2.17/1.59 WORST_CASE(?, O(n^1)) 2.17/1.60 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.17/1.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.17/1.60 2.17/1.60 2.17/1.60 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.17/1.60 2.17/1.60 (0) CpxIntTrs 2.17/1.60 (1) Koat Proof [FINISHED, 278 ms] 2.17/1.60 (2) BOUNDS(1, n^1) 2.17/1.60 2.17/1.60 2.17/1.60 ---------------------------------------- 2.17/1.60 2.17/1.60 (0) 2.17/1.60 Obligation: 2.17/1.60 Complexity Int TRS consisting of the following rules: 2.17/1.60 eval_t28_start(v_.0, v_.01, v_.1, v_.12, v_x, v_y) -> Com_1(eval_t28_bb0_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y)) :|: TRUE 2.17/1.60 eval_t28_bb0_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y) -> Com_1(eval_t28_bb1_in(v_x, v_y, v_.1, v_.12, v_x, v_y)) :|: TRUE 2.17/1.60 eval_t28_bb1_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y) -> Com_1(eval_t28_bb2_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y)) :|: v_.0 > v_.01 2.17/1.60 eval_t28_bb1_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y) -> Com_1(eval_t28_bb3_in(v_.0, v_.01, v_.1, v_.01, v_x, v_y)) :|: v_.0 <= v_.01 2.17/1.60 eval_t28_bb2_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y) -> Com_1(eval_t28_bb1_in(v_.0 + 999, v_.01 + 1000, v_.1, v_.12, v_x, v_y)) :|: TRUE 2.17/1.60 eval_t28_bb3_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y) -> Com_1(eval_t28_bb4_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y)) :|: v_.12 > 0 2.17/1.60 eval_t28_bb3_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y) -> Com_1(eval_t28_bb5_in(v_.0, v_.01, v_.0, v_.12, v_x, v_y)) :|: v_.12 <= 0 2.17/1.60 eval_t28_bb4_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y) -> Com_1(eval_t28_bb3_in(v_.0, v_.01, v_.1, v_.12 - 1, v_x, v_y)) :|: TRUE 2.17/1.60 eval_t28_bb5_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y) -> Com_1(eval_t28_bb6_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y)) :|: v_.1 < 0 2.17/1.60 eval_t28_bb5_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y) -> Com_1(eval_t28_bb7_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y)) :|: v_.1 >= 0 2.17/1.60 eval_t28_bb6_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y) -> Com_1(eval_t28_bb5_in(v_.0, v_.01, v_.1 + 1, v_.12, v_x, v_y)) :|: TRUE 2.17/1.60 eval_t28_bb7_in(v_.0, v_.01, v_.1, v_.12, v_x, v_y) -> Com_1(eval_t28_stop(v_.0, v_.01, v_.1, v_.12, v_x, v_y)) :|: TRUE 2.17/1.60 2.17/1.60 The start-symbols are:[eval_t28_start_6] 2.17/1.60 2.17/1.60 2.17/1.60 ---------------------------------------- 2.17/1.60 2.17/1.60 (1) Koat Proof (FINISHED) 2.17/1.60 YES(?, 8012*ar_1 + 8010*ar_3 + 18) 2.17/1.60 2.17/1.60 2.17/1.60 2.17/1.60 Initial complexity problem: 2.17/1.60 2.17/1.60 1: T: 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.17/1.60 2.17/1.60 start location: koat_start 2.17/1.60 2.17/1.60 leaf cost: 0 2.17/1.60 2.17/1.60 2.17/1.60 2.17/1.60 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.17/1.60 2.17/1.60 2: T: 2.17/1.60 2.17/1.60 (Comp: 1, Cost: 1) evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 (Comp: 1, Cost: 1) evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.17/1.60 2.17/1.60 start location: koat_start 2.17/1.60 2.17/1.60 leaf cost: 0 2.17/1.60 2.17/1.60 2.17/1.60 2.17/1.60 A polynomial rank function with 2.17/1.60 2.17/1.60 Pol(evalt28start) = 4 2.17/1.60 2.17/1.60 Pol(evalt28bb0in) = 4 2.17/1.60 2.17/1.60 Pol(evalt28bb1in) = 4 2.17/1.60 2.17/1.60 Pol(evalt28bb2in) = 4 2.17/1.60 2.17/1.60 Pol(evalt28bb3in) = 3 2.17/1.60 2.17/1.60 Pol(evalt28bb4in) = 3 2.17/1.60 2.17/1.60 Pol(evalt28bb5in) = 2 2.17/1.60 2.17/1.60 Pol(evalt28bb6in) = 2 2.17/1.60 2.17/1.60 Pol(evalt28bb7in) = 1 2.17/1.60 2.17/1.60 Pol(evalt28stop) = 0 2.17/1.60 2.17/1.60 Pol(koat_start) = 4 2.17/1.60 2.17/1.60 orients all transitions weakly and the transitions 2.17/1.60 2.17/1.60 evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ] 2.17/1.60 2.17/1.60 evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ] 2.17/1.60 2.17/1.60 evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ] 2.17/1.60 2.17/1.60 strictly and produces the following problem: 2.17/1.60 2.17/1.60 3: T: 2.17/1.60 2.17/1.60 (Comp: 1, Cost: 1) evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 (Comp: 1, Cost: 1) evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.17/1.60 