5.17/2.43 WORST_CASE(Omega(n^1), O(n^1)) 5.17/2.45 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 5.17/2.45 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.17/2.45 5.17/2.45 5.17/2.45 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 5.17/2.45 5.17/2.45 (0) CpxIntTrs 5.17/2.45 (1) Koat Proof [FINISHED, 223 ms] 5.17/2.45 (2) BOUNDS(1, n^1) 5.17/2.45 (3) Loat Proof [FINISHED, 611 ms] 5.17/2.45 (4) BOUNDS(n^1, INF) 5.17/2.45 5.17/2.45 5.17/2.45 ---------------------------------------- 5.17/2.45 5.17/2.45 (0) 5.17/2.45 Obligation: 5.17/2.45 Complexity Int TRS consisting of the following rules: 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 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 5.17/2.45 5.17/2.45 The start-symbols are:[eval_start_start_6] 5.17/2.45 5.17/2.45 5.17/2.45 ---------------------------------------- 5.17/2.45 5.17/2.45 (1) Koat Proof (FINISHED) 5.17/2.45 YES(?, 26*ar_1 + 24*ar_3 + 23) 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Initial complexity problem: 5.17/2.45 5.17/2.45 1: T: 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 start location: koat_start 5.17/2.45 5.17/2.45 leaf cost: 0 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Testing for reachability in the complexity graph removes the following transitions from problem 1: 5.17/2.45 5.17/2.45 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 ] 5.17/2.45 5.17/2.45 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)) 5.17/2.45 5.17/2.45 We thus obtain the following problem: 5.17/2.45 5.17/2.45 2: T: 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 start location: koat_start 5.17/2.45 5.17/2.45 leaf cost: 0 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Repeatedly propagating knowledge in problem 2 produces the following problem: 5.17/2.45 5.17/2.45 3: T: 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 start location: koat_start 5.17/2.45 5.17/2.45 leaf cost: 0 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 A polynomial rank function with 5.17/2.45 5.17/2.45 Pol(evalstartbb7in) = 1 5.17/2.45 5.17/2.45 Pol(evalstartstop) = 0 5.17/2.45 5.17/2.45 Pol(evalstartbb5in) = 2 5.17/2.45 5.17/2.45 Pol(evalstartbb4in) = 3 5.17/2.45 5.17/2.45 Pol(evalstartbb3in) = 3 5.17/2.45 5.17/2.45 Pol(evalstartbb2in) = 4 5.17/2.45 5.17/2.45 Pol(evalstartbb1in) = 4 5.17/2.45 5.17/2.45 Pol(evalstart4) = 4 5.17/2.45 5.17/2.45 Pol(evalstart3) = 4 5.17/2.45 5.17/2.45 Pol(evalstart2) = 4 5.17/2.45 5.17/2.45 Pol(evalstart1) = 4 5.17/2.45 5.17/2.45 Pol(evalstart0) = 4 5.17/2.45 5.17/2.45 Pol(evalstartbb0in) = 4 5.17/2.45 5.17/2.45 Pol(evalstartstart) = 4 5.17/2.45 5.17/2.45 Pol(koat_start) = 4 5.17/2.45 5.17/2.45 orients all transitions weakly and the transitions 5.17/2.45 5.17/2.45 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)) 5.17/2.45 5.17/2.45 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 ] 5.17/2.45 5.17/2.45 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 ] 5.17/2.45 5.17/2.45 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 ] 5.17/2.45 5.17/2.45 strictly and produces the following problem: 5.17/2.45 5.17/2.45 4: T: 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 start location: koat_start 5.17/2.45 5.17/2.45 leaf cost: 0 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 A polynomial rank function with 5.17/2.45 5.17/2.45 Pol(evalstartbb7in) = V_1 5.17/2.45 5.17/2.45 Pol(evalstartstop) = V_1 5.17/2.45 5.17/2.45 Pol(evalstartbb5in) = V_1 5.17/2.45 5.17/2.45 Pol(evalstartbb4in) = V_1 5.17/2.45 5.17/2.45 Pol(evalstartbb3in) = V_1 5.17/2.45 5.17/2.45 Pol(evalstartbb2in) = V_1 - 1 5.17/2.45 5.17/2.45 Pol(evalstartbb1in) = V_1 5.17/2.45 5.17/2.45 Pol(evalstart4) = V_2 5.17/2.45 5.17/2.45 Pol(evalstart3) = V_2 5.17/2.45 5.17/2.45 Pol(evalstart2) = V_2 5.17/2.45 5.17/2.45 Pol(evalstart1) = V_2 5.17/2.45 5.17/2.45 Pol(evalstart0) = V_2 5.17/2.45 5.17/2.45 Pol(evalstartbb0in) = V_2 5.17/2.45 5.17/2.45 