3.03/2.29 WORST_CASE(?, O(n^1)) 3.03/2.30 proof of /export/starexec/sandbox/output/output_files/bench.koat 3.03/2.30 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.03/2.30 3.03/2.30 3.03/2.30 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 3.03/2.30 3.03/2.30 (0) CpxIntTrs 3.03/2.30 (1) Koat Proof [FINISHED, 1083 ms] 3.03/2.30 (2) BOUNDS(1, n^1) 3.03/2.30 3.03/2.30 3.03/2.30 ---------------------------------------- 3.03/2.30 3.03/2.30 (0) 3.03/2.30 Obligation: 3.03/2.30 Complexity Int TRS consisting of the following rules: 3.03/2.30 eval_rank2_start(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb0_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: TRUE 3.03/2.30 eval_rank2_bb0_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb1_in(v_1, v_4, v_m, v_m, v_m, v_y.1)) :|: TRUE 3.03/2.30 eval_rank2_bb1_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb2_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: v_x.0 >= 2 3.03/2.30 eval_rank2_bb1_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb6_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: v_x.0 < 2 3.03/2.30 eval_rank2_bb2_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb3_in(v_x.0 - 1, v_4, v_m, v_x.0, v_y.0, v_y.0 + v_x.0 - 1)) :|: TRUE 3.03/2.30 eval_rank2_bb3_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb4_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: v_y.1 >= v_1 3.03/2.30 eval_rank2_bb3_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_.critedge_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: v_y.1 < v_1 3.03/2.30 eval_rank2_bb4_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_3(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: TRUE 3.03/2.30 eval_rank2_3(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_2(eval_nondet_start(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1), eval_rank2_4(v_1, nondef.0, v_m, v_x.0, v_y.0, v_y.1)) :|: TRUE 3.03/2.30 eval_rank2_4(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb5_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: v_4 > 0 3.03/2.30 eval_rank2_4(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_.critedge_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: v_4 <= 0 3.03/2.30 eval_rank2_bb5_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb3_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1 - 1)) :|: TRUE 3.03/2.30 eval_rank2_.critedge_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb1_in(v_1, v_4, v_m, v_1 - 1, v_y.1 - v_1 + 1, v_y.1)) :|: TRUE 3.03/2.30 eval_rank2_bb6_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_stop(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: TRUE 3.03/2.30 3.03/2.30 The start-symbols are:[eval_rank2_start_6] 3.03/2.30 3.03/2.30 3.03/2.30 ---------------------------------------- 3.03/2.30 3.03/2.30 (1) Koat Proof (FINISHED) 3.03/2.30 YES(?, 113*ar_1 + 6) 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 Initial complexity problem: 3.03/2.30 3.03/2.30 1: T: 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_1, ar_1, ar_1, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= 2 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 1 >= ar_0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_0 - 1, ar_2 + ar_0 - 1, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 >= ar_3 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_4 + 1 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= 1 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_5 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_3 - 1, ar_1, ar_4 - ar_3 + 1, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.03/2.30 3.03/2.30 start location: koat_start 3.03/2.30 3.03/2.30 leaf cost: 0 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 Repeatedly propagating knowledge in problem 1 produces the following problem: 3.03/2.30 3.03/2.30 2: T: 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 1) evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 1) evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_1, ar_1, ar_1, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= 2 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 1 >= ar_0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_0 - 1, ar_2 + ar_0 - 1, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 >= ar_3 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_4 + 1 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= 1 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_5 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_3 - 1, ar_1, ar_4 - ar_3 + 1, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.03/2.30 3.03/2.30 start location: koat_start 3.03/2.30 3.03/2.30 leaf cost: 0 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 A polynomial rank function with 3.03/2.30 3.03/2.30 Pol(evalrank2start) = 2 3.03/2.30 3.03/2.30 Pol(evalrank2bb0in) = 2 3.03/2.30 3.03/2.30 Pol(evalrank2bb1in) = 2 3.03/2.30 3.03/2.30 Pol(evalrank2bb2in) = 2 3.03/2.30 3.03/2.30 Pol(evalrank2bb6in) = 1 3.03/2.30 3.03/2.30 Pol(evalrank2bb3in) = 2 3.03/2.30 3.03/2.30 Pol(evalrank2bb4in) = 2 3.03/2.30 3.03/2.30 Pol(evalrank2critedgein) = 2 3.03/2.30 3.03/2.30 Pol(evalrank23) = 2 3.03/2.30 3.03/2.30 Pol(evalrank230) = 0 3.03/2.30 3.03/2.30 Pol(evalnondetstart) = 0 3.03/2.30 3.03/2.30 Pol(evalrank231) = 2 3.03/2.30 3.03/2.30 Pol(evalrank24) = 2 3.03/2.30 3.03/2.30 Pol(evalrank2bb5in) = 2 3.03/2.30 3.03/2.30 Pol(evalrank2stop) = 0 3.03/2.30 3.03/2.30 Pol(koat_start) = 2 3.03/2.30 3.03/2.30 orients all transitions weakly and the transitions 3.03/2.30 3.03/2.30 evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 1 >= ar_0 ] 3.03/2.30 3.03/2.30 strictly and produces the following problem: 3.03/2.30 3.03/2.30 3: T: 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 1) evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 1) evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_1, ar_1, ar_1, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= 2 ] 3.03/2.30 3.03/2.30 (Comp: 2, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 1 >= ar_0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_0 - 1, ar_2 + ar_0 - 1, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 >= ar_3 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_4 + 1 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= 1 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_5 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_3 - 1, ar_1, ar_4 - ar_3 + 1, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: 2, Cost: 1) evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.03/2.30 3.03/2.30 start location: koat_start 3.03/2.30 3.03/2.30 leaf cost: 0 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 Applied AI with 'oct' on problem 3 to obtain the following invariants: 3.03/2.30 3.03/2.30 For symbol evalrank23: X_5 - 1 >= 0 /\ X_4 + X_5 - 2 >= 0 /\ -X_4 + X_5 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_4 - 1 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 + 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 3.03/2.30 3.03/2.30 For symbol evalrank230: X_5 - 1 >= 0 /\ X_4 + X_5 - 2 >= 0 /\ -X_4 + X_5 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_4 - 1 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 + 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 3.03/2.30 3.03/2.30 For symbol evalrank231: X_5 - 1 >= 0 /\ X_4 + X_5 - 2 >= 0 /\ -X_4 + X_5 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_4 - 1 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 + 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 3.03/2.30 3.03/2.30 For symbol evalrank24: X_6 - X_7 >= 0 /\ -X_6 + X_7 >= 0 /\ X_5 - 1 >= 0 /\ X_4 + X_5 - 2 >= 0 /\ -X_4 + X_5 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_4 - 1 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 + 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 3.03/2.30 3.03/2.30 For symbol evalrank2bb1in: -X_1 + X_2 >= 0 3.03/2.30 3.03/2.30 For symbol evalrank2bb2in: X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 3.03/2.30 3.03/2.30 For symbol evalrank2bb3in: X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_4 - 1 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 + 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 3.03/2.30 3.03/2.30 For symbol evalrank2bb4in: X_5 - 1 >= 0 /\ X_4 + X_5 - 2 >= 0 /\ -X_4 + X_5 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_4 - 1 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 + 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 3.03/2.30 3.03/2.30 For symbol evalrank2bb5in: X_6 - X_7 >= 0 /\ X_7 - 1 >= 0 /\ X_6 + X_7 - 2 >= 0 /\ -X_6 + X_7 >= 0 /\ X_5 + X_7 - 2 >= 0 /\ X_4 + X_7 - 2 >= 0 /\ X_2 + X_7 - 3 >= 0 /\ X_1 + X_7 - 3 >= 0 /\ X_6 - 1 >= 0 /\ X_5 + X_6 - 2 >= 0 /\ X_4 + X_6 - 2 >= 0 /\ X_2 + X_6 - 3 >= 0 /\ X_1 + X_6 - 3 >= 0 /\ X_5 - 1 >= 0 /\ X_4 + X_5 - 2 >= 0 /\ -X_4 + X_5 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ -X_1 + X_5 + 1 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_4 - 1 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 + 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 3.03/2.30 3.03/2.30 For