WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\ Ar_2 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_0, Ar_1, Ar_2, Ar_5]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ] (Comp: ?, Cost: 1) eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\ Ar_2 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5)) start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ] (Comp: ?, Cost: 1) eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\ Ar_2 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 2 Pol(eval_ax_start) = 2 Pol(eval_ax_bb5_in) = 1 Pol(eval_ax_stop) = 0 Pol(eval_ax_13) = 2 Pol(eval_ax_bb1_in) = 2 Pol(eval_ax_12) = 2 Pol(eval_ax_bb4_in) = 2 Pol(eval_ax_bb3_in) = 2 Pol(eval_ax_bb2_in) = 2 Pol(eval_ax_6) = 2 Pol(eval_ax_5) = 2 Pol(eval_ax_4) = 2 Pol(eval_ax_3) = 2 Pol(eval_ax_2) = 2 Pol(eval_ax_1) = 2 Pol(eval_ax_0) = 2 Pol(eval_ax_bb0_in) = 2 orients all transitions weakly and the transitions eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5)) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 2, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ] (Comp: 2, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\ Ar_2 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_4 Pol(eval_ax_start) = V_4 - 2 Pol(eval_ax_bb5_in) = -V_3 + V_4 - 1 Pol(eval_ax_stop) = -V_3 + V_4 - 1 Pol(eval_ax_13) = -V_3 + V_4 - 1 Pol(eval_ax_bb1_in) = -V_1 + V_4 - 2 Pol(eval_ax_12) = -V_3 + V_4 - 1 Pol(eval_ax_bb4_in) = -V_1 + V_4 - 2 Pol(eval_ax_bb3_in) = -V_1 + V_4 - 2 Pol(eval_ax_bb2_in) = -V_1 + V_4 - 2 Pol(eval_ax_6) = V_4 - 2 Pol(eval_ax_5) = V_4 - 2 Pol(eval_ax_4) = V_4 - 2 Pol(eval_ax_3) = V_4 - 2 Pol(eval_ax_2) = V_4 - 2 Pol(eval_ax_1) = V_4 - 2 Pol(eval_ax_0) = V_4 - 2 Pol(eval_ax_bb0_in) = V_4 - 2 orients all transitions weakly and the transition eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\ Ar_2 < Ar_5 - 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 2, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ] (Comp: 2, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: Ar_5, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\ Ar_2 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5)) start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 2, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ] (Comp: 2, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: Ar_5, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\ Ar_2 < Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: Ar_5 + 1, Cost: 1) eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_ax_bb4_in) = 2 Pol(eval_ax_12) = 1 Pol(eval_ax_bb3_in) = 3 Pol(eval_ax_bb2_in) = 3 Pol(eval_ax_13) = 0 and size complexities S("eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5))", 0-0) = 0 S("eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5))", 0-0) = ? S("eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5))", 0-1) = 0 S("eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5))", 0-2) = ? S("eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-0) = ? S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-1) = ? S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-2) = ? S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-3) = Ar_5 S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ]", 0-0) = ? S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ]", 0-1) = ? S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ]", 0-2) = ? S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ]", 0-3) = Ar_5 S("eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5))", 0-0) = ? S("eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5))", 0-1) = ? S("eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5))", 0-2) = ? S("eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5))", 0-0) = ? S("eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5))", 0-1) = ? S("eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5))", 0-2) = ? S("eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5))", 0-3) = Ar_5 S("eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = ? S("eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = ? S("eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = ? S("eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\\ Ar_2 < Ar_5 - 1 ]", 0-0) = ? S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\\ Ar_2 < Ar_5 - 1 ]", 0-1) = ? S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\\ Ar_2 < Ar_5 - 1 ]", 0-2) = ? S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\\ Ar_2 < Ar_5 - 1 ]", 0-3) = Ar_5 S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-0) = ? S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-1) = ? S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-2) = ? S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-3) = Ar_5 S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ]", 0-0) = ? S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ]", 0-1) = ? S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ]", 0-2) = ? S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ]", 0-3) = Ar_5 S("eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = ? S("eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = ? S("eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = ? S("eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_5 orients the transitions eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5)) eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5)) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ] eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5)) weakly and the transitions eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5)) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ] eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5)) strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 2, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ] (Comp: 2, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: Ar_5, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\ Ar_2 < Ar_5 - 1 ] (Comp: 3*Ar_5 + 3, Cost: 1) eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 3*Ar_5 + 3, Cost: 1) eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5)) (Comp: 3*Ar_5 + 3, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ] (Comp: ?, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: Ar_5 + 1, Cost: 1) eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_ax_bb3_in) = -2*V_2 + 2*V_4 - 1 Pol(eval_ax_bb2_in) = -2*V_2 + 2*V_4 and size complexities S("eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = Ar_0 S("eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5))", 0-0) = 0 S("eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5))", 0-1) = Ar_1 S("eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5))", 0-2) = Ar_2 S("eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5))", 0-0) = 3*Ar_5 + 27 S("eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5))", 0-1) = 0 S("eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5))", 0-2) = 3*Ar_2 + 3*Ar_5 + 243 S("eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-0) = 3*Ar_5 + 27 S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-1) = ? S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-2) = 3*Ar_2 + 3*Ar_5 + 729 S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-3) = Ar_5 S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ]", 0-0) = 3*Ar_5 + 27 S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ]", 0-1) = ? S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ]", 0-2) = 3*Ar_2 + 3*Ar_5 + 2187 S("eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ]", 0-3) = Ar_5 S("eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5))", 0-0) = 3*Ar_5 + 27 S("eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5))", 0-1) = ? S("eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5))", 0-2) = 3*Ar_2 + 3*Ar_5 + 729 S("eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5))", 0-0) = 3*Ar_5 + 81 S("eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5))", 0-1) = ? S("eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5))", 0-2) = 3*Ar_5 + 27 S("eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5))", 0-3) = Ar_5 S("eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = 3*Ar_5 + 243 S("eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = ? S("eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = 3*Ar_5 + 27 S("eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\\ Ar_2 < Ar_5 - 1 ]", 0-0) = 3*Ar_5 + 27 S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\\ Ar_2 < Ar_5 - 1 ]", 0-1) = ? S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\\ Ar_2 < Ar_5 - 1 ]", 0-2) = 3*Ar_5 + 81 S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\\ Ar_2 < Ar_5 - 1 ]", 0-3) = Ar_5 S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-0) = 3*Ar_5 + 729 S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-1) = ? S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-2) = 3*Ar_5 + 81 S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ]", 0-3) = Ar_5 S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ]", 0-0) = 3*Ar_5 + 729 S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ]", 0-1) = ? S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ]", 0-2) = 3*Ar_5 + 81 S("eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ]", 0-3) = Ar_5 S("eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5))", 0-0) = 3*Ar_5 + 2187 S("eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5))", 0-1) = ? S("eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5))", 0-2) = 3*Ar_5 + 243 S("eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5))", 0-3) = Ar_5 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_5 orients the transitions eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5)) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] weakly and the transition eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 2, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ] (Comp: 2, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: Ar_5, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\ Ar_2 < Ar_5 - 1 ] (Comp: 3*Ar_5 + 3, Cost: 1) eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 3*Ar_5 + 3, Cost: 1) eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5)) (Comp: ?, Cost: 1) eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5)) (Comp: 3*Ar_5 + 3, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ] (Comp: 2*Ar_5^2 + 2*Ar_5, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: Ar_5 + 1, Cost: 1) eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5)) start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 8 produces the following problem: 9: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_stop(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 2, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_2 >= Ar_5 - 1 ] (Comp: 2, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb5_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: Ar_5, Cost: 1) eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(Ar_2, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 /\ Ar_2 < Ar_5 - 1 ] (Comp: 3*Ar_5 + 3, Cost: 1) eval_ax_12(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_13(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 3*Ar_5 + 3, Cost: 1) eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_12(Ar_0, Ar_1, Ar_0 + 1, Ar_5)) (Comp: 2*Ar_5^2 + 2*Ar_5, Cost: 1) eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, Ar_1 + 1, Ar_2, Ar_5)) (Comp: 3*Ar_5 + 3, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb4_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 >= Ar_5 - 1 ] (Comp: 2*Ar_5^2 + 2*Ar_5, Cost: 1) eval_ax_bb2_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb3_in(Ar_0, Ar_1, Ar_2, Ar_5)) [ Ar_1 < Ar_5 - 1 ] (Comp: Ar_5 + 1, Cost: 1) eval_ax_bb1_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb2_in(Ar_0, 0, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb1_in(0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_6(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_5(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_4(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_3(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_2(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_1(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_0(Ar_0, Ar_1, Ar_2, Ar_5)) (Comp: 1, Cost: 1) eval_ax_start(Ar_0, Ar_1, Ar_2, Ar_5) -> Com_1(eval_ax_bb0_in(Ar_0, Ar_1, Ar_2, Ar_5)) start location: koat_start leaf cost: 0 Complexity upper bound 15*Ar_5 + 4*Ar_5^2 + 25 Time: 1.539 sec (SMT: 1.462 sec)