Pol(evalstartstart) = V_2 5.17/2.45 5.17/2.45 Pol(koat_start) = V_2 5.17/2.45 5.17/2.45 orients all transitions weakly and the transition 5.17/2.45 5.17/2.45 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 ] 5.17/2.45 5.17/2.45 strictly and produces the following problem: 5.17/2.45 5.17/2.45 5: T: 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 start location: koat_start 5.17/2.45 5.17/2.45 leaf cost: 0 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Repeatedly propagating knowledge in problem 5 produces the following problem: 5.17/2.45 5.17/2.45 6: T: 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 start location: koat_start 5.17/2.45 5.17/2.45 leaf cost: 0 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 A polynomial rank function with 5.17/2.45 5.17/2.45 Pol(evalstartbb4in) = V_5 - 1 5.17/2.45 5.17/2.45 Pol(evalstartbb3in) = V_5 5.17/2.45 5.17/2.45 and size complexities 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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) = ? 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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) = ? 5.17/2.45 5.17/2.45 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) = ? 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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) = ? 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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) = ? 5.17/2.45 5.17/2.45 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) = ? 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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 5.17/2.45 5.17/2.45 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) = ? 5.17/2.45 5.17/2.45 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) = ? 5.17/2.45 5.17/2.45 orients the transitions 5.17/2.45 5.17/2.45 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)) 5.17/2.45 5.17/2.45 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 ] 5.17/2.45 5.17/2.45 weakly and the transition 5.17/2.45 5.17/2.45 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 ] 5.17/2.45 5.17/2.45 strictly and produces the following problem: 5.17/2.45 5.17/2.45 7: T: 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 start location: koat_start 5.17/2.45 5.17/2.45 leaf cost: 0 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Repeatedly propagating knowledge in problem 7 produces the following problem: 5.17/2.45 5.17/2.45 8: T: 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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)) 5.17/2.45 5.17/2.45 (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 ] 5.17/2.45 5.17/2.45 start location: koat_start 5.17/2.45 5.17/2.45 leaf cost: 0 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Complexity upper bound 26*ar_1 + 24*ar_3 + 23 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Time: 0.236 sec (SMT: 0.169 sec) 5.17/2.45 5.17/2.45 5.17/2.45 ---------------------------------------- 5.17/2.45 5.17/2.45 (2) 5.17/2.45 BOUNDS(1, n^1) 5.17/2.45 5.17/2.45 ---------------------------------------- 5.17/2.45 5.17/2.45 (3) Loat Proof (FINISHED) 5.17/2.45 5.17/2.45 5.17/2.45 ### Pre-processing the ITS problem ### 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Initial linear ITS problem 5.17/2.45 5.17/2.45 Start location: evalstartstart 5.17/2.45 5.17/2.45 0: evalstartstart -> evalstartbb0in : [], cost: 1 5.17/2.45 5.17/2.45 1: evalstartbb0in -> evalstart0 : [], cost: 1 5.17/2.45 5.17/2.45 2: evalstart0 -> evalstart1 : [], cost: 1 5.17/2.45 5.17/2.45 3: evalstart1 -> evalstart2 : [], cost: 1 5.17/2.45 5.17/2.45 4: evalstart2 -> evalstart3 : [], cost: 1 5.17/2.45 5.17/2.45 5: evalstart3 -> evalstart4 : [], cost: 1 5.17/2.45 5.17/2.45 6: evalstart4 -> evalstartbb1in : A'=B, C'=D, [], cost: 1 5.17/2.45 5.17/2.45 7: evalstartbb1in -> evalstartbb2in : [ A>=1 ], cost: 1 5.17/2.45 5.17/2.45 8: evalstartbb1in -> evalstartbb3in : E'=C, [ 