7.59/3.74 WORST_CASE(Omega(n^1), O(n^1)) 7.59/3.75 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 7.59/3.75 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.59/3.75 7.59/3.75 7.59/3.75 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 7.59/3.75 7.59/3.75 (0) CpxIntTrs 7.59/3.75 (1) Koat Proof [FINISHED, 912 ms] 7.59/3.75 (2) BOUNDS(1, n^1) 7.59/3.75 (3) Loat Proof [FINISHED, 1517 ms] 7.59/3.75 (4) BOUNDS(n^1, INF) 7.59/3.75 7.59/3.75 7.59/3.75 ---------------------------------------- 7.59/3.75 7.59/3.75 (0) 7.59/3.75 Obligation: 7.59/3.75 Complexity Int TRS consisting of the following rules: 7.59/3.75 eval_ex1_start(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_bb0_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_bb0_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_0(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_0(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_1(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_1(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_2(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_2(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_3(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_3(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_4(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_4(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_5(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_5(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_6(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_6(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_bb1_in(v_3, v_8, 0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_bb1_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_bb2_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: v_i_0 < v_n 7.59/3.75 eval_ex1_bb1_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_bb6_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: v_i_0 >= v_n 7.59/3.75 eval_ex1_bb2_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_bb3_in(v_3, v_8, v_i_0, v_i_0 + 1, 0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_bb3_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_bb4_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: v_i_1 < v_n 7.59/3.75 eval_ex1_bb3_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1__critedge_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: v_i_1 >= v_n 7.59/3.75 eval_ex1_bb4_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_9(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_9(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_10(nondef_0, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_10(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_bb5_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: v_3 > 0 7.59/3.75 eval_ex1_10(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1__critedge_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: v_3 <= 0 7.59/3.75 eval_ex1_bb5_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_bb3_in(v_3, v_8, v_i_0, v_i_1 + 1, v_j_0 + 1, v_n)) :|: TRUE 7.59/3.75 eval_ex1__critedge_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_15(v_3, v_i_1 - 1, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_15(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_16(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 eval_ex1_16(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_bb1_in(v_3, v_8, v_8, v_i_1, v_j_0, v_n)) :|: v_j_0 > 0 7.59/3.75 eval_ex1_16(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_bb1_in(v_3, v_8, v_i_1, v_i_1, v_j_0, v_n)) :|: v_j_0 <= 0 7.59/3.75 eval_ex1_bb6_in(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n) -> Com_1(eval_ex1_stop(v_3, v_8, v_i_0, v_i_1, v_j_0, v_n)) :|: TRUE 7.59/3.75 7.59/3.75 The start-symbols are:[eval_ex1_start_6] 7.59/3.75 7.59/3.75 7.59/3.75 ---------------------------------------- 7.59/3.75 7.59/3.75 (1) Koat Proof (FINISHED) 7.59/3.75 YES(?, 182*ar_1 + 13) 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Initial