/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 523 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 1637 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalperfectstart(A, B, C, D) -> Com_1(evalperfectentryin(A, B, C, D)) :|: TRUE evalperfectentryin(A, B, C, D) -> Com_1(evalperfectreturnin(A, B, C, D)) :|: 1 >= A evalperfectentryin(A, B, C, D) -> Com_1(evalperfectbb1in(A, B, C, D)) :|: A >= 2 evalperfectbb1in(A, B, C, D) -> Com_1(evalperfectbb8in(A, A, A - 1, D)) :|: TRUE evalperfectbb8in(A, B, C, D) -> Com_1(evalperfectbb4in(A, B, C, A)) :|: C >= 1 evalperfectbb8in(A, B, C, D) -> Com_1(evalperfectbb9in(B, B, C, D)) :|: 0 >= C evalperfectbb4in(A, B, C, D) -> Com_1(evalperfectbb3in(A, B, C, D)) :|: D >= C evalperfectbb4in(A, B, C, D) -> Com_1(evalperfectbb5in(A, B, C, D)) :|: C >= D + 1 evalperfectbb3in(A, B, C, D) -> Com_1(evalperfectbb4in(A, B, C, D - C)) :|: TRUE evalperfectbb5in(A, B, C, D) -> Com_1(evalperfectbb8in(A, B - C, C - 1, D)) :|: D >= 0 && D <= 0 evalperfectbb5in(A, B, C, D) -> Com_1(evalperfectbb8in(A, B, C - 1, D)) :|: 0 >= D + 1 evalperfectbb5in(A, B, C, D) -> Com_1(evalperfectbb8in(A, B, C - 1, D)) :|: D >= 1 evalperfectbb9in(A, B, C, D) -> Com_1(evalperfectreturnin(A, B, C, D)) :|: 0 >= A + 1 evalperfectbb9in(A, B, C, D) -> Com_1(evalperfectreturnin(A, B, C, D)) :|: A >= 1 evalperfectbb9in(A, B, C, D) -> Com_1(evalperfectreturnin(A, B, C, D)) :|: A >= 0 && A <= 0 evalperfectreturnin(A, B, C, D) -> Com_1(evalperfectstop(A, B, C, D)) :|: TRUE The start-symbols are:[evalperfectstart_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 29*Ar_0 + 8*Ar_0^2 + 45) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: ?, Cost: 1) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3)) (Comp: ?, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ] (Comp: ?, Cost: 1) evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(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) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3)) (Comp: ?, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ] (Comp: ?, Cost: 1) evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalperfectstart) = 3 Pol(evalperfectentryin) = 3 Pol(evalperfectreturnin) = 1 Pol(evalperfectbb1in) = 3 Pol(evalperfectbb8in) = 3 Pol(evalperfectbb4in) = 3 Pol(evalperfectbb9in) = 2 Pol(evalperfectbb3in) = 3 Pol(evalperfectbb5in) = 3 Pol(evalperfectstop) = 0 Pol(koat_start) = 3 orients all transitions weakly and the transitions evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ] evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ] evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3)) (Comp: ?, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ] (Comp: 3, Cost: 1) evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalperfectbb8in) = V_3 + 1 Pol(evalperfectbb4in) = V_3 Pol(evalperfectbb5in) = V_3 Pol(evalperfectbb3in) = V_3 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(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(evalperfectstart(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(evalperfectstart(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(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ]", 0-0) = 0 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ]", 0-1) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ]", 0-2) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ]", 0-3) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]", 0-0) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]", 0-1) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]", 0-2) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]", 0-3) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-0) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-1) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-2) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-3) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ]", 0-1) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ]", 0-2) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ]", 0-3) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-1) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-2) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-3) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ]", 0-1) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ]", 0-2) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ]", 0-3) = 0 S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2))", 0-0) = Ar_0 S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2))", 0-1) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2))", 0-2) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2))", 0-3) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ]", 0-1) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ]", 0-2) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ]", 0-3) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ]", 0-0) = Ar_0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ]", 0-1) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ]", 0-2) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ]", 0-3) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-0) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-1) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-2) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-3) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ]", 0-0) = Ar_0 S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ]", 0-1) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ]", 0-2) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ]", 0-3) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3))", 0-0) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3))", 0-1) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3))", 0-2) = Ar_0 + 1 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3))", 0-3) = Ar_3 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-0) = Ar_0 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-1) = Ar_1 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-2) = Ar_2 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-3) = Ar_3 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-1) = Ar_1 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-2) = Ar_2 