3.18/2.13 WORST_CASE(?, O(n^1)) 3.21/2.14 proof of /export/starexec/sandbox/output/output_files/bench.koat 3.21/2.14 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.21/2.14 3.21/2.14 3.21/2.14 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 3.21/2.14 3.21/2.14 (0) CpxIntTrs 3.21/2.14 (1) Koat Proof [FINISHED, 883 ms] 3.21/2.14 (2) BOUNDS(1, n^1) 3.21/2.14 3.21/2.14 3.21/2.14 ---------------------------------------- 3.21/2.14 3.21/2.14 (0) 3.21/2.14 Obligation: 3.21/2.14 Complexity Int TRS consisting of the following rules: 3.21/2.14 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 3.21/2.14 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 3.21/2.14 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 3.21/2.14 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 3.21/2.14 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 3.21/2.14 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 3.21/2.14 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 3.21/2.14 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 3.21/2.14 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 3.21/2.14 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 3.21/2.14 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 3.21/2.14 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 3.21/2.14 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 3.21/2.14 3.21/2.14 The start-symbols are:[eval_speedNestedMultiple_start_8] 3.21/2.14 3.21/2.14 3.21/2.14 ---------------------------------------- 3.21/2.14 3.21/2.14 (1) Koat Proof (FINISHED) 3.21/2.14 YES(?, 47*ar_1 + 47*ar_4 + 49*ar_3 + 49*ar_6 + 24) 3.21/2.14 3.21/2.14 3.21/2.14 3.21/2.14 Initial complexity problem: 3.21/2.14 3.21/2.14 1: T: 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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, j), evalspeedNestedMultiple01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, j)) 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 start location: koat_start 3.21/2.14 3.21/2.14 leaf cost: 0 3.21/2.14 3.21/2.14 3.21/2.14 3.21/2.14 Repeatedly propagating knowledge in problem 1 produces the following problem: 3.21/2.14 3.21/2.14 2: T: 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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, j), evalspeedNestedMultiple01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, j)) 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 start location: koat_start 3.21/2.14 3.21/2.14 leaf cost: 0 3.21/2.14 3.21/2.14 3.21/2.14 3.21/2.14 A polynomial rank function with 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplestart) = 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb0in) = 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb1in) = 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb2in) = 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb5in) = 1 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb3in) = 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplecritedgein) = 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiple0) = 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiple00) = 0 3.21/2.14 3.21/2.14 Pol(evalnondetstart) = 0 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiple01) = 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiple1) = 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb4in) = 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplestop) = 0 3.21/2.14 3.21/2.14 Pol(koat_start) = 2 3.21/2.14 3.21/2.14 orients all transitions weakly and the transitions 3.21/2.14 3.21/2.14 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)) 3.21/2.14 3.21/2.14 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 ] 3.21/2.14 3.21/2.14 strictly and produces the following problem: 3.21/2.14 3.21/2.14 3: T: 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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, j), evalspeedNestedMultiple01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, j)) 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 start location: koat_start 3.21/2.14 3.21/2.14 leaf cost: 0 3.21/2.14 3.21/2.14 3.21/2.14 3.21/2.14 Applied AI with 'oct' on problem 3 to obtain the following invariants: 3.21/2.14 3.21/2.14 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 3.21/2.14 3.21/2.14 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 3.21/2.14 3.21/2.14 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 3.21/2.14 3.21/2.14 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 3.21/2.14 3.21/2.14 For symbol evalspeedNestedMultiplebb1in: X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 3.21/2.14 3.21/2.14 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 3.21/2.14 3.21/2.14 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 3.21/2.14 3.21/2.14 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 3.21/2.14 3.21/2.14 For symbol evalspeedNestedMultiplebb5in: X_1 - X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 3.21/2.14 3.21/2.14 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 3.21/2.14 3.21/2.14 3.21/2.14 3.21/2.14 3.21/2.14 3.21/2.14 This yielded the following problem: 3.21/2.14 3.21/2.14 4: T: 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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, j), evalspeedNestedMultiple01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, j)) [ -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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 start location: koat_start 3.21/2.14 3.21/2.14 leaf cost: 0 3.21/2.14 3.21/2.14 3.21/2.14 3.21/2.14 A polynomial rank function with 3.21/2.14 3.21/2.14 Pol(koat_start) = -3*V_2 + 3*V_5 + 1 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplestart) = -3*V_2 + 3*V_5 + 1 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb5in) = -3*V_1 + 3*V_5 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplestop) = -3*V_1 + 3*V_5 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplecritedgein) = -3*V_1 + 3*V_5 - 1 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb1in) = -3*V_1 + 3*V_5 + 1 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb4in) = -3*V_1 + 3*V_5 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb2in) = -3*V_1 + 3*V_5 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiple1) = -3*V_1 + 3*V_5 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiple0) = -3*V_1 + 3*V_5 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiple00) = -3*V_1 + 3*V_2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiple01) = -3*V_1 + 3*V_5 3.21/2.14 3.21/2.14 Pol(evalnondetstart) = -3*V_1 + 3*V_2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb3in) = -3*V_1 + 3*V_5 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb0in) = -3*V_2 + 3*V_5 + 1 3.21/2.14 3.21/2.14 orients all transitions weakly and the transitions 3.21/2.14 3.21/2.14 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 ] 3.21/2.14 3.21/2.14 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 ] 3.21/2.14 3.21/2.14 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 ] 3.21/2.14 3.21/2.14 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 ] 3.21/2.14 3.21/2.14 strictly and produces the following problem: 3.21/2.14 3.21/2.14 5: T: 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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, j), evalspeedNestedMultiple01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, j)) [ -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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 start location: koat_start 3.21/2.14 3.21/2.14 leaf cost: 0 3.21/2.14 3.21/2.14 3.21/2.14 3.21/2.14 A polynomial rank function with 3.21/2.14 3.21/2.14 Pol(koat_start) = -5*V_2 - 7*V_4 + 5*V_5 + 7*V_7 + 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplestart) = -5*V_2 - 7*V_4 + 5*V_5 + 7*V_7 + 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb5in) = -5*V_1 - 7*V_3 + 5*V_5 + 7*V_7 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplestop) = -5*V_1 - 7*V_3 + 5*V_5 + 7*V_7 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplecritedgein) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 - 3 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb1in) = -5*V_1 - 7*V_3 + 5*V_5 + 7*V_7 + 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb4in) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 - 4 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb2in) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 + 2 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiple1) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 - 3 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiple0) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiple00) = 1 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiple01) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 - 2 3.21/2.14 3.21/2.14 Pol(evalnondetstart) = 0 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb3in) = -5*V_1 + 5*V_5 - 7*V_6 + 7*V_7 + 1 3.21/2.14 3.21/2.14 Pol(evalspeedNestedMultiplebb0in) = -5*V_2 - 7*V_4 + 5*V_5 + 7*V_7 + 2 3.21/2.14 3.21/2.14 orients all transitions weakly and the transitions 3.21/2.14 3.21/2.14 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 ] 3.21/2.14 3.21/2.14 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 ] 3.21/2.14 3.21/2.14 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 ] 3.21/2.14 3.21/2.14 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 ] 3.21/2.14 3.21/2.14 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 ] 3.21/2.14 3.21/2.14 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 ] 3.21/2.14 3.21/2.14 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, j), evalspeedNestedMultiple01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, j)) [ -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 ] 3.21/2.14 3.21/2.14 strictly and produces the following problem: 3.21/2.14 3.21/2.14 6: T: 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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, j), evalspeedNestedMultiple01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, j)) [ -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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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 ] 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 (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)) 3.21/2.14 3.21/2.14 start location: koat_start 3.21/2.14 3.21/2.14 leaf cost: 0 3.21/2.14 3.21/2.14 3.21/2.14 3.21/2.14 Complexity upper bound 47*ar_1 + 47*ar_4 + 49*ar_3 + 49*ar_6 + 24 3.21/2.14 3.21/2.14 3.21/2.14 3.21/2.14 Time: 0.847 sec (SMT: 0.591 sec) 3.21/2.14 3.21/2.14 3.21/2.14 ---------------------------------------- 3.21/2.14 3.21/2.14 (2) 3.21/2.14 BOUNDS(1, n^1) 3.21/2.16 EOF