6.76/3.24 WORST_CASE(Omega(n^2), O(n^2)) 6.76/3.25 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 6.76/3.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.76/3.25 6.76/3.25 6.76/3.25 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). 6.76/3.25 6.76/3.25 (0) CpxIntTrs 6.76/3.25 (1) Koat Proof [FINISHED, 221 ms] 6.76/3.25 (2) BOUNDS(1, n^2) 6.76/3.25 (3) Loat Proof [FINISHED, 1422 ms] 6.76/3.25 (4) BOUNDS(n^2, INF) 6.76/3.25 6.76/3.25 6.76/3.25 ---------------------------------------- 6.76/3.25 6.76/3.25 (0) 6.76/3.25 Obligation: 6.76/3.25 Complexity Int TRS consisting of the following rules: 6.76/3.25 eval_insertsort_start(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb0_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_bb0_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_0(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_0(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_1(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_1(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_2(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_2(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_3(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_3(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_4(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_4(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_5(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_5(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_6(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_6(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb1_in(v_20, v_3, 1, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_bb1_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb2_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: v_i_0 < v_length 6.76/3.25 eval_insertsort_bb1_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb7_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: v_i_0 >= v_length 6.76/3.25 eval_insertsort_bb2_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb3_in(v_20, nondef_0, v_i_0, v_i_0 - 1, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_bb3_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb4_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: v_j_0 >= 0 6.76/3.25 eval_insertsort_bb3_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb6_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: v_j_0 < 0 6.76/3.25 eval_insertsort_bb4_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb5_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: nondef_1 > v_3 6.76/3.25 eval_insertsort_bb4_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb6_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: nondef_1 <= v_3 6.76/3.25 eval_insertsort_bb5_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb3_in(v_20, v_3, v_i_0, v_j_0 - 1, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_bb6_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_25(v_i_0 + 1, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_25(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_26(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_26(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb1_in(v_20, v_3, v_20, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_bb7_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_stop(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 6.76/3.25 The start-symbols are:[eval_insertsort_start_5] 6.76/3.25 6.76/3.25 6.76/3.25 ---------------------------------------- 6.76/3.25 6.76/3.25 (1) Koat Proof (FINISHED) 6.76/3.25 YES(?, 229*ar_1 + 12*ar_1^2 + 13) 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Initial complexity problem: 6.76/3.25 6.76/3.25 1: T: 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 6.76/3.25 6.76/3.25 start location: koat_start 6.76/3.25 6.76/3.25 leaf cost: 0 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Repeatedly propagating knowledge in problem 1 produces the following problem: 6.76/3.25 6.76/3.25 2: T: 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 6.76/3.25 6.76/3.25 start location: koat_start 6.76/3.25 6.76/3.25 leaf cost: 0 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 A polynomial rank function with 6.76/3.25 6.76/3.25 