WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: ?, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_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_start_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_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: ?, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_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_start_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_start_start) = 2 Pol(eval_start_bb0_in) = 2 Pol(eval_start_0) = 2 Pol(eval_start_1) = 2 Pol(eval_start_2) = 2 Pol(eval_start_3) = 2 Pol(eval_start_4) = 2 Pol(eval_start_5) = 2 Pol(eval_start_6) = 2 Pol(eval_start_7) = 2 Pol(eval_start_8) = 2 Pol(eval_start_bb1_in) = 2 Pol(eval_start_bb2_in) = 2 Pol(eval_start_bb3_in) = 2 Pol(eval_start_bb4_in) = 2 Pol(eval_start_bb5_in) = 1 Pol(eval_start_stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3)) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ] (Comp: 2, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: 2, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_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_start_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_start_start) = 3*V_1 Pol(eval_start_bb0_in) = 3*V_1 Pol(eval_start_0) = 3*V_1 Pol(eval_start_1) = 3*V_1 Pol(eval_start_2) = 3*V_1 Pol(eval_start_3) = 3*V_1 Pol(eval_start_4) = 3*V_1 Pol(eval_start_5) = 3*V_1 Pol(eval_start_6) = 3*V_1 Pol(eval_start_7) = 3*V_1 Pol(eval_start_8) = 3*V_1 Pol(eval_start_bb1_in) = 3*V_1 - 3*V_4 - 1 Pol(eval_start_bb2_in) = 3*V_1 - 3*V_4 - 2 Pol(eval_start_bb3_in) = 3*V_1 - 3*V_4 - 2 Pol(eval_start_bb4_in) = 3*V_1 - 3*V_4 - 3 Pol(eval_start_bb5_in) = 3*V_1 - 3*V_4 - 2 Pol(eval_start_stop) = 3*V_1 - 3*V_4 - 2 Pol(koat_start) = 3*V_1 orients all transitions weakly and the transition eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: 3*Ar_0, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ] (Comp: 2, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: 2, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_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_start_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: 3*Ar_0, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ] (Comp: 2, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: 3*Ar_0, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: 2, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_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_start_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_start_bb2_in) = 1 Pol(eval_start_bb1_in) = 1 Pol(eval_start_bb3_in) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_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_start_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_start_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_start_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1))", 0-0) = Ar_0 S("eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1))", 0-1) = Ar_1 S("eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1))", 0-2) = ? S("eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1))", 0-3) = ? S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ]", 0-0) = Ar_0 S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ]", 0-1) = Ar_1 S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ]", 0-3) = ? S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ]", 0-0) = Ar_0 S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ]", 0-1) = Ar_1 S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ]", 0-2) = ? S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ]", 0-3) = ? S("eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1))", 0-0) = Ar_0 S("eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1))", 0-1) = Ar_1 S("eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1))", 0-2) = ? S("eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1))", 0-3) = ? S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ]", 0-0) = Ar_0 S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ]", 0-1) = Ar_1 S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ]", 0-2) = ? S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ]", 0-3) = ? S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]", 0-0) = Ar_0 S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]", 0-1) = Ar_1 S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]", 0-2) = ? S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]", 0-3) = ? S("eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, 0))", 0-0) = Ar_0 S("eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, 0))", 0-1) = Ar_1 S("eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, 0))", 0-2) = 0 S("eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, 0))", 0-3) = 0 S("eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] weakly and the transition eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] (Comp: 3*Ar_0 + 1, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: 3*Ar_0, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ] (Comp: 2, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: 3*Ar_0, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: 2, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_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_start_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_start_start) = 2*V_2 + 2 Pol(eval_start_bb0_in) = 2*V_2 + 2 Pol(eval_start_0) = 2*V_2 + 2 Pol(eval_start_1) = 2*V_2 + 2 Pol(eval_start_2) = 2*V_2 + 2 Pol(eval_start_3) = 2*V_2 + 2 Pol(eval_start_4) = 2*V_2 + 2 Pol(eval_start_5) = 2*V_2 + 2 Pol(eval_start_6) = 2*V_2 + 2 Pol(eval_start_7) = 2*V_2 + 2 Pol(eval_start_8) = 2*V_2 + 2 Pol(eval_start_bb1_in) = 2*V_2 - 2*V_3 + 2 Pol(eval_start_bb2_in) = 2*V_2 - 2*V_3 + 1 Pol(eval_start_bb3_in) = 2*V_2 - 2*V_3 Pol(eval_start_bb4_in) = 2*V_2 - 2*V_3 Pol(eval_start_bb5_in) = 2*V_2 - 2*V_3 Pol(eval_start_stop) = 2*V_2 - 2*V_3 Pol(koat_start) = 2*V_2 + 2 orients all transitions weakly and the transition eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: 2*Ar_1 + 2, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] (Comp: 3*Ar_0 + 1, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: 3*Ar_0, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ] (Comp: 2, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: 3*Ar_0, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: 2, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_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_start_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_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_start_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: 2*Ar_1 + 2, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] (Comp: 3*Ar_0 + 1, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: 2*Ar_1 + 2, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: 3*Ar_0, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_0 ] (Comp: 2, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: 3*Ar_0, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) (Comp: 2, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_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_start_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 4*Ar_1 + 9*Ar_0 + 20 Time: 1.491 sec (SMT: 1.410 sec)