WORST_CASE(?, O(n^6)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(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(evalfstart(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) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(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(evalfstart(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(evalfstart) = 2 Pol(evalfentryin) = 2 Pol(evalfbb10in) = 2 Pol(evalfbb8in) = 2 Pol(evalfreturnin) = 1 Pol(evalfbb6in) = 2 Pol(evalfbb4in) = 2 Pol(evalfbb7in) = 2 Pol(evalfbb3in) = 2 Pol(evalfbb5in) = 2 Pol(evalfstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(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(evalfstart(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(evalfstart) = 2*V_2 Pol(evalfentryin) = 2*V_2 Pol(evalfbb10in) = -2*V_1 + 2*V_2 + 1 Pol(evalfbb8in) = -2*V_1 + 2*V_2 Pol(evalfreturnin) = -2*V_1 + 2*V_2 + 1 Pol(evalfbb6in) = -2*V_1 + 2*V_2 Pol(evalfbb4in) = -2*V_1 + 2*V_2 Pol(evalfbb7in) = -2*V_1 + 2*V_2 Pol(evalfbb3in) = -2*V_1 + 2*V_2 Pol(evalfbb5in) = -2*V_1 + 2*V_2 Pol(evalfstop) = -2*V_1 + 2*V_2 + 1 Pol(koat_start) = 2*V_2 orients all transitions weakly and the transition evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2*Ar_1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(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(evalfstart(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(evalfbb8in) = 1 Pol(evalfbb6in) = 1 Pol(evalfbb10in) = 0 Pol(evalfbb7in) = 1 Pol(evalfbb4in) = 1 Pol(evalfbb5in) = 1 Pol(evalfbb3in) = 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-0) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-0) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-0) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transition evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2*Ar_1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(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(evalfstart(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(evalfbb8in) = V_1 - V_3 + 2 Pol(evalfbb6in) = V_1 - V_3 + 1 Pol(evalfbb7in) = V_1 - V_3 + 1 Pol(evalfbb4in) = V_1 - V_3 + 1 Pol(evalfbb5in) = V_1 - V_3 + 1 Pol(evalfbb3in) = V_1 - V_3 + 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 2*Ar_1 + 20 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = 2*Ar_1 + 4 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = 2*Ar_1 + 4 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = 2*Ar_1 + 4 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = 2*Ar_1 + 10 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 2*Ar_1 + 10 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transition evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2*Ar_1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 4*Ar_1^2 + 14*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(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(evalfstart(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(evalfbb7in) = 1 Pol(evalfbb8in) = 0 Pol(evalfbb6in) = 2 Pol(evalfbb4in) = 2 Pol(evalfbb5in) = 2 Pol(evalfbb3in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 2*Ar_1 + 20 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = 2*Ar_1 + 4 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = 2*Ar_1 + 4 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = 2*Ar_1 + 4 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = 2*Ar_1 + 10 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 2*Ar_1 + 10 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transition evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2*Ar_1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 4*Ar_1^2 + 14*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 8*Ar_1^2 + 28*Ar_1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(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(evalfstart(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(evalfbb6in) = 1 Pol(evalfbb7in) = 0 Pol(evalfbb4in) = 1 Pol(evalfbb5in) = 1 Pol(evalfbb3in) = 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 2*Ar_1 + 20 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 + 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = 2*Ar_1 + 4 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = 2*Ar_1 + 4 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = 2*Ar_1 + 4 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = 2*Ar_1 + 10 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 2*Ar_1 + 10 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = Ar_2 + 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transition evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2*Ar_1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 4*Ar_1^2 + 14*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] (Comp: 4*Ar_1^2 + 14*Ar_1, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 8*Ar_1^2 + 28*Ar_1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(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(evalfstart(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(evalfbb6in) = 3*V_2 - 3*V_4 + 1 Pol(evalfbb4in) = 3*V_2 - 3*V_4 Pol(evalfbb5in) = 3*V_2 - 3*V_4 - 1 Pol(evalfbb3in) = 3*V_2 - 3*V_4 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 2*Ar_1 + 20 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 + 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = 2*Ar_1 + 4 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = 2*Ar_1 + 4 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = 2*Ar_1 + 4 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = 2*Ar_1 + 10 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 2*Ar_1 + 10 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = Ar_2 + 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transition evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] strictly and produces the following problem: 9: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2*Ar_1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 4*Ar_1^2 + 14*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 