WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_start(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) eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_sipmabubble_start) = 2 Pol(eval_sipmabubble_bb0_in) = 2 Pol(eval_sipmabubble_0) = 2 Pol(eval_sipmabubble_1) = 2 Pol(eval_sipmabubble_2) = 2 Pol(eval_sipmabubble_3) = 2 Pol(eval_sipmabubble_4) = 2 Pol(eval_sipmabubble_5) = 2 Pol(eval_sipmabubble_6) = 2 Pol(eval_sipmabubble_bb1_in) = 2 Pol(eval_sipmabubble_bb2_in) = 2 Pol(eval_sipmabubble_bb7_in) = 1 Pol(eval_sipmabubble_bb3_in) = 2 Pol(eval_sipmabubble_bb6_in) = 2 Pol(eval_sipmabubble_bb4_in) = 2 Pol(eval_sipmabubble_bb5_in) = 2 Pol(eval_sipmabubble_29) = 2 Pol(eval_sipmabubble_30) = 2 Pol(eval_sipmabubble_stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3)) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ] (Comp: 2, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: 2, Cost: 1) eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_sipmabubble_start) = 6*V_4 + 1 Pol(eval_sipmabubble_bb0_in) = 6*V_4 + 1 Pol(eval_sipmabubble_0) = 6*V_4 + 1 Pol(eval_sipmabubble_1) = 6*V_4 + 1 Pol(eval_sipmabubble_2) = 6*V_4 + 1 Pol(eval_sipmabubble_3) = 6*V_4 + 1 Pol(eval_sipmabubble_4) = 6*V_4 + 1 Pol(eval_sipmabubble_5) = 6*V_4 + 1 Pol(eval_sipmabubble_6) = 6*V_4 + 1 Pol(eval_sipmabubble_bb1_in) = 6*V_2 + 1 Pol(eval_sipmabubble_bb2_in) = 6*V_2 - 1 Pol(eval_sipmabubble_bb7_in) = 6*V_2 + 1 Pol(eval_sipmabubble_bb3_in) = 6*V_2 - 1 Pol(eval_sipmabubble_bb6_in) = 6*V_2 - 2 Pol(eval_sipmabubble_bb4_in) = 6*V_2 - 1 Pol(eval_sipmabubble_bb5_in) = 6*V_2 - 1 Pol(eval_sipmabubble_29) = 6*V_1 + 3 Pol(eval_sipmabubble_30) = 6*V_1 + 2 Pol(eval_sipmabubble_stop) = 6*V_2 + 1 Pol(koat_start) = 6*V_4 + 1 orients all transitions weakly and the transition eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3)) (Comp: 6*Ar_3 + 1, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ] (Comp: 2, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: 2, Cost: 1) eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_sipmabubble_bb6_in) = 1 Pol(eval_sipmabubble_29) = 0 Pol(eval_sipmabubble_bb5_in) = 2 Pol(eval_sipmabubble_bb2_in) = 2 Pol(eval_sipmabubble_bb4_in) = 2 Pol(eval_sipmabubble_bb3_in) = 2 Pol(eval_sipmabubble_30) = -1 Pol(eval_sipmabubble_bb1_in) = -2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_start(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(eval_sipmabubble_start(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(eval_sipmabubble_start(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(eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-0) = ? S("eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-1) = ? S("eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-2) = ? S("eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-0) = ? S("eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-1) = ? S("eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-2) = ? S("eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ]", 0-0) = ? S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ]", 0-1) = ? S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ]", 0-2) = ? S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ]", 0-3) = Ar_3 S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ]", 0-0) = ? S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ]", 0-1) = ? S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ]", 0-2) = ? S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ]", 0-3) = Ar_3 S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ]", 0-0) = ? S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ]", 0-1) = ? S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ]", 0-2) = ? S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ]", 0-3) = Ar_3 S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ]", 0-0) = ? S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ]", 0-1) = ? S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ]", 0-2) = ? S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ]", 0-3) = Ar_3 S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ]", 0-0) = ? S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ]", 0-1) = ? S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ]", 0-2) = ? S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ]", 0-3) = Ar_3 S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ]", 0-0) = ? S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ]", 0-1) = ? S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ]", 0-2) = 0 S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ]", 0-3) = Ar_3 S("eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3))", 0-1) = Ar_3 S("eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3)) eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ] eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ] eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ] eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ] eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3)) weakly and the transitions eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3)) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3)) (Comp: 6*Ar_3 + 1, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ] (Comp: 2, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ] (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: 2, Cost: 1) eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (Comp: 1, Cost: 1) eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3)) (Comp: 6*Ar_3 + 1, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ] (Comp: 2, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ] (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3)) (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: 