/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 178 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_t07_start(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb0_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y)) :|: TRUE eval_t07_bb0_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb1_in(v_x, v_y, v_.1, v_.2, v_x, v_y)) :|: TRUE eval_t07_bb1_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb2_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y)) :|: v_.0 > 0 eval_t07_bb1_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb3_in(v_.0, v_.01, v_.01, v_.2, v_x, v_y)) :|: v_.0 <= 0 eval_t07_bb2_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb1_in(v_.0 - 1, v_.01 + 2, v_.1, v_.2, v_x, v_y)) :|: TRUE eval_t07_bb3_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb4_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y)) :|: v_.1 > 0 eval_t07_bb3_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb5_in(v_.0, v_.01, v_.1, v_.1, v_x, v_y)) :|: v_.1 <= 0 eval_t07_bb4_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb3_in(v_.0, v_.01, v_.1 - 1, v_.2, v_x, v_y)) :|: TRUE eval_t07_bb5_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb6_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y)) :|: v_.2 > 0 eval_t07_bb5_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb7_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y)) :|: v_.2 <= 0 eval_t07_bb6_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_bb5_in(v_.0, v_.01, v_.1, v_.2 - 1, v_x, v_y)) :|: TRUE eval_t07_bb7_in(v_.0, v_.01, v_.1, v_.2, v_x, v_y) -> Com_1(eval_t07_stop(v_.0, v_.01, v_.1, v_.2, v_x, v_y)) :|: TRUE The start-symbols are:[eval_t07_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 26*ar_1 + 24*ar_3 + 18) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] (Comp: ?, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) (Comp: ?, Cost: 1) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 1 ] (Comp: ?, Cost: 1) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ] (Comp: ?, Cost: 1) evalt07bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - 1)) (Comp: ?, Cost: 1) evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 1 ] evalt07bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - 1)) We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ] (Comp: ?, Cost: 1) evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] (Comp: ?, Cost: 1) evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] (Comp: ?, Cost: 1) evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ] (Comp: ?, Cost: 1) evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] (Comp: ?, Cost: 1) evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] (Comp: 1, Cost: 1) evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalt07bb7in) = 1 Pol(evalt07stop) = 0 Pol(evalt07bb5in) = 2 Pol(evalt07bb4in) = 3 Pol(evalt07bb3in) = 3 Pol(evalt07bb2in) = 4 Pol(evalt07bb1in) = 4 Pol(evalt07bb0in) = 4 Pol(evalt07start) = 4 Pol(koat_start) = 4 orients all transitions weakly and the transitions evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ] evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ] evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ] strictly and produces the following problem: 4: T: (Comp: 4, Cost: 1) evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 4, Cost: 1) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ] (Comp: ?, Cost: 1) evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) (Comp: 4, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] (Comp: ?, Cost: 1) evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5)) (Comp: 4, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] (Comp: 1, Cost: 1) evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalt07bb7in) = V_1 Pol(evalt07stop) = V_1 Pol(evalt07bb5in) = V_1 Pol(evalt07bb4in) = V_1 Pol(evalt07bb3in) = V_1 Pol(evalt07bb2in) = V_1 - 1 Pol(evalt07bb1in) = V_1 Pol(evalt07bb0in) = V_2 Pol(evalt07start) = V_2 Pol(koat_start) = V_2 orients all transitions weakly and the transition evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] strictly and produces the following problem: 5: T: (Comp: 4, Cost: 1) evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 4, Cost: 1) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ] (Comp: ?, Cost: 1) evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) (Comp: 4, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] (Comp: ?, Cost: 1) evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5)) (Comp: 4, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ] (Comp: ar_1, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] (Comp: 1, Cost: 1) evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (Comp: 4, Cost: 1) evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 4, Cost: 1) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ] (Comp: ?, Cost: 1) evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) (Comp: 4, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ] (Comp: ?, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] (Comp: ar_1, Cost: 1) evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5)) (Comp: 4, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ] (Comp: ar_1, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] (Comp: 1, Cost: 1) evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalt07bb4in) = V_5 - 1 Pol(evalt07bb3in) = V_5 and size complexities S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-3) = ar_3 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-4) = ar_4 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-5) = ar_5 S("evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-0) = ar_0 S("evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-1) = ar_1 S("evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-2) = ar_2 S("evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-3) = ar_3 S("evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-4) = ar_4 S("evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-5) = ar_5 