/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).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_perfect_start(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb0_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: TRUE eval_perfect_bb0_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_x <= 1 eval_perfect_bb0_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb1_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_x > 1 eval_perfect_bb1_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb2_in(v_x, v_x - 1, v_y2.1, v_x)) :|: TRUE eval_perfect_bb2_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb3_in(v_x, v_y1.0, v_x, v_y3.0)) :|: v_y1.0 > 0 eval_perfect_bb2_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb6_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y1.0 <= 0 eval_perfect_bb3_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb4_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y2.1 >= v_y1.0 eval_perfect_bb3_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb5_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y2.1 < v_y1.0 eval_perfect_bb4_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb3_in(v_x, v_y1.0, v_y2.1 - v_y1.0, v_y3.0)) :|: TRUE eval_perfect_bb5_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_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_perfect_bb5_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb2_in(v_x, v_y1.0 - 1, v_y2.1, v_y3.0)) :|: v_y2.1 < 0 eval_perfect_bb5_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb2_in(v_x, v_y1.0 - 1, v_y2.1, v_y3.0)) :|: v_y2.1 > 0 eval_perfect_bb6_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y3.0 < 0 eval_perfect_bb6_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y3.0 > 0 eval_perfect_bb6_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y3.0 >= 0 && v_y3.0 <= 0 eval_perfect_bb7_in(v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_perfect_stop(v_x, v_y1.0, v_y2.1, v_y3.0)) :|: TRUE The start-symbols are:[eval_perfect_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 13*Ar_0 + 4*Ar_0^2 + 28) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: ?, Cost: 1) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: ?, Cost: 1) evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(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) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: ?, Cost: 1) evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalperfectstart) = 3 Pol(evalperfectbb0in) = 3 Pol(evalperfectbb7in) = 1 Pol(evalperfectbb1in) = 3 Pol(evalperfectbb2in) = 3 Pol(evalperfectbb3in) = 3 Pol(evalperfectbb6in) = 2 Pol(evalperfectbb4in) = 3 Pol(evalperfectbb5in) = 3 Pol(evalperfectstop) = 0 Pol(koat_start) = 3 orients all transitions weakly and the transitions evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ] evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: 3, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: 3, Cost: 1) evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalperfectbb5in) = V_2 - 1 Pol(evalperfectbb2in) = V_2 Pol(evalperfectbb4in) = V_2 - 1 Pol(evalperfectbb3in) = V_2 - 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(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(evalperfectstart(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(evalperfectstart(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(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-0) = Ar_0 S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-1) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-2) = 0 S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-3) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-0) = Ar_0 S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-1) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-2) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-3) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-1) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-2) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-3) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-1) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-2) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-3) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-1) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-2) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-3) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-1) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-2) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-3) = 0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-0) = Ar_0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-1) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-2) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-3) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-1) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-2) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-3) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-0) = Ar_0 S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-1) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-2) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-3) = ? S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-0) = Ar_0 S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-1) = ? S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-2) = ? S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-3) = ? S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-0) = Ar_0 S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-1) = ? S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-2) = ? S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-3) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-0) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-1) = Ar_0 + 1 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-2) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-3) = Ar_3 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-0) = Ar_0 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-1) = Ar_1 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-2) = Ar_2 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-3) = Ar_3 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-1) = Ar_1 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-2) = Ar_2 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-3) = Ar_3 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] weakly and the transition evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) (Comp: Ar_0 + 1, Cost: 1) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: 3, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: 3, Cost: 1) evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalperfectbb5in) = 1 Pol(evalperfectbb2in) = 0 Pol(evalperfectbb4in) = 2 Pol(evalperfectbb3in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(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(evalperfectstart(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(evalperfectstart(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(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-0) = Ar_0 S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-1) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-2) = 0 S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ]", 0-3) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-0) = Ar_0 S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-1) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-2) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]", 0-3) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-1) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-2) = ? S("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]", 0-3) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-1) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-2) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ]", 0-3) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-1) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-2) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-3) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-1) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-2) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ]", 0-3) = 0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-0) = Ar_0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-1) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-2) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1))", 0-3) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-1) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-2) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]", 0-3) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-0) = Ar_0 S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-1) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-2) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]", 0-3) = ? S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-0) = Ar_0 S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-1) = ? S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-2) = ? S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]", 0-3) = ? S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-0) = Ar_0 S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-1) = ? S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-2) = ? S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ]", 0-3) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-0) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-1) = Ar_0 + 1 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-2) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3))", 0-3) = Ar_3 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-0) = Ar_0 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-1) = Ar_1 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-2) = Ar_2 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-3) = Ar_3 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-1) = Ar_1 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-2) = Ar_2 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-3) = Ar_3 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] weakly and the transitions evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(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) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) (Comp: Ar_0 + 1, Cost: 1) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_1 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) (Comp: 2*Ar_0 + 2, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2 - Ar_1, Ar_3)) [ Ar_3 = 0 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_3 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ] (Comp: 3, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 = 0 ] (Comp: 3, Cost: 1) evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(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 evalperfectbb1in: X_1 - 2 >= 0 For symbol evalperfectbb2in: 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 evalperfectbb3in: 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 evalperfectbb4in: 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 evalperfectbb5in: 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 evalperfectbb6in: 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(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 3, Cost: 1) evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 3, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(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) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(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) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(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) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) [ Ar_0 - 2 >= 0 ] (Comp: 1, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalperfectbb4in) = -2*V_2 + 2*V_4 + 1 Pol(evalperfectbb3in) = 2*V_4 and size complexities S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-1) = Ar_1 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-2) = Ar_2 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-3) = Ar_3 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-0) = Ar_0 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-1) = Ar_1 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-2) = Ar_2 S("evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-3) = Ar_3 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) [ Ar_0 - 2 >= 0 ]", 0-0) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) [ Ar_0 - 2 >= 0 ]", 0-1) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) [ Ar_0 - 2 >= 0 ]", 0-2) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) [ Ar_0 - 2 >= 0 ]", 0-3) = Ar_3 S("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(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("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(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("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(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("evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(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("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(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("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(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("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(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("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(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("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(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("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(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("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(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("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(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("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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("evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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("evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 + 3*Ar_0 + 2*Ar_0^2 S("evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(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(evalperfectstart(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(evalperfectstart(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(evalperfectstart(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(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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 ] evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(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 evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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 ] evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(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(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 3, Cost: 1) evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 3, Cost: 1) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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) evalperfectbb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(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) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(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: 2*Ar_0^2 + 2*Ar_0, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(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: 2*Ar_0^2 + 2*Ar_0, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(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) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb6in(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) evalperfectbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(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) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb2in(Ar_0, Ar_0 - 1, Ar_0, Ar_3)) [ Ar_0 - 2 >= 0 ] (Comp: 1, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb0in(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound 13*Ar_0 + 4*Ar_0^2 + 28 Time: 0.478 sec (SMT: 0.391 sec) ---------------------------------------- (2) BOUNDS(1, n^2)