0>=A ], cost: 1 5.17/2.45 5.17/2.45 9: evalstartbb2in -> evalstartbb1in : A'=-1+A, C'=2+C, [], cost: 1 5.17/2.45 5.17/2.45 10: evalstartbb3in -> evalstartbb4in : [ E>=1 ], cost: 1 5.17/2.45 5.17/2.45 11: evalstartbb3in -> evalstartbb5in : F'=E, [ 0>=E ], cost: 1 5.17/2.45 5.17/2.45 12: evalstartbb4in -> evalstartbb3in : E'=-1+E, [], cost: 1 5.17/2.45 5.17/2.45 13: evalstartbb5in -> evalstartbb6in : [ F>=1 ], cost: 1 5.17/2.45 5.17/2.45 14: evalstartbb5in -> evalstartbb7in : [ 0>=F ], cost: 1 5.17/2.45 5.17/2.45 15: evalstartbb6in -> evalstartbb5in : F'=-1+F, [], cost: 1 5.17/2.45 5.17/2.45 16: evalstartbb7in -> evalstartstop : [], cost: 1 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Removed unreachable and leaf rules: 5.17/2.45 5.17/2.45 Start location: evalstartstart 5.17/2.45 5.17/2.45 0: evalstartstart -> evalstartbb0in : [], cost: 1 5.17/2.45 5.17/2.45 1: evalstartbb0in -> evalstart0 : [], cost: 1 5.17/2.45 5.17/2.45 2: evalstart0 -> evalstart1 : [], cost: 1 5.17/2.45 5.17/2.45 3: evalstart1 -> evalstart2 : [], cost: 1 5.17/2.45 5.17/2.45 4: evalstart2 -> evalstart3 : [], cost: 1 5.17/2.45 5.17/2.45 5: evalstart3 -> evalstart4 : [], cost: 1 5.17/2.45 5.17/2.45 6: evalstart4 -> evalstartbb1in : A'=B, C'=D, [], cost: 1 5.17/2.45 5.17/2.45 7: evalstartbb1in -> evalstartbb2in : [ A>=1 ], cost: 1 5.17/2.45 5.17/2.45 8: evalstartbb1in -> evalstartbb3in : E'=C, [ 0>=A ], cost: 1 5.17/2.45 5.17/2.45 9: evalstartbb2in -> evalstartbb1in : A'=-1+A, C'=2+C, [], cost: 1 5.17/2.45 5.17/2.45 10: evalstartbb3in -> evalstartbb4in : [ E>=1 ], cost: 1 5.17/2.45 5.17/2.45 11: evalstartbb3in -> evalstartbb5in : F'=E, [ 0>=E ], cost: 1 5.17/2.45 5.17/2.45 12: evalstartbb4in -> evalstartbb3in : E'=-1+E, [], cost: 1 5.17/2.45 5.17/2.45 13: evalstartbb5in -> evalstartbb6in : [ F>=1 ], cost: 1 5.17/2.45 5.17/2.45 15: evalstartbb6in -> evalstartbb5in : F'=-1+F, [], cost: 1 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 ### Simplification by acceleration and chaining ### 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Eliminated locations (on linear paths): 5.17/2.45 5.17/2.45 Start location: evalstartstart 5.17/2.45 5.17/2.45 22: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 7 5.17/2.45 5.17/2.45 8: evalstartbb1in -> evalstartbb3in : E'=C, [ 0>=A ], cost: 1 5.17/2.45 5.17/2.45 23: evalstartbb1in -> evalstartbb1in : A'=-1+A, C'=2+C, [ A>=1 ], cost: 2 5.17/2.45 5.17/2.45 11: evalstartbb3in -> evalstartbb5in : F'=E, [ 0>=E ], cost: 1 5.17/2.45 5.17/2.45 24: evalstartbb3in -> evalstartbb3in : E'=-1+E, [ E>=1 ], cost: 2 5.17/2.45 5.17/2.45 25: evalstartbb5in -> evalstartbb5in : F'=-1+F, [ F>=1 ], cost: 2 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Accelerating simple loops of location 7. 5.17/2.45 5.17/2.45 Accelerating the following rules: 5.17/2.45 5.17/2.45 23: evalstartbb1in -> evalstartbb1in : A'=-1+A, C'=2+C, [ A>=1 ], cost: 2 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Accelerated rule 23 with metering function A, yielding the new rule 26. 5.17/2.45 5.17/2.45 Removing the simple loops: 23. 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Accelerating simple loops of location 9. 5.17/2.45 5.17/2.45 Accelerating the following rules: 5.17/2.45 5.17/2.45 24: evalstartbb3in -> evalstartbb3in : E'=-1+E, [ E>=1 ], cost: 2 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Accelerated rule 24 with metering function E, yielding the new rule 27. 5.17/2.45 5.17/2.45 Removing the simple loops: 24. 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Accelerating simple loops of location 11. 5.17/2.45 5.17/2.45 Accelerating the following rules: 5.17/2.45 5.17/2.45 25: evalstartbb5in -> evalstartbb5in : F'=-1+F, [ F>=1 ], cost: 2 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Accelerated rule 25 with metering function F, yielding the new rule 28. 5.17/2.45 5.17/2.45 Removing the simple loops: 25. 