WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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) evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalNestedMultiplestart) = 2 Pol(evalNestedMultipleentryin) = 2 Pol(evalNestedMultiplebb5in) = 2 Pol(evalNestedMultiplebb2in) = 2 Pol(evalNestedMultiplereturnin) = 1 Pol(evalNestedMultiplebb4in) = 2 Pol(evalNestedMultiplebb3in) = 2 Pol(evalNestedMultiplebb1in) = 2 Pol(evalNestedMultiplestop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4)) (Comp: 2, Cost: 1) evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalNestedMultiplestart) = -3*V_1 + 3*V_2 + 3 Pol(evalNestedMultipleentryin) = -3*V_1 + 3*V_2 + 3 Pol(evalNestedMultiplebb5in) = 3*V_1 - 3*V_2 + 3 Pol(evalNestedMultiplebb2in) = 3*V_1 - 3*V_2 + 2 Pol(evalNestedMultiplereturnin) = 3*V_1 - 3*V_2 + 3 Pol(evalNestedMultiplebb4in) = 3*V_1 - 3*V_2 + 1 Pol(evalNestedMultiplebb3in) = 3*V_1 - 3*V_2 + 2 Pol(evalNestedMultiplebb1in) = 3*V_1 - 3*V_2 + 2 Pol(evalNestedMultiplestop) = 3*V_1 - 3*V_2 + 3 Pol(koat_start) = -3*V_1 + 3*V_2 + 3 orients all transitions weakly and the transition evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4)) (Comp: 3*Ar_0 + 3*Ar_1 + 3, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4)) (Comp: 2, Cost: 1) evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalNestedMultiplebb4in) = 0 Pol(evalNestedMultiplebb5in) = -1 Pol(evalNestedMultiplebb3in) = 1 Pol(evalNestedMultiplebb1in) = 1 Pol(evalNestedMultiplebb2in) = 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = ? S("evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_3 S("evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4))", 0-0) = Ar_1 S("evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4))", 0-1) = ? S("evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4))", 0-2) = Ar_3 S("evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4))", 0-3) = ? S("evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4))", 0-4) = ? S("evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = Ar_1 S("evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = ? S("evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = Ar_3 S("evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_3 S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ]", 0-0) = Ar_1 S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ]", 0-1) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ]", 0-2) = Ar_3 S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ]", 0-3) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ]", 0-4) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ]", 0-0) = Ar_1 S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ]", 0-1) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ]", 0-2) = Ar_3 S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ]", 0-3) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ]", 0-4) = ? S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ]", 0-0) = Ar_1 S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ]", 0-1) = ? S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ]", 0-2) = Ar_3 S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ]", 0-3) = ? S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ]", 0-4) = ? S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ]", 0-0) = Ar_1 S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ]", 0-1) = ? S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ]", 0-2) = Ar_3 S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ]", 0-3) = ? S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ]", 0-4) = ? S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-0) = Ar_1 S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-1) = ? S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-2) = Ar_3 S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-3) = ? S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-4) = ? S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_1 S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = ? S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = Ar_3 S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = ? S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = ? S("evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4))", 0-0) = Ar_1 S("evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4))", 0-1) = Ar_0 S("evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4))", 0-2) = Ar_3 S("evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4))", 0-3) = Ar_2 S("evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4))", 0-4) = Ar_4 S("evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4)) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ] evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ] evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ] evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transition evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4)) (Comp: 3*Ar_0 + 3*Ar_1 + 3, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ] (Comp: 3*Ar_0 + 3*Ar_1 + 3, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4)) (Comp: 2, Cost: 1) evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalNestedMultiplebb4in) = 1 Pol(evalNestedMultiplebb5in) = 0 Pol(evalNestedMultiplebb3in) = 2 Pol(evalNestedMultiplebb1in) = 2 Pol(evalNestedMultiplebb2in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = ? S("evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_3 S("evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4))", 0-0) = Ar_1 S("evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4))", 0-1) = ? S("evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4))", 0-2) = Ar_3 S("evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4))", 0-3) = ? S("evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4))", 0-4) = ? S("evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = Ar_1 S("evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = ? S("evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = Ar_3 S("evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_3 S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ]", 0-0) = Ar_1 S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ]", 0-1) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ]", 0-2) = Ar_3 S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ]", 0-3) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ]", 0-4) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ]", 0-0) = Ar_1 S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ]", 0-1) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ]", 0-2) = Ar_3 S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ]", 0-3) = ? S("evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ]", 0-4) = ? S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ]", 0-0) = Ar_1 S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ]", 