symbol evalrank2bb6in: -X_1 + X_2 >= 0 /\ -X_1 + 1 >= 0 3.03/2.30 3.03/2.30 For symbol evalrank2critedgein: X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_4 - 1 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ -X_1 + X_4 + 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 2 >= 0 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 This yielded the following problem: 3.03/2.30 3.03/2.30 4: T: 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.03/2.30 3.03/2.30 (Comp: 2, Cost: 1) evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_3 - 1, ar_1, ar_4 - ar_3 + 1, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 2 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_3 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 3 >= 0 /\ ar_0 + ar_6 - 3 >= 0 /\ ar_5 - 1 >= 0 /\ ar_4 + ar_5 - 2 >= 0 /\ ar_3 + ar_5 - 2 >= 0 /\ ar_1 + ar_5 - 3 >= 0 /\ ar_0 + ar_5 - 3 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ 0 >= ar_5 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_5 >= 1 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_3 >= ar_4 + 1 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 >= ar_3 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_0 - 1, ar_2 + ar_0 - 1, ar_5, ar_6)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 2, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 ] 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 1) evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_1, ar_1, ar_1, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 1) evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 start location: koat_start 3.03/2.30 3.03/2.30 leaf cost: 0 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 A polynomial rank function with 3.03/2.30 3.03/2.30 Pol(koat_start) = 3*V_2 3.03/2.30 3.03/2.30 Pol(evalrank2start) = 3*V_2 3.03/2.30 3.03/2.30 Pol(evalrank2bb6in) = 3*V_1 3.03/2.30 3.03/2.30 Pol(evalrank2stop) = 3*V_1 3.03/2.30 3.03/2.30 Pol(evalrank2critedgein) = 3*V_4 - 1 3.03/2.30 3.03/2.30 Pol(evalrank2bb1in) = 3*V_1 3.03/2.30 3.03/2.30 Pol(evalrank2bb5in) = 3*V_4 + 1 3.03/2.30 3.03/2.30 Pol(evalrank2bb3in) = V_1 + 2*V_4 3.03/2.30 3.03/2.30 Pol(evalrank24) = 3*V_4 + 1 3.03/2.30 3.03/2.30 Pol(evalrank23) = 3*V_4 + 1 3.03/2.30 3.03/2.30 Pol(evalrank230) = 0 3.03/2.30 3.03/2.30 Pol(evalrank231) = 3*V_4 + 1 3.03/2.30 3.03/2.30 Pol(evalnondetstart) = 0 3.03/2.30 3.03/2.30 Pol(evalrank2bb4in) = V_1 + 2*V_4 3.03/2.30 3.03/2.30 Pol(evalrank2bb2in) = 3*V_1 - 1 3.03/2.30 3.03/2.30 Pol(evalrank2bb0in) = 3*V_2 3.03/2.30 3.03/2.30 orients all transitions weakly and the transitions 3.03/2.30 3.03/2.30 evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_3 - 1, ar_1, ar_4 - ar_3 + 1, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_3 >= ar_4 + 1 ] 3.03/2.30 3.03/2.30 evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_0 - 1, ar_2 + ar_0 - 1, ar_5, ar_6)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 ] 3.03/2.30 3.03/2.30 evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ 0 >= ar_5 ] 3.03/2.30 3.03/2.30 strictly and produces the following problem: 3.03/2.30 3.03/2.30 5: T: 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.03/2.30 3.03/2.30 (Comp: 2, Cost: 1) evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 3*ar_1, Cost: 1) evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_3 - 1, ar_1, ar_4 - ar_3 + 1, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 2 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_3 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 3 >= 0 /\ ar_0 + ar_6 - 3 >= 0 /\ ar_5 - 1 >= 0 /\ ar_4 + ar_5 - 2 >= 0 /\ ar_3 + ar_5 - 2 >= 0 /\ ar_1 + ar_5 - 3 >= 0 /\ ar_0 + ar_5 - 3 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 3*ar_1, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ 0 >= ar_5 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_5 >= 1 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 3*ar_1, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_3 >= ar_4 + 1 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 >= ar_3 ] 3.03/2.30 3.03/2.30 (Comp: 3*ar_1, Cost: 1) evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_0 - 1, ar_2 + ar_0 - 1, ar_5, ar_6)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 2, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 ] 3.03/2.30 3.03/2.30 (Comp: 3*ar_1, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 ] 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 1) evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_1, ar_1, ar_1, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 1) evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 start location: koat_start 3.03/2.30 3.03/2.30 leaf cost: 0 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 A polynomial rank function with 3.03/2.30 3.03/2.30 Pol(koat_start) = 14*V_2 3.03/2.30 3.03/2.30 Pol(evalrank2start) = 14*V_2 - 7 3.03/2.30 3.03/2.30 Pol(evalrank2bb6in) = 7*V_1 + 7*V_3 - 7 3.03/2.30 3.03/2.30 Pol(evalrank2stop) = 7*V_1 + 7*V_3 - 7 3.03/2.30 3.03/2.30 Pol(evalrank2critedgein) = 7*V_5 - 5 3.03/2.30 3.03/2.30 Pol(evalrank2bb1in) = 7*V_1 + 7*V_3 - 7 3.03/2.30 3.03/2.30 Pol(evalrank2bb5in) = 7*V_5 - 6 3.03/2.30 3.03/2.30 Pol(evalrank2bb3in) = 7*V_5 3.03/2.30 3.03/2.30 Pol(evalrank24) = 7*V_5 - 5 3.03/2.30 3.03/2.30 Pol(evalrank23) = 7*V_5 - 2 3.03/2.30 3.03/2.30 Pol(evalrank230) = 1 3.03/2.30 3.03/2.30 Pol(evalrank231) = 7*V_5 - 4 3.03/2.30 3.03/2.30 Pol(evalnondetstart) = 0 3.03/2.30 3.03/2.30 Pol(evalrank2bb4in) = 7*V_5 - 1 3.03/2.30 3.03/2.30 Pol(evalrank2bb2in) = 7*V_1 + 7*V_3 - 7 3.03/2.30 3.03/2.30 Pol(evalrank2bb0in) = 14*V_2 - 7 3.03/2.30 3.03/2.30 orients all transitions weakly and the transitions 3.03/2.30 3.03/2.30 evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 2 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_3 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 3 >= 0 /\ ar_0 + ar_6 - 3 >= 0 /\ ar_5 - 1 >= 0 /\ ar_4 + ar_5 - 2 >= 0 /\ ar_3 + ar_5 - 2 >= 0 /\ ar_1 + ar_5 - 3 >= 0 /\ ar_0 + ar_5 - 3 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 >= ar_3 ] 3.03/2.30 3.03/2.30 evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_5 >= 1 ] 3.03/2.30 3.03/2.30 evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 strictly and produces the following problem: 3.03/2.30 3.03/2.30 6: T: 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.03/2.30 3.03/2.30 (Comp: 2, Cost: 1) evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 3*ar_1, Cost: 1) evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_3 - 1, ar_1, ar_4 - ar_3 + 1, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 14*ar_1, Cost: 1) evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ ar_6 - 1 >= 0 /\ ar_5 + ar_6 - 2 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 + ar_6 - 2 >= 0 /\ ar_3 + ar_6 - 2 >= 0 /\ ar_1 + ar_6 - 3 >= 0 /\ ar_0 + ar_6 - 3 >= 0 /\ ar_5 - 1 >= 0 /\ ar_4 + ar_5 - 2 >= 0 /\ ar_3 + ar_5 - 2 >= 0 /\ ar_1 + ar_5 - 3 >= 0 /\ ar_0 + ar_5 - 3 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 3*ar_1, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ 0 >= ar_5 ] 3.03/2.30 3.03/2.30 (Comp: 14*ar_1, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 - ar_6 >= 0 /\ -ar_5 + ar_6 >= 0 /\ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_5 >= 1 ] 3.03/2.30 3.03/2.30 (Comp: 14*ar_1, Cost: 1) evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 14*ar_1, Cost: 1) evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 14*ar_1, Cost: 1) evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 14*ar_1, Cost: 1) evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 - 1 >= 0 /\ ar_3 + ar_4 - 2 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_1 + ar_4 - 3 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ -ar_0 + ar_4 + 1 >= 0 /\ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 3*ar_1, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_3 >= ar_4 + 1 ] 3.03/2.30 3.03/2.30 (Comp: 14*ar_1, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_0 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 3 >= 0 /\ -ar_0 + ar_3 + 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 /\ ar_4 >= ar_3 ] 3.03/2.30 3.03/2.30 (Comp: 3*ar_1, Cost: 1) evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_0 - 1, ar_2 + ar_0 - 1, ar_5, ar_6)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 2 >= 0 ] 3.03/2.30 3.03/2.30 (Comp: 2, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ 1 >= ar_0 ] 3.03/2.30 3.03/2.30 (Comp: 3*ar_1, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 2 ] 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 1) evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_1, ar_1, ar_1, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 1) evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 start location: koat_start 3.03/2.30 3.03/2.30 leaf cost: 0 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 Complexity upper bound 113*ar_1 + 6 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 Time: 1.029 sec (SMT: 0.775 sec) 3.03/2.30 3.03/2.30 3.03/2.30 ---------------------------------------- 3.03/2.30 3.03/2.30 (2) 3.03/2.30 BOUNDS(1, n^1) 3.15/2.33 EOF