2, Cost: 1) eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_sipmabubble_bb5_in) = V_2 - V_3 - 1 Pol(eval_sipmabubble_bb2_in) = V_2 - V_3 Pol(eval_sipmabubble_bb4_in) = V_2 - V_3 - 1 Pol(eval_sipmabubble_bb3_in) = V_2 - V_3 - 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_start(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(eval_sipmabubble_start(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(eval_sipmabubble_start(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(eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 13*Ar_0 + 13*Ar_3 + 742586 S("eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = 13*Ar_3 + 57122 S("eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-0) = 13*Ar_3 + 4394 S("eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-1) = 13*Ar_3 + 338 S("eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-2) = ? S("eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 13*Ar_3 + 338 S("eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = 13*Ar_3 + 57122 S("eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3))", 0-0) = 13*Ar_3 + 338 S("eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3))", 0-1) = 13*Ar_3 + 4394 S("eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-0) = 13*Ar_0 + 13*Ar_3 + 742586 S("eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-1) = 13*Ar_3 + 338 S("eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-2) = ? S("eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 13*Ar_0 + 13*Ar_3 + 742586 S("eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = 13*Ar_3 + 338 S("eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ]", 0-0) = 13*Ar_0 + 13*Ar_3 + 742586 S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ]", 0-1) = 13*Ar_3 + 338 S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ]", 0-2) = ? S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ]", 0-3) = Ar_3 S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ]", 0-0) = 13*Ar_0 + 13*Ar_3 + 742586 S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ]", 0-1) = 13*Ar_3 + 338 S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ]", 0-2) = ? S("eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ]", 0-3) = Ar_3 S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ]", 0-0) = 13*Ar_0 + 13*Ar_3 + 9653618 S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ]", 0-1) = 13*Ar_3 + 338 S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ]", 0-2) = ? S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ]", 0-3) = Ar_3 S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ]", 0-0) = 13*Ar_0 + 13*Ar_3 + 742586 S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ]", 0-1) = 13*Ar_3 + 338 S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ]", 0-2) = ? S("eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ]", 0-3) = Ar_3 S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ]", 0-0) = 13*Ar_0 + 13*Ar_3 + 57122 S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ]", 0-1) = 13*Ar_3 + 4394 S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ]", 0-2) = ? S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ]", 0-3) = Ar_3 S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ]", 0-0) = 13*Ar_0 + 13*Ar_3 + 57122 S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ]", 0-1) = 13*Ar_3 + 338 S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ]", 0-2) = 0 S("eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ]", 0-3) = Ar_3 S("eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3))", 0-1) = Ar_3 S("eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ] eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ] eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ] weakly and the transition eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3)) (Comp: 6*Ar_3 + 1, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ] (Comp: 2, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ] (Comp: 78*Ar_3^2 + 2041*Ar_3 + 338, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ] (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ] (Comp: ?, Cost: 1) eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3)) (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: 2, Cost: 1) eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 7 produces the following problem: 8: T: (Comp: 1, Cost: 1) eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_sipmabubble_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_3, Ar_2, Ar_3)) (Comp: 6*Ar_3 + 1, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= 0 ] (Comp: 2, Cost: 1) eval_sipmabubble_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 < 0 ] (Comp: 78*Ar_3^2 + 2041*Ar_3 + 338, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_1 - 1 ] (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_1 - 1 ] (Comp: 78*Ar_3^2 + 2041*Ar_3 + 338, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 > nondef_1 ] (Comp: 78*Ar_3^2 + 2041*Ar_3 + 338, Cost: 1) eval_sipmabubble_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ nondef_0 <= nondef_1 ] (Comp: 78*Ar_3^2 + 2041*Ar_3 + 338, Cost: 1) eval_sipmabubble_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 156*Ar_3^2 + 4082*Ar_3 + 676, Cost: 1) eval_sipmabubble_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_29(Ar_1 - 1, Ar_1, Ar_2, Ar_3)) (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 12*Ar_3 + 2, Cost: 1) eval_sipmabubble_30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: 2, Cost: 1) eval_sipmabubble_bb7_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_sipmabubble_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 12300*Ar_3 + 468*Ar_3^2 + 2050 Time: 1.620 sec (SMT: 1.539 sec)