WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] (Comp: ?, Cost: 1) evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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) evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] (Comp: ?, Cost: 1) evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalinsertsortstart) = 1 Pol(evalinsertsortentryin) = 1 Pol(evalinsertsortbb5in) = 1 Pol(evalinsertsortbbin) = 1 Pol(evalinsertsortreturnin) = 1 Pol(evalinsertsortbb2in) = 1 Pol(evalinsertsortbb4in) = 1 Pol(evalinsertsortbb3in) = 1 Pol(evalinsertsortbb1in) = 1 Pol(evalinsertsortstop) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3)) strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] (Comp: ?, Cost: 1) evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalinsertsortstart) = 1 Pol(evalinsertsortentryin) = 1 Pol(evalinsertsortbb5in) = 1 Pol(evalinsertsortbbin) = 1 Pol(evalinsertsortreturnin) = 0 Pol(evalinsertsortbb2in) = 1 Pol(evalinsertsortbb4in) = 1 Pol(evalinsertsortbb3in) = 1 Pol(evalinsertsortbb1in) = 1 Pol(evalinsertsortstop) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] (Comp: ?, Cost: 1) evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalinsertsortstart) = 4*V_2 Pol(evalinsertsortentryin) = 4*V_2 Pol(evalinsertsortbb5in) = -4*V_1 + 4*V_2 + 3 Pol(evalinsertsortbbin) = -4*V_1 + 4*V_2 + 2 Pol(evalinsertsortreturnin) = -4*V_1 + 4*V_2 + 3 Pol(evalinsertsortbb2in) = -4*V_1 + 4*V_2 + 1 Pol(evalinsertsortbb4in) = -4*V_1 + 4*V_2 Pol(evalinsertsortbb3in) = -4*V_1 + 4*V_2 + 1 Pol(evalinsertsortbb1in) = -4*V_1 + 4*V_2 + 1 Pol(evalinsertsortstop) = -4*V_1 + 4*V_2 + 3 Pol(koat_start) = 4*V_2 orients all transitions weakly and the transition evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] (Comp: ?, Cost: 1) evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (Comp: 1, Cost: 1) evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 4*Ar_1, Cost: 1) evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] (Comp: ?, Cost: 1) evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalinsertsortbb4in) = 0 Pol(evalinsertsortbb5in) = -1 Pol(evalinsertsortbb3in) = 1 Pol(evalinsertsortbb1in) = 1 Pol(evalinsertsortbb2in) = 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1))", 0-0) = ? S("evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1))", 0-1) = Ar_1 S("evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1))", 0-2) = ? S("evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1))", 0-3) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ]", 0-0) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ]", 0-1) = Ar_1 S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ]", 0-2) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ]", 0-3) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ]", 0-0) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ]", 0-2) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ]", 0-3) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ]", 0-0) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ]", 0-1) = Ar_1 S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ]", 0-2) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ]", 0-3) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-0) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-2) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-3) = ? S("evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1))", 0-0) = ? S("evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1))", 0-1) = Ar_1 S("evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1))", 0-2) = ? S("evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1))", 0-3) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-0) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-2) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3))", 0-0) = 1 S("evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) weakly and the transition evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 4*Ar_1, Cost: 1) evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] (Comp: ?, Cost: 1) evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalinsertsortbb4in) = 0 Pol(evalinsertsortbb5in) = -1 Pol(evalinsertsortbb3in) = 1 Pol(evalinsertsortbb1in) = 1 Pol(evalinsertsortbb2in) = 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1))", 0-0) = ? S("evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1))", 0-1) = Ar_1 S("evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1))", 0-2) = ? S("evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1))", 0-3) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ]", 0-0) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ]", 0-1) = Ar_1 S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ]", 0-2) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ]", 0-3) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ]", 0-0) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ]", 0-2) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ]", 0-3) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ]", 0-0) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ]", 0-1) = Ar_1 S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ]", 0-2) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ]", 0-3) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-0) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-2) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-3) = ? S("evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1))", 0-0) = ? S("evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1))", 0-1) = Ar_1 S("evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1))", 0-2) = ? S("evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1))", 0-3) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-0) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-2) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3))", 0-0) = 1 S("evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) weakly and the transition evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 1) evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 4*Ar_1, Cost: 1) evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1)) (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] (Comp: ?, Cost: 1) evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 8 produces the following problem: 9: T: (Comp: 1, Cost: 1) evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 4*Ar_1, Cost: 1) evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1)) (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] (Comp: ?, Cost: 1) evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) (Comp: 8*Ar_1, Cost: 1) evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalinsertsortbb3in) = 3*V_4 Pol(evalinsertsortbb1in) = 3*V_4 - 1 Pol(evalinsertsortbb2in) = 3*V_4 + 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 8*Ar_1 + 4160 S("evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-0) = 8*Ar_1 + 64 S("evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1))", 0-0) = 8*Ar_1 + 64 S("evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1))", 0-1) = Ar_1 S("evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1))", 0-2) = ? S("evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1))", 0-3) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ]", 0-0) = 8*Ar_1 + 64 S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ]", 0-1) = Ar_1 S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ]", 0-2) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ]", 0-3) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ]", 0-0) = 8*Ar_1 + 64 S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ]", 0-2) = ? S("evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ]", 0-3) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ]", 0-0) = 8*Ar_1 + 64 S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ]", 0-1) = Ar_1 S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ]", 0-2) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ]", 0-3) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-0) = 8*Ar_1 + 64 S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-2) = ? S("evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-3) = ? S("evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1))", 0-0) = 8*Ar_1 + 64 S("evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1))", 0-1) = Ar_1 S("evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1))", 0-2) = ? S("evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1))", 0-3) = 8*Ar_1 + 520 S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-0) = 8*Ar_1 + 520 S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-2) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-3) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = 8*Ar_1 + 64 S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = ? S("evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]", 0-3) = ? S("evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3))", 0-0) = 1 S("evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) weakly and the transition evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] strictly and produces the following problem: 10: T: (Comp: 1, Cost: 1) evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 4*Ar_1, Cost: 1) evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1)) (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: 96*Ar_1^2 + 6244*Ar_1, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] (Comp: ?, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] (Comp: ?, Cost: 1) evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) (Comp: 8*Ar_1, Cost: 1) evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 10 produces the following problem: 11: T: (Comp: 1, Cost: 1) evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(1, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalinsertsortbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 4*Ar_1, Cost: 1) evalinsertsortbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Fresh_0, Ar_0 - 1)) (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: 96*Ar_1^2 + 6244*Ar_1, Cost: 1) evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 ] (Comp: 96*Ar_1^2 + 6244*Ar_1, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= Ar_2 + 1 ] (Comp: 4*Ar_1, Cost: 1) evalinsertsortbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= E ] (Comp: 96*Ar_1^2 + 6244*Ar_1, Cost: 1) evalinsertsortbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb2in(Ar_0, Ar_1, Ar_2, Ar_3 - 1)) (Comp: 8*Ar_1, Cost: 1) evalinsertsortbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortbb5in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalinsertsortreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalinsertsortstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 18756*Ar_1 + 288*Ar_1^2 + 4 Time: 1.186 sec (SMT: 1.131 sec)