Pol(evalinsertsortstart) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb0in) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsort0) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsort1) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsort2) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsort3) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsort4) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsort5) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsort6) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb1in) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb2in) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb7in) = 1 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb3in) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb4in) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb6in) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb5in) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsort25) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsort26) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsortstop) = 0 6.76/3.25 6.76/3.25 Pol(koat_start) = 2 6.76/3.25 6.76/3.25 orients all transitions weakly and the transitions 6.76/3.25 6.76/3.25 evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 6.76/3.25 6.76/3.25 strictly and produces the following problem: 6.76/3.25 6.76/3.25 3: T: 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 6.76/3.25 6.76/3.25 (Comp: 2, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 2, Cost: 1) evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 6.76/3.25 6.76/3.25 start location: koat_start 6.76/3.25 6.76/3.25 leaf cost: 0 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 A polynomial rank function with 6.76/3.25 6.76/3.25 Pol(evalinsertsortstart) = V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb0in) = V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsort0) = V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsort1) = V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsort2) = V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsort3) = V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsort4) = V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsort5) = V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsort6) = V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb1in) = -V_1 + V_2 + 1 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb2in) = -V_1 + V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb7in) = -V_1 + V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb3in) = -V_1 + V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb4in) = -V_1 + V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb6in) = -V_1 + V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb5in) = -V_1 + V_2 6.76/3.25 6.76/3.25 Pol(evalinsertsort25) = V_2 - V_5 + 1 6.76/3.25 6.76/3.25 Pol(evalinsertsort26) = V_2 - V_5 + 1 6.76/3.25 6.76/3.25 Pol(evalinsertsortstop) = -V_1 + V_2 6.76/3.25 6.76/3.25 Pol(koat_start) = V_2 6.76/3.25 6.76/3.25 orients all transitions weakly and the transition 6.76/3.25 6.76/3.25 evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 6.76/3.25 6.76/3.25 strictly and produces the following problem: 6.76/3.25 6.76/3.25 4: T: 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ar_1, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 6.76/3.25 6.76/3.25 (Comp: 2, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 2, Cost: 1) evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 6.76/3.25 6.76/3.25 start location: koat_start 6.76/3.25 6.76/3.25 leaf cost: 0 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Repeatedly propagating knowledge in problem 4 produces the following problem: 6.76/3.25 6.76/3.25 5: T: 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ar_1, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 6.76/3.25 6.76/3.25 (Comp: 2, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 6.76/3.25 6.76/3.25 (Comp: ar_1, Cost: 1) evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 2, Cost: 1) evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 6.76/3.25 6.76/3.25 start location: koat_start 6.76/3.25 6.76/3.25 leaf cost: 0 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 A polynomial