6.20/2.83 WORST_CASE(Omega(n^1), O(n^1)) 6.20/2.84 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 6.20/2.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.20/2.84 6.20/2.84 6.20/2.84 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 6.20/2.84 6.20/2.84 (0) CpxIntTrs 6.20/2.84 (1) Koat Proof [FINISHED, 536 ms] 6.20/2.84 (2) BOUNDS(1, n^1) 6.20/2.84 (3) Loat Proof [FINISHED, 1114 ms] 6.20/2.84 (4) BOUNDS(n^1, INF) 6.20/2.84 6.20/2.84 6.20/2.84 ---------------------------------------- 6.20/2.84 6.20/2.84 (0) 6.20/2.84 Obligation: 6.20/2.84 Complexity Int TRS consisting of the following rules: 6.20/2.84 eval_start_start(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb0_in(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE 6.20/2.84 eval_start_bb0_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_0(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE 6.20/2.84 eval_start_0(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_1(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE 6.20/2.84 eval_start_1(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_2(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE 6.20/2.84 eval_start_2(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_3(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE 6.20/2.84 eval_start_3(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_4(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE 6.20/2.84 eval_start_4(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_5(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE 6.20/2.84 eval_start_5(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb1_in(v_n, v_y, v__1, v_1, v_n, v_y)) :|: TRUE 6.20/2.84 eval_start_bb1_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb2_in(v__0, v__01, v__1, v_1, v_n, v_y)) :|: v__0 < 0 6.20/2.84 eval_start_bb1_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb5_in(v__0, v__01, v__1, v_1, v_n, v_y)) :|: v__0 >= 0 6.20/2.84 eval_start_bb2_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb3_in(v__0, v__01, v__01 + 1000, v__0 + 1, v_n, v_y)) :|: TRUE 6.20/2.84 eval_start_bb3_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb4_in(v__0, v__01, v__1, v_1, v_n, v_y)) :|: v__1 >= 100 6.20/2.84 eval_start_bb3_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb1_in(v_1, v__1, v__1, v_1, v_n, v_y)) :|: v__1 < 100 6.20/2.84 eval_start_bb4_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_bb3_in(v__0, v__01, v__1 - 100, v_1, v_n, v_y)) :|: TRUE 6.20/2.84 eval_start_bb5_in(v__0, v__01, v__1, v_1, v_n, v_y) -> Com_1(eval_start_stop(v__0, v__01, v__1, v_1, v_n, v_y)) :|: TRUE 6.20/2.84 6.20/2.84 The start-symbols are:[eval_start_start_6] 6.20/2.84 6.20/2.84 6.20/2.84 ---------------------------------------- 6.20/2.84 6.20/2.84 (1) Koat Proof (FINISHED) 6.20/2.84 YES(?, 4003*ar_1 + 4*ar_3 + 12) 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Initial complexity problem: 6.20/2.84 6.20/2.84 1: T: 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstart5(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)) 6.20/2.84 6.20/2.84 (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)) [ 0 >= ar_0 + 1 ] 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb1in(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)) [ ar_0 >= 0 ] 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb2in(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 + 1000, ar_0 + 1)) 6.20/2.84 6.20/2.84 (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 >= 100 ] 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ] 6.20/2.84 6.20/2.84 (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 - 100, ar_5)) 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb5in(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)) 6.20/2.84 6.20/2.84 (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 ] 6.20/2.84 6.20/2.84 start location: koat_start 6.20/2.84 6.20/2.84 leaf cost: 0 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Repeatedly propagating knowledge in problem 1 produces the following problem: 6.20/2.84 6.20/2.84 2: T: 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart5(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)) 6.20/2.84 6.20/2.84 (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)) [ 0 >= ar_0 + 1 ] 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb1in(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)) [ ar_0 >= 0 ] 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb2in(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 + 1000, ar_0 + 1)) 6.20/2.84 6.20/2.84 (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 >= 100 ] 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ] 6.20/2.84 6.20/2.84 (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 - 100, ar_5)) 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb5in(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)) 6.20/2.84 6.20/2.84 (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 ] 6.20/2.84 6.20/2.84 start location: koat_start 6.20/2.84 6.20/2.84 leaf cost: 0 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 A polynomial rank function with 6.20/2.84 6.20/2.84 Pol(evalstartstart) = 2 6.20/2.84 6.20/2.84 Pol(evalstartbb0in) = 2 6.20/2.84 6.20/2.84 Pol(evalstart0) = 2 6.20/2.84 6.20/2.84 Pol(evalstart1) = 2 6.20/2.84 6.20/2.84 Pol(evalstart2) = 2 6.20/2.84 6.20/2.84 Pol(evalstart3) = 2 6.20/2.84 6.20/2.84 Pol(evalstart4) = 2 6.20/2.84 6.20/2.84 Pol(evalstart5) = 2 6.20/2.84 6.20/2.84 Pol(evalstartbb1in) = 2 6.20/2.84 6.20/2.84 Pol(evalstartbb2in) = 2 6.20/2.84 6.20/2.84 Pol(evalstartbb5in) = 1 6.20/2.84 6.20/2.84 Pol(evalstartbb3in) = 2 6.20/2.84 6.20/2.84 Pol(evalstartbb4in) = 2 6.20/2.84 6.20/2.84 Pol(evalstartstop) = 0 6.20/2.84 6.20/2.84 Pol(koat_start) = 2 6.20/2.84 6.20/2.84 orients all transitions weakly and the transitions 6.20/2.84 6.20/2.84 evalstartbb5in(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)) 6.20/2.84 6.20/2.84 evalstartbb1in(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)) [ ar_0 >= 0 ] 6.20/2.84 6.20/2.84 strictly and produces the following problem: 6.20/2.84 6.20/2.84 3: T: 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart5(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)) 6.20/2.84 6.20/2.84 (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)) [ 0 >= ar_0 + 1 ] 6.20/2.84 6.20/2.84 (Comp: 2, Cost: 1) evalstartbb1in(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)) [ ar_0 >= 0 ] 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb2in(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 + 1000, ar_0 + 1)) 6.20/2.84 6.20/2.84 (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 >= 100 ] 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ] 6.20/2.84 6.20/2.84 (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 - 100, ar_5)) 6.20/2.84 6.20/2.84 (Comp: 2, Cost: 1) evalstartbb5in(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)) 6.20/2.84 6.20/2.84 (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 ] 6.20/2.84 6.20/2.84 start location: koat_start 6.20/2.84 6.20/2.84 leaf cost: 0 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 A polynomial rank function with 6.20/2.84 6.20/2.84 Pol(evalstartstart) = -V_2 6.20/2.84 6.20/2.84 Pol(evalstartbb0in) = -V_2 6.20/2.84 6.20/2.84 Pol(evalstart0) = -V_2 6.20/2.84 6.20/2.84 Pol(evalstart1) = -V_2 6.20/2.84 6.20/2.84 Pol(evalstart2) = -V_2 6.20/2.84 6.20/2.84 Pol(evalstart3) = -V_2 6.20/2.84 6.20/2.84 Pol(evalstart4) = -V_2 6.20/2.84 6.20/2.84 Pol(evalstart5) = -V_2 6.20/2.84 6.20/2.84 Pol(evalstartbb1in) = -V_1 6.20/2.84 6.20/2.84 Pol(evalstartbb2in) = -V_1 - 1 6.20/2.84 6.20/2.84 Pol(evalstartbb5in) = -V_1 6.20/2.84 6.20/2.84 Pol(evalstartbb3in) = -V_6 6.20/2.84 6.20/2.84 Pol(evalstartbb4in) = -V_6 6.20/2.84 6.20/2.84 Pol(evalstartstop) = -V_1 6.20/2.84 6.20/2.84 Pol(koat_start) = -V_2 6.20/2.84 6.20/2.84 orients all transitions weakly and the transition 6.20/2.84 6.20/2.84 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)) [ 0 >= ar_0 + 1 ] 6.20/2.84 6.20/2.84 strictly and produces the following problem: 6.20/2.84 6.20/2.84 4: T: 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart5(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)) 6.20/2.84 6.20/2.84 (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)) [ 0 >= ar_0 + 1 ] 6.20/2.84 6.20/2.84 (Comp: 2, Cost: 1) evalstartbb1in(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)) [ ar_0 >= 0 ] 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb2in(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 + 1000, ar_0 + 1)) 6.20/2.84 6.20/2.84 (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 >= 100 ] 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ] 6.20/2.84 6.20/2.84 (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 - 100, ar_5)) 6.20/2.84 6.20/2.84 (Comp: 2, Cost: 1) evalstartbb5in(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)) 6.20/2.84 6.20/2.84 (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 ] 6.20/2.84 6.20/2.84 start location: koat_start 6.20/2.84 6.20/2.84 leaf cost: 0 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Repeatedly propagating knowledge in problem 4 produces the following problem: 6.20/2.84 6.20/2.84 5: T: 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart5(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)) 6.20/2.84 6.20/2.84 (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)) [ 0 >= ar_0 + 1 ] 6.20/2.84 6.20/2.84 (Comp: 2, Cost: 1) evalstartbb1in(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)) [ ar_0 >= 0 ] 6.20/2.84 6.20/2.84 (Comp: ar_1, Cost: 1) evalstartbb2in(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 + 1000, ar_0 + 1)) 6.20/2.84 6.20/2.84 (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 >= 100 ] 6.20/2.84 6.20/2.84 (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ] 6.20/2.84 6.20/2.84 (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 - 100, ar_5)) 6.20/2.84 6.20/2.84 (Comp: 2, Cost: 1) evalstartbb5in(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)) 6.20/2.84 6.20/2.84 (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 ] 6.20/2.84 6.20/2.84 start location: koat_start 6.20/2.84 6.20/2.84 leaf cost: 0 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 A polynomial rank function with 6.20/2.84 6.20/2.84 Pol(evalstartbb4in) = 1 6.20/2.84 6.20/2.84 Pol(evalstartbb3in) = 1 6.20/2.84 6.20/2.84 Pol(evalstartbb1in) = 0 6.20/2.84 6.20/2.84 and size complexities 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 S("evalstartbb5in(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 6.20/2.84 6.20/2.84 S("evalstartbb5in(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 6.20/2.84 6.20/2.84 S("evalstartbb5in(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) = ? 6.20/2.84 6.20/2.84 S("evalstartbb5in(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 6.20/2.84 6.20/2.84 S("evalstartbb5in(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) = ? 6.20/2.84 6.20/2.84 S("evalstartbb5in(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) = 2*ar_1 + 2*ar_5 6.20/2.84 6.20/2.84 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 - 100, ar_5))", 0-0) = 2*ar_1 6.20/2.84 6.20/2.84 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 - 100, ar_5))", 0-1) = ar_1 6.20/2.84 6.20/2.84 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 - 100, ar_5))", 0-2) = ? 6.20/2.84 6.20/2.84 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 - 100, ar_5))", 0-3) = ar_3 6.20/2.84 6.20/2.84 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 - 100, ar_5))", 0-4) = ? 6.20/2.84 6.20/2.84 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 - 100, ar_5))", 0-5) = 2*ar_1 6.20/2.84 6.20/2.84 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ]", 0-0) = 2*ar_1 6.20/2.84 6.20/2.84 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ]", 0-1) = ar_1 6.20/2.84 6.20/2.84 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ]", 0-2) = ? 6.20/2.84 6.20/2.84 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ]", 0-3) = ar_3 6.20/2.84 6.20/2.84 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ]", 0-4) = ? 6.20/2.84 6.20/2.84 S("evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ]", 0-5) = 2*ar_1 6.20/2.84 6.20/2.84 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 >= 100 ]", 0-0) = 2*ar_1 6.20/2.84 6.20/2.84 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 >= 100 ]", 0-1) = ar_1 6.20/2.84 6.20/2.84 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 >= 100 ]", 0-2) = ? 6.20/2.84 6.20/2.84 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 >= 100 ]", 0-3) = ar_3 6.20/2.84 6.20/2.84 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 >= 100 ]", 0-4) = ? 6.20/2.84 6.20/2.84 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 >= 100 ]", 0-5) = 2*ar_1 6.20/2.84 6.20/2.84 S("evalstartbb2in(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 + 1000, ar_0 + 1))", 0-0) = 2*ar_1 6.20/2.84 6.20/2.84 S("evalstartbb2in(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 + 1000, ar_0 + 1))", 0-1) = ar_1 6.20/2.84 6.20/2.84 S("evalstartbb2in(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 + 1000, ar_0 + 1))", 0-2) = ? 6.20/2.84 6.20/2.84 S("evalstartbb2in(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 + 1000, ar_0 + 1))", 0-3) = ar_3 6.20/2.84 6.20/2.84 S("evalstartbb2in(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 + 1000, ar_0 + 1))", 0-4) = ? 6.20/2.84 6.20/2.84 S("evalstartbb2in(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 + 1000, ar_0 + 1))", 0-5) = 2*ar_1 6.20/2.84 6.20/2.84 S("evalstartbb1in(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)) [ ar_0 >= 0 ]", 0-0) = 2*ar_1 6.20/2.84 6.20/2.84 S("evalstartbb1in(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)) [ ar_0 >= 0 ]", 0-1) = ar_1 6.20/2.84 6.20/2.84 S("evalstartbb1in(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)) [ ar_0 >= 0 ]", 0-2) = ? 6.20/2.84 6.20/2.84 S("evalstartbb1in(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)) [ ar_0 >= 0 ]", 0-3) = ar_3 6.20/2.84 6.20/2.84 S("evalstartbb1in(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)) [ ar_0 >= 0 ]", 0-4) = ? 6.20/2.84 6.20/2.84 S("evalstartbb1in(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)) [ ar_0 >= 0 ]", 0-5) = 2*ar_1 + 2*ar_5 6.20/2.84 6.20/2.84 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)) [ 0 >= ar_0 + 1 ]", 0-0) = 2*ar_1 6.20/2.84 6.20/2.84 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)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1 6.20/2.84 6.20/2.84 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)) [ 0 >= ar_0 + 1 ]", 0-2) = ? 6.20/2.84 6.20/2.84 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)) [ 0 >= ar_0 + 1 ]", 0-3) = ar_3 6.20/2.84 6.20/2.84 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)) [ 0 >= ar_0 + 1 ]", 0-4) = ? 