complexity problem: 7.59/3.75 7.59/3.75 1: T: 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_0 + 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_2 + 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex110(ar_0, ar_1, ar_2, ar_3, g, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex110(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex110(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb3in(ar_0, ar_1, ar_2 + 1, ar_3 + 1, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex115(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2 - 1)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex115(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(ar_5, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(ar_2, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_3 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 7.59/3.75 7.59/3.75 start location: koat_start 7.59/3.75 7.59/3.75 leaf cost: 0 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Repeatedly propagating knowledge in problem 1 produces the following problem: 7.59/3.75 7.59/3.75 2: T: 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_0 + 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_2 + 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex110(ar_0, ar_1, ar_2, ar_3, g, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex110(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex110(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb3in(ar_0, ar_1, ar_2 + 1, ar_3 + 1, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex115(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2 - 1)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex115(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(ar_5, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(ar_2, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_3 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 7.59/3.75 7.59/3.75 start location: koat_start 7.59/3.75 7.59/3.75 leaf cost: 0 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 A polynomial rank function with 7.59/3.75 7.59/3.75 Pol(evalex1start) = 2 7.59/3.75 7.59/3.75 Pol(evalex1bb0in) = 2 7.59/3.75 7.59/3.75 Pol(evalex10) = 2 7.59/3.75 7.59/3.75 Pol(evalex11) = 2 7.59/3.75 7.59/3.75 Pol(evalex12) = 2 7.59/3.75 7.59/3.75 Pol(evalex13) = 2 7.59/3.75 7.59/3.75 Pol(evalex14) = 2 7.59/3.75 7.59/3.75 Pol(evalex15) = 2 7.59/3.75 7.59/3.75 Pol(evalex16) = 2 7.59/3.75 7.59/3.75 Pol(evalex1bb1in) = 2 7.59/3.75 7.59/3.75 Pol(evalex1bb2in) = 2 7.59/3.75 7.59/3.75 Pol(evalex1bb6in) = 1 7.59/3.75 7.59/3.75 Pol(evalex1bb3in) = 2 7.59/3.75 7.59/3.75 Pol(evalex1bb4in) = 2 7.59/3.75 7.59/3.75 Pol(evalex1critedgein) = 2 7.59/3.75 7.59/3.75 Pol(evalex19) = 2 7.59/3.75 7.59/3.75 Pol(evalex110) = 2 7.59/3.75 7.59/3.75 Pol(evalex1bb5in) = 2 7.59/3.75 7.59/3.75 Pol(evalex115) = 2 7.59/3.75 7.59/3.75 Pol(evalex116) = 2 7.59/3.75 7.59/3.75 Pol(evalex1stop) = 0 7.59/3.75 7.59/3.75 Pol(koat_start) = 2 7.59/3.75 7.59/3.75 orients all transitions weakly and the transitions 7.59/3.75 7.59/3.75 evalex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 evalex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_1 ] 7.59/3.75 7.59/3.75 strictly and produces the following problem: 7.59/3.75 7.59/3.75 3: T: 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_0 + 1 ] 7.59/3.75 7.59/3.75 (Comp: 2, Cost: 1) evalex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_2 + 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex110(ar_0, ar_1, ar_2, ar_3, g, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex110(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex110(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb3in(ar_0, ar_1, ar_2 + 1, ar_3 + 1, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex115(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2 - 1)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex115(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(ar_5, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(ar_2, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_3 ] 7.59/3.75 7.59/3.75 (Comp: 2, Cost: 1) evalex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 7.59/3.75 7.59/3.75 start location: koat_start 7.59/3.75 7.59/3.75 leaf cost: 0 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Applied AI with 'oct' on problem 3 to obtain the following invariants: 7.59/3.75 7.59/3.75 For symbol evalex110: X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 2 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 7.59/3.75 7.59/3.75 For symbol evalex115: X_3 - X_6 - 1 >= 0 /\ X_2 - X_6 - 1 >= 0 /\ X_6 >= 0 /\ X_4 + X_6 >= 0 /\ -X_4 + X_6 >= 0 /\ X_3 + X_6 - 1 >= 0 /\ -X_3 + X_6 + 1 >= 0 /\ X_2 + X_6 - 1 >= 0 /\ X_1 + X_6 >= 0 /\ -X_1 + X_6 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 7.59/3.75 7.59/3.75 For symbol evalex116: X_3 - X_6 - 1 >= 0 /\ X_2 - X_6 - 1 >= 0 /\ X_6 >= 0 /\ X_4 + X_6 >= 0 /\ -X_4 + X_6 >= 0 /\ X_3 + X_6 - 1 >= 0 /\ -X_3 + X_6 + 1 >= 0 /\ X_2 + X_6 - 1 >= 0 /\ X_1 + X_6 >= 0 /\ -X_1 + X_6 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 7.59/3.75 7.59/3.75 For symbol evalex19: X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 2 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 7.59/3.75 7.59/3.75 For symbol evalex1bb1in: X_1 >= 0 7.59/3.75 7.59/3.75 For symbol evalex1bb2in: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 7.59/3.75 7.59/3.75 For symbol evalex1bb3in: X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 7.59/3.75 7.59/3.75 For symbol evalex1bb4in: X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 2 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 7.59/3.75 7.59/3.75 For symbol evalex1bb5in: X_5 - 1 >= 0 /\ X_4 + X_5 - 1 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 2 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 7.59/3.75 7.59/3.75 For symbol evalex1bb6in: X_1 - X_2 >= 0 /\ X_1 >= 0 7.59/3.75 7.59/3.75 For symbol evalex1critedgein: X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 >= 0 /\ X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 This yielded the following problem: 7.59/3.75 7.59/3.75 4: T: 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 7.59/3.75 7.59/3.75 (Comp: 2, Cost: 1) evalex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(ar_2, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_5 - 1 >= 0 /\ ar_1 - ar_5 - 1 >= 0 /\ ar_5 >= 0 /\ ar_3 + ar_5 >= 0 /\ -ar_3 + ar_5 >= 0 /\ ar_2 + ar_5 - 1 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 >= 0 /\ -ar_0 + ar_5 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_3 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(ar_5, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_5 - 1 >= 0 /\ ar_1 - ar_5 - 1 >= 0 /\ ar_5 >= 0 /\ ar_3 + ar_5 >= 0 /\ -ar_3 + ar_5 >= 0 /\ ar_2 + ar_5 - 1 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 >= 0 /\ -ar_0 + ar_5 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex115(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_5 - 1 >= 0 /\ ar_1 - ar_5 - 1 >= 0 /\ ar_5 >= 0 /\ ar_3 + ar_5 >= 0 /\ -ar_3 + ar_5 >= 0 /\ ar_2 + ar_5 - 1 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 >= 0 /\ -ar_0 + ar_5 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex115(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2 - 1)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb3in(ar_0, ar_1, ar_2 + 1, ar_3 + 1, ar_4, ar_5)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex110(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_4 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex110(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ ar_4 >= 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex110(ar_0, ar_1, ar_2, ar_3, g, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_2 + 1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4, ar_5)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: 2, Cost: 1) evalex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 0 /\ ar_0 >= ar_1 ] 