WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 < Ar_0 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) [ Ar_3 < Ar_0 /\ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= Ar_0 /\ Ar_3 < Ar_0 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_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_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3 + 1)) [ Ar_3 < Ar_0 /\ Ar_3 >= Ar_0 ] eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= Ar_0 /\ Ar_3 < Ar_0 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 < Ar_0 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(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_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 < Ar_0 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(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_speedSimpleMultipleDep_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_speedSimpleMultipleDep_bb3_in) = 1 Pol(eval_speedSimpleMultipleDep_stop) = 0 Pol(eval_speedSimpleMultipleDep_bb2_in) = 2 Pol(eval_speedSimpleMultipleDep_bb1_in) = 2 Pol(eval_speedSimpleMultipleDep_7) = 2 Pol(eval_speedSimpleMultipleDep_6) = 2 Pol(eval_speedSimpleMultipleDep_5) = 2 Pol(eval_speedSimpleMultipleDep_4) = 2 Pol(eval_speedSimpleMultipleDep_3) = 2 Pol(eval_speedSimpleMultipleDep_2) = 2 Pol(eval_speedSimpleMultipleDep_1) = 2 Pol(eval_speedSimpleMultipleDep_0) = 2 Pol(eval_speedSimpleMultipleDep_bb0_in) = 2 Pol(eval_speedSimpleMultipleDep_start) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_stop(Ar_0, Ar_1, Ar_2, Ar_3)) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] strictly and produces the following problem: 4: T: (Comp: 2, Cost: 1) eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 < Ar_0 ] (Comp: 2, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ] (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(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_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 4 to obtain the following invariants: For symbol eval_speedSimpleMultipleDep_bb1_in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_3 >= 0 For symbol eval_speedSimpleMultipleDep_bb2_in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 For symbol eval_speedSimpleMultipleDep_bb3_in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_3 >= 0 /\ -X_2 + X_3 >= 0 This yielded the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_2 < Ar_1 ] (Comp: 2, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_3 < Ar_0 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_3 >= Ar_0 ] (Comp: 2, Cost: 1) eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_2 + 2 Pol(eval_speedSimpleMultipleDep_start) = V_2 + 2 Pol(eval_speedSimpleMultipleDep_bb0_in) = V_2 + 2 Pol(eval_speedSimpleMultipleDep_0) = V_2 + 2 Pol(eval_speedSimpleMultipleDep_1) = V_2 + 2 Pol(eval_speedSimpleMultipleDep_2) = V_2 + 2 Pol(eval_speedSimpleMultipleDep_3) = V_2 + 2 Pol(eval_speedSimpleMultipleDep_4) = V_2 + 2 Pol(eval_speedSimpleMultipleDep_5) = V_2 + 2 Pol(eval_speedSimpleMultipleDep_6) = V_2 + 2 Pol(eval_speedSimpleMultipleDep_7) = V_2 + 2 Pol(eval_speedSimpleMultipleDep_bb1_in) = V_2 - V_3 + 2 Pol(eval_speedSimpleMultipleDep_bb2_in) = V_2 - V_3 + 2 Pol(eval_speedSimpleMultipleDep_bb3_in) = V_2 - V_3 + 2 Pol(eval_speedSimpleMultipleDep_stop) = V_2 - V_3 + 2 orients all transitions weakly and the transition eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_3 >= Ar_0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_2 < Ar_1 ] (Comp: 2, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_3 < Ar_0 ] (Comp: Ar_1 + 2, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_3 >= Ar_0 ] (Comp: 2, Cost: 1) eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_speedSimpleMultipleDep_bb2_in) = 3*V_1 - 3*V_4 - 2 Pol(eval_speedSimpleMultipleDep_bb1_in) = 3*V_1 - 3*V_4 - 1 and size complexities S("eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 ]", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 ]", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 ]", 0-2) = Ar_1 S("eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 ]", 0-3) = 0 S("eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_3 >= Ar_0 ]", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_3 >= Ar_0 ]", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_3 >= Ar_0 ]", 0-2) = Ar_1 S("eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_3 >= Ar_0 ]", 0-3) = 0 S("eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_3 < Ar_0 ]", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_3 < Ar_0 ]", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_3 < Ar_0 ]", 0-2) = Ar_1 S("eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_3 < Ar_0 ]", 0-3) = Ar_0 S("eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-2) = Ar_1 S("eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-3) = 0 S("eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_2 < Ar_1 ]", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_2 < Ar_1 ]", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_2 < Ar_1 ]", 0-2) = Ar_1 S("eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_2 < Ar_1 ]", 0-3) = Ar_0 S("eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, 0, 0))", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, 0, 0))", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, 0, 0))", 0-2) = 0 S("eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, 0, 0))", 0-3) = 0 S("eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_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_speedSimpleMultipleDep_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_speedSimpleMultipleDep_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_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_3 < Ar_0 ] eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_2 < Ar_1 ] weakly and the transition eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_3 < Ar_0 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: ?, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_2 < Ar_1 ] (Comp: 2, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: 3*Ar_0*Ar_1 + 9*Ar_0 + Ar_1 + 3, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_3 < Ar_0 ] (Comp: Ar_1 + 2, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_3 >= Ar_0 ] (Comp: 2, Cost: 1) eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 7 produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) eval_speedSimpleMultipleDep_7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, 0, 0)) (Comp: 2*Ar_1 + 3*Ar_0*Ar_1 + 9*Ar_0 + 6, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_2 < Ar_1 ] (Comp: 2, Cost: 1) eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: 3*Ar_0*Ar_1 + 9*Ar_0 + Ar_1 + 3, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_3 < Ar_0 ] (Comp: Ar_1 + 2, Cost: 1) eval_speedSimpleMultipleDep_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_bb1_in(Ar_0, Ar_1, Ar_2 + 1, 0)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_3 >= Ar_0 ] (Comp: 2, Cost: 1) eval_speedSimpleMultipleDep_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_speedSimpleMultipleDep_stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 4*Ar_1 + 6*Ar_0*Ar_1 + 18*Ar_0 + 25 Time: 2.981 sec (SMT: 2.868 sec)