WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_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_abc_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_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_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_abc_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_abc_start) = 1 Pol(eval_abc_bb0_in) = 1 Pol(eval_abc_0) = 1 Pol(eval_abc_1) = 1 Pol(eval_abc_2) = 1 Pol(eval_abc_3) = 1 Pol(eval_abc_4) = 1 Pol(eval_abc_bb1_in) = 1 Pol(eval_abc_bb2_in) = 1 Pol(eval_abc_bb5_in) = 0 Pol(eval_abc_bb3_in) = 1 Pol(eval_abc_bb4_in) = 1 Pol(eval_abc_8) = 1 Pol(eval_abc_9) = 1 Pol(eval_abc_stop) = -1 Pol(koat_start) = 1 orients all transitions weakly and the transition eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ] (Comp: 1, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_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_abc_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (Comp: 1, Cost: 1) eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ] (Comp: 1, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_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_abc_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_abc_start) = 5*V_4 Pol(eval_abc_bb0_in) = 5*V_4 Pol(eval_abc_0) = 5*V_4 Pol(eval_abc_1) = 5*V_4 Pol(eval_abc_2) = 5*V_4 Pol(eval_abc_3) = 5*V_4 Pol(eval_abc_4) = 5*V_4 Pol(eval_abc_bb1_in) = -5*V_2 + 5*V_4 + 1 Pol(eval_abc_bb2_in) = -5*V_2 + 5*V_4 Pol(eval_abc_bb5_in) = -5*V_2 + 5*V_4 + 1 Pol(eval_abc_bb3_in) = -5*V_2 + 5*V_4 Pol(eval_abc_bb4_in) = -5*V_2 + 5*V_4 - 1 Pol(eval_abc_8) = -5*V_1 + 5*V_4 + 3 Pol(eval_abc_9) = -5*V_1 + 5*V_4 + 2 Pol(eval_abc_stop) = -5*V_2 + 5*V_4 + 1 Pol(koat_start) = 5*V_4 orients all transitions weakly and the transition eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3)) (Comp: 5*Ar_3, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ] (Comp: 1, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_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_abc_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_abc_bb4_in) = 3 Pol(eval_abc_8) = 2 Pol(eval_abc_bb3_in) = 4 Pol(eval_abc_bb2_in) = 4 Pol(eval_abc_9) = 1 Pol(eval_abc_bb1_in) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_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_abc_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_abc_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_abc_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-0) = ? S("eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-1) = ? S("eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-2) = ? S("eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-0) = ? S("eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-1) = ? S("eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-2) = ? S("eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-3) = Ar_3 S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ]", 0-0) = ? S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ]", 0-1) = ? S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ]", 0-2) = ? S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ]", 0-3) = Ar_3 S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ]", 0-0) = ? S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ]", 0-1) = ? S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ]", 0-2) = ? S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ]", 0-3) = Ar_3 S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ]", 0-0) = ? S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ]", 0-1) = ? S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ]", 0-2) = ? S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ]", 0-3) = Ar_3 S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ]", 0-0) = ? S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ]", 0-1) = ? S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ]", 0-2) = ? S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ]", 0-3) = Ar_3 S("eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3))", 0-1) = 1 S("eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3)) eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ] eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ] eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3)) weakly and the transitions eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3)) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ] eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3)) strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3)) (Comp: 5*Ar_3, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ] (Comp: 1, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ] (Comp: 20*Ar_3, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 20*Ar_3, Cost: 1) eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 20*Ar_3, Cost: 1) eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 20*Ar_3, Cost: 1) eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_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_abc_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_abc_bb3_in) = -2*V_3 + 2*V_4 Pol(eval_abc_bb2_in) = -2*V_3 + 2*V_4 + 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_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_abc_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_abc_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_abc_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 20*Ar_0 + 20*Ar_3 + 3200000 S("eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = 20*Ar_3 + 160400 S("eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-0) = 20*Ar_3 + 8000 S("eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-1) = 20*Ar_3 + 400 S("eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-2) = ? S("eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 20*Ar_3 + 400 S("eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = 20*Ar_3 + 160000 S("eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3))", 0-0) = 20*Ar_3 + 400 S("eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3))", 0-1) = 20*Ar_3 + 8000 S("eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-0) = 20*Ar_0 + 20*Ar_3 + 3200000 S("eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-1) = 20*Ar_3 + 400 S("eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-2) = ? S("eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-3) = Ar_3 S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ]", 0-0) = 20*Ar_0 + 20*Ar_3 + 64000000 S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ]", 0-1) = 20*Ar_3 + 400 S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ]", 0-2) = ? S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ]", 0-3) = Ar_3 S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ]", 0-0) = 20*Ar_0 + 20*Ar_3 + 3200000 S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ]", 0-1) = 20*Ar_3 + 400 S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ]", 0-2) = ? S("eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ]", 0-3) = Ar_3 S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ]", 0-0) = 20*Ar_0 + 20*Ar_3 + 160000 S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ]", 0-1) = 20*Ar_3 + 8020 S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ]", 0-2) = ? S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ]", 0-3) = Ar_3 S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ]", 0-0) = 20*Ar_0 + 20*Ar_3 + 160000 S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ]", 0-1) = 20*Ar_3 + 400 S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ]", 0-2) = 20*Ar_3 + 8020 S("eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ]", 0-3) = Ar_3 S("eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3))", 0-1) = 1 S("eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ] weakly and the transition eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) eval_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3)) (Comp: 5*Ar_3, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ] (Comp: 1, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ] (Comp: 210*Ar_3^2 + 80205*Ar_3, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ] (Comp: 20*Ar_3, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ] (Comp: ?, Cost: 1) eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 20*Ar_3, Cost: 1) eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 20*Ar_3, Cost: 1) eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 20*Ar_3, Cost: 1) eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_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_abc_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_abc_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, 1, Ar_2, Ar_3)) (Comp: 5*Ar_3, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_1, Ar_3)) [ Ar_1 <= Ar_3 ] (Comp: 1, Cost: 1) eval_abc_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 > Ar_3 ] (Comp: 210*Ar_3^2 + 80205*Ar_3, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 <= Ar_3 ] (Comp: 20*Ar_3, Cost: 1) eval_abc_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 > Ar_3 ] (Comp: 210*Ar_3^2 + 80205*Ar_3, Cost: 1) eval_abc_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb2_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 20*Ar_3, Cost: 1) eval_abc_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_8(Ar_1 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 20*Ar_3, Cost: 1) eval_abc_8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 20*Ar_3, Cost: 1) eval_abc_9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_bb1_in(Ar_0, Ar_0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_abc_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_abc_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_abc_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 160495*Ar_3 + 420*Ar_3^2 + 9 Time: 1.296 sec (SMT: 1.235 sec)