36*Ar_1^3 + 250*Ar_1^2 + 434*Ar_1, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] (Comp: 4*Ar_1^2 + 14*Ar_1, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 8*Ar_1^2 + 28*Ar_1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(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(evalfstart(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(evalfbb5in) = 1 Pol(evalfbb6in) = 0 Pol(evalfbb4in) = 2 Pol(evalfbb3in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 2*Ar_1 + 20 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 + 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = 2*Ar_1 + 4 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = 2*Ar_1 + 4 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = 2*Ar_1 + 4 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = 2*Ar_1 + 10 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 2*Ar_1 + 10 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = Ar_2 + 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transitions evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] strictly and produces the following problem: 10: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2*Ar_1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 4*Ar_1^2 + 14*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 36*Ar_1^3 + 250*Ar_1^2 + 434*Ar_1, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] (Comp: 4*Ar_1^2 + 14*Ar_1, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: 72*Ar_1^3 + 500*Ar_1^2 + 868*Ar_1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: 72*Ar_1^3 + 500*Ar_1^2 + 868*Ar_1, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 8*Ar_1^2 + 28*Ar_1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(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(evalfstart(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(evalfbb4in) = 2*V_4 - 2*V_5 + 1 Pol(evalfbb3in) = 2*V_4 - 2*V_5 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 2*Ar_1 + 20 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 + 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 + 869*Ar_1 + 72*Ar_1^3 + 500*Ar_1^2 + 20 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = 2*Ar_1 + 4 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = 869*Ar_1 + 72*Ar_1^3 + 500*Ar_1^2 + 20 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = 2*Ar_1 + 4 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = 869*Ar_1 + 72*Ar_1^3 + 500*Ar_1^2 + 5 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = 2*Ar_1 + 4 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = 869*Ar_1 + 72*Ar_1^3 + 500*Ar_1^2 + 5 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = 869*Ar_1 + 72*Ar_1^3 + 500*Ar_1^2 + 5 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = 869*Ar_1 + 72*Ar_1^3 + 500*Ar_1^2 + 5 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-3) = 869*Ar_1 + 72*Ar_1^3 + 500*Ar_1^2 + 20 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-1) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-3) = 869*Ar_1 + 72*Ar_1^3 + 500*Ar_1^2 + 5 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = Ar_3 + 869*Ar_1 + 72*Ar_1^3 + 500*Ar_1^2 + 20 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = 2*Ar_1 + 10 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 2*Ar_1 + 10 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = Ar_2 + 8*Ar_1^2 + 28*Ar_1 + 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = Ar_3 + 869*Ar_1 + 72*Ar_1^3 + 500*Ar_1^2 + 20 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-0) = 2*Ar_1 + 4 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-1) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-3) = Ar_3 + 869*Ar_1 + 72*Ar_1^3 + 500*Ar_1^2 + 20 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transition evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] strictly and produces the following problem: 11: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2*Ar_1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 4*Ar_1^2 + 14*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 36*Ar_1^3 + 250*Ar_1^2 + 434*Ar_1, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] (Comp: 4*Ar_1^2 + 14*Ar_1, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: 375064*Ar_1^4 + 868968*Ar_1^3 + 757542*Ar_1^2 + 5184*Ar_1^6 + 72000*Ar_1^5 + 5642*Ar_1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: 72*Ar_1^3 + 500*Ar_1^2 + 868*Ar_1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: 72*Ar_1^3 + 500*Ar_1^2 + 868*Ar_1, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 8*Ar_1^2 + 28*Ar_1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(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(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 11 produces the following problem: 12: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2*Ar_1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 4*Ar_1^2 + 14*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_0 + 1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_1, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 36*Ar_1^3 + 250*Ar_1^2 + 434*Ar_1, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 >= Ar_3 ] (Comp: 4*Ar_1^2 + 14*Ar_1, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 ] (Comp: 375064*Ar_1^4 + 868968*Ar_1^3 + 757542*Ar_1^2 + 5184*Ar_1^6 + 72000*Ar_1^5 + 5642*Ar_1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: 72*Ar_1^3 + 500*Ar_1^2 + 868*Ar_1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: 375064*Ar_1^4 + 868968*Ar_1^3 + 757542*Ar_1^2 + 5184*Ar_1^6 + 72000*Ar_1^5 + 5642*Ar_1, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: 72*Ar_1^3 + 500*Ar_1^2 + 868*Ar_1, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 8*Ar_1^2 + 28*Ar_1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(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(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 13514*Ar_1 + 1516350*Ar_1^2 + 1738116*Ar_1^3 + 750128*Ar_1^4 + 10368*Ar_1^6 + 144000*Ar_1^5 + 6 Time: 1.780 sec (SMT: 1.660 sec)