/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 712 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 1549 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 The start-symbols are:[eval_ex1_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 182*Ar_1 + 13) Initial complexity problem: 1: T: (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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 ] (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 ] (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)) (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 ] (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 ] (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)) (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, Fresh_0, Ar_5)) (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 ] (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 ] (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)) (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)) (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)) (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 ] (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 ] (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)) (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 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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 ] (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 ] (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)) (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 ] (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 ] (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)) (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, Fresh_0, Ar_5)) (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 ] (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 ] (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)) (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)) (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)) (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 ] (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 ] (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)) (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 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalex1start) = 2 Pol(evalex1bb0in) = 2 Pol(evalex10) = 2 Pol(evalex11) = 2 Pol(evalex12) = 2 Pol(evalex13) = 2 Pol(evalex14) = 2 Pol(evalex15) = 2 Pol(evalex16) = 2 Pol(evalex1bb1in) = 2 Pol(evalex1bb2in) = 2 Pol(evalex1bb6in) = 1 Pol(evalex1bb3in) = 2 Pol(evalex1bb4in) = 2 Pol(evalex1critedgein) = 2 Pol(evalex19) = 2 Pol(evalex110) = 2 Pol(evalex1bb5in) = 2 Pol(evalex115) = 2 Pol(evalex116) = 2 Pol(evalex1stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions 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)) 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 ] strictly and produces the following problem: 3: T: (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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 ] (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 ] (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)) (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 ] (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 ] (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)) (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, Fresh_0, Ar_5)) (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 ] (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 ] (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)) (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)) (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)) (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 ] (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 ] (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)) (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 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: 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 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 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 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 For symbol evalex1bb1in: X_1 >= 0 For symbol evalex1bb2in: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 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 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 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 For symbol evalex1bb6in: X_1 - X_2 >= 0 /\ X_1 >= 0 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 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalex1start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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, Fresh_0, 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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 