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-3) = Ar_3 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ] evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ] evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ] evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) weakly and the transition evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3)) (Comp: Ar_0 + 2, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ] (Comp: 3, Cost: 1) evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalperfectbb5in) = 1 Pol(evalperfectbb8in) = 0 Pol(evalperfectbb4in) = 2 Pol(evalperfectbb3in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(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(evalperfectstart(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(evalperfectstart(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(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ]", 0-0) = 0 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ]", 0-1) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ]", 0-2) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ]", 0-3) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]", 0-0) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]", 0-1) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]", 0-2) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]", 0-3) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-0) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-1) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-2) = ? S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-3) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ]", 0-1) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ]", 0-2) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ]", 0-3) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-1) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-2) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ]", 0-3) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ]", 0-1) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ]", 0-2) = ? S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ]", 0-3) = 0 S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2))", 0-0) = Ar_0 S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2))", 0-1) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2))", 0-2) = ? S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2))", 0-3) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ]", 0-1) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ]", 0-2) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ]", 0-3) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ]", 0-0) = Ar_0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ]", 0-1) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ]", 0-2) = ? S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ]", 0-3) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-0) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-1) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-2) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]", 0-3) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ]", 0-0) = Ar_0 S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ]", 0-1) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ]", 0-2) = ? S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ]", 0-3) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3))", 0-0) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3))", 0-1) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3))", 0-2) = Ar_0 + 1 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3))", 0-3) = Ar_3 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-0) = Ar_0 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-1) = Ar_1 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-2) = Ar_2 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-3) = Ar_3 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-1) = Ar_1 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-2) = Ar_2 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-3) = Ar_3 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ] evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ] evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ] evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) weakly and the transitions evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ] evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ] evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3)) (Comp: Ar_0 + 2, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_2 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 ] (Comp: 2*Ar_0 + 4, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) (Comp: 2*Ar_0 + 4, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_3 = 0 ] (Comp: 2*Ar_0 + 4, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ 0 >= Ar_3 + 1 ] (Comp: 2*Ar_0 + 4, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_3 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ] (Comp: 3, Cost: 1) evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 5 to obtain the following invariants: For symbol evalperfectbb1in: X_1 - 2 >= 0 For symbol evalperfectbb3in: X_1 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_1 + X_4 - 3 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalperfectbb4in: X_1 - X_4 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalperfectbb5in: X_3 - X_4 - 1 >= 0 /\ X_1 - X_4 - 2 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalperfectbb8in: X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_1 - X_2 >= 0 /\ X_1 - 2 >= 0 For symbol evalperfectbb9in: -X_3 >= 0 /\ X_3 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 + X_2 >= 0 This yielded the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 3, Cost: 1) evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 = 0 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 4, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 >= 1 ] (Comp: 2*Ar_0 + 4, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: 2*Ar_0 + 4, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) [ Ar_0 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 ] (Comp: 2*Ar_0 + 4, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 >= Ar_2 ] (Comp: 3, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ 0 >= Ar_2 ] (Comp: Ar_0 + 2, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_2 >= 1 ] (Comp: 1, Cost: 1) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3)) [ Ar_0 - 2 >= 0 ] (Comp: 1, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalperfectbb4in) = -2*V_3 + 2*V_4 + 2 Pol(evalperfectbb3in) = -2*V_3 + 2*V_4 + 1 and size complexities S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-1) = Ar_1 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-2) = Ar_2 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ]", 0-3) = Ar_3 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-0) = Ar_0 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-1) = Ar_1 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-2) = Ar_2 S("evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ]", 0-3) = Ar_3 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3)) [ Ar_0 - 2 >= 0 ]", 0-0) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3)) [ Ar_0 - 2 >= 0 ]", 0-1) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3)) [ Ar_0 - 2 >= 0 ]", 0-2) = Ar_0 S("evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3)) [ Ar_0 - 2 >= 0 ]", 0-3) = Ar_3 S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 >= 1 ]", 0-0) = Ar_0 S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 >= 1 ]", 0-1) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 >= 1 ]", 0-2) = Ar_0 S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 >= 1 ]", 0-3) = Ar_0 S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_2 ]", 0-0) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_2 ]", 0-1) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_2 ]", 0-2) = 0 S("evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_2 ]", 0-3) = Ar_0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= Ar_2 ]", 0-0) = Ar_0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= Ar_2 ]", 0-1) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= Ar_2 ]", 0-2) = Ar_0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= Ar_2 ]", 0-3) = Ar_0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 >= Ar_3 + 1 ]", 0-1) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 >= Ar_3 + 1 ]", 0-2) = Ar_0 S("evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_2 >= Ar_3 + 1 ]", 0-3) = Ar_0 S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 3 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-0) = Ar_0 S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 3 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-1) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 3 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-2) = Ar_0 S("evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) [ Ar_0 - Ar_3 >= 0 /\\ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 2 >= 0 /\\ -Ar_2 + Ar_3 >= 0 /\\ Ar_0 + Ar_3 - 3 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 ]", 0-3) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 = 0 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 = 0 ]", 0-1) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 = 0 ]", 0-2) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 = 0 ]", 0-3) = 0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_3 + 1 ]", 0-1) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_3 + 1 ]", 0-2) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ 0 >= Ar_3 + 1 ]", 0-3) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= 1 ]", 0-0) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= 1 ]", 0-1) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= 1 ]", 0-2) = Ar_0 S("evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\\ Ar_0 - Ar_3 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 - 2 >= 0 /\\ Ar_3 >= 1 ]", 0-3) = Ar_0 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 ]", 0-0) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 ]", 0-1) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 ]", 0-2) = 0 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 ]", 0-3) = Ar_0 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 1 ]", 0-0) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 1 ]", 0-1) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 1 ]", 0-2) = 0 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 1 ]", 0-3) = Ar_0 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 = 0 ]", 0-0) = 0 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 = 0 ]", 0-1) = 0 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 = 0 ]", 0-2) = 0 S("evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 = 0 ]", 0-3) = Ar_0 S("evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 5*Ar_0 + 2*Ar_0^2 S("evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 + 5*Ar_0 + 2*Ar_0^2 S("evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_0 + Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(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(evalperfectstart(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(evalperfectstart(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(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 >= Ar_2 ] evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) [ Ar_0 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 ] weakly and the transitions evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 >= Ar_2 ] evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) [ Ar_0 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 3, Cost: 1) evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 = 0 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 1 ] (Comp: 3, Cost: 1) evalperfectbb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 4, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 >= 1 ] (Comp: 2*Ar_0 + 4, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ 0 >= Ar_3 + 1 ] (Comp: 2*Ar_0 + 4, Cost: 1) evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_1 - Ar_2, Ar_2 - 1, Ar_3)) [ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 = 0 ] (Comp: 4*Ar_0^2 + 10*Ar_0 + 4, Cost: 1) evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_2)) [ Ar_0 - Ar_3 >= 0 /\ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 2 >= 0 /\ -Ar_2 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 