WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestart(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) evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalSimpleMultiplestart) = 2 Pol(evalSimpleMultipleentryin) = 2 Pol(evalSimpleMultiplebb3in) = 2 Pol(evalSimpleMultiplebbin) = 2 Pol(evalSimpleMultiplereturnin) = 1 Pol(evalSimpleMultiplebb1in) = 2 Pol(evalSimpleMultiplebb2in) = 2 Pol(evalSimpleMultiplestop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3)) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalSimpleMultiplestart) = V_4 + 1 Pol(evalSimpleMultipleentryin) = V_4 + 1 Pol(evalSimpleMultiplebb3in) = -V_1 + V_4 + 1 Pol(evalSimpleMultiplebbin) = -V_1 + V_4 + 1 Pol(evalSimpleMultiplereturnin) = -V_1 + V_4 + 1 Pol(evalSimpleMultiplebb1in) = -V_1 + V_4 Pol(evalSimpleMultiplebb2in) = -V_1 + V_4 + 1 Pol(evalSimpleMultiplestop) = -V_1 + V_4 + 1 Pol(koat_start) = V_4 + 1 orients all transitions weakly and the transition evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] (Comp: Ar_3 + 1, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestart(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) evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 ] (Comp: Ar_3 + 1, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 ] (Comp: Ar_3 + 1, Cost: 1) evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 5 to obtain the following invariants: For symbol evalSimpleMultiplebb1in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalSimpleMultiplebb2in: X_1 - X_4 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalSimpleMultiplebb3in: X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalSimpleMultiplebbin: X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalSimpleMultiplereturnin: X_2 - X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0 This yielded the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: Ar_3 + 1, Cost: 1) evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: Ar_3 + 1, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 2*V_3 Pol(evalSimpleMultiplestart) = 2*V_3 Pol(evalSimpleMultiplereturnin) = -2*V_2 + 2*V_3 Pol(evalSimpleMultiplestop) = -2*V_2 + 2*V_3 Pol(evalSimpleMultiplebb2in) = -2*V_2 + 2*V_3 - 1 Pol(evalSimpleMultiplebb3in) = -2*V_2 + 2*V_3 Pol(evalSimpleMultiplebb1in) = -2*V_2 + 2*V_3 Pol(evalSimpleMultiplebbin) = -2*V_2 + 2*V_3 Pol(evalSimpleMultipleentryin) = 2*V_3 orients all transitions weakly and the transition evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 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(evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2*Ar_2, Cost: 1) evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: Ar_3 + 1, Cost: 1) evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: Ar_3 + 1, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3)) 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(evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2*Ar_2, Cost: 1) evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: Ar_3 + 1, Cost: 1) evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: Ar_3 + 2*Ar_2 + 2, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: Ar_3 + 1, Cost: 1) evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ] (Comp: Ar_3 + 2*Ar_2 + 2, Cost: 1) evalSimpleMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalSimpleMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalSimpleMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound 6*Ar_2 + 4*Ar_3 + 12 Time: 2.019 sec (SMT: 1.948 sec)