6.20/2.84 6.20/2.84 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)) [ 0 >= ar_0 + 1 ]", 0-5) = 2*ar_1 + 2*ar_5 6.20/2.84 6.20/2.84 S("evalstart5(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 6.20/2.84 6.20/2.84 S("evalstart5(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 6.20/2.84 6.20/2.84 S("evalstart5(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 6.20/2.84 6.20/2.84 S("evalstart5(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 6.20/2.84 6.20/2.84 S("evalstart5(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 6.20/2.84 6.20/2.84 S("evalstart5(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 6.20/2.84 6.20/2.84 S("evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-0) = ar_0 6.20/2.84 6.20/2.84 S("evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-1) = ar_1 6.20/2.84 6.20/2.84 S("evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-2) = ar_2 6.20/2.84 6.20/2.84 S("evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-3) = ar_3 6.20/2.84 6.20/2.84 S("evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-4) = ar_4 6.20/2.84 6.20/2.84 S("evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-5) = ar_5 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 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 6.20/2.84 6.20/2.84 orients the transitions 6.20/2.84 6.20/2.84 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 - 100, ar_5)) 6.20/2.84 6.20/2.84 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 >= 100 ] 6.20/2.84 6.20/2.84 evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ] 6.20/2.84 6.20/2.84 weakly and the transition 6.20/2.84 6.20/2.84 evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ] 6.20/2.84 6.20/2.84 strictly and produces the following problem: 6.20/2.84 6.20/2.84 6: T: 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart5(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)) 6.20/2.84 6.20/2.84 (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)) [ 0 >= ar_0 + 1 ] 6.20/2.84 6.20/2.84 (Comp: 2, Cost: 1) evalstartbb1in(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)) [ ar_0 >= 0 ] 6.20/2.84 6.20/2.84 (Comp: ar_1, Cost: 1) evalstartbb2in(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 + 1000, ar_0 + 1)) 6.20/2.84 6.20/2.84 (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 >= 100 ] 6.20/2.84 6.20/2.84 (Comp: ar_1, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ 99 >= ar_4 ] 6.20/2.84 6.20/2.84 (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 - 100, ar_5)) 6.20/2.84 6.20/2.84 (Comp: 2, Cost: 1) evalstartbb5in(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)) 6.20/2.84 6.20/2.84 (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 ] 6.20/2.84 6.20/2.84 start location: koat_start 6.20/2.84 6.20/2.84 leaf cost: 0 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Applied AI with 'oct' on problem 6 to obtain the following invariants: 6.20/2.84 6.20/2.84 For symbol evalstartbb1in: X_1 - X_2 >= 0 6.20/2.84 6.20/2.84 For symbol evalstartbb2in: -X_2 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 - 2 >= 0 /\ -X_1 - 1 >= 0 6.20/2.84 6.20/2.84 For symbol evalstartbb3in: -X_6 >= 0 /\ -X_2 - X_6 - 1 >= 0 /\ X_1 - X_6 + 1 >= 0 /\ -X_1 - X_6 - 1 >= 0 /\ -X_2 + X_6 - 1 >= 0 /\ -X_1 + X_6 - 1 >= 0 /\ X_3 - X_5 + 1000 >= 0 /\ -X_2 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 - 2 >= 0 /\ -X_1 - 1 >= 0 6.20/2.84 6.20/2.84 For symbol evalstartbb4in: -X_6 >= 0 /\ X_5 - X_6 - 100 >= 0 /\ X_3 - X_6 + 900 >= 0 /\ -X_2 - X_6 - 1 >= 0 /\ X_1 - X_6 + 1 >= 0 /\ -X_1 - X_6 - 1 >= 0 /\ -X_2 + X_6 - 1 >= 0 /\ -X_1 + X_6 - 1 >= 0 /\ X_3 - X_5 + 1000 >= 0 /\ X_5 - 100 >= 0 /\ X_3 + X_5 + 800 >= 0 /\ -X_2 + X_5 - 101 >= 0 /\ -X_1 + X_5 - 101 >= 0 /\ X_3 + 900 >= 0 /\ -X_2 + X_3 + 899 >= 0 /\ -X_1 + X_3 + 899 >= 0 /\ -X_2 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 - 2 >= 0 /\ -X_1 - 1 >= 0 6.20/2.84 6.20/2.84 For symbol evalstartbb5in: X_1 - X_2 >= 0 /\ X_1 >= 0 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 This yielded the following problem: 6.20/2.84 6.20/2.84 7: T: 6.20/2.84 6.20/2.84 (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 ] 6.20/2.84 6.20/2.84 (Comp: 2, Cost: 1) evalstartbb5in(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)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ] 6.20/2.84 6.20/2.84 (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 - 100, ar_5)) [ -ar_5 >= 0 /\ ar_4 - ar_5 - 100 >= 0 /\ ar_2 - ar_5 + 900 >= 0 /\ -ar_1 - ar_5 - 1 >= 0 /\ ar_0 - ar_5 + 1 >= 0 /\ -ar_0 - ar_5 - 1 >= 0 /\ -ar_1 + ar_5 - 1 >= 0 /\ -ar_0 + ar_5 - 1 >= 0 /\ ar_2 - ar_4 + 1000 >= 0 /\ ar_4 - 100 >= 0 /\ ar_2 + ar_4 + 800 >= 0 /\ -ar_1 + ar_4 - 101 >= 0 /\ -ar_0 + ar_4 - 101 >= 0 /\ ar_2 + 900 >= 0 /\ -ar_1 + ar_2 + 899 >= 0 /\ -ar_0 + ar_2 + 899 >= 0 /\ -ar_1 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 - ar_1 - 2 >= 0 /\ -ar_0 - 1 >= 0 ] 6.20/2.84 6.20/2.84 (Comp: ar_1, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ -ar_5 >= 0 /\ -ar_1 - ar_5 - 1 >= 0 /\ ar_0 - ar_5 + 1 >= 0 /\ -ar_0 - ar_5 - 1 >= 0 /\ -ar_1 + ar_5 - 1 >= 0 /\ -ar_0 + ar_5 - 1 >= 0 /\ ar_2 - ar_4 + 1000 >= 0 /\ -ar_1 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 - ar_1 - 2 >= 0 /\ -ar_0 - 1 >= 0 /\ 99 >= ar_4 ] 6.20/2.84 6.20/2.84 (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_5 >= 0 /\ -ar_1 - ar_5 - 1 >= 0 /\ ar_0 - ar_5 + 1 >= 0 /\ -ar_0 - ar_5 - 1 >= 0 /\ -ar_1 + ar_5 - 1 >= 0 /\ -ar_0 + ar_5 - 1 >= 0 /\ ar_2 - ar_4 + 1000 >= 0 /\ -ar_1 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 - ar_1 - 2 >= 0 /\ -ar_0 - 1 >= 0 /\ ar_4 >= 100 ] 6.20/2.84 6.20/2.84 (Comp: ar_1, Cost: 1) evalstartbb2in(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 + 1000, ar_0 + 1)) [ -ar_1 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 - ar_1 - 2 >= 0 /\ -ar_0 - 1 >= 0 ] 6.20/2.84 6.20/2.84 (Comp: 2, Cost: 1) evalstartbb1in(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)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ] 6.20/2.84 6.20/2.84 (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 - ar_1 >= 0 /\ 0 >= ar_0 + 1 ] 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart5(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)) 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 start location: koat_start 6.20/2.84 6.20/2.84 leaf cost: 0 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 A polynomial rank function with 6.20/2.84 6.20/2.84 Pol(koat_start) = -2000*V_2 + 2*V_4 6.20/2.84 6.20/2.84 Pol(evalstartstart) = -2000*V_2 + 2*V_4 6.20/2.84 6.20/2.84 Pol(evalstartbb5in) = -2000*V_1 + 2*V_3 6.20/2.84 6.20/2.84 Pol(evalstartstop) = -2000*V_1 + 2*V_3 6.20/2.84 6.20/2.84 Pol(evalstartbb4in) = 2*V_5 - 2000*V_6 - 100 6.20/2.84 6.20/2.84 Pol(evalstartbb3in) = 2*V_5 - 2000*V_6 6.20/2.84 6.20/2.84 Pol(evalstartbb1in) = -2000*V_1 + 2*V_3 6.20/2.84 6.20/2.84 Pol(evalstartbb2in) = -2000*V_1 + 2*V_3 6.20/2.84 6.20/2.84 Pol(evalstart5) = -2000*V_2 + 2*V_4 6.20/2.84 6.20/2.84 Pol(evalstart4) = -2000*V_2 + 2*V_4 6.20/2.84 6.20/2.84 Pol(evalstart3) = -2000*V_2 + 2*V_4 6.20/2.84 6.20/2.84 Pol(evalstart2) = -2000*V_2 + 2*V_4 6.20/2.84 6.20/2.84 Pol(evalstart1) = -2000*V_2 + 2*V_4 6.20/2.84 6.20/2.84 Pol(evalstart0) = -2000*V_2 + 2*V_4 6.20/2.84 6.20/2.84 Pol(evalstartbb0in) = -2000*V_2 + 2*V_4 6.20/2.84 6.20/2.84 orients all transitions weakly and the transitions 6.20/2.84 6.20/2.84 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 - 100, ar_5)) [ -ar_5 >= 0 /\ ar_4 - ar_5 - 100 >= 0 /\ ar_2 - ar_5 + 900 >= 0 /\ -ar_1 - ar_5 - 1 >= 0 /\ ar_0 - ar_5 + 1 >= 0 /\ -ar_0 - ar_5 - 1 >= 0 /\ -ar_1 + ar_5 - 1 >= 0 /\ -ar_0 + ar_5 - 1 >= 0 /\ ar_2 - ar_4 + 1000 >= 0 /\ ar_4 - 100 >= 0 /\ ar_2 + ar_4 + 800 >= 0 /\ -ar_1 + ar_4 - 101 >= 0 /\ -ar_0 + ar_4 - 101 >= 0 /\ ar_2 + 900 >= 0 /\ -ar_1 + ar_2 + 899 >= 0 /\ -ar_0 + ar_2 + 899 >= 0 /\ -ar_1 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 - ar_1 - 2 >= 0 /\ -ar_0 - 1 >= 0 ] 6.20/2.84 6.20/2.84 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_5 >= 0 /\ -ar_1 - ar_5 - 1 >= 0 /\ ar_0 - ar_5 + 1 >= 0 /\ -ar_0 - ar_5 - 1 >= 0 /\ -ar_1 + ar_5 - 1 >= 0 /\ -ar_0 + ar_5 - 1 >= 0 /\ ar_2 - ar_4 + 1000 >= 0 /\ -ar_1 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 - ar_1 - 2 >= 0 /\ -ar_0 - 1 >= 0 /\ ar_4 >= 100 ] 6.20/2.84 6.20/2.84 strictly and produces the following problem: 6.20/2.84 6.20/2.84 8: T: 6.20/2.84 6.20/2.84 (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 ] 6.20/2.84 6.20/2.84 (Comp: 2, Cost: 1) evalstartbb5in(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)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ] 6.20/2.84 6.20/2.84 (Comp: 2000*ar_1 + 2*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 - 100, ar_5)) [ -ar_5 >= 0 /\ ar_4 - ar_5 - 100 >= 0 /\ ar_2 - ar_5 + 900 >= 0 /\ -ar_1 - ar_5 - 1 >= 0 /\ ar_0 - ar_5 + 1 >= 0 /\ -ar_0 - ar_5 - 1 >= 0 /\ -ar_1 + ar_5 - 1 >= 0 /\ -ar_0 + ar_5 - 1 >= 0 /\ ar_2 - ar_4 + 1000 >= 0 /\ ar_4 - 100 >= 0 /\ ar_2 + ar_4 + 800 >= 0 /\ -ar_1 + ar_4 - 101 >= 0 /\ -ar_0 + ar_4 - 101 >= 0 /\ ar_2 + 900 >= 0 /\ -ar_1 + ar_2 + 899 >= 0 /\ -ar_0 + ar_2 + 899 >= 0 /\ -ar_1 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 - ar_1 - 2 >= 0 /\ -ar_0 - 1 >= 0 ] 6.20/2.84 6.20/2.84 (Comp: ar_1, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstartbb1in(ar_5, ar_1, ar_4, ar_3, ar_4, ar_5)) [ -ar_5 >= 0 /\ -ar_1 - ar_5 - 1 >= 0 /\ ar_0 - ar_5 + 1 >= 0 /\ -ar_0 - ar_5 - 1 >= 0 /\ -ar_1 + ar_5 - 1 >= 0 /\ -ar_0 + ar_5 - 1 >= 0 /\ ar_2 - ar_4 + 1000 >= 0 /\ -ar_1 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 - ar_1 - 2 >= 0 /\ -ar_0 - 1 >= 0 /\ 99 >= ar_4 ] 6.20/2.84 6.20/2.84 (Comp: 2000*ar_1 + 2*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_5 >= 0 /\ -ar_1 - ar_5 - 1 >= 0 /\ ar_0 - ar_5 + 1 >= 0 /\ -ar_0 - ar_5 - 1 >= 0 /\ -ar_1 + ar_5 - 1 >= 0 /\ -ar_0 + ar_5 - 1 >= 0 /\ ar_2 - ar_4 + 1000 >= 0 /\ -ar_1 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 - ar_1 - 2 >= 0 /\ -ar_0 - 1 >= 0 /\ ar_4 >= 100 ] 6.20/2.84 6.20/2.84 (Comp: ar_1, Cost: 1) evalstartbb2in(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 + 1000, ar_0 + 1)) [ -ar_1 - 1 >= 0 /\ ar_0 - ar_1 >= 0 /\ -ar_0 - ar_1 - 2 >= 0 /\ -ar_0 - 1 >= 0 ] 6.20/2.84 6.20/2.84 (Comp: 2, Cost: 1) evalstartbb1in(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)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ] 6.20/2.84 6.20/2.84 (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 - ar_1 >= 0 /\ 0 >= ar_0 + 1 ] 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart5(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)) 6.20/2.84 6.20/2.84 (Comp: 1, Cost: 1) evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 (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)) 6.20/2.84 6.20/2.84 start location: koat_start 6.20/2.84 6.20/2.84 leaf cost: 0 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Complexity upper bound 4003*ar_1 + 4*ar_3 + 12 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Time: 0.516 sec (SMT: 0.375 sec) 6.20/2.84 6.20/2.84 6.20/2.84 ---------------------------------------- 6.20/2.84 6.20/2.84 (2) 6.20/2.84 BOUNDS(1, n^1) 6.20/2.84 6.20/2.84 ---------------------------------------- 6.20/2.84 6.20/2.84 (3) Loat Proof (FINISHED) 6.20/2.84 6.20/2.84 6.20/2.84 ### Pre-processing the ITS problem ### 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Initial linear ITS problem 6.20/2.84 6.20/2.84 Start location: evalstartstart 6.20/2.84 6.20/2.84 0: evalstartstart -> evalstartbb0in : [], cost: 1 6.20/2.84 6.20/2.84 1: evalstartbb0in -> evalstart0 : [], cost: 1 6.20/2.84 6.20/2.84 2: evalstart0 -> evalstart1 : [], cost: 1 6.20/2.84 6.20/2.84 3: evalstart1 -> evalstart2 : [], cost: 1 6.20/2.84 6.20/2.84 4: evalstart2 -> evalstart3 : [], cost: 1 6.20/2.84 6.20/2.84 5: evalstart3 -> evalstart4 : [], cost: 1 6.20/2.84 6.20/2.84 6: evalstart4 -> evalstart5 : [], cost: 1 6.20/2.84 6.20/2.84 7: evalstart5 -> evalstartbb1in : A'=B, C'=D, [], cost: 1 6.20/2.84 6.20/2.84 8: evalstartbb1in -> evalstartbb2in : [ 0>=1+A ], cost: 1 6.20/2.84 6.20/2.84 9: evalstartbb1in -> evalstartbb5in : [ A>=0 ], cost: 1 6.20/2.84 6.20/2.84 10: evalstartbb2in -> evalstartbb3in : E'=1000+C, F'=1+A, [], cost: 1 6.20/2.84 6.20/2.84 11: evalstartbb3in -> evalstartbb4in : [ E>=100 ], cost: 1 6.20/2.84 6.20/2.84 12: evalstartbb3in -> evalstartbb1in : A'=F, C'=E, [ 99>=E ], cost: 1 6.20/2.84 6.20/2.84 13: evalstartbb4in -> evalstartbb3in : E'=-100+E, [], cost: 1 6.20/2.84 6.20/2.84 14: evalstartbb5in -> evalstartstop : [], cost: 1 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Removed unreachable and leaf rules: 6.20/2.84 6.20/2.84 Start location: evalstartstart 6.20/2.84 6.20/2.84 0: evalstartstart -> evalstartbb0in : [], cost: 1 6.20/2.84 6.20/2.84 1: evalstartbb0in -> evalstart0 : [], cost: 1 6.20/2.84 6.20/2.84 2: evalstart0 -> evalstart1 : [], cost: 1 6.20/2.84 6.20/2.84 3: evalstart1 -> evalstart2 : [], cost: 1 6.20/2.84 6.20/2.84 4: evalstart2 -> evalstart3 : [], cost: 1 6.20/2.84 6.20/2.84 5: evalstart3 -> evalstart4 : [], cost: 1 6.20/2.84 6.20/2.84 6: evalstart4 -> evalstart5 : [], cost: 1 6.20/2.84 6.20/2.84 7: evalstart5 -> evalstartbb1in : A'=B, C'=D, [], cost: 1 6.20/2.84 6.20/2.84 8: evalstartbb1in -> evalstartbb2in : [ 0>=1+A ], cost: 1 6.20/2.84 6.20/2.84 10: evalstartbb2in -> evalstartbb3in : E'=1000+C, F'=1+A, [], cost: 1 6.20/2.84 6.20/2.84 11: evalstartbb3in -> evalstartbb4in : [ E>=100 ], cost: 1 6.20/2.84 6.20/2.84 12: evalstartbb3in -> evalstartbb1in : A'=F, C'=E, [ 99>=E ], cost: 1 6.20/2.84 6.20/2.84 13: evalstartbb4in -> evalstartbb3in : E'=-100+E, [], cost: 1 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 ### Simplification by acceleration and chaining ### 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Eliminated locations (on linear paths): 6.20/2.84 6.20/2.84 Start location: evalstartstart 6.20/2.84 6.20/2.84 21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 6.20/2.84 6.20/2.84 22: evalstartbb1in -> evalstartbb3in : E'=1000+C, F'=1+A, [ 0>=1+A ], cost: 2 6.20/2.84 6.20/2.84 12: evalstartbb3in -> evalstartbb1in : A'=F, C'=E, [ 99>=E ], cost: 1 6.20/2.84 6.20/2.84 23: evalstartbb3in -> evalstartbb3in : E'=-100+E, [ E>=100 ], cost: 2 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Accelerating simple loops of location 10. 6.20/2.84 6.20/2.84 Accelerating the following rules: 6.20/2.84 6.20/2.84 23: evalstartbb3in -> evalstartbb3in : E'=-100+E, [ E>=100 ], cost: 2 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Accelerated rule 23 with metering function meter (where 100*meter==-99+E), yielding the new rule 24. 6.20/2.84 6.20/2.84 Removing the simple loops: 23. 