/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^2)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 483 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_perfect1_start(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb0_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: TRUE eval_perfect1_bb0_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_x <= 1 eval_perfect1_bb0_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb1_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_x > 1 eval_perfect1_bb1_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb2_in(v_x, v_x - 1, v_y2.1, v_x)) :|: TRUE eval_perfect1_bb2_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb3_in(v_x, v_y1.0, v_x, v_y3.0)) :|: v_y1.0 > 0 eval_perfect1_bb2_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb6_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y1.0 <= 0 eval_perfect1_bb3_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb4_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y2.1 >= v_y1.0 eval_perfect1_bb3_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb5_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y2.1 < v_y1.0 eval_perfect1_bb4_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb3_in(v_x, v_y1.0, v_y2.1 - v_y1.0, v_y3.0)) :|: TRUE eval_perfect1_bb5_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb2_in(v_x, v_y1.0 - 1, v_y2.1, v_y3.0 - v_y1.0)) :|: v_y2.1 >= 0 && v_y2.1 <= 0 eval_perfect1_bb5_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb2_in(v_x, v_y1.0 - 1, v_y2.1, v_y3.0)) :|: v_y2.1 < 0 eval_perfect1_bb5_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb2_in(v_x, v_y1.0 - 1, v_y2.1, v_y3.0)) :|: v_y2.1 > 0 eval_perfect1_bb6_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y3.0 < 0 eval_perfect1_bb6_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y3.0 > 0 eval_perfect1_bb6_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y3.0 >= 0 && v_y3.0 <= 0 eval_perfect1_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect1_stop(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: TRUE The start-symbols are:[eval_perfect1_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 19*Ar_0 + 8*Ar_0^2 + 30) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: ?, Cost: 1) evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) (Comp: ?, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: ?, Cost: 1) evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) (Comp: ?, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: ?, Cost: 1) evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalperfect1start) = 3 Pol(evalperfect1bb0in) = 3 Pol(evalperfect1bb7in) = 1 Pol(evalperfect1bb1in) = 3 Pol(evalperfect1bb2in) = 3 Pol(evalperfect1bb3in) = 3 Pol(evalperfect1bb6in) = 2 Pol(evalperfect1bb4in) = 3 Pol(evalperfect1bb5in) = 3 Pol(evalperfect1stop) = 0 Pol(koat_start) = 3 orients all transitions weakly and the transitions evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3)) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ] evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] (Comp: 3, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) (Comp: ?, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: 3, Cost: 1) evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalperfect1bb5in) = V_2 - 1 Pol(evalperfect1bb2in) = V_2 Pol(evalperfect1bb4in) = V_2 - 1 Pol(evalperfect1bb3in) = V_2 - 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-0) = Ar_0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-1) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-2) = 0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-3) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-0) = Ar_0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-1) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-2) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-3) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-1) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-2) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-3) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-0) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-1) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-2) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-3) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-1) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-2) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-3) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-0) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-1) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-2) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-3) = 0 S("evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-0) = Ar_0 S("evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-1) = ? S("evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-2) = ? S("evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-3) = ? S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-1) = ? S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-2) = ? S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-3) = ? S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-0) = Ar_0 S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-1) = ? S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-2) = ? S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-3) = ? S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-0) = Ar_0 S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-1) = ? S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-2) = ? S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-3) = ? S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-0) = Ar_0 S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-1) = ? S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-2) = ? S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-3) = Ar_0 S("evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-0) = Ar_0 S("evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-1) = Ar_0 + 1 S("evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-2) = Ar_0 S("evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-3) = Ar_3 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-0) = Ar_0 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-1) = Ar_1 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-2) = Ar_2 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-3) = Ar_3 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-1) = Ar_1 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-2) = Ar_2 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-3) = Ar_3 S("evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] weakly and the transition evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) (Comp: Ar_0 + 1, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] (Comp: 3, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) (Comp: ?, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: 3, Cost: 1) evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalperfect1bb5in) = 1 Pol(evalperfect1bb2in) = 0 Pol(evalperfect1bb4in) = 2 Pol(evalperfect1bb3in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-0) = Ar_0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-1) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-2) = 0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-3) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-0) = Ar_0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-1) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-2) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-3) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-1) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-2) = ? S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-3) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-0) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-1) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-2) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-3) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-1) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-2) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-3) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-0) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-1) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-2) = ? S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-3) = 0 S("evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-0) = Ar_0 S("evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-1) = ? S("evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-2) = ? S("evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-3) = ? S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-1) = ? S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-2) = ? S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-3) = ? S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-0) = Ar_0 S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-1) = ? S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-2) = ? S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-3) = ? S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-0) = Ar_0 