/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).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, 537 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 1126 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_start_start(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_bb0_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y)) :|: TRUE eval_start_bb0_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_0(v__0, v__01, v__1, v_1, v_2, v_x, v_y)) :|: TRUE eval_start_0(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_1(v__0, v__01, v__1, v_1, v_2, v_x, v_y)) :|: TRUE eval_start_1(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_2(v__0, v__01, v__1, v_1, v_2, v_x, v_y)) :|: TRUE eval_start_2(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_3(v__0, v__01, v__1, v_1, v_2, v_x, v_y)) :|: TRUE eval_start_3(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_4(v__0, v__01, v__1, v_1, v_2, v_x, v_y)) :|: TRUE eval_start_4(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_5(v__0, v__01, v__1, v_1, v_2, v_x, v_y)) :|: TRUE eval_start_5(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_bb1_in(v_x, v_y, v__1, v_1, v_2, v_x, v_y)) :|: TRUE eval_start_bb1_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_bb2_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y)) :|: v__0 > 0 eval_start_bb1_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_bb6_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y)) :|: v__0 <= 0 eval_start_bb2_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_7(v__0, v__01, v__1, v__0 - 1, v_2, v_x, v_y)) :|: TRUE eval_start_7(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_8(v__0, v__01, v__1, v_1, nondef_0, v_x, v_y)) :|: TRUE eval_start_8(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_bb3_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y)) :|: v_2 > 0 eval_start_8(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_bb4_in(v__0, v__01, v__01, v_1, v_2, v_x, v_y)) :|: v_2 <= 0 eval_start_bb3_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_bb1_in(v_1, v__01 + 1, v__1, v_1, v_2, v_x, v_y)) :|: TRUE eval_start_bb4_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_bb5_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y)) :|: v__1 > 0 eval_start_bb4_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_bb1_in(v_1, v__1, v__1, v_1, v_2, v_x, v_y)) :|: v__1 <= 0 eval_start_bb5_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_bb4_in(v__0, v__01, v__1 - 1, v_1, v_2, v_x, v_y)) :|: TRUE eval_start_bb6_in(v__0, v__01, v__1, v_1, v_2, v_x, v_y) -> Com_1(eval_start_stop(v__0, v__01, v__1, v_1, v_2, v_x, v_y)) :|: TRUE The start-symbols are:[eval_start_start_7] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 11*Ar_1 + 4*Ar_3 + 19) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6)) (Comp: ?, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ] (Comp: ?, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ] (Comp: ?, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1)) (Comp: ?, Cost: 1) evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 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) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6)) (Comp: ?, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ] (Comp: ?, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ] (Comp: ?, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1)) (Comp: ?, Cost: 1) evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalstartstart) = 2 Pol(evalstartbb0in) = 2 Pol(evalstart0) = 2 Pol(evalstart1) = 2 Pol(evalstart2) = 2 Pol(evalstart3) = 2 Pol(evalstart4) = 2 Pol(evalstart5) = 2 Pol(evalstartbb1in) = 2 Pol(evalstartbb2in) = 2 Pol(evalstartbb6in) = 1 Pol(evalstart7) = 2 Pol(evalstart8) = 2 Pol(evalstartbb3in) = 2 Pol(evalstartbb4in) = 2 Pol(evalstartbb5in) = 2 Pol(evalstartstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6)) (Comp: ?, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ] (Comp: ?, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ] (Comp: ?, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1)) (Comp: 2, Cost: 1) evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalstartstart) = V_2 + 1 Pol(evalstartbb0in) = V_2 + 1 Pol(evalstart0) = V_2 + 1 Pol(evalstart1) = V_2 + 1 Pol(evalstart2) = V_2 + 1 Pol(evalstart3) = V_2 + 1 Pol(evalstart4) = V_2 + 1 Pol(evalstart5) = V_2 + 1 Pol(evalstartbb1in) = V_1 + 1 