2.17/1.60 (Comp: 4, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.17/1.60 2.17/1.60 (Comp: 4, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ] 2.17/1.60 2.17/1.60 (Comp: 4, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ] 2.17/1.60 2.17/1.60 (Comp: ?, Cost: 1) evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) 2.17/1.60 2.17/1.60 (Comp: 4, Cost: 1) evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.60 2.17/1.60 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.17/1.60 2.17/1.60 start location: koat_start 2.17/1.60 2.17/1.60 leaf cost: 0 2.17/1.60 2.17/1.60 2.17/1.60 2.17/1.60 A polynomial rank function with 2.17/1.60 2.17/1.60 Pol(evalt28start) = V_2 - V_4 2.17/1.60 2.17/1.60 Pol(evalt28bb0in) = V_2 - V_4 2.17/1.60 2.17/1.60 Pol(evalt28bb1in) = V_1 - V_3 2.17/1.60 2.17/1.60 Pol(evalt28bb2in) = V_1 - V_3 - 1 2.17/1.60 2.17/1.60 Pol(evalt28bb3in) = V_1 - V_3 2.17/1.60 2.17/1.60 Pol(evalt28bb4in) = V_1 - V_3 2.17/1.60 2.17/1.60 Pol(evalt28bb5in) = 2*V_1 - V_3 - V_6 2.17/1.60 2.17/1.60 Pol(evalt28bb6in) = 2*V_1 - V_3 - V_6 - 1 2.17/1.60 2.17/1.60 Pol(evalt28bb7in) = 2*V_1 - V_3 - V_6 2.17/1.60 2.17/1.60 Pol(evalt28stop) = 2*V_1 - V_3 - V_6 2.17/1.60 2.17/1.60 Pol(koat_start) = V_2 - V_4 2.17/1.61 2.17/1.61 orients all transitions weakly and the transition 2.17/1.61 2.17/1.61 evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.17/1.61 2.17/1.61 strictly and produces the following problem: 2.17/1.61 2.17/1.61 4: T: 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 1) evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 1) evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ar_1 + ar_3, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ] 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ] 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ] 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.17/1.61 2.17/1.61 start location: koat_start 2.17/1.61 2.17/1.61 leaf cost: 0 2.17/1.61 2.17/1.61 2.17/1.61 2.17/1.61 Repeatedly propagating knowledge in problem 4 produces the following problem: 2.17/1.61 2.17/1.61 5: T: 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 1) evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 1) evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ar_1 + ar_3, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ] 2.17/1.61 2.17/1.61 (Comp: ar_1 + ar_3, Cost: 1) evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ] 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ] 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.17/1.61 2.17/1.61 start location: koat_start 2.17/1.61 2.17/1.61 leaf cost: 0 2.17/1.61 2.17/1.61 2.17/1.61 2.17/1.61 A polynomial rank function with 2.17/1.61 2.17/1.61 Pol(evalt28start) = -V_2 2.17/1.61 2.17/1.61 Pol(evalt28bb0in) = -V_2 2.17/1.61 2.17/1.61 Pol(evalt28bb1in) = -V_1 2.17/1.61 2.17/1.61 Pol(evalt28bb2in) = -V_1 2.17/1.61 2.17/1.61 Pol(evalt28bb3in) = -V_1 2.17/1.61 2.17/1.61 Pol(evalt28bb4in) = -V_1 2.17/1.61 2.17/1.61 Pol(evalt28bb5in) = -V_6 2.17/1.61 2.17/1.61 Pol(evalt28bb6in) = -V_6 - 1 2.17/1.61 2.17/1.61 Pol(evalt28bb7in) = -V_6 2.17/1.61 2.17/1.61 Pol(evalt28stop) = -V_6 2.17/1.61 2.17/1.61 Pol(koat_start) = -V_2 2.17/1.61 2.17/1.61 orients all transitions weakly and the transition 2.17/1.61 2.17/1.61 evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ] 2.17/1.61 2.17/1.61 strictly and produces the following problem: 2.17/1.61 2.17/1.61 6: T: 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 1) evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 1) evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ar_1 + ar_3, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ] 2.17/1.61 2.17/1.61 (Comp: ar_1 + ar_3, Cost: 1) evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ] 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ar_1, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ] 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.17/1.61 2.17/1.61 start location: koat_start 2.17/1.61 2.17/1.61 leaf cost: 0 2.17/1.61 2.17/1.61 2.17/1.61 2.17/1.61 Repeatedly propagating knowledge in problem 6 produces the following problem: 2.17/1.61 2.17/1.61 7: T: 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 1) evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 1) evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ar_1 + ar_3, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ] 2.17/1.61 2.17/1.61 (Comp: ar_1 + ar_3, Cost: 1) evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ] 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ar_1, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ] 2.17/1.61 2.17/1.61 (Comp: ar_1, Cost: 1) evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.17/1.61 2.17/1.61 start location: koat_start 2.17/1.61 2.17/1.61 leaf cost: 0 2.17/1.61 2.17/1.61 2.17/1.61 2.17/1.61 A polynomial rank function with 2.17/1.61 2.17/1.61 Pol(evalt28bb4in) = V_5 - 1 2.17/1.61 2.17/1.61 Pol(evalt28bb3in) = V_5 2.17/1.61 2.17/1.61 and size complexities 2.17/1.61 2.17/1.61 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-0) = ar_0 2.17/1.61 2.17/1.61 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-2) = ar_2 2.17/1.61 2.17/1.61 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-4) = ar_4 2.17/1.61 2.17/1.61 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-5) = ar_5 2.17/1.61 2.17/1.61 S("evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-0) = 1000*ar_1 + 1000*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-2) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-4) = ? 2.17/1.61 2.17/1.61 S("evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-5) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1))", 0-0) = 1000*ar_1 + 1000*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1))", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1))", 0-2) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1))", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1))", 0-4) = ? 2.17/1.61 2.17/1.61 S("evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1))", 0-5) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ]", 0-0) = 1000*ar_1 + 1000*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ]", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ]", 0-2) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ]", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ]", 0-4) = ? 2.17/1.61 2.17/1.61 S("evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ]", 0-5) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ]", 0-0) = 1000*ar_1 + 1000*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ]", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ]", 0-2) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ]", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ]", 0-4) = ? 2.17/1.61 2.17/1.61 S("evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ]", 0-5) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5))", 0-0) = 1000*ar_1 + 1000*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5))", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5))", 0-2) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5))", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5))", 0-4) = ? 2.17/1.61 2.17/1.61 S("evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5))", 0-5) = ar_5 2.17/1.61 2.17/1.61 S("evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ]", 0-0) = 1000*ar_1 + 1000*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ]", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ]", 0-2) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ]", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ]", 0-4) = ? 2.17/1.61 2.17/1.61 S("evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ]", 0-5) = 1000*ar_1 + 1000*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-0) = 1000*ar_1 + 1000*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-2) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-4) = ? 2.17/1.61 2.17/1.61 S("evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-5) = ar_5 2.17/1.61 2.17/1.61 S("evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5))", 0-0) = 1000*ar_1 + 1000*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5))", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5))", 0-2) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5))", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5))", 0-4) = ar_4 2.17/1.61 2.17/1.61 S("evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5))", 0-5) = ar_5 2.17/1.61 2.17/1.61 S("evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ]", 0-0) = 1000*ar_1 + 1000*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ]", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ]", 