/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 683 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_speedNestedMultiple_start(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speedNestedMultiple_bb0_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: TRUE eval_speedNestedMultiple_bb0_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speedNestedMultiple_bb1_in(v_x, v_y, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: TRUE eval_speedNestedMultiple_bb1_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speedNestedMultiple_bb2_in(v_.0, v_.01, v_.01, v_2, v_m, v_n, v_x, v_y)) :|: v_.0 < v_n eval_speedNestedMultiple_bb1_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speedNestedMultiple_bb5_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: v_.0 >= v_n eval_speedNestedMultiple_bb2_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speedNestedMultiple_bb3_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: v_.1 < v_m eval_speedNestedMultiple_bb2_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speedNestedMultiple_.critedge_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: v_.1 >= v_m eval_speedNestedMultiple_bb3_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speedNestedMultiple_0(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: TRUE eval_speedNestedMultiple_0(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_2(eval_nondet_start(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y), eval_speedNestedMultiple_1(v_.0, v_.01, v_.1, nondef.0, v_m, v_n, v_x, v_y)) :|: TRUE eval_speedNestedMultiple_1(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speedNestedMultiple_bb4_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: v_2 > 0 eval_speedNestedMultiple_1(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speedNestedMultiple_.critedge_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: v_2 <= 0 eval_speedNestedMultiple_bb4_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speedNestedMultiple_bb2_in(v_.0, v_.01, v_.1 + 1, v_2, v_m, v_n, v_x, v_y)) :|: TRUE eval_speedNestedMultiple_.critedge_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speedNestedMultiple_bb1_in(v_.0 + 1, v_.1, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: TRUE eval_speedNestedMultiple_bb5_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speedNestedMultiple_stop(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: TRUE The start-symbols are:[eval_speedNestedMultiple_start_8] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 47*Ar_1 + 47*Ar_4 + 49*Ar_3 + 49*Ar_6 + 24) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiplebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_6 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_5 >= Ar_6 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_8, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_2(evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0), evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0)) (Comp: ?, Cost: 1) evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_7 >= 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 >= Ar_7 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_0 + 1, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 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) evalspeedNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: 1, Cost: 1) evalspeedNestedMultiplebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_6 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_5 >= Ar_6 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_8, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_2(evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0), evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0)) (Comp: ?, Cost: 1) evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_7 >= 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 >= Ar_7 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_0 + 1, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalspeedNestedMultiplestart) = 2 Pol(evalspeedNestedMultiplebb0in) = 2 Pol(evalspeedNestedMultiplebb1in) = 2 Pol(evalspeedNestedMultiplebb2in) = 2 Pol(evalspeedNestedMultiplebb5in) = 1 Pol(evalspeedNestedMultiplebb3in) = 2 Pol(evalspeedNestedMultiplecritedgein) = 2 Pol(evalspeedNestedMultiple0) = 2 Pol(evalspeedNestedMultiple00) = 0 Pol(evalnondetstart) = 0 Pol(evalspeedNestedMultiple01) = 2 Pol(evalspeedNestedMultiple1) = 2 Pol(evalspeedNestedMultiplebb4in) = 2 Pol(evalspeedNestedMultiplestop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_0 >= Ar_4 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalspeedNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: 1, Cost: 1) evalspeedNestedMultiplebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_4 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_6 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_5 >= Ar_6 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_8, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_2(evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0), evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0)) (Comp: ?, Cost: 1) evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_7 >= 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 >= Ar_7 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_0 + 1, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: 2, Cost: 1) evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalspeedNestedMultiple0: -X_6 + X_7 - 1 >= 0 /\ -X_4 + X_7 - 1 >= 0 /\ -X_3 + X_7 - 1 >= 0 /\ -X_4 + X_6 >= 0 /\ -X_3 + X_6 >= 0 /\ -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedNestedMultiple00: -X_6 + X_7 - 1 >= 0 /\ -X_4 + X_7 - 1 >= 0 /\ -X_3 + X_7 - 1 >= 0 /\ -X_4 + X_6 >= 0 /\ -X_3 + X_6 >= 0 /\ -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedNestedMultiple01: -X_6 + X_7 - 1 >= 0 /\ -X_4 + X_7 - 1 >= 0 /\ -X_3 + X_7 - 1 >= 0 /\ -X_4 + X_6 >= 0 /\ -X_3 + X_6 >= 0 /\ -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedNestedMultiple1: X_8 - X_9 >= 0 /\ -X_8 + X_9 >= 0 /\ -X_6 + X_7 - 1 >= 0 /\ -X_4 + X_7 - 1 >= 0 /\ -X_3 + X_7 - 1 >= 0 /\ -X_4 + X_6 >= 0 /\ -X_3 + X_6 >= 0 /\ -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedNestedMultiplebb1in: X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedNestedMultiplebb2in: -X_4 + X_6 >= 0 /\ -X_3 + X_6 >= 0 /\ -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedNestedMultiplebb3in: -X_6 + X_7 - 1 >= 0 /\ -X_4 + X_7 - 1 >= 0 /\ -X_3 + X_7 - 1 >= 0 /\ -X_4 + X_6 >= 0 /\ -X_3 + X_6 >= 0 /\ -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedNestedMultiplebb4in: X_8 - X_9 >= 0 /\ X_9 - 1 >= 0 /\ X_8 + X_9 - 2 >= 0 /\ -X_8 + X_9 >= 0 /\ X_8 - 1 >= 0 /\ -X_6 + X_7 - 1 >= 0 /\ -X_4 + X_7 - 1 >= 0 /\ -X_3 + X_7 - 1 >= 0 /\ -X_4 + X_6 >= 0 /\ -X_3 + X_6 >= 0 /\ -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedNestedMultiplebb5in: X_1 - X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedNestedMultiplecritedgein: -X_4 + X_6 >= 0 /\ -X_3 + X_6 >= 0 /\ -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_0 - Ar_4 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_0 + 1, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7, Ar_8)) [ Ar_7 - Ar_8 >= 0 /\ Ar_8 - 1 >= 0 /\ Ar_7 + Ar_8 - 2 >= 0 /\ -Ar_7 + Ar_8 >= 0 /\ Ar_7 - 1 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_7 - Ar_8 >= 0 /\ -Ar_7 + Ar_8 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 0 >= Ar_7 ] (Comp: ?, Cost: 1) evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_7 - Ar_8 >= 0 /\ -Ar_7 + Ar_8 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_7 >= 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_2(evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0), evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_8, Ar_8)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_5 >= Ar_6 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_6 >= Ar_5 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_4 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedNestedMultiplebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: 1, Cost: 1) evalspeedNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = -3*V_2 + 3*V_5 + 1 Pol(evalspeedNestedMultiplestart) = -3*V_2 + 3*V_5 + 1 Pol(evalspeedNestedMultiplebb5in) = -3*V_1 + 3*V_5 Pol(evalspeedNestedMultiplestop) = -3*V_1 + 3*V_5 Pol(evalspeedNestedMultiplecritedgein) = -3*V_1 + 3*V_5 - 1 Pol(evalspeedNestedMultiplebb1in) = -3*V_1 + 3*V_5 + 1 Pol(evalspeedNestedMultiplebb4in) = -3*V_1 + 3*V_5 Pol(evalspeedNestedMultiplebb2in) = -3*V_1 + 3*V_5 Pol(evalspeedNestedMultiple1) = -3*V_1 + 3*V_5 Pol(evalspeedNestedMultiple0) = -3*V_1 + 3*V_5 Pol(evalspeedNestedMultiple00) = -3*V_1 + 3*V_2 Pol(evalspeedNestedMultiple01) = -3*V_1 + 3*V_5 Pol(evalnondetstart) = -3*V_1 + 3*V_2 Pol(evalspeedNestedMultiplebb3in) = -3*V_1 + 3*V_5 Pol(evalspeedNestedMultiplebb0in) = -3*V_2 + 3*V_5 + 1 orients all transitions weakly and the transitions evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_0 + 1, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_5 >= Ar_6 ] evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_4 >= Ar_0 + 1 ] evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_7 - Ar_8 >= 0 /\ -Ar_7 + Ar_8 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 0 >= Ar_7 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_0 - Ar_4 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: 3*Ar_1 + 3*Ar_4 + 1, Cost: 1) evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_0 + 1, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7, Ar_8)) [ Ar_7 - Ar_8 >= 0 /\ Ar_8 - 1 >= 0 /\ Ar_7 + Ar_8 - 2 >= 0 /\ -Ar_7 + Ar_8 >= 0 /\ Ar_7 - 1 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: 3*Ar_1 + 3*Ar_4 + 1, Cost: 1) evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_7 - Ar_8 >= 0 /\ -Ar_7 + Ar_8 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 0 >= Ar_7 ] (Comp: ?, Cost: 1) evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_7 - Ar_8 >= 0 /\ -Ar_7 + Ar_8 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_7 >= 1 ] (Comp: ?, Cost: 1) evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_2(evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0), evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_8, Ar_8)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: 