S("evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))", 0-0) = ar_1 S("evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))", 0-1) = ar_1 S("evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))", 0-2) = ar_3 S("evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))", 0-3) = ar_3 S("evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))", 0-4) = ar_4 S("evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5))", 0-5) = ar_5 S("evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]", 0-0) = 2*ar_1 S("evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]", 0-1) = ar_1 S("evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]", 0-2) = 3*ar_1 + 3*ar_3 S("evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]", 0-3) = ar_3 S("evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]", 0-4) = ar_4 S("evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ]", 0-5) = ar_5 S("evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ]", 0-0) = 2*ar_1 S("evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ]", 0-1) = ar_1 S("evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ]", 0-2) = 3*ar_1 + 3*ar_3 S("evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ]", 0-3) = ar_3 S("evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ]", 0-4) = 3*ar_1 + 3*ar_3 S("evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ]", 0-5) = ar_5 S("evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5))", 0-0) = 2*ar_1 S("evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5))", 0-1) = ar_1 S("evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5))", 0-2) = 3*ar_1 + 3*ar_3 S("evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5))", 0-3) = ar_3 S("evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5))", 0-4) = ar_4 S("evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5))", 0-5) = ar_5 S("evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-0) = 2*ar_1 S("evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-1) = ar_1 S("evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-2) = 3*ar_1 + 3*ar_3 S("evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-3) = ar_3 S("evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-4) = ? S("evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-5) = ar_5 S("evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ]", 0-0) = 2*ar_1 S("evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ]", 0-1) = ar_1 S("evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ]", 0-2) = 3*ar_1 + 3*ar_3 S("evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ]", 0-3) = ar_3 S("evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ]", 0-4) = ? S("evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ]", 0-5) = ? S("evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5))", 0-0) = 2*ar_1 S("evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5))", 0-1) = ar_1 S("evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5))", 0-2) = 3*ar_1 + 3*ar_3 S("evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5))", 0-3) = ar_3 S("evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5))", 0-4) = ? S("evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5))", 0-5) = ar_5 S("evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ]", 0-0) = 2*ar_1 S("evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ]", 0-1) = ar_1 S("evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ]", 0-2) = 3*ar_1 + 3*ar_3 S("evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ]", 0-3) = ar_3 S("evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ]", 0-4) = ? S("evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ]", 0-5) = ? S("evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-0) = 2*ar_1 S("evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-1) = ar_1 S("evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-2) = 3*ar_1 + 3*ar_3 S("evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-3) = ar_3 S("evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-4) = ? S("evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))", 0-5) = ? orients the transitions evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] weakly and the transition evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] strictly and produces the following problem: 7: T: (Comp: 4, Cost: 1) evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 4, Cost: 1) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ] (Comp: ?, Cost: 1) evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) (Comp: 4, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ] (Comp: 12*ar_1 + 12*ar_3, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] (Comp: ar_1, Cost: 1) evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5)) (Comp: 4, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ] (Comp: ar_1, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] (Comp: 1, Cost: 1) evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 7 produces the following problem: 8: T: (Comp: 4, Cost: 1) evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 4, Cost: 1) evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_5 ] (Comp: 12*ar_1 + 12*ar_3, Cost: 1) evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) (Comp: 4, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) [ 0 >= ar_4 ] (Comp: 12*ar_1 + 12*ar_3, Cost: 1) evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] (Comp: ar_1, Cost: 1) evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_0 - 1, ar_1, ar_2 + 2, ar_3, ar_4, ar_5)) (Comp: 4, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb3in(ar_0, ar_1, ar_2, ar_3, ar_2, ar_5)) [ 0 >= ar_0 ] (Comp: ar_1, Cost: 1) evalt07bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 ] (Comp: 1, Cost: 1) evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt07start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 26*ar_1 + 24*ar_3 + 18 Time: 0.147 sec (SMT: 0.111 sec) ---------------------------------------- (2) BOUNDS(1, n^1)