Pol(evalstartbb2in) = V_1 Pol(evalstartbb6in) = V_1 Pol(evalstart7) = V_5 + 1 Pol(evalstart8) = V_5 + 1 Pol(evalstartbb3in) = V_5 + 1 Pol(evalstartbb4in) = V_5 + 1 Pol(evalstartbb5in) = V_5 + 1 Pol(evalstartstop) = V_1 Pol(koat_start) = V_2 + 1 orients all transitions weakly and the transition evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: Ar_1 + 1, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6)) (Comp: ?, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ] (Comp: ?, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ] (Comp: ?, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1)) (Comp: 2, Cost: 1) evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: Ar_1 + 1, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) (Comp: Ar_1 + 1, Cost: 1) evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6)) (Comp: Ar_1 + 1, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ] (Comp: Ar_1 + 1, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ] (Comp: ?, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1)) (Comp: 2, Cost: 1) evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalstartbb5in) = 1 Pol(evalstartbb4in) = 1 Pol(evalstartbb1in) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ]", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ]", 0-5) = Ar_5 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ]", 0-6) = Ar_6 S("evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-0) = 2*Ar_1 + 16 S("evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-1) = Ar_1 S("evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-2) = ? S("evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-3) = Ar_3 S("evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-4) = 2*Ar_1 + 2*Ar_4 + 32 S("evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-5) = ? S("evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-6) = ? S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1))", 0-0) = 2*Ar_1 + 64 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1))", 0-1) = Ar_1 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1))", 0-2) = ? S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1))", 0-3) = Ar_3 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1))", 0-4) = 2*Ar_1 + 4 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1))", 0-5) = ? S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1))", 0-6) = ? S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ]", 0-0) = 2*Ar_1 + 4 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ]", 0-1) = Ar_1 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ]", 0-2) = ? S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ]", 0-3) = Ar_3 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ]", 0-4) = 2*Ar_1 + 8 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ]", 0-5) = ? S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ]", 0-6) = ? S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ]", 0-0) = 2*Ar_1 + 64 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ]", 0-1) = Ar_1 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ]", 0-2) = ? S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ]", 0-3) = Ar_3 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ]", 0-4) = 2*Ar_1 + 4 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ]", 0-5) = ? S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ]", 0-6) = ? S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6))", 0-0) = 2*Ar_1 + 4 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6))", 0-1) = Ar_1 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6))", 0-2) = ? S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6))", 0-3) = Ar_3 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6))", 0-4) = 2*Ar_1 + 8 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6))", 0-5) = ? S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6))", 0-6) = ? S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ]", 0-0) = 2*Ar_1 + 32 S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ]", 0-1) = Ar_1 S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ]", 0-2) = ? S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ]", 0-3) = Ar_3 S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ]", 0-4) = 2*Ar_1 + 4 S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ]", 0-5) = ? S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ]", 0-6) = ? S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ]", 0-0) = 2*Ar_1 + 32 S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ]", 0-1) = Ar_1 S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ]", 0-2) = ? S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ]", 0-3) = Ar_3 S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ]", 0-4) = 2*Ar_1 + 4 S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ]", 0-5) = ? S("evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ]", 0-6) = ? S("evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6))", 0-0) = 2*Ar_1 + 16 S("evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6))", 0-1) = Ar_1 S("evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6))", 0-2) = ? S("evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6))", 0-3) = Ar_3 S("evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6))", 0-4) = 2*Ar_1 + 4 S("evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6))", 0-5) = ? S("evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6))", 0-6) = ? S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6))", 0-0) = 2*Ar_1 + 8 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6))", 0-1) = Ar_1 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6))", 0-2) = ? S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6))", 0-3) = Ar_3 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6))", 0-4) = 2*Ar_1 + 4 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6))", 0-5) = ? S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6))", 0-6) = ? S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ]", 0-0) = 2*Ar_1 + 8 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ]", 0-1) = Ar_1 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ]", 0-2) = ? S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ]", 0-3) = Ar_3 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ]", 0-4) = 2*Ar_1 + 2*Ar_4 + 16 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ]", 0-5) = ? S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ]", 0-6) = ? S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ]", 0-0) = 2*Ar_1 + 4 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ]", 0-1) = Ar_1 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ]", 0-2) = ? S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ]", 0-3) = Ar_3 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ]", 0-4) = 2*Ar_1 + 2*Ar_4 + 16 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ]", 0-5) = ? S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ]", 0-6) = ? S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6))", 0-0) = Ar_1 S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6))", 0-1) = Ar_1 S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6))", 0-2) = Ar_3 S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6))", 0-3) = Ar_3 S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6))", 0-4) = Ar_4 S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6))", 0-5) = Ar_5 S("evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6))", 0-6) = Ar_6 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-0) = Ar_0 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-1) = Ar_1 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-2) = Ar_2 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-3) = Ar_3 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-4) = Ar_4 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-5) = Ar_5 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-6) = Ar_6 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-0) = Ar_0 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-1) = Ar_1 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-2) = Ar_2 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-3) = Ar_3 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-4) = Ar_4 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-5) = Ar_5 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-6) = Ar_6 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-0) = Ar_0 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-1) = Ar_1 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-2) = Ar_2 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-3) = Ar_3 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-4) = Ar_4 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-5) = Ar_5 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-6) = Ar_6 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-0) = Ar_0 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-1) = Ar_1 