14*V_2 Pol(evalex1start) = 14*V_2 Pol(evalex1bb6in) = -14*V_1 + 14*V_2 Pol(evalex1stop) = -14*V_1 + 14*V_2 Pol(evalex116) = 14*V_2 - 14*V_3 + 9*V_4 + 6 Pol(evalex1bb1in) = -14*V_1 + 14*V_2 Pol(evalex115) = 14*V_2 - 14*V_3 + 9*V_4 + 7 Pol(evalex1critedgein) = 14*V_2 - 14*V_3 + 9*V_4 + 8 Pol(evalex1bb5in) = 14*V_2 - 14*V_3 + 9*V_4 + 8 Pol(evalex1bb3in) = 14*V_2 - 14*V_3 + 9*V_4 + 12 Pol(evalex110) = 14*V_2 - 14*V_3 + 9*V_4 + 9 Pol(evalex19) = 14*V_2 - 14*V_3 + 9*V_4 + 10 Pol(evalex1bb4in) = 14*V_2 - 14*V_3 + 9*V_4 + 11 Pol(evalex1bb2in) = -14*V_1 + 14*V_2 - 1 Pol(evalex16) = 14*V_2 Pol(evalex15) = 14*V_2 Pol(evalex14) = 14*V_2 Pol(evalex13) = 14*V_2 Pol(evalex12) = 14*V_2 Pol(evalex11) = 14*V_2 Pol(evalex10) = 14*V_2 Pol(evalex1bb0in) = 14*V_2 orients all transitions weakly and the transitions 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] evalex19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalex110(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0, 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalex1start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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, Fresh_0, 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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) start location: koat_start leaf cost: 0 Complexity upper bound 182*Ar_1 + 13 Time: 0.763 sec (SMT: 0.519 sec) ---------------------------------------- (2) BOUNDS(1, n^1) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalex1start 0: evalex1start -> evalex1bb0in : [], cost: 1 1: evalex1bb0in -> evalex10 : [], cost: 1 2: evalex10 -> evalex11 : [], cost: 1 3: evalex11 -> evalex12 : [], cost: 1 4: evalex12 -> evalex13 : [], cost: 1 5: evalex13 -> evalex14 : [], cost: 1 6: evalex14 -> evalex15 : [], cost: 1 7: evalex15 -> evalex16 : [], cost: 1 8: evalex16 -> evalex1bb1in : A'=0, [], cost: 1 9: evalex1bb1in -> evalex1bb2in : [ B>=1+A ], cost: 1 10: evalex1bb1in -> evalex1bb6in : [ A>=B ], cost: 1 11: evalex1bb2in -> evalex1bb3in : C'=1+A, D'=0, [], cost: 1 12: evalex1bb3in -> evalex1bb4in : [ B>=1+C ], cost: 1 13: evalex1bb3in -> evalex1critedgein : [ C>=B ], cost: 1 14: evalex1bb4in -> evalex19 : [], cost: 1 15: evalex19 -> evalex110 : E'=free, [], cost: 1 16: evalex110 -> evalex1bb5in : [ E>=1 ], cost: 1 17: evalex110 -> evalex1critedgein : [ 0>=E ], cost: 1 18: evalex1bb5in -> evalex1bb3in : C'=1+C, D'=1+D, [], cost: 1 19: evalex1critedgein -> evalex115 : F'=-1+C, [], cost: 1 20: evalex115 -> evalex116 : [], cost: 1 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 23: evalex1bb6in -> evalex1stop : [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: evalex1start -> evalex1bb0in : [], cost: 1 Removed unreachable and leaf rules: Start location: evalex1start 0: evalex1start -> evalex1bb0in : [], cost: 1 1: evalex1bb0in -> evalex10 : [], cost: 1 2: evalex10 -> evalex11 : [], cost: 1 3: evalex11 -> evalex12 : [], cost: 1 4: evalex12 -> evalex13 : [], cost: 1 5: evalex13 -> evalex14 : [], cost: 1 6: evalex14 -> evalex15 : [], cost: 1 7: evalex15 -> evalex16 : [], cost: 1 8: evalex16 -> evalex1bb1in : A'=0, [], cost: 1 9: evalex1bb1in -> evalex1bb2in : [ B>=1+A ], cost: 1 11: evalex1bb2in -> evalex1bb3in : C'=1+A, D'=0, [], cost: 1 12: evalex1bb3in -> evalex1bb4in : [ B>=1+C ], cost: 1 13: evalex1bb3in -> evalex1critedgein : [ C>=B ], cost: 1 14: evalex1bb4in -> evalex19 : [], cost: 1 15: evalex19 -> evalex110 : E'=free, [], cost: 1 16: evalex110 -> evalex1bb5in : [ E>=1 ], cost: 1 17: evalex110 -> evalex1critedgein : [ 0>=E ], cost: 1 18: evalex1bb5in -> evalex1bb3in : C'=1+C, D'=1+D, [], cost: 1 19: evalex1critedgein -> evalex115 : F'=-1+C, [], cost: 1 20: evalex115 -> evalex116 : [], cost: 1 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalex1start 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 32: evalex1bb1in -> evalex1bb3in : C'=1+A, D'=0, [ B>=1+A ], cost: 2 13: evalex1bb3in -> evalex1critedgein : [ C>=B ], cost: 1 34: evalex1bb3in -> evalex110 : E'=free, [ B>=1+C ], cost: 3 17: evalex110 -> evalex1critedgein : [ 0>=E ], cost: 1 35: evalex110 -> evalex1bb3in : C'=1+C, D'=1+D, [ E>=1 ], cost: 2 36: evalex1critedgein -> evalex116 : F'=-1+C, [], cost: 2 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalex1start 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 32: evalex1bb1in -> evalex1bb3in : C'=1+A, D'=0, [ B>=1+A ], cost: 2 38: evalex1bb3in -> evalex1bb3in : C'=1+C, D'=1+D, E'=free, [ B>=1+C && free>=1 ], cost: 5 39: evalex1bb3in -> evalex116 : F'=-1+C, [ C>=B ], cost: 3 40: evalex1bb3in -> evalex116 : E'=free, F'=-1+C, [ B>=1+C && 0>=free ], cost: 6 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 Accelerating simple loops of location 11. Accelerating the following rules: 38: evalex1bb3in -> evalex1bb3in : C'=1+C, D'=1+D, E'=free, [ B>=1+C && free>=1 ], cost: 5 Accelerated rule 38 with metering function -C+B, yielding the new rule 41. Removing the simple loops: 38. Accelerated all simple loops using metering functions (where possible): Start location: evalex1start 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 32: evalex1bb1in -> evalex1bb3in : C'=1+A, D'=0, [ B>=1+A ], cost: 2 39: evalex1bb3in -> evalex116 : F'=-1+C, [ C>=B ], cost: 3 40: evalex1bb3in -> evalex116 : E'=free, F'=-1+C, [ B>=1+C && 0>=free ], cost: 6 41: evalex1bb3in -> evalex1bb3in : C'=B, D'=-C+D+B, E'=free, [ B>=1+C && free>=1 ], cost: -5*C+5*B 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 Chained accelerated rules (with incoming rules): Start location: evalex1start 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 32: evalex1bb1in -> evalex1bb3in : C'=1+A, D'=0, [ B>=1+A ], cost: 2 42: evalex1bb1in -> evalex1bb3in : C'=B, D'=-1-A+B, E'=free, [ B>=2+A && free>=1 ], cost: -3-5*A+5*B 39: evalex1bb3in -> evalex116 : F'=-1+C, [ C>=B ], cost: 3 40: evalex1bb3in -> evalex116 : E'=free, F'=-1+C, [ B>=1+C && 0>=free ], cost: 6 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalex1start 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 43: evalex1bb1in -> evalex116 : C'=1+A, D'=0, F'=A, [ B>=1+A && 1+A>=B ], cost: 5 44: evalex1bb1in -> evalex116 : C'=1+A, D'=0, E'=free, F'=A, [ B>=2+A && 0>=free ], cost: 8 45: evalex1bb1in -> evalex116 : C'=B, D'=-1-A+B, E'=free, F'=-1+B, [ B>=2+A && free>=1 ], cost: -5*A+5*B 46: evalex1bb1in -> [22] : [ B>=2+A && free>=1 ], cost: -3-5*A+5*B 21: evalex116 -> evalex1bb1in : A'=F, [ D>=1 ], cost: 1 22: evalex116 -> evalex1bb1in : A'=C, [ 0>=D ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalex1start 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 46: evalex1bb1in -> [22] : [ B>=2+A && free>=1 ], cost: -3-5*A+5*B 47: evalex1bb1in -> evalex1bb1in : A'=1+A, C'=1+A, D'=0, F'=A, [ B>=1+A && 1+A>=B ], cost: 6 48: evalex1bb1in -> evalex1bb1in : A'=1+A, C'=1+A, D'=0, E'=free, F'=A, [ B>=2+A && 0>=free ], cost: 9 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 50: evalex1bb1in -> [23] : [ B>=2+A && free>=1 ], cost: -5*A+5*B Accelerating simple loops of location 9. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 47: evalex1bb1in -> evalex1bb1in : A'=1+A, C'=1+A, D'=0, F'=A, [ 1+A-B==0 ], cost: 6 48: evalex1bb1in -> evalex1bb1in : A'=1+A, C'=1+A, D'=0, E'=free, F'=A, [ B>=2+A && 0>=free ], cost: 9 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 Accelerated rule 47 with metering function -A+B, yielding the new rule 51. Accelerated rule 48 with metering function -1-A+B, yielding the new rule 52. Found no metering function for rule 49. Removing the simple loops: 47 48. Accelerated all simple loops using metering functions (where possible): Start location: evalex1start 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 46: evalex1bb1in -> [22] : [ B>=2+A && free>=1 ], cost: -3-5*A+5*B 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 50: evalex1bb1in -> [23] : [ B>=2+A && free>=1 ], cost: -5*A+5*B 51: evalex1bb1in -> evalex1bb1in : A'=B, C'=B, D'=0, F'=-1+B, [ 1+A-B==0 ], cost: -6*A+6*B 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 Chained accelerated rules (with incoming rules): Start location: evalex1start 31: evalex1start -> evalex1bb1in : A'=0, [], cost: 9 53: evalex1start -> evalex1bb1in : A'=-1+B, C'=B, D'=-1+B, E'=free, F'=-1+B, [ B>=2 && free>=1 ], cost: 10+5*B 54: evalex1start -> evalex1bb1in : A'=B, C'=B, D'=0, F'=-1+B, [ 1-B==0 ], cost: 9+6*B 55: evalex1start -> evalex1bb1in : A'=-1+B, C'=-1+B, D'=0, E'=free, F'=-2+B, [ B>=2 && 0>=free ], cost: 9*B 46: evalex1bb1in -> [22] : [ B>=2+A && free>=1 ], cost: -3-5*A+5*B 50: evalex1bb1in -> [23] : [ B>=2+A && free>=1 ], cost: -5*A+5*B Eliminated locations (on tree-shaped paths): Start location: evalex1start 56: evalex1start -> [22] : A'=0, [ B>=2 && free>=1 ], cost: 6+5*B 57: evalex1start -> [23] : A'=0, [ B>=2 && free>=1 ], cost: 9+5*B 58: evalex1start -> [25] : [ B>=2 && free>=1 ], cost: 10+5*B 59: evalex1start -> [25] : [ 1-B==0 ], cost: 9+6*B 60: evalex1start -> [25] : [ B>=2 && 0>=free ], cost: 9*B ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalex1start 58: evalex1start -> [25] : [ B>=2 && free>=1 ], cost: 10+5*B 59: evalex1start -> [25] : [ 1-B==0 ], cost: 9+6*B 60: evalex1start -> [25] : [ B>=2 && 0>=free ], cost: 9*B Computing asymptotic complexity for rule 58 Solved the limit problem by the following transformations: Created initial limit problem: -1+B (+/+!), free (+/+!), 10+5*B (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {free==1,B==n} resulting limit problem: [solved] Solution: free / 1 B / n Resulting cost 10+5*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 10+5*n Rule cost: 10+5*B Rule guard: [ B>=2 && free>=1 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)