rank function with 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb6in) = 3 6.76/3.25 6.76/3.25 Pol(evalinsertsort25) = 2 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb5in) = 4 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb3in) = 4 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb4in) = 4 6.76/3.25 6.76/3.25 Pol(evalinsertsort26) = 1 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb1in) = 0 6.76/3.25 6.76/3.25 and size complexities 6.76/3.25 6.76/3.25 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-0) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-4) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-0) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-4) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4))", 0-0) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4))", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4))", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4))", 0-4) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ]", 0-0) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ]", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ]", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ]", 0-4) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ]", 0-0) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ]", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ]", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ]", 0-4) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-0) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-4) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ]", 0-0) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ]", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ]", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ]", 0-4) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4))", 0-0) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4))", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4))", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4))", 0-4) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-0) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-4) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-0) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-4) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-0) = 1 6.76/3.25 6.76/3.25 S("evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 orients the transitions 6.76/3.25 6.76/3.25 evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1)) 6.76/3.25 6.76/3.25 evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4)) 6.76/3.25 6.76/3.25 evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ] 6.76/3.25 6.76/3.25 evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ] 6.76/3.25 6.76/3.25 evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] 6.76/3.25 6.76/3.25 evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ] 6.76/3.25 6.76/3.25 evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 weakly and the transitions 6.76/3.25 6.76/3.25 evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1)) 6.76/3.25 6.76/3.25 evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ] 6.76/3.25 6.76/3.25 evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] 6.76/3.25 6.76/3.25 evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 strictly and produces the following problem: 6.76/3.25 6.76/3.25 6: T: 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ar_1, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 6.76/3.25 6.76/3.25 (Comp: 2, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 6.76/3.25 6.76/3.25 (Comp: ar_1, Cost: 1) evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ] 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ] 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1)) 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 2, Cost: 1) evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 6.76/3.25 6.76/3.25 start location: koat_start 6.76/3.25 6.76/3.25 leaf cost: 0 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 A polynomial rank function with 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb5in) = V_4 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb3in) = V_4 + 1 6.76/3.25 6.76/3.25 Pol(evalinsertsortbb4in) = V_4 6.76/3.25 6.76/3.25 