7.59/3.75 7.59/3.75 (Comp: ?, Cost: 1) evalex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 start location: koat_start 7.59/3.75 7.59/3.75 leaf cost: 0 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 A polynomial rank function with 7.59/3.75 7.59/3.75 Pol(koat_start) = 14*V_2 7.59/3.75 7.59/3.75 Pol(evalex1start) = 14*V_2 7.59/3.75 7.59/3.75 Pol(evalex1bb6in) = -14*V_1 + 14*V_2 7.59/3.75 7.59/3.75 Pol(evalex1stop) = -14*V_1 + 14*V_2 7.59/3.75 7.59/3.75 Pol(evalex116) = 14*V_2 - 8*V_3 + 9*V_4 - 6*V_6 7.59/3.75 7.59/3.75 Pol(evalex1bb1in) = -14*V_1 + 14*V_2 7.59/3.75 7.59/3.75 Pol(evalex115) = 14*V_2 - 8*V_3 + 9*V_4 - 6*V_6 + 1 7.59/3.75 7.59/3.75 Pol(evalex1critedgein) = 14*V_2 - 14*V_3 + 9*V_4 + 8 7.59/3.75 7.59/3.75 Pol(evalex1bb5in) = 14*V_2 - 14*V_3 + 9*V_4 + 8 7.59/3.75 7.59/3.75 Pol(evalex1bb3in) = 14*V_2 - 14*V_3 + 9*V_4 + 12 7.59/3.75 7.59/3.75 Pol(evalex110) = 14*V_2 - 14*V_3 + 9*V_4 + 9 7.59/3.75 7.59/3.75 Pol(evalex19) = 14*V_2 - 14*V_3 + 9*V_4 + 10 7.59/3.75 7.59/3.75 Pol(evalex1bb4in) = 14*V_2 - 14*V_3 + 9*V_4 + 11 7.59/3.75 7.59/3.75 Pol(evalex1bb2in) = -14*V_1 + 14*V_2 - 1 7.59/3.75 7.59/3.75 Pol(evalex16) = 14*V_2 7.59/3.75 7.59/3.75 Pol(evalex15) = 14*V_2 7.59/3.75 7.59/3.75 Pol(evalex14) = 14*V_2 7.59/3.75 7.59/3.75 Pol(evalex13) = 14*V_2 7.59/3.75 7.59/3.75 Pol(evalex12) = 14*V_2 7.59/3.75 7.59/3.75 Pol(evalex11) = 14*V_2 7.59/3.75 7.59/3.75 Pol(evalex10) = 14*V_2 7.59/3.75 7.59/3.75 Pol(evalex1bb0in) = 14*V_2 7.59/3.75 7.59/3.75 orients all transitions weakly and the transitions 7.59/3.75 7.59/3.75 evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex115(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2 - 1)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 evalex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb3in(ar_0, ar_1, ar_2 + 1, ar_3 + 1, ar_4, ar_5)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 evalex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 evalex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_1 ] 7.59/3.75 7.59/3.75 evalex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_2 + 1 ] 7.59/3.75 7.59/3.75 evalex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4, ar_5)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 evalex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.59/3.75 7.59/3.75 evalex19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex110(ar_0, ar_1, ar_2, ar_3, g, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(ar_5, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_5 - 1 >= 0 /\ ar_1 - ar_5 - 1 >= 0 /\ ar_5 >= 0 /\ ar_3 + ar_5 >= 0 /\ -ar_3 + ar_5 >= 0 /\ ar_2 + ar_5 - 1 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 >= 0 /\ -ar_0 + ar_5 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= 1 ] 7.59/3.75 7.59/3.75 evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(ar_2, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_5 - 1 >= 0 /\ ar_1 - ar_5 - 1 >= 0 /\ ar_5 >= 0 /\ ar_3 + ar_5 >= 0 /\ -ar_3 + ar_5 >= 0 /\ ar_2 + ar_5 - 1 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 >= 0 /\ -ar_0 + ar_5 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_3 ] 7.59/3.75 7.59/3.75 evalex115(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_5 - 1 >= 0 /\ ar_1 - ar_5 - 1 >= 0 /\ ar_5 >= 0 /\ ar_3 + ar_5 >= 0 /\ -ar_3 + ar_5 >= 0 /\ ar_2 + ar_5 - 1 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 >= 0 /\ -ar_0 + ar_5 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 evalex110(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_4 ] 7.59/3.75 7.59/3.75 evalex110(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ ar_4 >= 1 ] 7.59/3.75 7.59/3.75 strictly and produces the following problem: 7.59/3.75 7.59/3.75 5: T: 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 7.59/3.75 7.59/3.75 (Comp: 2, Cost: 1) evalex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(ar_2, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_5 - 1 >= 0 /\ ar_1 - ar_5 - 1 >= 0 /\ ar_5 >= 0 /\ ar_3 + ar_5 >= 0 /\ -ar_3 + ar_5 >= 0 /\ ar_2 + ar_5 - 1 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 >= 0 /\ -ar_0 + ar_5 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_3 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(ar_5, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_5 - 1 >= 0 /\ ar_1 - ar_5 - 1 >= 0 /\ ar_5 >= 0 /\ ar_3 + ar_5 >= 0 /\ -ar_3 + ar_5 >= 0 /\ ar_2 + ar_5 - 1 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 >= 0 /\ -ar_0 + ar_5 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= 1 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex115(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex116(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_5 - 1 >= 0 /\ ar_1 - ar_5 - 1 >= 0 /\ ar_5 >= 0 /\ ar_3 + ar_5 >= 0 /\ -ar_3 + ar_5 >= 0 /\ ar_2 + ar_5 - 1 >= 0 /\ -ar_2 + ar_5 + 1 >= 0 /\ ar_1 + ar_5 - 1 >= 0 /\ ar_0 + ar_5 >= 0 /\ -ar_0 + ar_5 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex115(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2 - 1)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb3in(ar_0, ar_1, ar_2 + 1, ar_3 + 1, ar_4, ar_5)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex110(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_4 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex110(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ ar_4 >= 1 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex110(ar_0, ar_1, ar_2, ar_3, g, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 2 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_1 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_2 + 1 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb3in(ar_0, ar_1, ar_0 + 1, 0, ar_4, ar_5)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ] 7.59/3.75 7.59/3.75 (Comp: 2, Cost: 1) evalex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 0 /\ ar_0 >= ar_1 ] 7.59/3.75 7.59/3.75 (Comp: 14*ar_1, Cost: 1) evalex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ] 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb1in(0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 (Comp: 1, Cost: 1) evalex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 7.59/3.75 7.59/3.75 start location: koat_start 7.59/3.75 7.59/3.75 leaf cost: 0 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Complexity upper bound 182*ar_1 + 13 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Time: 0.964 sec (SMT: 0.690 sec) 7.59/3.75 7.59/3.75 7.59/3.75 ---------------------------------------- 7.59/3.75 7.59/3.75 (2) 7.59/3.75 BOUNDS(1, n^1) 7.59/3.75 7.59/3.75 ---------------------------------------- 7.59/3.75 7.59/3.75 (3) Loat Proof (FINISHED) 7.59/3.75 7.59/3.75 7.59/3.75 ### Pre-processing the ITS problem ### 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Initial linear ITS problem 7.59/3.75 7.59/3.75 Start location: evalex1start 7.59/3.75 7.59/3.75 0: evalex1start -> evalex1bb0in : [], cost: 1 7.59/3.75 7.59/3.75 1: evalex1bb0in -> evalex10 : [], cost: 1 7.59/3.75 7.59/3.75 2: evalex10 -> evalex11 : [], cost: 1 7.59/3.75 7.59/3.75 3: evalex11 -> evalex12 : [], cost: 1 7.59/3.75 7.59/3.75 4: evalex12 -> evalex13 : [], cost: 1 7.59/3.75 7.59/3.75 5: evalex13 -> evalex14 : [], cost: 1 7.59/3.75 7.59/3.75 6: evalex14 -> evalex15 : [], cost: 1 7.59/3.75 7.59/3.75 7: evalex15 -> evalex16 : [], cost: 1 7.59/3.75 7.59/3.75 8: evalex16 -> evalex1bb1in : A'=0, [], cost: 1 7.59/3.75 7.59/3.75 9: evalex1bb1in -> evalex1bb2in : [ B>=1+A ], cost: 1 7.59/3.75 7.59/3.75 10: evalex1bb1in -> evalex1bb6in : [ A>=B ], cost: 1 7.59/3.75 7.59/3.75 11: evalex1bb2in -> evalex1bb3in : C'=1+A, D'=0, [], cost: 1 7.59/3.75 7.59/3.75 12: evalex1bb3in -> evalex1bb4in : [ B>=1+C ], cost: 1 7.59/3.75 7.59/3.75 13: evalex1bb3in -> evalex1critedgein : [ C>=B ], cost: 1 7.59/3.75 7.59/3.75 14: evalex1bb4in -> evalex19 : [], cost: 1 7.59/3.75 7.59/3.75 15: evalex19 -> evalex110 : E'=free, [], cost: 1 7.59/3.75 7.59/3.75 16: evalex110 -> evalex1bb5in : [ E>=1 ], cost: 1 7.59/3.75 7.59/3.75 17: evalex110 -> evalex1critedgein : [ 0>=E ], cost: 1 7.59/3.75 7.59/3.75 18: evalex1bb5in -> evalex1bb3in : C'=1+C, D'=1+D, [], cost: 1 7.59/3.75 7.59/3.75 19: evalex1critedgein -> evalex115 : F'=-1+C, [], cost: 1 7.59/3.75 7.59/3.75 20: evalex115 -> evalex116 : [], cost: 1 7.59/3.75 7.59/3.75 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 7.59/3.75 7.59/3.75 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 7.59/3.75 7.59/3.75 23: evalex1bb6in -> evalex1stop : [], cost: 1 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Removed unreachable and leaf rules: 7.59/3.75 7.59/3.75 Start location: evalex1start 7.59/3.75 7.59/3.75 0: evalex1start -> evalex1bb0in : [], cost: 1 7.59/3.75 7.59/3.75 1: evalex1bb0in -> evalex10 : [], cost: 1 7.59/3.75 7.59/3.75 2: evalex10 -> evalex11 : [], cost: 1 7.59/3.75 7.59/3.75 3: evalex11 -> evalex12 : [], cost: 1 7.59/3.75 7.59/3.75 4: evalex12 -> evalex13 : [], cost: 1 7.59/3.75 7.59/3.75 5: evalex13 -> evalex14 : [], cost: 1 7.59/3.75 7.59/3.75 6: evalex14 -> evalex15 : [], cost: 1 7.59/3.75 7.59/3.75 7: evalex15 -> evalex16 : [], cost: 1 7.59/3.75 7.59/3.75 8: evalex16 -> evalex1bb1in : A'=0, [], cost: 1 7.59/3.75 7.59/3.75 9: evalex1bb1in -> evalex1bb2in : [ B>=1+A ], cost: 1 7.59/3.75 7.59/3.75 11: evalex1bb2in -> evalex1bb3in : C'=1+A, D'=0, [], cost: 1 7.59/3.75 7.59/3.75 12: evalex1bb3in -> evalex1bb4in : [ B>=1+C ], cost: 1 7.59/3.75 7.59/3.75 13: evalex1bb3in -> evalex1critedgein : [ C>=B ], cost: 1 7.59/3.75 7.59/3.75 14: evalex1bb4in -> evalex19 : [], cost: 1 7.59/3.75 7.59/3.75 15: evalex19 -> evalex110 : E'=free, [], cost: 1 7.59/3.75 7.59/3.75 16: evalex110 -> evalex1bb5in : [ E>=1 ], cost: 1 7.59/3.75 7.59/3.75 17: evalex110 -> evalex1critedgein : [ 0>=E ], cost: 1 7.59/3.75 7.59/3.75 18: evalex1bb5in -> evalex1bb3in : C'=1+C, D'=1+D, [], cost: 1 7.59/3.75 7.59/3.75 19: evalex1critedgein -> evalex115 : F'=-1+C, [], cost: 1 7.59/3.75 7.59/3.75 20: evalex115 -> evalex116 : [], cost: 1 7.59/3.75 7.59/3.75 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 7.59/3.75 7.59/3.75 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 ### Simplification by acceleration and chaining ### 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Eliminated locations (on linear paths): 7.59/3.75 7.59/3.75 Start location: evalex1start 7.59/3.75 7.59/3.75 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 7.59/3.75 7.59/3.75 32: evalex1bb1in -> evalex1bb3in : C'=1+A, D'=0, [ B>=1+A ], cost: 2 7.59/3.75 7.59/3.75 13: evalex1bb3in -> evalex1critedgein : [ C>=B ], cost: 1 7.59/3.75 7.59/3.75 34: evalex1bb3in -> evalex110 : E'=free, [ B>=1+C ], cost: 3 7.59/3.75 7.59/3.75 17: evalex110 -> evalex1critedgein : [ 0>=E ], cost: 1 7.59/3.75 7.59/3.75 35: evalex110 -> evalex1bb3in : C'=1+C, D'=1+D, [ E>=1 ], cost: 2 7.59/3.75 7.59/3.75 36: evalex1critedgein -> evalex116 : F'=-1+C, [], cost: 2 7.59/3.75 7.59/3.75 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 7.59/3.75 7.59/3.75 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Eliminated locations (on tree-shaped paths): 7.59/3.75 7.59/3.75 Start location: evalex1start 7.59/3.75 7.59/3.75 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 7.59/3.75 7.59/3.75 32: evalex1bb1in -> evalex1bb3in : C'=1+A, D'=0, [ B>=1+A ], cost: 2 7.59/3.75 7.59/3.75 38: evalex1bb3in -> evalex1bb3in : C'=1+C, D'=1+D, E'=free, [ B>=1+C && free>=1 ], cost: 5 7.59/3.75 7.59/3.75 39: evalex1bb3in -> evalex116 : F'=-1+C, [ C>=B ], cost: 3 7.59/3.75 7.59/3.75 40: evalex1bb3in -> evalex116 : E'=free, F'=-1+C, [ B>=1+C && 0>=free ], cost: 6 7.59/3.75 7.59/3.75 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 7.59/3.75 7.59/3.75 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Accelerating simple loops of location 11. 7.59/3.75 7.59/3.75 Accelerating the following rules: 7.59/3.75 7.59/3.75 38: evalex1bb3in -> evalex1bb3in : C'=1+C, D'=1+D, E'=free, [ B>=1+C && free>=1 ], cost: 5 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Accelerated rule 38 with metering function -C+B, yielding the new rule 41. 