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-2) = Ar_2 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-3) = Ar_3 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-4) = Ar_4 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-5) = Ar_5 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-6) = Ar_6 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-0) = Ar_0 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-1) = Ar_1 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-2) = Ar_2 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-3) = Ar_3 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-4) = Ar_4 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-5) = Ar_5 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-6) = Ar_6 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-0) = Ar_0 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-1) = Ar_1 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-2) = Ar_2 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-3) = Ar_3 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-4) = Ar_4 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-5) = Ar_5 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-6) = Ar_6 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-0) = Ar_0 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-1) = Ar_1 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-2) = Ar_2 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-3) = Ar_3 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-4) = Ar_4 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-5) = Ar_5 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6))", 0-6) = Ar_6 orients the transitions evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1)) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ] evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ] weakly and the transition evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: Ar_1 + 1, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 1 ] (Comp: 2, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) (Comp: Ar_1 + 1, Cost: 1) evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6)) (Comp: Ar_1 + 1, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 1 ] (Comp: Ar_1 + 1, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ 0 >= Ar_5 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_6 >= 1 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_6 ] (Comp: ?, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1)) (Comp: 2, Cost: 1) evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 6 to obtain the following invariants: For symbol evalstart7: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 >= 0 /\ X_2 + X_5 - 1 >= 0 /\ X_1 + X_5 - 1 >= 0 /\ -X_1 + X_5 + 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalstart8: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 >= 0 /\ X_2 + X_5 - 1 >= 0 /\ X_1 + X_5 - 1 >= 0 /\ -X_1 + X_5 + 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalstartbb1in: -X_1 + X_2 >= 0 For symbol evalstartbb2in: X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalstartbb3in: X_6 - 1 >= 0 /\ X_5 + X_6 - 1 >= 0 /\ X_2 + X_6 - 2 >= 0 /\ X_1 + X_6 - 2 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 >= 0 /\ X_2 + X_5 - 1 >= 0 /\ X_1 + X_5 - 1 >= 0 /\ -X_1 + X_5 + 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalstartbb4in: X_3 - X_7 >= 0 /\ -X_6 >= 0 /\ X_5 - X_6 >= 0 /\ X_2 - X_6 - 1 >= 0 /\ X_1 - X_6 - 1 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 >= 0 /\ X_2 + X_5 - 1 >= 0 /\ X_1 + X_5 - 1 >= 0 /\ -X_1 + X_5 + 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalstartbb5in: X_3 - X_7 >= 0 /\ X_7 - 1 >= 0 /\ -X_6 + X_7 - 1 >= 0 /\ X_5 + X_7 - 1 >= 0 /\ X_3 + X_7 - 2 >= 0 /\ X_2 + X_7 - 2 >= 0 /\ X_1 + X_7 - 2 >= 0 /\ -X_6 >= 0 /\ X_5 - X_6 >= 0 /\ X_3 - X_6 - 1 >= 0 /\ X_2 - X_6 - 1 >= 0 /\ X_1 - X_6 - 1 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 >= 0 /\ X_3 + X_5 - 1 >= 0 /\ X_2 + X_5 - 1 >= 0 /\ X_1 + X_5 - 1 >= 0 /\ -X_1 + X_5 + 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalstartbb6in: -X_1 + X_2 >= 0 /\ -X_1 >= 0 This yielded the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ -Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1)) [ Ar_2 - Ar_6 >= 0 /\ Ar_6 - 1 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ Ar_4 + Ar_6 - 1 >= 0 /\ Ar_2 + Ar_6 - 2 >= 0 /\ Ar_1 + Ar_6 - 2 >= 0 /\ Ar_0 + Ar_6 - 2 >= 0 /\ -Ar_5 >= 0 /\ Ar_4 - Ar_5 >= 0 /\ Ar_2 - Ar_5 - 1 >= 0 /\ Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 - 1 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 - 1 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_2 - Ar_6 >= 0 /\ -Ar_5 >= 0 /\ Ar_4 - Ar_5 >= 0 /\ Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 - 1 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_6 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_2 - Ar_6 >= 0 /\ -Ar_5 >= 0 /\ Ar_4 - Ar_5 >= 0 /\ Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 - 1 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_6 >= 1 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 - 1 >= 0 /\ Ar_4 + Ar_5 - 1 >= 0 /\ Ar_1 + Ar_5 - 2 >= 0 /\ Ar_0 + Ar_5 - 2 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: Ar_1 + 1, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_5 ] (Comp: Ar_1 + 1, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_5 >= 1 ] (Comp: Ar_1 + 1, Cost: 1) evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 2*V_2 + 2*V_4 Pol(evalstartstart) = 2*V_2 + 2*V_4 Pol(evalstartbb6in) = 2*V_1 + 2*V_3 Pol(evalstartstop) = 2*V_1 + 2*V_3 Pol(evalstartbb5in) = 2*V_1 + 2*V_7 - 1 Pol(evalstartbb4in) = 2*V_1 + 2*V_7 Pol(evalstartbb1in) = 2*V_1 + 2*V_3 Pol(evalstartbb3in) = 2*V_3 + 2*V_5 + 2 Pol(evalstart8) = 2*V_1 + 2*V_3 Pol(evalstart7) = 2*V_1 + 2*V_3 Pol(evalstartbb2in) = 2*V_1 + 2*V_3 Pol(evalstart5) = 2*V_2 + 2*V_4 Pol(evalstart4) = 2*V_2 + 2*V_4 Pol(evalstart3) = 2*V_2 + 2*V_4 Pol(evalstart2) = 2*V_2 + 2*V_4 Pol(evalstart1) = 2*V_2 + 2*V_4 Pol(evalstart0) = 2*V_2 + 2*V_4 Pol(evalstartbb0in) = 2*V_2 + 2*V_4 orients all transitions weakly and the transitions evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1)) [ Ar_2 - Ar_6 >= 0 /\ Ar_6 - 1 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ Ar_4 + Ar_6 - 1 >= 0 /\ Ar_2 + Ar_6 - 2 >= 0 /\ Ar_1 + Ar_6 - 2 >= 0 /\ Ar_0 + Ar_6 - 2 >= 0 /\ -Ar_5 >= 0 /\ Ar_4 - Ar_5 >= 0 /\ Ar_2 - Ar_5 - 1 >= 0 /\ Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 - 1 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 - 1 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_2 - Ar_6 >= 0 /\ -Ar_5 >= 0 /\ Ar_4 - Ar_5 >= 0 /\ Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 - 1 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_6 >= 1 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ -Ar_0 >= 0 ] (Comp: 2*Ar_1 + 2*Ar_3, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6 - 1)) [ Ar_2 - Ar_6 >= 0 /\ Ar_6 - 1 >= 0 /\ -Ar_5 + Ar_6 - 1 >= 0 /\ Ar_4 + Ar_6 - 1 >= 0 /\ Ar_2 + Ar_6 - 2 >= 0 /\ Ar_1 + Ar_6 - 2 >= 0 /\ Ar_0 + Ar_6 - 2 >= 0 /\ -Ar_5 >= 0 /\ Ar_4 - Ar_5 >= 0 /\ Ar_2 - Ar_5 - 1 >= 0 /\ Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 - 1 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_2 + Ar_4 - 1 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_6, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_2 - Ar_6 >= 0 /\ -Ar_5 >= 0 /\ Ar_4 - Ar_5 >= 0 /\ Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 - 1 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_6 ] (Comp: 2*Ar_1 + 2*Ar_3, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_2 - Ar_6 >= 0 /\ -Ar_5 >= 0 /\ Ar_4 - Ar_5 >= 0 /\ Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 - 1 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_6 >= 1 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_4, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 - 1 >= 0 /\ Ar_4 + Ar_5 - 1 >= 0 /\ Ar_1 + Ar_5 - 2 >= 0 /\ Ar_0 + Ar_5 - 2 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: Ar_1 + 1, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_5 ] (Comp: Ar_1 + 1, Cost: 1) evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_5 >= 1 ] (Comp: Ar_1 + 1, Cost: 1) evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, Ar_6)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_4 >= 0 /\ Ar_1 + Ar_4 - 1 >= 0 /\ Ar_0 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 + 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - 1, Ar_5, Ar_6)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 ] (Comp: Ar_1 + 1, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) start location: koat_start leaf cost: 0 Complexity upper bound 11*Ar_1 + 4*Ar_3 + 19 Time: 0.589 sec (SMT: 0.370 sec) ---------------------------------------- (2) BOUNDS(1, n^1) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalstartstart 0: evalstartstart -> evalstartbb0in : [], cost: 1 1: evalstartbb0in -> evalstart0 : [], cost: 1 2: evalstart0 -> evalstart1 : [], cost: 1 3: evalstart1 -> evalstart2 : [], cost: 1 4: evalstart2 -> evalstart3 : [], cost: 1 5: evalstart3 -> evalstart4 : [], cost: 1 6: evalstart4 -> evalstart5 : [], cost: 1 7: evalstart5 -> evalstartbb1in : A'=B, C'=D, [], cost: 1 8: evalstartbb1in -> evalstartbb2in : [ A>=1 ], cost: 1 9: evalstartbb1in -> evalstartbb6in : [ 0>=A ], cost: 1 10: evalstartbb2in -> evalstart7 : E'=-1+A, [], cost: 1 11: evalstart7 -> evalstart8 : F'=free, [], cost: 1 12: evalstart8 -> evalstartbb3in : [ F>=1 ], cost: 1 13: evalstart8 -> evalstartbb4in : G'=C, [ 0>=F ], cost: 1 14: evalstartbb3in -> evalstartbb1in : A'=E, C'=1+C, [], cost: 1 15: evalstartbb4in -> evalstartbb5in : [ G>=1 ], cost: 1 16: evalstartbb4in -> evalstartbb1in : A'=E, C'=G, [ 0>=G ], cost: 1 17: evalstartbb5in -> evalstartbb4in : G'=-1+G, [], cost: 1 18: evalstartbb6in -> evalstartstop : [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: evalstartstart -> evalstartbb0in : [], cost: 1 Removed unreachable and leaf rules: Start location: evalstartstart 0: evalstartstart -> evalstartbb0in : [], cost: 1 1: evalstartbb0in -> evalstart0 : [], cost: 1 2: evalstart0 -> evalstart1 : [], cost: 1 3: evalstart1 -> evalstart2 : [], cost: 1 4: evalstart2 -> evalstart3 : [], cost: 1 5: evalstart3 -> evalstart4 : [], cost: 1 6: evalstart4 -> evalstart5 : [], cost: 1 7: evalstart5 -> evalstartbb1in : A'=B, C'=D, [], cost: 1 8: evalstartbb1in -> evalstartbb2in : [ A>=1 ], cost: 1 10: evalstartbb2in -> evalstart7 : E'=-1+A, [], cost: 1 11: evalstart7 -> evalstart8 : F'=free, [], cost: 1 12: evalstart8 -> evalstartbb3in : [ F>=1 ], cost: 1 13: evalstart8 -> evalstartbb4in : G'=C, [ 0>=F ], cost: 1 14: evalstartbb3in -> evalstartbb1in : A'=E, C'=1+C, [], cost: 1 15: evalstartbb4in -> evalstartbb5in : [ G>=1 ], cost: 1 16: evalstartbb4in -> evalstartbb1in : A'=E, C'=G, [ 0>=G ], cost: 1 17: evalstartbb5in -> evalstartbb4in : G'=-1+G, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalstartstart 25: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 27: evalstartbb1in -> evalstart8 : E'=-1+A, F'=free, [ A>=1 ], cost: 3 13: evalstart8 -> evalstartbb4in : G'=C, [ 0>=F ], cost: 1 28: evalstart8 -> evalstartbb1in : A'=E, C'=1+C, [ F>=1 ], cost: 2 16: evalstartbb4in -> evalstartbb1in : A'=E, C'=G, [ 0>=G ], cost: 1 29: evalstartbb4in -> evalstartbb4in : G'=-1+G, [ G>=1 ], cost: 2 Accelerating simple loops of location 13. Accelerating the following rules: 29: evalstartbb4in -> evalstartbb4in : G'=-1+G, [ G>=1 ], cost: 2 Accelerated rule 29 with metering function G, yielding the new rule 30. Removing the simple loops: 29. Accelerated all simple loops using metering functions (where possible): Start location: evalstartstart 25: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 27: evalstartbb1in -> evalstart8 : E'=-1+A, F'=free, [ A>=1 ], cost: 3 13: evalstart8 -> evalstartbb4in : G'=C, [ 0>=F ], cost: 1 28: evalstart8 -> evalstartbb1in : A'=E, C'=1+C, [ F>=1 ], cost: 2 16: evalstartbb4in -> evalstartbb1in : A'=E, C'=G, [ 0>=G ], cost: 1 30: evalstartbb4in -> evalstartbb4in : G'=0, [ G>=1 ], cost: 2*G Chained accelerated rules (with incoming rules): Start location: evalstartstart 25: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 27: evalstartbb1in -> evalstart8 : E'=-1+A, F'=free, [ A>=1 ], cost: 3 13: evalstart8 -> evalstartbb4in : G'=C, [ 0>=F ], cost: 1 28: evalstart8 -> evalstartbb1in : A'=E, C'=1+C, [ F>=1 ], cost: 2 31: evalstart8 -> evalstartbb4in : G'=0, [ 0>=F && C>=1 ], cost: 1+2*C 16: evalstartbb4in -> evalstartbb1in : A'=E, C'=G, [ 0>=G ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalstartstart 25: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 32: evalstartbb1in -> evalstartbb4in : E'=-1+A, F'=free, G'=C, [ A>=1 && 0>=free ], cost: 4 33: evalstartbb1in -> evalstartbb1in : A'=-1+A, C'=1+C, E'=-1+A, F'=free, [ A>=1 && free>=1 ], cost: 5 34: evalstartbb1in -> evalstartbb4in : E'=-1+A, F'=free, G'=0, [ A>=1 && 0>=free && C>=1 ], cost: 4+2*C 16: evalstartbb4in -> evalstartbb1in : A'=E, C'=G, [ 0>=G ], cost: 1 Accelerating simple loops of location 8. Accelerating the following rules: 33: evalstartbb1in -> evalstartbb1in : A'=-1+A, C'=1+C, E'=-1+A, F'=free, [ A>=1 && free>=1 ], cost: 5 Accelerated rule 33 