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Accelerated all simple loops using metering functions (where possible): 5.17/2.45 5.17/2.45 Start location: evalstartstart 5.17/2.45 5.17/2.45 22: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 7 5.17/2.45 5.17/2.45 8: evalstartbb1in -> evalstartbb3in : E'=C, [ 0>=A ], cost: 1 5.17/2.45 5.17/2.45 26: evalstartbb1in -> evalstartbb1in : A'=0, C'=C+2*A, [ A>=1 ], cost: 2*A 5.17/2.45 5.17/2.45 11: evalstartbb3in -> evalstartbb5in : F'=E, [ 0>=E ], cost: 1 5.17/2.45 5.17/2.45 27: evalstartbb3in -> evalstartbb3in : E'=0, [ E>=1 ], cost: 2*E 5.17/2.45 5.17/2.45 28: evalstartbb5in -> evalstartbb5in : F'=0, [ F>=1 ], cost: 2*F 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Chained accelerated rules (with incoming rules): 5.17/2.45 5.17/2.45 Start location: evalstartstart 5.17/2.45 5.17/2.45 22: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 7 5.17/2.45 5.17/2.45 29: evalstartstart -> evalstartbb1in : A'=0, C'=D+2*B, [ B>=1 ], cost: 7+2*B 5.17/2.45 5.17/2.45 8: evalstartbb1in -> evalstartbb3in : E'=C, [ 0>=A ], cost: 1 5.17/2.45 5.17/2.45 30: evalstartbb1in -> evalstartbb3in : E'=0, [ 0>=A && C>=1 ], cost: 1+2*C 5.17/2.45 5.17/2.45 11: evalstartbb3in -> evalstartbb5in : F'=E, [ 0>=E ], cost: 1 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Removed unreachable locations (and leaf rules with constant cost): 5.17/2.45 5.17/2.45 Start location: evalstartstart 5.17/2.45 5.17/2.45 22: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 7 5.17/2.45 5.17/2.45 29: evalstartstart -> evalstartbb1in : A'=0, C'=D+2*B, [ B>=1 ], cost: 7+2*B 5.17/2.45 5.17/2.45 30: evalstartbb1in -> evalstartbb3in : E'=0, [ 0>=A && C>=1 ], cost: 1+2*C 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Eliminated locations (on tree-shaped paths): 5.17/2.45 5.17/2.45 Start location: evalstartstart 5.17/2.45 5.17/2.45 31: evalstartstart -> evalstartbb3in : A'=B, C'=D, E'=0, [ 0>=B && D>=1 ], cost: 8+2*D 5.17/2.45 5.17/2.45 32: evalstartstart -> evalstartbb3in : A'=0, C'=D+2*B, E'=0, [ B>=1 && D+2*B>=1 ], cost: 8+2*D+6*B 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 ### Computing asymptotic complexity ### 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Fully simplified ITS problem 5.17/2.45 5.17/2.45 Start location: evalstartstart 5.17/2.45 5.17/2.45 31: evalstartstart -> evalstartbb3in : A'=B, C'=D, E'=0, [ 0>=B && D>=1 ], cost: 8+2*D 5.17/2.45 5.17/2.45 32: evalstartstart -> evalstartbb3in : A'=0, C'=D+2*B, E'=0, [ B>=1 && D+2*B>=1 ], cost: 8+2*D+6*B 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Computing asymptotic complexity for rule 31 5.17/2.45 5.17/2.45 Solved the limit problem by the following transformations: 5.17/2.45 5.17/2.45 Created initial limit problem: 5.17/2.45 5.17/2.45 D (+/+!), 1-B (+/+!), 8+2*D (+) [not solved] 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 removing all constraints (solved by SMT) 5.17/2.45 5.17/2.45 resulting limit problem: [solved] 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 applying transformation rule (C) using substitution {D==n,B==0} 5.17/2.45 5.17/2.45 resulting limit problem: 5.17/2.45 5.17/2.45 [solved] 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Solution: 5.17/2.45 5.17/2.45 D / n 5.17/2.45 5.17/2.45 B / 0 5.17/2.45 5.17/2.45 Resulting cost 8+2*n has complexity: Poly(n^1) 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Found new complexity Poly(n^1). 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 Obtained the following overall complexity (w.r.t. the length of the input n): 5.17/2.45 5.17/2.45 Complexity: Poly(n^1) 5.17/2.45 5.17/2.45 Cpx degree: 1 5.17/2.45 5.17/2.45 Solved cost: 8+2*n 5.17/2.45 5.17/2.45 Rule cost: 8+2*D 5.17/2.45 5.17/2.45 Rule guard: [ 0>=B && D>=1 ] 5.17/2.45 5.17/2.45 5.17/2.45 5.17/2.45 WORST_CASE(Omega(n^1),?) 5.17/2.45 5.17/2.45 5.17/2.45 ---------------------------------------- 5.17/2.45 5.17/2.45 (4) 5.17/2.45 BOUNDS(n^1, INF) 5.39/2.49 EOF