and size complexities 6.76/3.25 6.76/3.25 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = 4*ar_1 + 272 6.76/3.25 6.76/3.25 S("evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = 4*ar_1 + 4*ar_4 + 1024 6.76/3.25 6.76/3.25 S("evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-0) = 4*ar_1 + 16 6.76/3.25 6.76/3.25 S("evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4))", 0-4) = 4*ar_1 + 64 6.76/3.25 6.76/3.25 S("evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = 4*ar_1 + 256 6.76/3.25 6.76/3.25 S("evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = 4*ar_1 + 16 6.76/3.25 6.76/3.25 S("evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-0) = 4*ar_1 + 64 6.76/3.25 6.76/3.25 S("evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1))", 0-4) = 4*ar_1 + 16 6.76/3.25 6.76/3.25 S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4))", 0-0) = 4*ar_1 + 16 6.76/3.25 6.76/3.25 S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4))", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4))", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4))", 0-4) = 4*ar_1 + 4*ar_4 + 4096 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ]", 0-0) = 4*ar_1 + 16 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ]", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ]", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ]", 0-4) = 4*ar_1 + 4*ar_4 + 16384 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ]", 0-0) = 4*ar_1 + 16 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ]", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ]", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ]", 0-4) = 4*ar_1 + 4*ar_4 + 4096 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-0) = 4*ar_1 + 16 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ]", 0-4) = 4*ar_1 + 4*ar_4 + 16384 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ]", 0-0) = 4*ar_1 + 16 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ]", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ]", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ]", 0-4) = 4*ar_1 + 4*ar_4 + 4096 6.76/3.25 6.76/3.25 S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4))", 0-0) = 4*ar_1 + 16 6.76/3.25 6.76/3.25 S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4))", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4))", 0-3) = 4*ar_1 + 68 6.76/3.25 6.76/3.25 S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4))", 0-4) = 4*ar_1 + 4*ar_4 + 1024 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-0) = 4*ar_1 + 68 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-4) = 4*ar_1 + 4*ar_4 + 256 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-0) = 4*ar_1 + 16 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-2) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-3) = ? 6.76/3.25 6.76/3.25 S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-4) = 4*ar_1 + 4*ar_4 + 256 6.76/3.25 6.76/3.25 S("evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-0) = 1 6.76/3.25 6.76/3.25 S("evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 6.76/3.25 6.76/3.25 S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 6.76/3.25 6.76/3.25 S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 6.76/3.25 6.76/3.25 S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 6.76/3.25 6.76/3.25 S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 6.76/3.25 6.76/3.25 orients the transitions 6.76/3.25 6.76/3.25 evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4)) 6.76/3.25 6.76/3.25 evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ] 6.76/3.25 6.76/3.25 evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ] 6.76/3.25 6.76/3.25 weakly and the transition 6.76/3.25 6.76/3.25 evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ] 6.76/3.25 6.76/3.25 strictly and produces the following problem: 6.76/3.25 6.76/3.25 7: T: 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ar_1, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 6.76/3.25 6.76/3.25 (Comp: 2, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 6.76/3.25 6.76/3.25 (Comp: ar_1, Cost: 1) evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 4*ar_1^2 + 69*ar_1, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ] 