0-2) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ]", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ]", 0-4) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ]", 0-5) = ar_5 2.17/1.61 2.17/1.61 S("evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]", 0-0) = 1000*ar_1 + 1000*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]", 0-2) = 1001*ar_1 + 1001*ar_3 2.17/1.61 2.17/1.61 S("evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]", 0-4) = ar_4 2.17/1.61 2.17/1.61 S("evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ]", 0-5) = ar_5 2.17/1.61 2.17/1.61 S("evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))", 0-0) = ar_1 2.17/1.61 2.17/1.61 S("evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))", 0-2) = ar_3 2.17/1.61 2.17/1.61 S("evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))", 0-4) = ar_4 2.17/1.61 2.17/1.61 S("evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))", 0-5) = ar_5 2.17/1.61 2.17/1.61 S("evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-0) = ar_0 2.17/1.61 2.17/1.61 S("evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-1) = ar_1 2.17/1.61 2.17/1.61 S("evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-2) = ar_2 2.17/1.61 2.17/1.61 S("evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-3) = ar_3 2.17/1.61 2.17/1.61 S("evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-4) = ar_4 2.17/1.61 2.17/1.61 S("evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-5) = ar_5 2.17/1.61 2.17/1.61 orients the transitions 2.17/1.61 2.17/1.61 evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 2.17/1.61 2.17/1.61 evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.17/1.61 2.17/1.61 weakly and the transition 2.17/1.61 2.17/1.61 evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.17/1.61 2.17/1.61 strictly and produces the following problem: 2.17/1.61 2.17/1.61 8: T: 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 1) evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 1) evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ar_1 + ar_3, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ] 2.17/1.61 2.17/1.61 (Comp: ar_1 + ar_3, Cost: 1) evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 4004*ar_1 + 4004*ar_3, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ] 2.17/1.61 2.17/1.61 (Comp: ?, Cost: 1) evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ar_1, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ] 2.17/1.61 2.17/1.61 (Comp: ar_1, Cost: 1) evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.17/1.61 2.17/1.61 start location: koat_start 2.17/1.61 2.17/1.61 leaf cost: 0 2.17/1.61 2.17/1.61 2.17/1.61 2.17/1.61 Repeatedly propagating knowledge in problem 8 produces the following problem: 2.17/1.61 2.17/1.61 9: T: 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 1) evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 1) evalt28bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ar_1 + ar_3, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ ar_2 >= ar_0 ] 2.17/1.61 2.17/1.61 (Comp: ar_1 + ar_3, Cost: 1) evalt28bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb1in(ar_0 + 999, ar_1, ar_2 + 1000, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 4004*ar_1 + 4004*ar_3, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0)) [ 0 >= ar_4 ] 2.17/1.61 2.17/1.61 (Comp: 4004*ar_1 + 4004*ar_3, Cost: 1) evalt28bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 2.17/1.61 2.17/1.61 (Comp: ar_1, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 + 1 ] 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 0 ] 2.17/1.61 2.17/1.61 (Comp: ar_1, Cost: 1) evalt28bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1)) 2.17/1.61 2.17/1.61 (Comp: 4, Cost: 1) evalt28bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.17/1.61 2.17/1.61 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt28start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.17/1.61 2.17/1.61 start location: koat_start 2.17/1.61 2.17/1.61 leaf cost: 0 2.17/1.61 2.17/1.61 2.17/1.61 2.17/1.61 Complexity upper bound 8012*ar_1 + 8010*ar_3 + 18 2.17/1.61 2.17/1.61 2.17/1.61 2.17/1.61 Time: 0.232 sec (SMT: 0.177 sec) 2.17/1.61 2.17/1.61 2.17/1.61 ---------------------------------------- 2.17/1.61 2.17/1.61 (2) 2.17/1.61 BOUNDS(1, n^1) 2.17/1.62 EOF