7.59/3.75 7.59/3.75 Removing the simple loops: 38. 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Accelerated all simple loops using metering functions (where possible): 7.59/3.75 7.59/3.75 Start location: evalex1start 7.59/3.75 7.59/3.75 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 7.59/3.75 7.59/3.75 32: evalex1bb1in -> evalex1bb3in : C'=1+A, D'=0, [ B>=1+A ], cost: 2 7.59/3.75 7.59/3.75 39: evalex1bb3in -> evalex116 : F'=-1+C, [ C>=B ], cost: 3 7.59/3.75 7.59/3.75 40: evalex1bb3in -> evalex116 : E'=free, F'=-1+C, [ B>=1+C && 0>=free ], cost: 6 7.59/3.75 7.59/3.75 41: evalex1bb3in -> evalex1bb3in : C'=B, D'=-C+D+B, E'=free, [ B>=1+C && free>=1 ], cost: -5*C+5*B 7.59/3.75 7.59/3.75 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 7.59/3.75 7.59/3.75 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Chained accelerated rules (with incoming rules): 7.59/3.75 7.59/3.75 Start location: evalex1start 7.59/3.75 7.59/3.75 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 7.59/3.75 7.59/3.75 32: evalex1bb1in -> evalex1bb3in : C'=1+A, D'=0, [ B>=1+A ], cost: 2 7.59/3.75 7.59/3.75 42: evalex1bb1in -> evalex1bb3in : C'=B, D'=-1-A+B, E'=free, [ B>=2+A && free>=1 ], cost: -3-5*A+5*B 7.59/3.75 7.59/3.75 39: evalex1bb3in -> evalex116 : F'=-1+C, [ C>=B ], cost: 3 7.59/3.75 7.59/3.75 40: evalex1bb3in -> evalex116 : E'=free, F'=-1+C, [ B>=1+C && 0>=free ], cost: 6 7.59/3.75 7.59/3.75 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 7.59/3.75 7.59/3.75 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Eliminated locations (on tree-shaped paths): 7.59/3.75 7.59/3.75 Start location: evalex1start 7.59/3.75 7.59/3.75 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 7.59/3.75 7.59/3.75 43: evalex1bb1in -> evalex116 : C'=1+A, D'=0, F'=A, [ B>=1+A && 1+A>=B ], cost: 5 7.59/3.75 7.59/3.75 44: evalex1bb1in -> evalex116 : C'=1+A, D'=0, E'=free, F'=A, [ B>=2+A && 0>=free ], cost: 8 7.59/3.75 7.59/3.75 45: evalex1bb1in -> evalex116 : C'=B, D'=-1-A+B, E'=free, F'=-1+B, [ B>=2+A && free>=1 ], cost: -5*A+5*B 7.59/3.75 7.59/3.75 46: evalex1bb1in -> [22] : [ B>=2+A && free>=1 ], cost: -3-5*A+5*B 7.59/3.75 7.59/3.75 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 7.59/3.75 7.59/3.75 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Eliminated locations (on tree-shaped paths): 7.59/3.75 7.59/3.75 Start location: evalex1start 7.59/3.75 7.59/3.75 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 7.59/3.75 7.59/3.75 46: evalex1bb1in -> [22] : [ B>=2+A && free>=1 ], cost: -3-5*A+5*B 7.59/3.75 7.59/3.75 47: evalex1bb1in -> evalex1bb1in : A'=1+A, C'=1+A, D'=0, F'=A, [ B>=1+A && 1+A>=B ], cost: 6 7.59/3.75 7.59/3.75 48: evalex1bb1in -> evalex1bb1in : A'=1+A, C'=1+A, D'=0, E'=free, F'=A, [ B>=2+A && 0>=free ], cost: 9 7.59/3.75 7.59/3.75 49: evalex1bb1in -> evalex1bb1in : A'=-1+B, C'=B, D'=-1-A+B, E'=free, F'=-1+B, [ B>=2+A && free>=1 ], cost: 1-5*A+5*B 7.59/3.75 7.59/3.75 50: evalex1bb1in -> [23] : [ B>=2+A && free>=1 ], cost: -5*A+5*B 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Accelerating simple loops of location 9. 7.59/3.75 7.59/3.75 Simplified some of the simple loops (and removed duplicate rules). 7.59/3.75 7.59/3.75 Accelerating the following rules: 7.59/3.75 7.59/3.75 47: evalex1bb1in -> evalex1bb1in : A'=1+A, C'=1+A, D'=0, F'=A, [ 1+A-B==0 ], cost: 6 7.59/3.75 7.59/3.75 48: evalex1bb1in -> evalex1bb1in : A'=1+A, C'=1+A, D'=0, E'=free, F'=A, [ B>=2+A && 0>=free ], cost: 9 7.59/3.75 7.59/3.75 49: evalex1bb1in -> evalex1bb1in : A'=-1+B, C'=B, D'=-1-A+B, E'=free, F'=-1+B, [ B>=2+A && free>=1 ], cost: 1-5*A+5*B 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Accelerated rule 47 with metering function -A+B, yielding the new rule 51. 7.59/3.75 7.59/3.75 Accelerated rule 48 with metering function -1-A+B, yielding the new rule 52. 7.59/3.75 7.59/3.75 Found no metering function for rule 49. 7.59/3.75 7.59/3.75 Removing the simple loops: 47 48. 