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ] 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1)) 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 2, Cost: 1) evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 6.76/3.25 6.76/3.25 start location: koat_start 6.76/3.25 6.76/3.25 leaf cost: 0 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Repeatedly propagating knowledge in problem 7 produces the following problem: 6.76/3.25 6.76/3.25 8: T: 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 1) evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ar_1, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 6.76/3.25 6.76/3.25 (Comp: 2, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 6.76/3.25 6.76/3.25 (Comp: ar_1, Cost: 1) evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 4*ar_1^2 + 69*ar_1, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ] 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] 6.76/3.25 6.76/3.25 (Comp: 4*ar_1^2 + 69*ar_1, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ] 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ] 6.76/3.25 6.76/3.25 (Comp: 4*ar_1^2 + 69*ar_1, Cost: 1) evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1)) 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 4*ar_1, Cost: 1) evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 2, Cost: 1) evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 6.76/3.25 6.76/3.25 start location: koat_start 6.76/3.25 6.76/3.25 leaf cost: 0 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Complexity upper bound 229*ar_1 + 12*ar_1^2 + 13 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Time: 0.286 sec (SMT: 0.208 sec) 6.76/3.25 6.76/3.25 6.76/3.25 ---------------------------------------- 6.76/3.25 6.76/3.25 (2) 6.76/3.25 BOUNDS(1, n^2) 6.76/3.25 6.76/3.25 ---------------------------------------- 6.76/3.25 6.76/3.25 (3) Loat Proof (FINISHED) 6.76/3.25 6.76/3.25 6.76/3.25 ### Pre-processing the ITS problem ### 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Initial linear ITS problem 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 0: evalinsertsortstart -> evalinsertsortbb0in : [], cost: 1 6.76/3.25 6.76/3.25 1: evalinsertsortbb0in -> evalinsertsort0 : [], cost: 1 6.76/3.25 6.76/3.25 2: evalinsertsort0 -> evalinsertsort1 : [], cost: 1 6.76/3.25 6.76/3.25 3: evalinsertsort1 -> evalinsertsort2 : [], cost: 1 6.76/3.25 6.76/3.25 4: evalinsertsort2 -> evalinsertsort3 : [], cost: 1 6.76/3.25 6.76/3.25 5: evalinsertsort3 -> evalinsertsort4 : [], cost: 1 6.76/3.25 6.76/3.25 6: evalinsertsort4 -> evalinsertsort5 : [], cost: 1 6.76/3.25 6.76/3.25 7: evalinsertsort5 -> evalinsertsort6 : [], cost: 1 6.76/3.25 6.76/3.25 8: evalinsertsort6 -> evalinsertsortbb1in : A'=1, [], cost: 1 6.76/3.25 6.76/3.25 9: evalinsertsortbb1in -> evalinsertsortbb2in : [ B>=1+A ], cost: 1 6.76/3.25 6.76/3.25 10: evalinsertsortbb1in -> evalinsertsortbb7in : [ A>=B ], cost: 1 6.76/3.25 6.76/3.25 11: evalinsertsortbb2in -> evalinsertsortbb3in : C'=free, D'=-1+A, [], cost: 1 6.76/3.25 6.76/3.25 12: evalinsertsortbb3in -> evalinsertsortbb4in : [ D>=0 ], cost: 1 6.76/3.25 6.76/3.25 13: evalinsertsortbb3in -> evalinsertsortbb6in : [ 0>=1+D ], cost: 1 6.76/3.25 6.76/3.25 14: evalinsertsortbb4in -> evalinsertsortbb5in : [ free_1>=1+C ], cost: 1 6.76/3.25 6.76/3.25 15: evalinsertsortbb4in -> evalinsertsortbb6in : [ C>=free_2 ], cost: 1 6.76/3.25 6.76/3.25 16: evalinsertsortbb5in -> evalinsertsortbb3in : D'=-1+D, [], cost: 1 6.76/3.25 6.76/3.25 17: evalinsertsortbb6in -> evalinsertsort25 : E'=1+A, [], cost: 1 6.76/3.25 6.76/3.25 18: evalinsertsort25 -> evalinsertsort26 : [], cost: 1 6.76/3.25 6.76/3.25 19: evalinsertsort26 -> evalinsertsortbb1in : A'=E, [], cost: 1 6.76/3.25 6.76/3.25 20: evalinsertsortbb7in -> evalinsertsortstop : [], cost: 1 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Removed unreachable and leaf rules: 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 0: evalinsertsortstart -> evalinsertsortbb0in : [], cost: 1 6.76/3.25 6.76/3.25 1: evalinsertsortbb0in -> evalinsertsort0 : [], cost: 1 6.76/3.25 6.76/3.25 2: evalinsertsort0 -> evalinsertsort1 : [], cost: 1 6.76/3.25 6.76/3.25 3: evalinsertsort1 -> evalinsertsort2 : [], cost: 1 6.76/3.25 