptotic complexity for rule 28 Solved the limit problem by the following transformations: Created initial limit problem: 5+3*C-3*A (+), 1-A (+/+!), C-A (+/+!), 1+A (+/+!) [not solved] applying transformation rule (C) using substitution {A==0} resulting limit problem: 1 (+/+!), C (+/+!), 5+3*C (+) [not solved] applying transformation rule (C) using substitution {C==1+A} resulting limit problem: 1 (+/+!), 8+3*A (+), 1+A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 8+3*A (+), 1+A (+/+!) [not solved] applying transformation rule (D), replacing 8+3*A (+) by 3*A (+) resulting limit problem: 3*A (+), 1+A (+/+!) [not solved] applying transformation rule (D), replacing 1+A (+/+!) by A (+) resulting limit problem: 3*A (+), A (+) [not solved] applying transformation rule (A), replacing 3*A (+) by A (+) and 3 (+!) using + limit vector (+,+!) resulting limit problem: 3 (+!), A (+) [not solved] applying transformation rule (B), deleting 3 (+!) resulting limit problem: A (+) [solved] Solution: C / 1+n A / 0 Resulting cost 8+3*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Computing asymptotic complexity for rule 29 Simplified the guard: 29: evalstartstart -> evalstartbb1in : B'=C-A*k-k, D'=C-A*k-k, E'=0, [ A>=1 && k>0 && 1+C-k-(-1+k)*A>=1+A ], cost: 5+2*A*k+3*k Solved the limit problem by the following transformations: Created initial limit problem: 5+2*A*k+3*k (+), 1+C-A-k-(-1+k)*A (+/+!), A (+/+!), k (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==2*n,A==1,k==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 5+2*A*k+3*k (+), 1+C-A-k-(-1+k)*A (+/+!), A (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {k==1} resulting limit problem: 1 (+/+!), 8+2*A (+), A (+/+!), C-A (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 8+2*A (+), A (+/+!), C-A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==n,A==-1+n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 5+2*A*k+3*k (+), 1+C-A-k-(-1+k)*A (+/+!), A (+/+!), k (+/+!) [not solved] applying transformation rule (C) using substitution {A==1} resulting limit problem: 1 (+/+!), 1+C-2*k (+/+!), k (+/+!), 5+5*k (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 1+C-2*k (+/+!), k (+/+!), 5+5*k (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==2*n,k==n} resulting limit problem: [solved] Solution: C / 2*n A / 1 k / n Resulting cost 5+5*n has complexity: Poly(n^1) Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 8+3*n Rule cost: 5+3*C-3*A Rule guard: [ -A==0 && C>=1+A ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)