/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).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, 124 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 705 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__2, v_x, v_y) -> Com_1(eval_start_bb0_in(v__0, v__01, v__1, v__2, v_x, v_y)) :|: TRUE eval_start_bb0_in(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_0(v__0, v__01, v__1, v__2, v_x, v_y)) :|: TRUE eval_start_0(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_1(v__0, v__01, v__1, v__2, v_x, v_y)) :|: TRUE eval_start_1(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_2(v__0, v__01, v__1, v__2, v_x, v_y)) :|: TRUE eval_start_2(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_3(v__0, v__01, v__1, v__2, v_x, v_y)) :|: TRUE eval_start_3(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_4(v__0, v__01, v__1, v__2, v_x, v_y)) :|: TRUE eval_start_4(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_bb1_in(v_x, v_y, v__1, v__2, v_x, v_y)) :|: TRUE eval_start_bb1_in(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_bb2_in(v__0, v__01, v__1, v__2, v_x, v_y)) :|: v__0 > 0 eval_start_bb1_in(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_bb3_in(v__0, v__01, v__01, v__2, v_x, v_y)) :|: v__0 <= 0 eval_start_bb2_in(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_bb1_in(v__0 - 1, v__01 + 2, v__1, v__2, v_x, v_y)) :|: TRUE eval_start_bb3_in(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_bb4_in(v__0, v__01, v__1, v__2, v_x, v_y)) :|: v__1 > 0 eval_start_bb3_in(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_bb5_in(v__0, v__01, v__1, v__1, v_x, v_y)) :|: v__1 <= 0 eval_start_bb4_in(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_bb3_in(v__0, v__01, v__1 - 1, v__2, v_x, v_y)) :|: TRUE eval_start_bb5_in(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_bb6_in(v__0, v__01, v__1, v__2, v_x, v_y)) :|: v__2 > 0 eval_start_bb5_in(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_bb7_in(v__0, v__01, v__1, v__2, v_x, v_y)) :|: v__2 <= 0 eval_start_bb6_in(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_bb5_in(v__0, v__01, v__1, v__2 - 1, v_x, v_y)) :|: TRUE eval_start_bb7_in(v__0, v__01, v__1, v__2, v_x, v_y) -> Com_1(eval_start_stop(v__0, v__01, v__1, v__2, v_x, v_y)) :|: TRUE The start-symbols are:[eval_start_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 26*Ar_1 + 24*Ar_3 + 23) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5)) (Comp: ?, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 1 ] (Comp: ?, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ] (Comp: ?, Cost: 1) evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 - 1)) (Comp: ?, Cost: 1) evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(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(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 1 ] evalstartbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 - 1)) We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5)) (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(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(evalstartstart(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 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5)) (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(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(evalstartstart(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(evalstartbb7in) = 1 Pol(evalstartstop) = 0 Pol(evalstartbb5in) = 2 Pol(evalstartbb4in) = 3 Pol(evalstartbb3in) = 3 Pol(evalstartbb2in) = 4 Pol(evalstartbb1in) = 4 Pol(evalstart4) = 4 Pol(evalstart3) = 4 Pol(evalstart2) = 4 Pol(evalstart1) = 4 Pol(evalstart0) = 4 Pol(evalstartbb0in) = 4 Pol(evalstartstart) = 4 Pol(koat_start) = 4 orients all transitions weakly and the transitions evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ] evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ] evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 4, Cost: 1) evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 4, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5)) (Comp: 4, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5)) (Comp: 4, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(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(evalstartstart(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(evalstartbb7in) = V_1 Pol(evalstartstop) = V_1 Pol(evalstartbb5in) = V_1 Pol(evalstartbb4in) = V_1 Pol(evalstartbb3in) = V_1 Pol(evalstartbb2in) = V_1 - 1 Pol(evalstartbb1in) = V_1 Pol(evalstart4) = V_2 Pol(evalstart3) = V_2 Pol(evalstart2) = V_2 Pol(evalstart1) = V_2 Pol(evalstart0) = V_2 Pol(evalstartbb0in) = V_2 Pol(evalstartstart) = V_2 Pol(koat_start) = V_2 orients all transitions weakly and the transition evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ] strictly and produces the following problem: 5: T: (Comp: 4, Cost: 1) evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 4, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5)) (Comp: 4, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: ?, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5)) (Comp: 4, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ] (Comp: Ar_1, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(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(evalstartstart(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 5 produces the following problem: 6: T: (Comp: 4, Cost: 1) evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 4, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5)) (Comp: 4, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ] (Comp: ?, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: Ar_1, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5)) (Comp: 4, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ] (Comp: Ar_1, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(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(evalstartstart(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(evalstartbb4in) = V_5 - 1 Pol(evalstartbb3in) = V_5 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ]", 0-0) = 2*Ar_1 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ]", 0-1) = Ar_1 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ]", 0-2) = 3*Ar_1 + 3*Ar_3 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ]", 0-3) = Ar_3 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ]", 0-4) = Ar_4 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ]", 0-5) = Ar_5 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ]", 0-0) = 2*Ar_1 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ]", 0-1) = Ar_1 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ]", 0-2) = 3*Ar_1 + 3*Ar_3 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ]", 0-3) = Ar_3 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ]", 0-4) = 3*Ar_1 + 3*Ar_3 S("evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ]", 0-5) = Ar_5 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5))", 0-0) = 2*Ar_1 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5))", 0-2) = 3*Ar_1 + 3*Ar_3 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-0) = 2*Ar_1 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-1) = Ar_1 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-2) = 3*Ar_1 + 3*Ar_3 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-3) = Ar_3 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-4) = ? S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-5) = Ar_5 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ]", 0-0) = 2*Ar_1 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ]", 0-1) = Ar_1 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ]", 0-2) = 3*Ar_1 + 3*Ar_3 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ]", 0-3) = Ar_3 S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ]", 0-4) = ? S("evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ]", 0-5) = ? S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5))", 0-0) = 2*Ar_1 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5))", 0-1) = Ar_1 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5))", 0-2) = 3*Ar_1 + 3*Ar_3 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5))", 0-3) = Ar_3 S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5))", 0-4) = ? S("evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5))", 0-5) = Ar_5 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ]", 0-0) = 2*Ar_1 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ]", 0-1) = Ar_1 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ]", 0-2) = 3*Ar_1 + 3*Ar_3 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ]", 0-3) = Ar_3 S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ]", 0-4) = ? S("evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ]", 0-5) = ? S("evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = 2*Ar_1 S("evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = 3*Ar_1 + 3*Ar_3 S("evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = ? orients the transitions evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5)) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] weakly and the transition evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] strictly and produces the following problem: 7: T: (Comp: 4, Cost: 1) evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 4, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ] (Comp: ?, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5)) (Comp: 4, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ] (Comp: 12*Ar_1 + 12*Ar_3, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: Ar_1, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5)) (Comp: 4, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ] (Comp: Ar_1, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(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(evalstartstart(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 7 produces the following problem: 8: T: (Comp: 4, Cost: 1) evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 4, Cost: 1) evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_5 ] (Comp: 12*Ar_1 + 12*Ar_3, Cost: 1) evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5)) (Comp: 4, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_4)) [ 0 >= Ar_4 ] (Comp: 12*Ar_1 + 12*Ar_3, Cost: 1) evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: Ar_1, Cost: 1) evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_0 - 1, Ar_1, Ar_2 + 2, Ar_3, Ar_4, Ar_5)) (Comp: 4, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_5)) [ 0 >= Ar_0 ] (Comp: Ar_1, Cost: 1) evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalstartbb0in(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(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 26*Ar_1 + 24*Ar_3 + 23 Time: 0.177 sec (SMT: 0.115 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 -> evalstartbb1in : A'=B, C'=D, [], cost: 1 7: evalstartbb1in -> evalstartbb2in : [ A>=1 ], cost: 1 8: evalstartbb1in -> evalstartbb3in : E'=C, [ 0>=A ], cost: 1 9: evalstartbb2in -> evalstartbb1in : A'=-1+A, C'=2+C, [], cost: 1 10: evalstartbb3in -> evalstartbb4in : [ E>=1 ], cost: 1 11: evalstartbb3in -> evalstartbb5in : F'=E, [ 0>=E ], cost: 1 12: evalstartbb4in -> evalstartbb3in : E'=-1+E, [], cost: 1 13: evalstartbb5in -> evalstartbb6in : [ F>=1 ], cost: 1 14: evalstartbb5in -> evalstartbb7in : [ 0>=F ], cost: 1 15: evalstartbb6in -> evalstartbb5in : F'=-1+F, [], cost: 1 16: evalstartbb7in -> 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 -> evalstartbb1in : A'=B, C'=D, [], cost: 1 7: evalstartbb1in -> evalstartbb2in : [ A>=1 ], cost: 1 8: evalstartbb1in -> evalstartbb3in : E'=C, [ 0>=A ], cost: 1 9: evalstartbb2in -> evalstartbb1in : A'=-1+A, C'=2+C, [], cost: 1 10: evalstartbb3in -> evalstartbb4in : [ E>=1 ], cost: 1 11: evalstartbb3in -> evalstartbb5in : F'=E, [ 0>=E ], cost: 1 12: evalstartbb4in -> evalstartbb3in : E'=-1+E, [], cost: 1 13: evalstartbb5in -> evalstartbb6in : [ F>=1 ], cost: 1 15: evalstartbb6in -> evalstartbb5in : F'=-1+F, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalstartstart 22: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 7 8: evalstartbb1in -> evalstartbb3in : E'=C, [ 0>=A ], cost: 1 23: evalstartbb1in -> evalstartbb1in : A'=-1+A, C'=2+C, [ A>=1 ], cost: 2 11: evalstartbb3in -> evalstartbb5in : F'=E, [ 0>=E ], cost: 1 24: evalstartbb3in -> evalstartbb3in : E'=-1+E, [ E>=1 ], cost: 2 25: evalstartbb5in -> evalstartbb5in : F'=-1+F, [ F>=1 ], cost: 2 Accelerating simple loops of location 7. Accelerating the following rules: 23: evalstartbb1in -> evalstartbb1in : A'=-1+A, C'=2+C, [ A>=1 ], cost: 2 Accelerated rule 23 with metering function A, yielding the new rule 26. Removing the simple loops: 23. Accelerating simple loops of location 9. Accelerating the following rules: 24: evalstartbb3in -> evalstartbb3in : E'=-1+E, [ E>=1 ], cost: 2 Accelerated rule 24 with metering function E, yielding the new rule 27. Removing the simple loops: 24. Accelerating simple loops of location 11. Accelerating the following rules: 25: evalstartbb5in -> evalstartbb5in : F'=-1+F, [ F>=1 ], cost: 2 Accelerated rule 25 with metering function F, yielding the new rule 28. Removing the simple loops: 25. Accelerated all simple loops using metering functions (where possible): Start location: evalstartstart 22: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 7 8: evalstartbb1in -> evalstartbb3in : E'=C, [ 0>=A ], cost: 1 26: evalstartbb1in -> evalstartbb1in : A'=0, C'=C+2*A, [ A>=1 ], cost: 2*A 11: evalstartbb3in -> evalstartbb5in : F'=E, [ 0>=E ], cost: 1 27: evalstartbb3in -> evalstartbb3in : E'=0, [ E>=1 ], cost: 2*E 28: evalstartbb5in -> evalstartbb5in : F'=0, [ F>=1 ], cost: 2*F Chained accelerated rules (with incoming rules): Start location: evalstartstart 22: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 7 29: evalstartstart -> evalstartbb1in : A'=0, C'=D+2*B, [ B>=1 ], cost: 7+2*B 8: evalstartbb1in -> evalstartbb3in : E'=C, [ 0>=A ], cost: 1 30: evalstartbb1in -> evalstartbb3in : E'=0, [ 0>=A && C>=1 ], cost: 1+2*C 11: evalstartbb3in -> evalstartbb5in : F'=E, [ 0>=E ], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: evalstartstart 22: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 7 29: evalstartstart -> evalstartbb1in : A'=0, C'=D+2*B, [ B>=1 ], cost: 7+2*B 30: evalstartbb1in -> evalstartbb3in : E'=0, [ 0>=A && C>=1 ], cost: 1+2*C Eliminated locations (on tree-shaped paths): Start location: evalstartstart 31: evalstartstart -> evalstartbb3in : A'=B, C'=D, E'=0, [ 0>=B && D>=1 ], cost: 8+2*D 32: evalstartstart -> evalstartbb3in : A'=0, C'=D+2*B, E'=0, [ B>=1 && D+2*B>=1 ], cost: 8+2*D+6*B ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalstartstart 31: evalstartstart -> evalstartbb3in : A'=B, C'=D, E'=0, [ 0>=B && D>=1 ], cost: 8+2*D 32: evalstartstart -> evalstartbb3in : A'=0, C'=D+2*B, E'=0, [ B>=1 && D+2*B>=1 ], cost: 8+2*D+6*B Computing asymptotic complexity for rule 31 Solved the limit problem by the following transformations: Created initial limit problem: 1-B (+/+!), D (+/+!), 8+2*D (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {D==n,B==0} resulting limit problem: [solved] Solution: D / n B / 0 Resulting cost 8+2*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+2*n Rule cost: 8+2*D Rule guard: [ 0>=B && D>=1 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)