6.76/3.25 4: evalinsertsort2 -> evalinsertsort3 : [], cost: 1 6.76/3.25 6.76/3.25 5: evalinsertsort3 -> evalinsertsort4 : [], cost: 1 6.76/3.25 6.76/3.25 6: evalinsertsort4 -> evalinsertsort5 : [], cost: 1 6.76/3.25 6.76/3.25 7: evalinsertsort5 -> evalinsertsort6 : [], cost: 1 6.76/3.25 6.76/3.25 8: evalinsertsort6 -> evalinsertsortbb1in : A'=1, [], cost: 1 6.76/3.25 6.76/3.25 9: evalinsertsortbb1in -> evalinsertsortbb2in : [ B>=1+A ], cost: 1 6.76/3.25 6.76/3.25 11: evalinsertsortbb2in -> evalinsertsortbb3in : C'=free, D'=-1+A, [], cost: 1 6.76/3.25 6.76/3.25 12: evalinsertsortbb3in -> evalinsertsortbb4in : [ D>=0 ], cost: 1 6.76/3.25 6.76/3.25 13: evalinsertsortbb3in -> evalinsertsortbb6in : [ 0>=1+D ], cost: 1 6.76/3.25 6.76/3.25 14: evalinsertsortbb4in -> evalinsertsortbb5in : [ free_1>=1+C ], cost: 1 6.76/3.25 6.76/3.25 15: evalinsertsortbb4in -> evalinsertsortbb6in : [ C>=free_2 ], cost: 1 6.76/3.25 6.76/3.25 16: evalinsertsortbb5in -> evalinsertsortbb3in : D'=-1+D, [], cost: 1 6.76/3.25 6.76/3.25 17: evalinsertsortbb6in -> evalinsertsort25 : E'=1+A, [], cost: 1 6.76/3.25 6.76/3.25 18: evalinsertsort25 -> evalinsertsort26 : [], cost: 1 6.76/3.25 6.76/3.25 19: evalinsertsort26 -> evalinsertsortbb1in : A'=E, [], cost: 1 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Simplified all rules, resulting in: 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 0: evalinsertsortstart -> evalinsertsortbb0in : [], cost: 1 6.76/3.25 6.76/3.25 1: evalinsertsortbb0in -> evalinsertsort0 : [], cost: 1 6.76/3.25 6.76/3.25 2: evalinsertsort0 -> evalinsertsort1 : [], cost: 1 6.76/3.25 6.76/3.25 3: evalinsertsort1 -> evalinsertsort2 : [], cost: 1 6.76/3.25 6.76/3.25 4: evalinsertsort2 -> evalinsertsort3 : [], cost: 1 6.76/3.25 6.76/3.25 5: evalinsertsort3 -> evalinsertsort4 : [], cost: 1 6.76/3.25 6.76/3.25 6: evalinsertsort4 -> evalinsertsort5 : [], cost: 1 6.76/3.25 6.76/3.25 7: evalinsertsort5 -> evalinsertsort6 : [], cost: 1 6.76/3.25 6.76/3.25 8: evalinsertsort6 -> evalinsertsortbb1in : A'=1, [], cost: 1 6.76/3.25 6.76/3.25 9: evalinsertsortbb1in -> evalinsertsortbb2in : [ B>=1+A ], cost: 1 6.76/3.25 6.76/3.25 11: evalinsertsortbb2in -> evalinsertsortbb3in : C'=free, D'=-1+A, [], cost: 1 6.76/3.25 6.76/3.25 12: evalinsertsortbb3in -> evalinsertsortbb4in : [ D>=0 ], cost: 1 6.76/3.25 6.76/3.25 13: evalinsertsortbb3in -> evalinsertsortbb6in : [ 0>=1+D ], cost: 1 6.76/3.25 6.76/3.25 14: evalinsertsortbb4in -> evalinsertsortbb5in : [], cost: 1 6.76/3.25 6.76/3.25 15: evalinsertsortbb4in -> evalinsertsortbb6in : [], cost: 1 6.76/3.25 6.76/3.25 16: evalinsertsortbb5in -> evalinsertsortbb3in : D'=-1+D, [], cost: 1 6.76/3.25 6.76/3.25 17: evalinsertsortbb6in -> evalinsertsort25 : E'=1+A, [], cost: 1 6.76/3.25 6.76/3.25 18: evalinsertsort25 -> evalinsertsort26 : [], cost: 1 6.76/3.25 6.76/3.25 19: evalinsertsort26 -> evalinsertsortbb1in : A'=E, [], cost: 1 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 ### Simplification by acceleration and chaining ### 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Eliminated locations (on linear paths): 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 28: evalinsertsortstart -> evalinsertsortbb1in : A'=1, [], cost: 9 6.76/3.25 6.76/3.25 29: evalinsertsortbb1in -> evalinsertsortbb3in : C'=free, D'=-1+A, [ B>=1+A ], cost: 2 6.76/3.25 6.76/3.25 12: evalinsertsortbb3in -> evalinsertsortbb4in : [ D>=0 ], cost: 1 6.76/3.25 6.76/3.25 13: evalinsertsortbb3in -> evalinsertsortbb6in : [ 0>=1+D ], cost: 1 6.76/3.25 6.76/3.25 15: evalinsertsortbb4in -> evalinsertsortbb6in : [], cost: 1 6.76/3.25 6.76/3.25 30: evalinsertsortbb4in -> evalinsertsortbb3in : D'=-1+D, [], cost: 2 6.76/3.25 6.76/3.25 32: evalinsertsortbb6in -> evalinsertsortbb1in : A'=1+A, E'=1+A, [], cost: 3 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Eliminated locations (on tree-shaped paths): 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 28: evalinsertsortstart -> evalinsertsortbb1in : A'=1, [], cost: 9 6.76/3.25 6.76/3.25 29: evalinsertsortbb1in -> evalinsertsortbb3in : C'=free, D'=-1+A, [ B>=1+A ], cost: 2 6.76/3.25 6.76/3.25 34: evalinsertsortbb3in -> evalinsertsortbb3in : D'=-1+D, [ D>=0 ], cost: 3 6.76/3.25 6.76/3.25 35: evalinsertsortbb3in -> evalinsertsortbb1in : A'=1+A, E'=1+A, [ 0>=1+D ], cost: 4 6.76/3.25 6.76/3.25 36: evalinsertsortbb3in -> evalinsertsortbb1in : A'=1+A, E'=1+A, [ D>=0 ], cost: 5 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Accelerating simple loops of location 11. 