WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 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) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfstart) = 1 Pol(evalfentryin) = 1 Pol(evalfbb4in) = 1 Pol(evalfbb2in) = 1 Pol(evalfreturnin) = 0 Pol(evalfbb1in) = 1 Pol(evalfbb3in) = 1 Pol(evalfstop) = -1 Pol(koat_start) = 1 orients all transitions weakly and the transition evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 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(evalfbb4in) = -2*V_1 + 2*V_2 + 1 Pol(evalfbb2in) = -2*V_1 + 2*V_2 - 1 Pol(evalfreturnin) = -2*V_1 + 2*V_2 + 1 Pol(evalfbb1in) = -2*V_1 + 2*V_2 - 1 Pol(evalfbb3in) = -2*V_1 + 2*V_2 - 1 Pol(evalfstop) = -2*V_1 + 2*V_2 + 1 Pol(koat_start) = 2*V_2 orients all transitions weakly and the transition evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2)) (Comp: 2*Ar_1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb3in) = 1 Pol(evalfbb4in) = 0 Pol(evalfbb2in) = 2 Pol(evalfbb1in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 S("evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2))", 0-0) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2))", 0-2) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2))", 0-0) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2))", 0-2) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1))", 0-0) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1))", 0-1) = Ar_1 S("evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1))", 0-2) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]", 0-0) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]", 0-2) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ]", 0-0) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ]", 0-1) = Ar_1 S("evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ]", 0-0) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ]", 0-2) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2))", 0-0) = 1 S("evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 orients the transitions evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2)) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1)) weakly and the transitions evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2)) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2)) (Comp: 2*Ar_1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: 4*Ar_1, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: 4*Ar_1, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb2in) = 2*V_2 - 2*V_3 + 2 Pol(evalfbb1in) = 2*V_2 - 2*V_3 + 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 S("evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2))", 0-0) = 4*Ar_1 + 272 S("evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2))", 0-2) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2))", 0-0) = 4*Ar_1 + 16 S("evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2))", 0-2) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1))", 0-0) = 4*Ar_1 + 16 S("evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1))", 0-1) = Ar_1 S("evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1))", 0-2) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]", 0-0) = 4*Ar_1 + 16 S("evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]", 0-2) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ]", 0-0) = 4*Ar_1 + 16 S("evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ]", 0-1) = Ar_1 S("evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = 4*Ar_1 + 68 S("evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ]", 0-0) = 4*Ar_1 + 16 S("evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ]", 0-2) = 4*Ar_1 + 68 S("evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2))", 0-0) = 1 S("evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 orients the transitions evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1)) weakly and the transition evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2)) (Comp: 2*Ar_1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 20*Ar_1^2 + 276*Ar_1, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: 4*Ar_1, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: 4*Ar_1, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 7 produces the following problem: 8: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(1, Ar_1, Ar_2)) (Comp: 2*Ar_1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 20*Ar_1^2 + 276*Ar_1, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 ] (Comp: 4*Ar_1, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ] (Comp: 20*Ar_1^2 + 276*Ar_1, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: 4*Ar_1, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalfbb4in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 562*Ar_1 + 40*Ar_1^2 + 4 Time: 0.756 sec (SMT: 0.710 sec)