0-1) = ? S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ]", 0-2) = Ar_3 S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ]", 0-3) = ? S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ]", 0-4) = ? S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ]", 0-0) = Ar_1 S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ]", 0-1) = ? S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ]", 0-2) = Ar_3 S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ]", 0-3) = ? S("evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ]", 0-4) = ? S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-0) = Ar_1 S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-1) = ? S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-2) = Ar_3 S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-3) = ? S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-4) = ? S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_1 S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = ? S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = Ar_3 S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = ? S("evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = ? S("evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4))", 0-0) = Ar_1 S("evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4))", 0-1) = Ar_0 S("evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4))", 0-2) = Ar_3 S("evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4))", 0-3) = Ar_2 S("evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4))", 0-4) = Ar_4 S("evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4)) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ] evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ] evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ] evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transitions evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4)) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4)) (Comp: 3*Ar_0 + 3*Ar_1 + 3, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 9*Ar_0 + 9*Ar_1 + 9, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_2 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ F >= 1 ] (Comp: 3*Ar_0 + 3*Ar_1 + 3, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: 9*Ar_0 + 9*Ar_1 + 9, Cost: 1) evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4)) (Comp: 2, Cost: 1) evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 6 to obtain the following invariants: For symbol evalNestedMultiplebb1in: X_3 - X_5 - 1 >= 0 /\ -X_4 + X_5 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol evalNestedMultiplebb2in: -X_4 + X_5 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol evalNestedMultiplebb3in: X_3 - X_5 - 1 >= 0 /\ -X_4 + X_5 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol evalNestedMultiplebb4in: -X_4 + X_5 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol evalNestedMultiplereturnin: -X_1 + X_2 >= 0 This yielded the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + Ar_1 >= 0 ] (Comp: 9*Ar_0 + 9*Ar_1 + 9, Cost: 1) evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4)) [ -Ar_3 + Ar_4 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: ?, Cost: 1) evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_2 - Ar_4 - 1 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: 3*Ar_0 + 3*Ar_1 + 3, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 - 1 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 - 1 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ F >= 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 - 1 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ 0 >= F + 1 ] (Comp: ?, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_3 + Ar_4 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: 9*Ar_0 + 9*Ar_1 + 9, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_3 + Ar_4 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: 2, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 3*Ar_0 + 3*Ar_1 + 3, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = -V_1 + V_2 - 3*V_3 + 3*V_4 Pol(evalNestedMultiplestart) = -V_1 + V_2 - 3*V_3 + 3*V_4 Pol(evalNestedMultiplereturnin) = V_1 - V_2 + 3*V_3 - 3*V_4 Pol(evalNestedMultiplestop) = V_1 - V_2 + 3*V_3 - 3*V_4 Pol(evalNestedMultiplebb4in) = V_1 - V_2 + 3*V_3 - 3*V_5 - 1 Pol(evalNestedMultiplebb5in) = V_1 - V_2 + 3*V_3 - 3*V_4 Pol(evalNestedMultiplebb1in) = V_1 - V_2 + 3*V_3 - 3*V_5 - 2 Pol(evalNestedMultiplebb2in) = V_1 - V_2 + 3*V_3 - 3*V_5 Pol(evalNestedMultiplebb3in) = V_1 - V_2 + 3*V_3 - 3*V_5 - 1 Pol(evalNestedMultipleentryin) = -V_1 + V_2 - 3*V_3 + 3*V_4 orients all transitions weakly and the transitions evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 - 1 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ F >= 1 ] evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 - 1 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ 0 >= F + 1 ] evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_3 + Ar_4 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_2 - Ar_4 - 1 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + Ar_1 >= 0 ] (Comp: 9*Ar_0 + 9*Ar_1 + 9, Cost: 1) evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_0, Ar_1 + 1, Ar_2, Ar_4, Ar_4)) [ -Ar_3 + Ar_4 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: Ar_0 + Ar_1 + 3*Ar_2 + 3*Ar_3, Cost: 1) evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_2 - Ar_4 - 1 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: 3*Ar_0 + 3*Ar_1 + 3, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 - 1 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 ] (Comp: Ar_0 + Ar_1 + 3*Ar_2 + 3*Ar_3, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 - 1 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ F >= 1 ] (Comp: Ar_0 + Ar_1 + 3*Ar_2 + 3*Ar_3, Cost: 1) evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_4 - 1 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ 0 >= F + 1 ] (Comp: Ar_0 + Ar_1 + 3*Ar_2 + 3*Ar_3, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_3 + Ar_4 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_2 >= Ar_4 + 1 ] (Comp: 9*Ar_0 + 9*Ar_1 + 9, Cost: 1) evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_3 + Ar_4 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_4 >= Ar_2 ] (Comp: 2, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplereturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 3*Ar_0 + 3*Ar_1 + 3, Cost: 1) evalNestedMultiplebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_3)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultiplebb5in(Ar_1, Ar_0, Ar_3, Ar_2, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultiplestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) start location: koat_start leaf cost: 0 Complexity upper bound 28*Ar_0 + 28*Ar_1 + 12*Ar_2 + 12*Ar_3 + 30 Time: 2.722 sec (SMT: 2.598 sec)