WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1) -> Com_1(evalsipmabubbleentryin(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubbleentryin(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1)) [ 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) evalsipmabubblestart(Ar_0, Ar_1) -> Com_1(evalsipmabubbleentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubbleentryin(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalsipmabubblestart) = 1 Pol(evalsipmabubbleentryin) = 1 Pol(evalsipmabubblebb6in) = 1 Pol(evalsipmabubblebb4in) = 1 Pol(evalsipmabubblereturnin) = 1 Pol(evalsipmabubblebb1in) = 1 Pol(evalsipmabubblebb5in) = 1 Pol(evalsipmabubblebb2in) = 1 Pol(evalsipmabubblebb3in) = 1 Pol(evalsipmabubblestop) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1)) strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1) -> Com_1(evalsipmabubbleentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubbleentryin(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalsipmabubblestart) = 1 Pol(evalsipmabubbleentryin) = 1 Pol(evalsipmabubblebb6in) = 1 Pol(evalsipmabubblebb4in) = 1 Pol(evalsipmabubblereturnin) = 0 Pol(evalsipmabubblebb1in) = 1 Pol(evalsipmabubblebb5in) = 1 Pol(evalsipmabubblebb2in) = 1 Pol(evalsipmabubblebb3in) = 1 Pol(evalsipmabubblestop) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1) -> Com_1(evalsipmabubbleentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubbleentryin(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalsipmabubblestart) = 3*V_1 + 3 Pol(evalsipmabubbleentryin) = 3*V_1 + 3 Pol(evalsipmabubblebb6in) = 3*V_1 + 3 Pol(evalsipmabubblebb4in) = 3*V_1 + 2 Pol(evalsipmabubblereturnin) = 3*V_1 + 3 Pol(evalsipmabubblebb1in) = 3*V_1 + 2 Pol(evalsipmabubblebb5in) = 3*V_1 + 1 Pol(evalsipmabubblebb2in) = 3*V_1 + 2 Pol(evalsipmabubblebb3in) = 3*V_1 + 2 Pol(evalsipmabubblestop) = 3*V_1 + 3 Pol(koat_start) = 3*V_1 + 3 orients all transitions weakly and the transition evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1) -> Com_1(evalsipmabubbleentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubbleentryin(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1)) (Comp: 3*Ar_0 + 3, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalsipmabubblebb5in) = 1 Pol(evalsipmabubblebb6in) = 0 Pol(evalsipmabubblebb4in) = 2 Pol(evalsipmabubblebb1in) = 2 Pol(evalsipmabubblebb3in) = 2 Pol(evalsipmabubblebb2in) = 2 and size complexities S("koat_start(Ar_0, Ar_1) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1 S("evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1))", 0-0) = ? S("evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1))", 0-1) = ? S("evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1))", 0-0) = ? S("evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1))", 0-1) = ? S("evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1))", 0-0) = ? S("evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1))", 0-1) = ? S("evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1))", 0-0) = ? S("evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1))", 0-1) = ? S("evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ]", 0-0) = ? S("evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ]", 0-1) = ? S("evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ]", 0-0) = ? S("evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ]", 0-1) = ? S("evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]", 0-0) = ? S("evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]", 0-1) = ? S("evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = ? S("evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = ? S("evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-0) = ? S("evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-1) = ? S("evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ]", 0-0) = ? S("evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ]", 0-1) = 0 S("evalsipmabubbleentryin(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1))", 0-0) = Ar_0 S("evalsipmabubbleentryin(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1))", 0-1) = Ar_1 S("evalsipmabubblestart(Ar_0, Ar_1) -> Com_1(evalsipmabubbleentryin(Ar_0, Ar_1))", 0-0) = Ar_0 S("evalsipmabubblestart(Ar_0, Ar_1) -> Com_1(evalsipmabubbleentryin(Ar_0, Ar_1))", 0-1) = Ar_1 orients the transitions evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1)) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1)) evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ] evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ] weakly and the transitions evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1)) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1) -> Com_1(evalsipmabubbleentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubbleentryin(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1)) (Comp: 3*Ar_0 + 3, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 6*Ar_0 + 6, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1)) (Comp: 6*Ar_0 + 6, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalsipmabubblebb4in) = V_1 - V_2 + 1 Pol(evalsipmabubblebb1in) = V_1 - V_2 Pol(evalsipmabubblebb3in) = V_1 - V_2 Pol(evalsipmabubblebb2in) = V_1 - V_2 and size complexities S("koat_start(Ar_0, Ar_1) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1 S("evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1))", 0-0) = 7*Ar_0 + 14406 S("evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1))", 0-1) = ? S("evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1))", 0-0) = 7*Ar_0 + 294 S("evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1))", 0-1) = ? S("evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1))", 0-0) = 7*Ar_0 + 294 S("evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1))", 0-1) = ? S("evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1))", 0-0) = 7*Ar_0 + 294 S("evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1))", 0-1) = ? S("evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ]", 0-0) = 7*Ar_0 + 294 S("evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ]", 0-1) = ? S("evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ]", 0-0) = 7*Ar_0 + 294 S("evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ]", 0-1) = ? S("evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]", 0-0) = 7*Ar_0 + 294 S("evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ]", 0-1) = ? S("evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 7*Ar_0 + 294 S("evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = ? S("evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-0) = 7*Ar_0 + 2058 S("evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]", 0-1) = ? S("evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ]", 0-0) = 7*Ar_0 + 294 S("evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ]", 0-1) = 0 S("evalsipmabubbleentryin(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1))", 0-0) = Ar_0 S("evalsipmabubbleentryin(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1))", 0-1) = Ar_1 S("evalsipmabubblestart(Ar_0, Ar_1) -> Com_1(evalsipmabubbleentryin(Ar_0, Ar_1))", 0-0) = Ar_0 S("evalsipmabubblestart(Ar_0, Ar_1) -> Com_1(evalsipmabubbleentryin(Ar_0, Ar_1))", 0-1) = Ar_1 orients the transitions evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1)) evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ] evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ] weakly and the transition evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1) -> Com_1(evalsipmabubbleentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubbleentryin(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1)) (Comp: 3*Ar_0 + 3, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: 21*Ar_0^2 + 906*Ar_0 + 885, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 6*Ar_0 + 6, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1)) (Comp: 6*Ar_0 + 6, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1)) [ 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) evalsipmabubblestart(Ar_0, Ar_1) -> Com_1(evalsipmabubbleentryin(Ar_0, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubbleentryin(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1)) (Comp: 3*Ar_0 + 3, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, 0)) [ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1) -> Com_1(evalsipmabubblereturnin(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ] (Comp: 21*Ar_0^2 + 906*Ar_0 + 885, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb1in(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 6*Ar_0 + 6, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 ] (Comp: 21*Ar_0^2 + 906*Ar_0 + 885, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1)) [ C >= D + 1 ] (Comp: 21*Ar_0^2 + 906*Ar_0 + 885, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) [ D >= C ] (Comp: 21*Ar_0^2 + 906*Ar_0 + 885, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1)) (Comp: 42*Ar_0^2 + 1812*Ar_0 + 1770, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1 + 1)) (Comp: 6*Ar_0 + 6, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1) -> Com_1(evalsipmabubblebb6in(Ar_0 - 1, Ar_1)) (Comp: 1, Cost: 1) evalsipmabubblereturnin(Ar_0, Ar_1) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 5451*Ar_0 + 126*Ar_0^2 + 5329 Time: 0.757 sec (SMT: 0.721 sec)