S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-1) = ? S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-2) = ? S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-3) = ? S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-0) = Ar_0 S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-1) = ? S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-2) = ? S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-3) = Ar_0 S("evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-0) = Ar_0 S("evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-1) = Ar_0 + 1 S("evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-2) = Ar_0 S("evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-3) = Ar_3 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-0) = Ar_0 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-1) = Ar_1 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-2) = Ar_2 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-3) = Ar_3 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-1) = Ar_1 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-2) = Ar_2 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-3) = Ar_3 S("evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] weakly and the transitions evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) (Comp: Ar_0 + 1, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] (Comp: 3, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) (Comp: 2*Ar_0 + 2, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: 3, Cost: 1) evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 5 to obtain the following invariants: For symbol evalperfect1bb1in: X_1 - 2 >= 0 For symbol evalperfect1bb2in: X_1 - X_3 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 2 >= 0 For symbol evalperfect1bb3in: X_1 - X_4 >= 0 /\ X_1 - X_3 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 2 >= 0 For symbol evalperfect1bb4in: X_1 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ -X_2 + X_4 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ X_1 - X_3 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 2 >= 0 For symbol evalperfect1bb5in: X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 - 2 >= 0 /\ X_1 - X_3 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 2 >= 0 For symbol evalperfect1bb6in: X_1 - X_3 >= 0 /\ -X_2 >= 0 /\ X_1 - X_2 - 2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 2 >= 0 This yielded the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 3, Cost: 1) evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 - 2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_2 = 0 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 - 2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_2 >= 1 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 - 2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 2 >= 0 /\ 0 >= Ar_2 + 1 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 >= 1 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 >= Ar_1 ] (Comp: 3, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 2 >= 0 /\ 0 >= Ar_1 ] (Comp: Ar_0 + 1, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) [ Ar_0 - 2 >= 0 ] (Comp: 1, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalperfect1bb4in) = 2*V_4 Pol(evalperfect1bb3in) = 2*V_2 + 2*V_4 - 1 and size complexities S("evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-1) = Ar_1 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-2) = Ar_2 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-3) = Ar_3 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-0) = Ar_0 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-1) = Ar_1 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-2) = Ar_2 S("evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-3) = Ar_3 S("evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) [ Ar_0 - 2 >= 0 ]", 0-0) = Ar_0 S("evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) [ Ar_0 - 2 >= 0 ]", 0-1) = Ar_0 S("evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) [ Ar_0 - 2 >= 0 ]", 0-2) = Ar_0 S("evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) [ Ar_0 - 2 >= 0 ]", 0-3) = Ar_3 S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0 S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = Ar_0 S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_1 >= 1 ]", 0-2) = 3*Ar_0 + 2*Ar_0^2 S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_1 >= 1 ]", 0-3) = Ar_0 S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_1 ]", 0-0) = Ar_0 S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_1 ]", 0-1) = 0 S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_1 ]", 0-2) = 3*Ar_0 + 2*Ar_0^2 S("evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_1 ]", 0-3) = Ar_0 S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-0) = Ar_0 S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-1) = Ar_0 S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-2) = 3*Ar_0 + 2*Ar_0^2 S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-3) = Ar_0 S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-1) = Ar_0 S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-2) = 3*Ar_0 + 2*Ar_0^2 S("evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-3) = Ar_0 S("evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ -Ar_1 + Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-0) = Ar_0 S("evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ -Ar_1 + Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-1) = Ar_0 S("evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ -Ar_1 + Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-2) = 3*Ar_0 + 2*Ar_0^2 S("evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ -Ar_1 + Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 3 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-3) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 = 0 ]", 0-0) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 = 0 ]", 0-1) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 = 0 ]", 0-2) = 3*Ar_0 + 2*Ar_0^2 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 = 0 ]", 0-3) = 0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_3 + 1 ]", 0-1) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_3 + 1 ]", 0-2) = 3*Ar_0 + 2*Ar_0^2 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_3 + 1 ]", 0-3) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= 1 ]", 0-0) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= 1 ]", 0-1) = Ar_0 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= 1 ]", 0-2) = 3*Ar_0 + 2*Ar_0^2 S("evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= 1 ]", 0-3) = Ar_0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_2 + 1 ]", 0-1) = 0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_2 + 1 ]", 0-2) = 3*Ar_0 + 2*Ar_0^2 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_2 + 1 ]", 0-3) = Ar_0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 >= 1 ]", 0-0) = Ar_0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 >= 1 ]", 0-1) = 0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 >= 1 ]", 0-2) = 3*Ar_0 + 2*Ar_0^2 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 >= 1 ]", 0-3) = Ar_0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 = 0 ]", 0-0) = Ar_0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 = 0 ]", 0-1) = 0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 = 0 ]", 0-2) = 0 S("evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\\ -Ar_1 >= 0 /\\ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 = 0 ]", 0-3) = Ar_0 S("evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 + 3*Ar_0 + 2*Ar_0^2 S("evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_0 + Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ] evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 >= Ar_1 ] weakly and the transitions evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ] evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 >= Ar_1 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 3, Cost: 1) evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 - 2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_2 = 0 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 - 2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_2 >= 1 ] (Comp: 3, Cost: 1) evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 - 2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 2 >= 0 /\ 0 >= Ar_2 + 1 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 >= 1 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 = 0 ] (Comp: 4*Ar_0^2 + 5*Ar_0 + 1, Cost: 1) evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_1 >= Ar_3 + 1 ] (Comp: 4*Ar_0^2 + 5*Ar_0 + 1, Cost: 1) evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 >= Ar_1 ] (Comp: 3, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 2 >= 0 /\ 0 >= Ar_1 ] (Comp: Ar_0 + 1, Cost: 1) evalperfect1bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 - Ar_2 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) [ Ar_0 - 2 >= 0 ] (Comp: 1, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfect1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfect1bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound 19*Ar_0 + 8*Ar_0^2 + 30 Time: 0.473 sec (SMT: 0.388 sec) ---------------------------------------- (2) BOUNDS(1, n^2)