6.76/3.25 6.76/3.25 Accelerating the following rules: 6.76/3.25 6.76/3.25 34: evalinsertsortbb3in -> evalinsertsortbb3in : D'=-1+D, [ D>=0 ], cost: 3 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Accelerated rule 34 with metering function 1+D, yielding the new rule 37. 6.76/3.25 6.76/3.25 Removing the simple loops: 34. 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Accelerated all simple loops using metering functions (where possible): 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 28: evalinsertsortstart -> evalinsertsortbb1in : A'=1, [], cost: 9 6.76/3.25 6.76/3.25 29: evalinsertsortbb1in -> evalinsertsortbb3in : C'=free, D'=-1+A, [ B>=1+A ], cost: 2 6.76/3.25 6.76/3.25 35: evalinsertsortbb3in -> evalinsertsortbb1in : A'=1+A, E'=1+A, [ 0>=1+D ], cost: 4 6.76/3.25 6.76/3.25 36: evalinsertsortbb3in -> evalinsertsortbb1in : A'=1+A, E'=1+A, [ D>=0 ], cost: 5 6.76/3.25 6.76/3.25 37: evalinsertsortbb3in -> evalinsertsortbb3in : D'=-1, [ D>=0 ], cost: 3+3*D 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Chained accelerated rules (with incoming rules): 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 28: evalinsertsortstart -> evalinsertsortbb1in : A'=1, [], cost: 9 6.76/3.25 6.76/3.25 29: evalinsertsortbb1in -> evalinsertsortbb3in : C'=free, D'=-1+A, [ B>=1+A ], cost: 2 6.76/3.25 6.76/3.25 38: evalinsertsortbb1in -> evalinsertsortbb3in : C'=free, D'=-1, [ B>=1+A && -1+A>=0 ], cost: 2+3*A 6.76/3.25 6.76/3.25 35: evalinsertsortbb3in -> evalinsertsortbb1in : A'=1+A, E'=1+A, [ 0>=1+D ], cost: 4 6.76/3.25 6.76/3.25 36: evalinsertsortbb3in -> evalinsertsortbb1in : A'=1+A, E'=1+A, [ D>=0 ], cost: 5 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Eliminated locations (on tree-shaped paths): 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 28: evalinsertsortstart -> evalinsertsortbb1in : A'=1, [], cost: 9 6.76/3.25 6.76/3.25 39: evalinsertsortbb1in -> evalinsertsortbb1in : A'=1+A, C'=free, D'=-1+A, E'=1+A, [ B>=1+A && 0>=A ], cost: 6 6.76/3.25 6.76/3.25 40: evalinsertsortbb1in -> evalinsertsortbb1in : A'=1+A, C'=free, D'=-1+A, E'=1+A, [ B>=1+A && -1+A>=0 ], cost: 7 6.76/3.25 6.76/3.25 41: evalinsertsortbb1in -> evalinsertsortbb1in : A'=1+A, C'=free, D'=-1, E'=1+A, [ B>=1+A && -1+A>=0 ], cost: 6+3*A 6.76/3.25 6.76/3.25 42: evalinsertsortbb1in -> [20] : [ B>=1+A && -1+A>=0 ], cost: 2+3*A 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Accelerating simple loops of location 9. 6.76/3.25 6.76/3.25 Accelerating the following rules: 6.76/3.25 6.76/3.25 39: evalinsertsortbb1in -> evalinsertsortbb1in : A'=1+A, C'=free, D'=-1+A, E'=1+A, [ B>=1+A && 0>=A ], cost: 6 6.76/3.25 6.76/3.25 40: evalinsertsortbb1in -> evalinsertsortbb1in : A'=1+A, C'=free, D'=-1+A, E'=1+A, [ B>=1+A && -1+A>=0 ], cost: 7 6.76/3.25 6.76/3.25 41: evalinsertsortbb1in -> evalinsertsortbb1in : A'=1+A, C'=free, D'=-1, E'=1+A, [ B>=1+A && -1+A>=0 ], cost: 6+3*A 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Accelerated rule 39 with backward acceleration, yielding the new rule 43. 6.76/3.25 6.76/3.25 Accelerated rule 39 with backward acceleration, yielding the new rule 44. 6.76/3.25 6.76/3.25 Accelerated rule 40 with metering function -A+B, yielding the new rule 45. 6.76/3.25 6.76/3.25 Accelerated rule 41 with metering function -A+B, yielding the new rule 46. 6.76/3.25 6.76/3.25 Removing the simple loops: 39 40 41. 