WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval_ndecr_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb0_in(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_ndecr_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_0(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_ndecr_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_1(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_ndecr_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_2(Ar_2 - 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_ndecr_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_3(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_ndecr_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_4(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_ndecr_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb1_in(Ar_0, Ar_0, Ar_2)) (Comp: ?, Cost: 1) eval_ndecr_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 > 1 ] (Comp: ?, Cost: 1) eval_ndecr_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 <= 1 ] (Comp: ?, Cost: 1) eval_ndecr_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb1_in(Ar_0, Ar_1 - 1, Ar_2)) (Comp: ?, Cost: 1) eval_ndecr_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_start(Ar_0, Ar_1, Ar_2)) [ 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_ndecr_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb0_in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_0(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_1(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_2(Ar_2 - 1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_3(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_4(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb1_in(Ar_0, Ar_0, Ar_2)) (Comp: ?, Cost: 1) eval_ndecr_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 > 1 ] (Comp: ?, Cost: 1) eval_ndecr_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 <= 1 ] (Comp: ?, Cost: 1) eval_ndecr_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb1_in(Ar_0, Ar_1 - 1, Ar_2)) (Comp: ?, Cost: 1) eval_ndecr_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_ndecr_start) = 2 Pol(eval_ndecr_bb0_in) = 2 Pol(eval_ndecr_0) = 2 Pol(eval_ndecr_1) = 2 Pol(eval_ndecr_2) = 2 Pol(eval_ndecr_3) = 2 Pol(eval_ndecr_4) = 2 Pol(eval_ndecr_bb1_in) = 2 Pol(eval_ndecr_bb2_in) = 2 Pol(eval_ndecr_bb3_in) = 1 Pol(eval_ndecr_stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions eval_ndecr_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_stop(Ar_0, Ar_1, Ar_2)) eval_ndecr_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 <= 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) eval_ndecr_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb0_in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_0(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_1(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_2(Ar_2 - 1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_3(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_4(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb1_in(Ar_0, Ar_0, Ar_2)) (Comp: ?, Cost: 1) eval_ndecr_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 > 1 ] (Comp: 2, Cost: 1) eval_ndecr_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 <= 1 ] (Comp: ?, Cost: 1) eval_ndecr_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb1_in(Ar_0, Ar_1 - 1, Ar_2)) (Comp: 2, Cost: 1) eval_ndecr_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_ndecr_start) = 2*V_3 Pol(eval_ndecr_bb0_in) = 2*V_3 Pol(eval_ndecr_0) = 2*V_3 Pol(eval_ndecr_1) = 2*V_3 Pol(eval_ndecr_2) = 2*V_1 + 2 Pol(eval_ndecr_3) = 2*V_1 + 2 Pol(eval_ndecr_4) = 2*V_1 + 2 Pol(eval_ndecr_bb1_in) = 2*V_2 + 2 Pol(eval_ndecr_bb2_in) = 2*V_2 + 1 Pol(eval_ndecr_bb3_in) = 2*V_2 + 2 Pol(eval_ndecr_stop) = 2*V_2 + 2 Pol(koat_start) = 2*V_3 orients all transitions weakly and the transition eval_ndecr_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 > 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) eval_ndecr_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb0_in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_0(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_1(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_2(Ar_2 - 1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_3(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_4(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb1_in(Ar_0, Ar_0, Ar_2)) (Comp: 2*Ar_2, Cost: 1) eval_ndecr_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 > 1 ] (Comp: 2, Cost: 1) eval_ndecr_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 <= 1 ] (Comp: ?, Cost: 1) eval_ndecr_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb1_in(Ar_0, Ar_1 - 1, Ar_2)) (Comp: 2, Cost: 1) eval_ndecr_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_start(Ar_0, Ar_1, Ar_2)) [ 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_ndecr_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb0_in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_0(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_1(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_2(Ar_2 - 1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_3(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_4(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_ndecr_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb1_in(Ar_0, Ar_0, Ar_2)) (Comp: 2*Ar_2, Cost: 1) eval_ndecr_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 > 1 ] (Comp: 2, Cost: 1) eval_ndecr_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 <= 1 ] (Comp: 2*Ar_2, Cost: 1) eval_ndecr_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_bb1_in(Ar_0, Ar_1 - 1, Ar_2)) (Comp: 2, Cost: 1) eval_ndecr_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ndecr_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 4*Ar_2 + 11 Time: 0.687 sec (SMT: 0.666 sec)