3*Ar_1 + 3*Ar_4 + 1, Cost: 1) evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_5 >= Ar_6 ] (Comp: ?, Cost: 1) evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_6 >= Ar_5 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_4 ] (Comp: 3*Ar_1 + 3*Ar_4 + 1, Cost: 1) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_4 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedNestedMultiplebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: 1, Cost: 1) evalspeedNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = -5*V_2 - 7*V_4 + 5*V_5 + 7*V_7 + 2 Pol(evalspeedNestedMultiplestart) = -5*V_2 - 7*V_4 + 5*V_5 + 7*V_7 + 2 Pol(evalspeedNestedMultiplebb5in) = -5*V_1 - 7*V_3 + 5*V_5 + 7*V_7 Pol(evalspeedNestedMultiplestop) = -5*V_1 - 7*V_3 + 5*V_5 + 7*V_7 Pol(evalspeedNestedMultiplecritedgein) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 - 3 Pol(evalspeedNestedMultiplebb1in) = -5*V_1 - 7*V_3 + 5*V_5 + 7*V_7 + 2 Pol(evalspeedNestedMultiplebb4in) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 - 4 Pol(evalspeedNestedMultiplebb2in) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 + 2 Pol(evalspeedNestedMultiple1) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 - 3 Pol(evalspeedNestedMultiple0) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 Pol(evalspeedNestedMultiple00) = 1 Pol(evalspeedNestedMultiple01) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 - 2 Pol(evalnondetstart) = 0 Pol(evalspeedNestedMultiplebb3in) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 + 1 Pol(evalspeedNestedMultiplebb0in) = -5*V_2 - 7*V_4 + 5*V_5 + 7*V_7 + 2 orients all transitions weakly and the transitions evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7, Ar_8)) [ Ar_7 - Ar_8 >= 0 /\ Ar_8 - 1 >= 0 /\ Ar_7 + Ar_8 - 2 >= 0 /\ -Ar_7 + Ar_8 >= 0 /\ Ar_7 - 1 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_6 >= Ar_5 + 1 ] evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_7 - Ar_8 >= 0 /\ -Ar_7 + Ar_8 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_7 >= 1 ] evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_8, Ar_8)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_2(evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0), evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_0 - Ar_4 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: 3*Ar_1 + 3*Ar_4 + 1, Cost: 1) evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_0 + 1, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: 5*Ar_1 + 7*Ar_3 + 5*Ar_4 + 7*Ar_6 + 2, Cost: 1) evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7, Ar_8)) [ Ar_7 - Ar_8 >= 0 /\ Ar_8 - 1 >= 0 /\ Ar_7 + Ar_8 - 2 >= 0 /\ -Ar_7 + Ar_8 >= 0 /\ Ar_7 - 1 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: 3*Ar_1 + 3*Ar_4 + 1, Cost: 1) evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_7 - Ar_8 >= 0 /\ -Ar_7 + Ar_8 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 0 >= Ar_7 ] (Comp: 5*Ar_1 + 7*Ar_3 + 5*Ar_4 + 7*Ar_6 + 2, Cost: 1) evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_7 - Ar_8 >= 0 /\ -Ar_7 + Ar_8 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_7 >= 1 ] (Comp: 5*Ar_1 + 7*Ar_3 + 5*Ar_4 + 7*Ar_6 + 2, Cost: 1) evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_2(evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0), evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: 5*Ar_1 + 7*Ar_3 + 5*Ar_4 + 7*Ar_6 + 2, Cost: 1) evalspeedNestedMultiple01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_8, Ar_8)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: 5*Ar_1 + 7*Ar_3 + 5*Ar_4 + 7*Ar_6 + 2, Cost: 1) evalspeedNestedMultiple00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: 5*Ar_1 + 7*Ar_3 + 5*Ar_4 + 7*Ar_6 + 2, Cost: 1) evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiple0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_5 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_6 - 1 >= 0 /\ -Ar_2 + Ar_6 - 1 >= 0 /\ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ] (Comp: 3*Ar_1 + 3*Ar_4 + 1, Cost: 1) evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplecritedgein(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_5 >= Ar_6 ] (Comp: 5*Ar_1 + 7*Ar_3 + 5*Ar_4 + 7*Ar_6 + 2, Cost: 1) evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ -Ar_3 + Ar_5 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_6 >= Ar_5 + 1 ] (Comp: 2, Cost: 1) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_4 ] (Comp: 3*Ar_1 + 3*Ar_4 + 1, Cost: 1) evalspeedNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_4 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedNestedMultiplebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: 1, Cost: 1) evalspeedNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(evalspeedNestedMultiplebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) start location: koat_start leaf cost: 0 Complexity upper bound 47*Ar_1 + 47*Ar_4 + 49*Ar_3 + 49*Ar_6 + 24 Time: 0.685 sec (SMT: 0.450 sec) ---------------------------------------- (2) BOUNDS(1, n^1)