WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(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(evalNestedMultipleDepstart(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) evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(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(evalNestedMultipleDepstart(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(evalNestedMultipleDepstart) = 1 Pol(evalNestedMultipleDepentryin) = 1 Pol(evalNestedMultipleDepbb3in) = 1 Pol(evalNestedMultipleDepbbin) = 1 Pol(evalNestedMultipleDepreturnin) = 0 Pol(evalNestedMultipleDepbb2in) = 1 Pol(evalNestedMultipleDepbb1in) = 1 Pol(evalNestedMultipleDepstop) = -1 Pol(koat_start) = 1 orients all transitions weakly and the transition evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(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(evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (Comp: 1, Cost: 1) evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(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(evalNestedMultipleDepstart(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(evalNestedMultipleDepstart) = 3*V_2 Pol(evalNestedMultipleDepentryin) = 3*V_2 Pol(evalNestedMultipleDepbb3in) = -3*V_1 + 3*V_2 - 2 Pol(evalNestedMultipleDepbbin) = -3*V_1 + 3*V_2 - 3 Pol(evalNestedMultipleDepreturnin) = -3*V_1 + 3*V_2 - 2 Pol(evalNestedMultipleDepbb2in) = 3*V_2 - 3*V_3 - 1 Pol(evalNestedMultipleDepbb1in) = 3*V_2 - 3*V_3 - 1 Pol(evalNestedMultipleDepstop) = -3*V_1 + 3*V_2 - 2 Pol(koat_start) = 3*V_2 orients all transitions weakly and the transition evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 3*Ar_1, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(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(evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (Comp: 1, Cost: 1) evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 3*Ar_1, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: 3*Ar_1, Cost: 1) evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(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(evalNestedMultipleDepstart(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(evalNestedMultipleDepbb2in) = 1 Pol(evalNestedMultipleDepbb3in) = 0 Pol(evalNestedMultipleDepbb1in) = 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstart(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(evalNestedMultipleDepstart(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(evalNestedMultipleDepstart(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(evalNestedMultipleDepstart(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(evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 3*Ar_1 S("evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = 3*Ar_1 + 3*Ar_2 S("evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = 3*Ar_1 S("evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = 3*Ar_1 S("evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = Ar_4 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = 3*Ar_1 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = 3*Ar_1 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = Ar_4 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = 3*Ar_1 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = 3*Ar_1 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = Ar_4 S("evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-0) = 3*Ar_1 S("evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-1) = Ar_1 S("evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-2) = 3*Ar_1 S("evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-3) = 0 S("evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-4) = Ar_4 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-0) = 3*Ar_1 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-2) = 3*Ar_1 + 3*Ar_2 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-4) = Ar_4 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = 3*Ar_1 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = 3*Ar_1 + 3*Ar_2 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-4) = Ar_4 S("evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 0 S("evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) weakly and the transition evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 3*Ar_1, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: 3*Ar_1, Cost: 1) evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: ?, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: 3*Ar_1, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(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(evalNestedMultipleDepstart(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(evalNestedMultipleDepbb2in) = -2*V_4 + 2*V_5 Pol(evalNestedMultipleDepbb1in) = -2*V_4 + 2*V_5 - 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstart(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(evalNestedMultipleDepstart(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(evalNestedMultipleDepstart(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(evalNestedMultipleDepstart(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(evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 3*Ar_1 S("evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = 3*Ar_1 + 3*Ar_2 S("evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = 3*Ar_1 S("evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = 3*Ar_1 S("evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = Ar_4 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = 3*Ar_1 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = 3*Ar_1 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = Ar_4 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = 3*Ar_1 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = 3*Ar_1 S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = Ar_4 S("evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-0) = 3*Ar_1 S("evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-1) = Ar_1 S("evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-2) = 3*Ar_1 S("evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-3) = 0 S("evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4))", 0-4) = Ar_4 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-0) = 3*Ar_1 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-2) = 3*Ar_1 + 3*Ar_2 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ]", 0-4) = Ar_4 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = 3*Ar_1 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = 3*Ar_1 + 3*Ar_2 S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ]", 0-4) = Ar_4 S("evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 0 S("evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) weakly and the transition evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 1) evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 3*Ar_1, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: 3*Ar_1, Cost: 1) evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: 6*Ar_1*Ar_4, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: 3*Ar_1, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(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(evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 8 produces the following problem: 9: T: (Comp: 1, Cost: 1) evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 3*Ar_1, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalNestedMultipleDepbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: 3*Ar_1, Cost: 1) evalNestedMultipleDepbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_0 + 1, 0, Ar_4)) (Comp: 6*Ar_1*Ar_4, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: 3*Ar_1, Cost: 1) evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb3in(Ar_2, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: 6*Ar_1*Ar_4, Cost: 1) evalNestedMultipleDepbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepbb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 1, Cost: 1) evalNestedMultipleDepreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalNestedMultipleDepstop(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(evalNestedMultipleDepstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 9*Ar_1 + 12*Ar_1*Ar_4 + 4 Time: 1.022 sec (SMT: 0.959 sec)