WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_3, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 > 100 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 <= 100 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_0 + Ar_4 + 50, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_2, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 ] (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 < 0 ] (Comp: ?, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_3, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 > 100 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 <= 100 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_0 + Ar_4 + 50, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_2, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 ] (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 < 0 ] (Comp: ?, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_start_start) = 7 Pol(eval_start_bb0_in) = 7 Pol(eval_start_0) = 7 Pol(eval_start_1) = 7 Pol(eval_start_2) = 7 Pol(eval_start_3) = 7 Pol(eval_start_bb1_in) = 7 Pol(eval_start_bb2_in) = 7 Pol(eval_start_bb3_in) = 6 Pol(eval_start_8) = 5 Pol(eval_start_9) = 4 Pol(eval_start_10) = 3 Pol(eval_start_bb4_in) = 2 Pol(eval_start_bb5_in) = 2 Pol(eval_start_bb6_in) = 1 Pol(eval_start_stop) = 0 Pol(koat_start) = 7 orients all transitions weakly and the transitions eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 < 0 ] eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_0 + Ar_4 + 50, Ar_3, Ar_4)) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 <= 100 ] eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_2, Ar_2, Ar_3, Ar_4)) strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_3, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 > 100 ] (Comp: 7, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 <= 100 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_0 + Ar_4 + 50, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_2, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 ] (Comp: 7, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 < 0 ] (Comp: ?, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_start_start) = 101*V_5 + 15352 Pol(eval_start_bb0_in) = 101*V_5 + 15352 Pol(eval_start_0) = 101*V_5 + 15352 Pol(eval_start_1) = 101*V_5 + 15352 Pol(eval_start_2) = 101*V_5 + 15352 Pol(eval_start_3) = 101*V_5 + 15352 Pol(eval_start_bb1_in) = 101*V_5 + 15352 Pol(eval_start_bb2_in) = 101*V_5 + 15352 Pol(eval_start_bb3_in) = 101*V_1 + 101*V_5 + 5252 Pol(eval_start_8) = 101*V_3 + 202 Pol(eval_start_9) = 101*V_3 + 202 Pol(eval_start_10) = 101*V_3 + 202 Pol(eval_start_bb4_in) = 101*V_2 + 202 Pol(eval_start_bb5_in) = 101*V_2 + 101 Pol(eval_start_bb6_in) = 101*V_2 + 202 Pol(eval_start_stop) = 101*V_2 + 202 Pol(koat_start) = 101*V_5 + 15352 orients all transitions weakly and the transition eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_3, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 > 100 ] (Comp: 7, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 <= 100 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_0 + Ar_4 + 50, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_2, Ar_2, Ar_3, Ar_4)) (Comp: 101*Ar_4 + 15352, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 ] (Comp: 7, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 < 0 ] (Comp: ?, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_3, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 > 100 ] (Comp: 7, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 <= 100 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_0 + Ar_4 + 50, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_2, Ar_2, Ar_3, Ar_4)) (Comp: 101*Ar_4 + 15352, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 ] (Comp: 7, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 < 0 ] (Comp: 101*Ar_4 + 15352, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_start_start) = 2*V_4 + 2 Pol(eval_start_bb0_in) = 2*V_4 + 2 Pol(eval_start_0) = 2*V_4 + 2 Pol(eval_start_1) = 2*V_4 + 2 Pol(eval_start_2) = 2*V_4 + 2 Pol(eval_start_3) = 2*V_4 + 2 Pol(eval_start_bb1_in) = 2*V_1 + 2 Pol(eval_start_bb2_in) = 2*V_1 + 1 Pol(eval_start_bb3_in) = 2*V_1 Pol(eval_start_8) = 2*V_1 Pol(eval_start_9) = 2*V_1 Pol(eval_start_10) = 2*V_1 Pol(eval_start_bb4_in) = 2*V_1 Pol(eval_start_bb5_in) = 2*V_1 Pol(eval_start_bb6_in) = 2*V_1 Pol(eval_start_stop) = 2*V_1 Pol(koat_start) = 2*V_4 + 2 orients all transitions weakly and the transition eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 > 100 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_3, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2*Ar_3 + 2, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 > 100 ] (Comp: 7, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 <= 100 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_0 + Ar_4 + 50, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_2, Ar_2, Ar_3, Ar_4)) (Comp: 101*Ar_4 + 15352, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 ] (Comp: 7, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 < 0 ] (Comp: 101*Ar_4 + 15352, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_3, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2*Ar_3 + 2, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 > 100 ] (Comp: 7, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 <= 100 ] (Comp: 2*Ar_3 + 2, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb1_in(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_0 + Ar_4 + 50, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_9(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_2, Ar_2, Ar_3, Ar_4)) (Comp: 101*Ar_4 + 15352, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 0 ] (Comp: 7, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 < 0 ] (Comp: 101*Ar_4 + 15352, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 7, Cost: 1) eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 4*Ar_3 + 202*Ar_4 + 30763 Time: 1.816 sec (SMT: 1.742 sec)