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Accelerated all simple loops using metering functions (where possible): 6.20/2.84 6.20/2.84 Start location: evalstartstart 6.20/2.84 6.20/2.84 21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 6.20/2.84 6.20/2.84 22: evalstartbb1in -> evalstartbb3in : E'=1000+C, F'=1+A, [ 0>=1+A ], cost: 2 6.20/2.84 6.20/2.84 12: evalstartbb3in -> evalstartbb1in : A'=F, C'=E, [ 99>=E ], cost: 1 6.20/2.84 6.20/2.84 24: evalstartbb3in -> evalstartbb3in : E'=-100*meter+E, [ E>=100 && 100*meter==-99+E && meter>=1 ], cost: 2*meter 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Chained accelerated rules (with incoming rules): 6.20/2.84 6.20/2.84 Start location: evalstartstart 6.20/2.84 6.20/2.84 21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 6.20/2.84 6.20/2.84 22: evalstartbb1in -> evalstartbb3in : E'=1000+C, F'=1+A, [ 0>=1+A ], cost: 2 6.20/2.84 6.20/2.84 25: evalstartbb1in -> evalstartbb3in : E'=1000+C-100*meter, F'=1+A, [ 0>=1+A && 1000+C>=100 && 100*meter==901+C && meter>=1 ], cost: 2+2*meter 6.20/2.84 6.20/2.84 12: evalstartbb3in -> evalstartbb1in : A'=F, C'=E, [ 99>=E ], cost: 1 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Eliminated locations (on tree-shaped paths): 6.20/2.84 6.20/2.84 Start location: evalstartstart 6.20/2.84 6.20/2.84 21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 6.20/2.84 6.20/2.84 26: evalstartbb1in -> evalstartbb1in : A'=1+A, C'=1000+C, E'=1000+C, F'=1+A, [ 0>=1+A && 99>=1000+C ], cost: 3 6.20/2.84 6.20/2.84 27: evalstartbb1in -> evalstartbb1in : A'=1+A, C'=1000+C-100*meter, E'=1000+C-100*meter, F'=1+A, [ 0>=1+A && 1000+C>=100 && 100*meter==901+C && meter>=1 ], cost: 3+2*meter 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Accelerating simple loops of location 8. 6.20/2.84 6.20/2.84 Accelerating the following rules: 6.20/2.84 6.20/2.84 26: evalstartbb1in -> evalstartbb1in : A'=1+A, C'=1000+C, E'=1000+C, F'=1+A, [ 0>=1+A && 99>=1000+C ], cost: 3 6.20/2.84 6.20/2.84 27: evalstartbb1in -> evalstartbb1in : A'=1+A, C'=1000+C-100*meter, E'=1000+C-100*meter, F'=1+A, [ 0>=1+A && 1000+C>=100 && 100*meter==901+C && meter>=1 ], cost: 3+2*meter 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Accelerated rule 26 with metering function meter_1 (where 1000*meter_1==-900-C) (after adding A<=C), yielding the new rule 28. 6.20/2.84 6.20/2.84 Accelerated rule 26 with backward acceleration, yielding the new rule 29. 6.20/2.84 6.20/2.84 During metering: Instantiating temporary variables by {meter==1} 6.20/2.84 6.20/2.84 Accelerated rule 27 with metering function meter_2 (where 900*meter_2==-801-C), yielding the new rule 30. 6.20/2.84 6.20/2.84 During metering: Instantiating temporary variables by {k==-1-A,meter==1} 6.20/2.84 6.20/2.84 Removing the simple loops: 26 27. 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Accelerated all simple loops using metering functions (where possible): 6.20/2.84 6.20/2.84 Start location: evalstartstart 6.20/2.84 6.20/2.84 21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 6.20/2.84 6.20/2.84 28: evalstartbb1in -> evalstartbb1in : A'=A+meter_1, C'=C+1000*meter_1, E'=C+1000*meter_1, F'=A+meter_1, [ 0>=1+A && 99>=1000+C && A<=C && 1000*meter_1==-900-C && meter_1>=1 ], cost: 3*meter_1 6.20/2.84 6.20/2.84 29: evalstartbb1in -> evalstartbb1in : A'=k+A, C'=C+1000*k, E'=C+1000*k, F'=k+A, [ 0>=1+A && 99>=1000+C && k>0 && 0>=k+A && 99>=C+1000*k ], cost: 3*k 6.20/2.84 6.20/2.84 30: evalstartbb1in -> evalstartbb1in : A'=A+meter_2, C'=C+900*meter_2, E'=C+900*meter_2, F'=A+meter_2, [ 0>=1+A && 100==901+C && 900*meter_2==-801-C && meter_2>=1 ], cost: 5*meter_2 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Chained accelerated rules (with incoming rules): 6.20/2.84 6.20/2.84 Start location: evalstartstart 6.20/2.84 6.20/2.84 21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8 6.20/2.84 6.20/2.84 31: evalstartstart -> evalstartbb1in : A'=meter_1+B, C'=D+1000*meter_1, E'=D+1000*meter_1, F'=meter_1+B, [ 0>=1+B && 99>=1000+D && B<=D && 1000*meter_1==-900-D && meter_1>=1 ], cost: 8+3*meter_1 6.20/2.84 6.20/2.84 32: evalstartstart -> evalstartbb1in : A'=k+B, C'=1000*k+D, E'=1000*k+D, F'=k+B, [ 0>=1+B && 99>=1000+D && k>0 && 0>=k+B && 99>=1000*k+D ], cost: 8+3*k 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Removed unreachable locations (and leaf rules with constant cost): 6.20/2.84 6.20/2.84 Start location: evalstartstart 6.20/2.84 6.20/2.84 31: evalstartstart -> evalstartbb1in : A'=meter_1+B, C'=D+1000*meter_1, E'=D+1000*meter_1, F'=meter_1+B, [ 0>=1+B && 99>=1000+D && B<=D && 1000*meter_1==-900-D && meter_1>=1 ], cost: 8+3*meter_1 6.20/2.84 6.20/2.84 32: evalstartstart -> evalstartbb1in : A'=k+B, C'=1000*k+D, E'=1000*k+D, F'=k+B, [ 0>=1+B && 99>=1000+D && k>0 && 0>=k+B && 99>=1000*k+D ], cost: 8+3*k 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 ### Computing asymptotic complexity ### 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Fully simplified ITS problem 6.20/2.84 6.20/2.84 Start location: evalstartstart 6.20/2.84 