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Accelerated all simple loops using metering functions (where possible): 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 28: evalinsertsortstart -> evalinsertsortbb1in : A'=1, [], cost: 9 6.76/3.25 6.76/3.25 42: evalinsertsortbb1in -> [20] : [ B>=1+A && -1+A>=0 ], cost: 2+3*A 6.76/3.25 6.76/3.25 43: evalinsertsortbb1in -> evalinsertsortbb1in : A'=B, C'=free, D'=-2+B, E'=B, [ B>=1+A && 0>=A && 0>=-1+B ], cost: -6*A+6*B 6.76/3.25 6.76/3.25 44: evalinsertsortbb1in -> evalinsertsortbb1in : A'=1, C'=free, D'=-1, E'=1, [ B>=1+A && 0>=A && B>=1 ], cost: 6-6*A 6.76/3.25 6.76/3.25 45: evalinsertsortbb1in -> evalinsertsortbb1in : A'=B, C'=free, D'=-2+B, E'=B, [ B>=1+A && -1+A>=0 ], cost: -7*A+7*B 6.76/3.25 6.76/3.25 46: evalinsertsortbb1in -> evalinsertsortbb1in : A'=B, C'=free, D'=-1, E'=B, [ B>=1+A && -1+A>=0 ], cost: 3/2*(A-B)^2-9/2*A-3*A*(A-B)+9/2*B 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Chained accelerated rules (with incoming rules): 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 28: evalinsertsortstart -> evalinsertsortbb1in : A'=1, [], cost: 9 6.76/3.25 6.76/3.25 47: evalinsertsortstart -> evalinsertsortbb1in : A'=B, C'=free, D'=-2+B, E'=B, [ B>=2 ], cost: 2+7*B 6.76/3.25 6.76/3.25 48: evalinsertsortstart -> evalinsertsortbb1in : A'=B, C'=free, D'=-1, E'=B, [ B>=2 ], cost: 3/2+3/2*(-1+B)^2+15/2*B 6.76/3.25 6.76/3.25 42: evalinsertsortbb1in -> [20] : [ B>=1+A && -1+A>=0 ], cost: 2+3*A 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Eliminated locations (on tree-shaped paths): 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 49: evalinsertsortstart -> [20] : A'=1, [ B>=2 ], cost: 14 6.76/3.25 6.76/3.25 50: evalinsertsortstart -> [22] : [ B>=2 ], cost: 2+7*B 6.76/3.25 6.76/3.25 51: evalinsertsortstart -> [22] : [ B>=2 ], cost: 3/2+3/2*(-1+B)^2+15/2*B 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Applied pruning (of leafs and parallel rules): 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 50: evalinsertsortstart -> [22] : [ B>=2 ], cost: 2+7*B 6.76/3.25 6.76/3.25 51: evalinsertsortstart -> [22] : [ B>=2 ], cost: 3/2+3/2*(-1+B)^2+15/2*B 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 ### Computing asymptotic complexity ### 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Fully simplified ITS problem 6.76/3.25 6.76/3.25 Start location: evalinsertsortstart 6.76/3.25 6.76/3.25 50: evalinsertsortstart -> [22] : [ B>=2 ], cost: 2+7*B 6.76/3.25 6.76/3.25 51: evalinsertsortstart -> [22] : [ B>=2 ], cost: 3/2+3/2*(-1+B)^2+15/2*B 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Computing asymptotic complexity for rule 50 6.76/3.25 6.76/3.25 Solved the limit problem by the following transformations: 6.76/3.25 6.76/3.25 Created initial limit problem: 6.76/3.25 6.76/3.25 -1+B (+/+!), 2+7*B (+) [not solved] 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 removing all constraints (solved by SMT) 6.76/3.25 6.76/3.25 resulting limit problem: [solved] 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 applying transformation rule (C) using substitution {B==n} 6.76/3.25 6.76/3.25 resulting limit problem: 6.76/3.25 6.76/3.25 [solved] 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Solution: 6.76/3.25 6.76/3.25 B / n 6.76/3.25 6.76/3.25 Resulting cost 2+7*n has complexity: Poly(n^1) 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Found new complexity Poly(n^1). 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Computing asymptotic complexity for rule 51 6.76/3.25 6.76/3.25 Solved the limit problem by the following transformations: 6.76/3.25 6.76/3.25 Created initial limit problem: 6.76/3.25 6.76/3.25 -1+B (+/+!), 3+3/2*B^2+9/2*B (+) [not solved] 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 removing all constraints (solved by SMT) 6.76/3.25 6.76/3.25 resulting limit problem: [solved] 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 applying transformation rule (C) using substitution {B==n} 6.76/3.25 6.76/3.25 resulting limit problem: 6.76/3.25 6.76/3.25 [solved] 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Solution: 6.76/3.25 6.76/3.25 B / n 6.76/3.25 6.76/3.25 Resulting cost 3+3/2*n^2+9/2*n has complexity: Poly(n^2) 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Found new complexity Poly(n^2). 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Obtained the following overall complexity (w.r.t. the length of the input n): 6.76/3.25 6.76/3.25 Complexity: Poly(n^2) 6.76/3.25 6.76/3.25 Cpx degree: 2 6.76/3.25 6.76/3.25 Solved cost: 3+3/2*n^2+9/2*n 6.76/3.25 6.76/3.25 Rule cost: 3/2+3/2*(-1+B)^2+15/2*B 6.76/3.25 6.76/3.25 Rule guard: [ B>=2 ] 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 WORST_CASE(Omega(n^2),?) 6.76/3.25 6.76/3.25 6.76/3.25 ---------------------------------------- 6.76/3.25 6.76/3.25 (4) 6.76/3.25 BOUNDS(n^2, INF) 6.76/3.28 EOF