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Accelerated all simple loops using metering functions (where possible): 7.59/3.75 7.59/3.75 Start location: evalex1start 7.59/3.75 7.59/3.75 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 7.59/3.75 7.59/3.75 46: evalex1bb1in -> [22] : [ B>=2+A && free>=1 ], cost: -3-5*A+5*B 7.59/3.75 7.59/3.75 49: evalex1bb1in -> evalex1bb1in : A'=-1+B, C'=B, D'=-1-A+B, E'=free, F'=-1+B, [ B>=2+A && free>=1 ], cost: 1-5*A+5*B 7.59/3.75 7.59/3.75 50: evalex1bb1in -> [23] : [ B>=2+A && free>=1 ], cost: -5*A+5*B 7.59/3.75 7.59/3.75 51: evalex1bb1in -> evalex1bb1in : A'=B, C'=B, D'=0, F'=-1+B, [ 1+A-B==0 ], cost: -6*A+6*B 7.59/3.75 7.59/3.75 52: evalex1bb1in -> evalex1bb1in : A'=-1+B, C'=-1+B, D'=0, E'=free, F'=-2+B, [ B>=2+A && 0>=free ], cost: -9-9*A+9*B 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Chained accelerated rules (with incoming rules): 7.59/3.75 7.59/3.75 Start location: evalex1start 7.59/3.75 7.59/3.75 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 7.59/3.75 7.59/3.75 53: evalex1start -> evalex1bb1in : A'=-1+B, C'=B, D'=-1+B, E'=free, F'=-1+B, [ B>=2 && free>=1 ], cost: 10+5*B 7.59/3.75 7.59/3.75 54: evalex1start -> evalex1bb1in : A'=B, C'=B, D'=0, F'=-1+B, [ 1-B==0 ], cost: 9+6*B 7.59/3.75 7.59/3.75 55: evalex1start -> evalex1bb1in : A'=-1+B, C'=-1+B, D'=0, E'=free, F'=-2+B, [ B>=2 && 0>=free ], cost: 9*B 7.59/3.75 7.59/3.75 46: evalex1bb1in -> [22] : [ B>=2+A && free>=1 ], cost: -3-5*A+5*B 7.59/3.75 7.59/3.75 50: evalex1bb1in -> [23] : [ B>=2+A && free>=1 ], cost: -5*A+5*B 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Eliminated locations (on tree-shaped paths): 7.59/3.75 7.59/3.75 Start location: evalex1start 7.59/3.75 7.59/3.75 56: evalex1start -> [22] : A'=0, [ B>=2 && free>=1 ], cost: 6+5*B 7.59/3.75 7.59/3.75 57: evalex1start -> [23] : A'=0, [ B>=2 && free>=1 ], cost: 9+5*B 7.59/3.75 7.59/3.75 58: evalex1start -> [25] : [ B>=2 && free>=1 ], cost: 10+5*B 7.59/3.75 7.59/3.75 59: evalex1start -> [25] : [ 1-B==0 ], cost: 9+6*B 7.59/3.75 7.59/3.75 60: evalex1start -> [25] : [ B>=2 && 0>=free ], cost: 9*B 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 ### Computing asymptotic complexity ### 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Fully simplified ITS problem 7.59/3.75 7.59/3.75 Start location: evalex1start 7.59/3.75 7.59/3.75 58: evalex1start -> [25] : [ B>=2 && free>=1 ], cost: 10+5*B 7.59/3.75 7.59/3.75 59: evalex1start -> [25] : [ 1-B==0 ], cost: 9+6*B 7.59/3.75 7.59/3.75 60: evalex1start -> [25] : [ B>=2 && 0>=free ], cost: 9*B 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Computing asymptotic complexity for rule 58 7.59/3.75 7.59/3.75 Solved the limit problem by the following transformations: 7.59/3.75 7.59/3.75 Created initial limit problem: 7.59/3.75 7.59/3.75 10+5*B (+), -1+B (+/+!), free (+/+!) [not solved] 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 removing all constraints (solved by SMT) 7.59/3.75 7.59/3.75 resulting limit problem: [solved] 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 applying transformation rule (C) using substitution {free==n,B==n} 7.59/3.75 7.59/3.75 resulting limit problem: 7.59/3.75 7.59/3.75 [solved] 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Solution: 7.59/3.75 7.59/3.75 free / n 7.59/3.75 7.59/3.75 B / n 7.59/3.75 7.59/3.75 Resulting cost 10+5*n has complexity: Poly(n^1) 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Found new complexity Poly(n^1). 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 Obtained the following overall complexity (w.r.t. the length of the input n): 7.59/3.75 7.59/3.75 Complexity: Poly(n^1) 7.59/3.75 7.59/3.75 Cpx degree: 1 7.59/3.75 7.59/3.75 Solved cost: 10+5*n 7.59/3.75 7.59/3.75 Rule cost: 10+5*B 7.59/3.75 7.59/3.75 Rule guard: [ B>=2 && free>=1 ] 7.59/3.75 7.59/3.75 7.59/3.75 7.59/3.75 WORST_CASE(Omega(n^1),?) 7.59/3.75 7.59/3.75 7.59/3.75 ---------------------------------------- 7.59/3.75 7.59/3.75 (4) 7.59/3.75 BOUNDS(n^1, INF) 7.76/3.78 EOF