6.20/2.84 31: evalstartstart -> evalstartbb1in : A'=meter_1+B, C'=D+1000*meter_1, E'=D+1000*meter_1, F'=meter_1+B, [ 0>=1+B && 99>=1000+D && B<=D && 1000*meter_1==-900-D && meter_1>=1 ], cost: 8+3*meter_1 6.20/2.84 6.20/2.84 32: evalstartstart -> evalstartbb1in : A'=k+B, C'=1000*k+D, E'=1000*k+D, F'=k+B, [ 0>=1+B && 99>=1000+D && k>0 && 0>=k+B && 99>=1000*k+D ], cost: 8+3*k 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Computing asymptotic complexity for rule 31 6.20/2.84 6.20/2.84 Simplified the guard: 6.20/2.84 6.20/2.84 31: evalstartstart -> evalstartbb1in : A'=meter_1+B, C'=D+1000*meter_1, E'=D+1000*meter_1, F'=meter_1+B, [ 99>=1000+D && B<=D && 1000*meter_1==-900-D ], cost: 8+3*meter_1 6.20/2.84 6.20/2.84 Solved the limit problem by the following transformations: 6.20/2.84 6.20/2.84 Created initial limit problem: 6.20/2.84 6.20/2.84 901+D+1000*meter_1 (+/+!), 1+D-B (+/+!), -899-D-1000*meter_1 (+/+!), 8+3*meter_1 (+), -900-D (+/+!) [not solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 applying transformation rule (C) using substitution {D==-900-1000*meter_1} 6.20/2.84 6.20/2.84 resulting limit problem: 6.20/2.84 6.20/2.84 1 (+/+!), 8+3*meter_1 (+), -899-1000*meter_1-B (+/+!), 1000*meter_1 (+/+!) [not solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 applying transformation rule (B), deleting 1 (+/+!) 6.20/2.84 6.20/2.84 resulting limit problem: 6.20/2.84 6.20/2.84 8+3*meter_1 (+), -899-1000*meter_1-B (+/+!), 1000*meter_1 (+/+!) [not solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 removing all constraints (solved by SMT) 6.20/2.84 6.20/2.84 resulting limit problem: [solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 applying transformation rule (C) using substitution {meter_1==n,B==-1001*n} 6.20/2.84 6.20/2.84 resulting limit problem: 6.20/2.84 6.20/2.84 [solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Solved the limit problem by the following transformations: 6.20/2.84 6.20/2.84 Created initial limit problem: 6.20/2.84 6.20/2.84 901+D+1000*meter_1 (+/+!), 1+D-B (+/+!), -899-D-1000*meter_1 (+/+!), 8+3*meter_1 (+), -900-D (+/+!) [not solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 applying transformation rule (C) using substitution {D==-900-1000*meter_1} 6.20/2.84 6.20/2.84 resulting limit problem: 6.20/2.84 6.20/2.84 1 (+/+!), 8+3*meter_1 (+), -899-1000*meter_1-B (+/+!), 1000*meter_1 (+/+!) [not solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 applying transformation rule (B), deleting 1 (+/+!) 6.20/2.84 6.20/2.84 resulting limit problem: 6.20/2.84 6.20/2.84 8+3*meter_1 (+), -899-1000*meter_1-B (+/+!), 1000*meter_1 (+/+!) [not solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 removing all constraints (solved by SMT) 6.20/2.84 6.20/2.84 resulting limit problem: [solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 applying transformation rule (C) using substitution {meter_1==n,B==-1001*n} 6.20/2.84 6.20/2.84 resulting limit problem: 6.20/2.84 6.20/2.84 [solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Solution: 6.20/2.84 6.20/2.84 D / -900-1000*n 6.20/2.84 6.20/2.84 meter_1 / n 6.20/2.84 6.20/2.84 B / -1001*n 6.20/2.84 6.20/2.84 Resulting cost 8+3*n has complexity: Poly(n^1) 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Found new complexity Poly(n^1). 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Computing asymptotic complexity for rule 32 6.20/2.84 6.20/2.84 Simplified the guard: 6.20/2.84 6.20/2.84 32: evalstartstart -> evalstartbb1in : A'=k+B, C'=1000*k+D, E'=1000*k+D, F'=k+B, [ k>0 && 0>=k+B && 99>=1000*k+D ], cost: 8+3*k 6.20/2.84 6.20/2.84 Solved the limit problem by the following transformations: 6.20/2.84 6.20/2.84 Created initial limit problem: 6.20/2.84 6.20/2.84 100-1000*k-D (+/+!), 1-k-B (+/+!), k (+/+!), 8+3*k (+) [not solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 removing all constraints (solved by SMT) 6.20/2.84 6.20/2.84 resulting limit problem: [solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 applying transformation rule (C) using substitution {k==n,D==-1000*n,B==-n} 6.20/2.84 6.20/2.84 resulting limit problem: 6.20/2.84 6.20/2.84 [solved] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Solution: 6.20/2.84 6.20/2.84 k / n 6.20/2.84 6.20/2.84 D / -1000*n 6.20/2.84 6.20/2.84 B / -n 6.20/2.84 6.20/2.84 Resulting cost 8+3*n has complexity: Poly(n^1) 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 Obtained the following overall complexity (w.r.t. the length of the input n): 6.20/2.84 6.20/2.84 Complexity: Poly(n^1) 6.20/2.84 6.20/2.84 Cpx degree: 1 6.20/2.84 6.20/2.84 Solved cost: 8+3*n 6.20/2.84 6.20/2.84 Rule cost: 8+3*meter_1 6.20/2.84 6.20/2.84 Rule guard: [ 99>=1000+D && B<=D && 1000*meter_1==-900-D ] 6.20/2.84 6.20/2.84 6.20/2.84 6.20/2.84 WORST_CASE(Omega(n^1),?) 6.20/2.84 6.20/2.84 6.20/2.84 ---------------------------------------- 6.20/2.84 6.20/2.84 (4) 6.20/2.84 BOUNDS(n^1, INF) 6.20/2.86 EOF