with metering function A, yielding the new rule 35. Removing the simple loops: 33. Accelerated all simple loops using metering functions (where possible): Start location: evalstartstart 25: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 32: evalstartbb1in -> evalstartbb4in : E'=-1+A, F'=free, G'=C, [ A>=1 && 0>=free ], cost: 4 34: evalstartbb1in -> evalstartbb4in : E'=-1+A, F'=free, G'=0, [ A>=1 && 0>=free && C>=1 ], cost: 4+2*C 35: evalstartbb1in -> evalstartbb1in : A'=0, C'=C+A, E'=0, F'=free, [ A>=1 && free>=1 ], cost: 5*A 16: evalstartbb4in -> evalstartbb1in : A'=E, C'=G, [ 0>=G ], cost: 1 Chained accelerated rules (with incoming rules): Start location: evalstartstart 25: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 37: evalstartstart -> evalstartbb1in : A'=0, C'=D+B, E'=0, F'=free, [ B>=1 && free>=1 ], cost: 8+5*B 32: evalstartbb1in -> evalstartbb4in : E'=-1+A, F'=free, G'=C, [ A>=1 && 0>=free ], cost: 4 34: evalstartbb1in -> evalstartbb4in : E'=-1+A, F'=free, G'=0, [ A>=1 && 0>=free && C>=1 ], cost: 4+2*C 16: evalstartbb4in -> evalstartbb1in : A'=E, C'=G, [ 0>=G ], cost: 1 36: evalstartbb4in -> evalstartbb1in : A'=0, C'=G+E, E'=0, F'=free, [ 0>=G && E>=1 && free>=1 ], cost: 1+5*E Eliminated locations (on tree-shaped paths): Start location: evalstartstart 25: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 37: evalstartstart -> evalstartbb1in : A'=0, C'=D+B, E'=0, F'=free, [ B>=1 && free>=1 ], cost: 8+5*B 38: evalstartbb1in -> evalstartbb1in : A'=-1+A, C'=C, E'=-1+A, F'=free, G'=C, [ A>=1 && 0>=free && 0>=C ], cost: 5 39: evalstartbb1in -> evalstartbb1in : A'=-1+A, C'=0, E'=-1+A, F'=free, G'=0, [ A>=1 && 0>=free && C>=1 ], cost: 5+2*C 40: evalstartbb1in -> [19] : [ A>=1 && 0>=free && C>=1 ], cost: 4+2*C Accelerating simple loops of location 8. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 38: evalstartbb1in -> evalstartbb1in : A'=-1+A, E'=-1+A, F'=free, G'=C, [ A>=1 && 0>=free && 0>=C ], cost: 5 39: evalstartbb1in -> evalstartbb1in : A'=-1+A, C'=0, E'=-1+A, F'=free, G'=0, [ A>=1 && 0>=free && C>=1 ], cost: 5+2*C Accelerated rule 38 with metering function A, yielding the new rule 41. Found no metering function for rule 39. Removing the simple loops: 38. Accelerated all simple loops using metering functions (where possible): Start location: evalstartstart 25: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 37: evalstartstart -> evalstartbb1in : A'=0, C'=D+B, E'=0, F'=free, [ B>=1 && free>=1 ], cost: 8+5*B 39: evalstartbb1in -> evalstartbb1in : A'=-1+A, C'=0, E'=-1+A, F'=free, G'=0, [ A>=1 && 0>=free && C>=1 ], cost: 5+2*C 40: evalstartbb1in -> [19] : [ A>=1 && 0>=free && C>=1 ], cost: 4+2*C 41: evalstartbb1in -> evalstartbb1in : A'=0, E'=0, F'=free, G'=C, [ A>=1 && 0>=free && 0>=C ], cost: 5*A Chained accelerated rules (with incoming rules): Start location: evalstartstart 25: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 37: evalstartstart -> evalstartbb1in : A'=0, C'=D+B, E'=0, F'=free, [ B>=1 && free>=1 ], cost: 8+5*B 42: evalstartstart -> evalstartbb1in : A'=-1+B, C'=0, E'=-1+B, F'=free, G'=0, [ B>=1 && 0>=free && D>=1 ], cost: 13+2*D 43: evalstartstart -> evalstartbb1in : A'=0, C'=D, E'=0, F'=free, G'=D, [ B>=1 && 0>=free && 0>=D ], cost: 8+5*B 40: evalstartbb1in -> [19] : [ A>=1 && 0>=free && C>=1 ], cost: 4+2*C Eliminated locations (on tree-shaped paths): Start location: evalstartstart 44: evalstartstart -> [19] : A'=B, C'=D, [ B>=1 && 0>=free && D>=1 ], cost: 12+2*D 45: evalstartstart -> [21] : [ B>=1 && free>=1 ], cost: 8+5*B 46: evalstartstart -> [21] : [ B>=1 && 0>=free && D>=1 ], cost: 13+2*D 47: evalstartstart -> [21] : [ B>=1 && 0>=free && 0>=D ], cost: 8+5*B ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalstartstart 45: evalstartstart -> [21] : [ B>=1 && free>=1 ], cost: 8+5*B 46: evalstartstart -> [21] : [ B>=1 && 0>=free && D>=1 ], cost: 13+2*D 47: evalstartstart -> [21] : [ B>=1 && 0>=free && 0>=D ], cost: 8+5*B Computing asymptotic complexity for rule 45 Solved the limit problem by the following transformations: Created initial limit problem: 8+5*B (+), B (+/+!), free (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {B==n,free==n} resulting limit problem: [solved] Solution: B / n free / n Resulting cost 8+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: 8+5*n Rule cost: 8+5*B Rule guard: [ B>=1 && free>=1 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)