/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 382 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_speed_popl10_nested_single_start(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb0_in(v_3, v_n, v_x.0, v_x.1)) :|: TRUE eval_speed_popl10_nested_single_bb0_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb1_in(v_3, v_n, 0, v_x.1)) :|: TRUE eval_speed_popl10_nested_single_bb1_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb2_in(v_3, v_n, v_x.0, v_x.1)) :|: v_x.0 < v_n eval_speed_popl10_nested_single_bb1_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb6_in(v_3, v_n, v_x.0, v_x.1)) :|: v_x.0 >= v_n eval_speed_popl10_nested_single_bb2_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb3_in(v_3, v_n, v_x.0, v_x.0 + 1)) :|: TRUE eval_speed_popl10_nested_single_bb3_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb4_in(v_3, v_n, v_x.0, v_x.1)) :|: v_x.1 < v_n eval_speed_popl10_nested_single_bb3_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb1_in(v_3, v_n, v_x.1, v_x.1)) :|: v_x.1 >= v_n eval_speed_popl10_nested_single_bb4_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_2(v_3, v_n, v_x.0, v_x.1)) :|: TRUE eval_speed_popl10_nested_single_2(v_3, v_n, v_x.0, v_x.1) -> Com_2(eval_nondet_start(v_3, v_n, v_x.0, v_x.1), eval_speed_popl10_nested_single_3(nondef.0, v_n, v_x.0, v_x.1)) :|: TRUE eval_speed_popl10_nested_single_3(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb1_in(v_3, v_n, v_x.1, v_x.1)) :|: v_3 > 0 eval_speed_popl10_nested_single_3(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb5_in(v_3, v_n, v_x.0, v_x.1)) :|: v_3 <= 0 eval_speed_popl10_nested_single_bb5_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb3_in(v_3, v_n, v_x.0, v_x.1 + 1)) :|: TRUE eval_speed_popl10_nested_single_bb6_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_stop(v_3, v_n, v_x.0, v_x.1)) :|: TRUE The start-symbols are:[eval_speed_popl10_nested_single_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 88*Ar_1 + 6) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_0 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsingle2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalspeedpopl10nestedsingle20(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalspeedpopl10nestedsingle21(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglestop(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(evalspeedpopl10nestedsinglestart(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) evalspeedpopl10nestedsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10nestedsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_0 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsingle2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalspeedpopl10nestedsingle20(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalspeedpopl10nestedsingle21(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglestop(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(evalspeedpopl10nestedsinglestart(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(evalspeedpopl10nestedsinglestart) = 2 Pol(evalspeedpopl10nestedsinglebb0in) = 2 Pol(evalspeedpopl10nestedsinglebb1in) = 2 Pol(evalspeedpopl10nestedsinglebb2in) = 2 Pol(evalspeedpopl10nestedsinglebb6in) = 1 Pol(evalspeedpopl10nestedsinglebb3in) = 2 Pol(evalspeedpopl10nestedsinglebb4in) = 2 Pol(evalspeedpopl10nestedsingle2) = 2 Pol(evalspeedpopl10nestedsingle20) = 0 Pol(evalnondetstart) = 0 Pol(evalspeedpopl10nestedsingle21) = 2 Pol(evalspeedpopl10nestedsingle3) = 2 Pol(evalspeedpopl10nestedsinglebb5in) = 2 Pol(evalspeedpopl10nestedsinglestop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalspeedpopl10nestedsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalspeedpopl10nestedsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb6in(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) evalspeedpopl10nestedsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10nestedsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedpopl10nestedsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_0 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsingle2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalspeedpopl10nestedsingle20(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalspeedpopl10nestedsingle21(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalspeedpopl10nestedsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglestop(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(evalspeedpopl10nestedsinglestart(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 evalspeedpopl10nestedsingle2: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10nestedsingle20: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10nestedsingle21: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10nestedsingle3: X_4 - X_5 >= 0 /\ -X_4 + X_5 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10nestedsinglebb1in: X_1 >= 0 For symbol evalspeedpopl10nestedsinglebb2in: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10nestedsinglebb3in: X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 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 evalspeedpopl10nestedsinglebb4in: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10nestedsinglebb5in: -X_5 >= 0 /\ X_4 - X_5 >= 0 /\ -X_4 - X_5 >= 0 /\ X_3 - X_5 - 1 >= 0 /\ X_2 - X_5 - 2 >= 0 /\ X_1 - X_5 >= 0 /\ -X_4 + X_5 >= 0 /\ -X_4 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 2 >= 0 /\ X_1 - X_4 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10nestedsinglebb6in: X_1 - X_2 >= 0 /\ X_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(evalspeedpopl10nestedsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalspeedpopl10nestedsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_3 - Ar_4 >= 0 /\ -Ar_3 - Ar_4 >= 0 /\ Ar_2 - Ar_4 - 1 >= 0 /\ Ar_1 - Ar_4 - 2 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_1 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalspeedpopl10nestedsingle20(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalspeedpopl10nestedsingle21(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsingle2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 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_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 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_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_0 + 1, Ar_3, Ar_4)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalspeedpopl10nestedsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpopl10nestedsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10nestedsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 8*V_2 Pol(evalspeedpopl10nestedsinglestart) = 8*V_2 Pol(evalspeedpopl10nestedsinglebb6in) = -8*V_1 + 8*V_2 Pol(evalspeedpopl10nestedsinglestop) = -8*V_1 + 8*V_2 Pol(evalspeedpopl10nestedsinglebb5in) = 8*V_2 - 8*V_3 - 1 Pol(evalspeedpopl10nestedsinglebb3in) = 8*V_2 - 8*V_3 + 6 Pol(evalspeedpopl10nestedsingle3) = 8*V_2 - 8*V_3 + 1 Pol(evalspeedpopl10nestedsinglebb1in) = -8*V_1 + 8*V_2 Pol(evalspeedpopl10nestedsingle2) = 8*V_2 - 8*V_3 + 4 Pol(evalspeedpopl10nestedsingle20) = 1 Pol(evalspeedpopl10nestedsingle21) = 8*V_2 - 8*V_3 + 2 Pol(evalnondetstart) = 0 Pol(evalspeedpopl10nestedsinglebb4in) = 8*V_2 - 8*V_3 + 5 Pol(evalspeedpopl10nestedsinglebb2in) = -8*V_1 + 8*V_2 - 1 Pol(evalspeedpopl10nestedsinglebb0in) = 8*V_2 orients all transitions weakly and the transitions evalspeedpopl10nestedsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_3 - Ar_4 >= 0 /\ -Ar_3 - Ar_4 >= 0 /\ Ar_2 - Ar_4 - 1 >= 0 /\ Ar_1 - Ar_4 - 2 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_1 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] evalspeedpopl10nestedsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsingle2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 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_1 >= Ar_2 + 1 ] evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 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_2 >= Ar_1 ] evalspeedpopl10nestedsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_0 + 1, Ar_3, Ar_4)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] evalspeedpopl10nestedsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 ] evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] evalspeedpopl10nestedsingle21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] evalspeedpopl10nestedsingle20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] evalspeedpopl10nestedsingle2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalspeedpopl10nestedsingle20(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalspeedpopl10nestedsingle21(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] 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(evalspeedpopl10nestedsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalspeedpopl10nestedsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 8*Ar_1, Cost: 1) evalspeedpopl10nestedsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_3 - Ar_4 >= 0 /\ -Ar_3 - Ar_4 >= 0 /\ Ar_2 - Ar_4 - 1 >= 0 /\ Ar_1 - Ar_4 - 2 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_1 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 8*Ar_1, Cost: 1) evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 ] (Comp: 8*Ar_1, Cost: 1) evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: 8*Ar_1, Cost: 1) evalspeedpopl10nestedsingle2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalspeedpopl10nestedsingle20(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalspeedpopl10nestedsingle21(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 8*Ar_1, Cost: 1) evalspeedpopl10nestedsingle21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsingle3(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 8*Ar_1, Cost: 1) evalspeedpopl10nestedsingle20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 8*Ar_1, Cost: 1) evalspeedpopl10nestedsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsingle2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 8*Ar_1, Cost: 1) evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 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_2 >= Ar_1 ] (Comp: 8*Ar_1, Cost: 1) evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 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_1 >= Ar_2 + 1 ] (Comp: 8*Ar_1, Cost: 1) evalspeedpopl10nestedsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(Ar_0, Ar_1, Ar_0 + 1, Ar_3, Ar_4)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalspeedpopl10nestedsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: 8*Ar_1, Cost: 1) evalspeedpopl10nestedsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpopl10nestedsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10nestedsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10nestedsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) start location: koat_start leaf cost: 0 Complexity upper bound 88*Ar_1 + 6 Time: 0.369 sec (SMT: 0.284 sec) ---------------------------------------- (2) BOUNDS(1, n^1)