3 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 ] (Comp: 2*Ar_0 + 4, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_2 >= Ar_3 + 1 ] (Comp: 4*Ar_0^2 + 10*Ar_0 + 4, Cost: 1) evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_3 >= Ar_2 ] (Comp: 3, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb9in(Ar_1, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ 0 >= Ar_2 ] (Comp: Ar_0 + 2, Cost: 1) evalperfectbb8in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb4in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_2 >= 1 ] (Comp: 1, Cost: 1) evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb8in(Ar_0, Ar_0, Ar_0 - 1, Ar_3)) [ Ar_0 - 2 >= 0 ] (Comp: 1, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 1) evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_0 ] (Comp: 1, Cost: 1) evalperfectstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalperfectentryin(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound 29*Ar_0 + 8*Ar_0^2 + 45 Time: 0.503 sec (SMT: 0.398 sec) ---------------------------------------- (2) BOUNDS(1, n^2) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalperfectstart 0: evalperfectstart -> evalperfectentryin : [], cost: 1 1: evalperfectentryin -> evalperfectreturnin : [ 1>=A ], cost: 1 2: evalperfectentryin -> evalperfectbb1in : [ A>=2 ], cost: 1 3: evalperfectbb1in -> evalperfectbb8in : B'=A, C'=-1+A, [], cost: 1 4: evalperfectbb8in -> evalperfectbb4in : D'=A, [ C>=1 ], cost: 1 5: evalperfectbb8in -> evalperfectbb9in : A'=B, [ 0>=C ], cost: 1 6: evalperfectbb4in -> evalperfectbb3in : [ D>=C ], cost: 1 7: evalperfectbb4in -> evalperfectbb5in : [ C>=1+D ], cost: 1 8: evalperfectbb3in -> evalperfectbb4in : D'=-C+D, [], cost: 1 9: evalperfectbb5in -> evalperfectbb8in : B'=-C+B, C'=-1+C, [ D==0 ], cost: 1 10: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ 0>=1+D ], cost: 1 11: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ D>=1 ], cost: 1 12: evalperfectbb9in -> evalperfectreturnin : [ 0>=1+A ], cost: 1 13: evalperfectbb9in -> evalperfectreturnin : [ A>=1 ], cost: 1 14: evalperfectbb9in -> evalperfectreturnin : [ A==0 ], cost: 1 15: evalperfectreturnin -> evalperfectstop : [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: evalperfectstart -> evalperfectentryin : [], cost: 1 Removed unreachable and leaf rules: Start location: evalperfectstart 0: evalperfectstart -> evalperfectentryin : [], cost: 1 2: evalperfectentryin -> evalperfectbb1in : [ A>=2 ], cost: 1 3: evalperfectbb1in -> evalperfectbb8in : B'=A, C'=-1+A, [], cost: 1 4: evalperfectbb8in -> evalperfectbb4in : D'=A, [ C>=1 ], cost: 1 6: evalperfectbb4in -> evalperfectbb3in : [ D>=C ], cost: 1 7: evalperfectbb4in -> evalperfectbb5in : [ C>=1+D ], cost: 1 8: evalperfectbb3in -> evalperfectbb4in : D'=-C+D, [], cost: 1 9: evalperfectbb5in -> evalperfectbb8in : B'=-C+B, C'=-1+C, [ D==0 ], cost: 1 10: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ 0>=1+D ], cost: 1 11: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ D>=1 ], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalperfectstart 17: evalperfectstart -> evalperfectbb8in : B'=A, C'=-1+A, [ A>=2 ], cost: 3 4: evalperfectbb8in -> evalperfectbb4in : D'=A, [ C>=1 ], cost: 1 7: evalperfectbb4in -> evalperfectbb5in : [ C>=1+D ], cost: 1 18: evalperfectbb4in -> evalperfectbb4in : D'=-C+D, [ D>=C ], cost: 2 9: evalperfectbb5in -> evalperfectbb8in : B'=-C+B, C'=-1+C, [ D==0 ], cost: 1 10: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ 0>=1+D ], cost: 1 11: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ D>=1 ], cost: 1 Accelerating simple loops of location 4. Accelerating the following rules: 18: evalperfectbb4in -> evalperfectbb4in : D'=-C+D, [ D>=C ], cost: 2 Found no metering function for rule 18. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: evalperfectstart 17: evalperfectstart -> evalperfectbb8in : B'=A, C'=-1+A, [ A>=2 ], cost: 3 4: evalperfectbb8in -> evalperfectbb4in : D'=A, [ C>=1 ], cost: 1 7: evalperfectbb4in -> evalperfectbb5in : [ C>=1+D ], cost: 1 18: evalperfectbb4in -> evalperfectbb4in : D'=-C+D, [ D>=C ], cost: 2 9: evalperfectbb5in -> evalperfectbb8in : B'=-C+B, C'=-1+C, [ D==0 ], cost: 1 10: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ 0>=1+D ], cost: 1 11: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ D>=1 ], cost: 1 Chained accelerated rules (with incoming rules): Start location: evalperfectstart 17: evalperfectstart -> evalperfectbb8in : B'=A, C'=-1+A, [ A>=2 ], cost: 3 4: evalperfectbb8in -> evalperfectbb4in : D'=A, [ C>=1 ], cost: 1 19: evalperfectbb8in -> evalperfectbb4in : D'=-C+A, [ C>=1 && A>=C ], cost: 3 7: evalperfectbb4in -> evalperfectbb5in : [ C>=1+D ], cost: 1 9: evalperfectbb5in -> evalperfectbb8in : B'=-C+B, C'=-1+C, [ D==0 ], cost: 1 10: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ 0>=1+D ], cost: 1 11: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ D>=1 ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalperfectstart 17: evalperfectstart -> evalperfectbb8in : B'=A, C'=-1+A, [ A>=2 ], cost: 3 20: evalperfectbb8in -> evalperfectbb5in : D'=A, [ C>=1 && C>=1+A ], cost: 2 21: evalperfectbb8in -> evalperfectbb5in : D'=-C+A, [ C>=1 && A>=C && C>=1-C+A ], cost: 4 9: evalperfectbb5in -> evalperfectbb8in : B'=-C+B, C'=-1+C, [ D==0 ], cost: 1 10: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ 0>=1+D ], cost: 1 11: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ D>=1 ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalperfectstart 17: evalperfectstart -> evalperfectbb8in : B'=A, C'=-1+A, [ A>=2 ], cost: 3 22: evalperfectbb8in -> evalperfectbb8in : B'=-C+B, C'=-1+C, D'=A, [ C>=1 && C>=1+A && A==0 ], cost: 3 23: evalperfectbb8in -> evalperfectbb8in : C'=-1+C, D'=A, [ C>=1 && C>=1+A && 0>=1+A ], cost: 3 24: evalperfectbb8in -> evalperfectbb8in : C'=-1+C, D'=A, [ C>=1 && C>=1+A && A>=1 ], cost: 3 25: evalperfectbb8in -> evalperfectbb8in : B'=-C+B, C'=-1+C, D'=-C+A, [ C>=1 && C>=1-C+A && -C+A==0 ], cost: 5 26: evalperfectbb8in -> evalperfectbb8in : C'=-1+C, D'=-C+A, [ C>=1 && C>=1-C+A && -C+A>=1 ], cost: 5 Accelerating simple loops of location 3. Accelerating the following rules: 22: evalperfectbb8in -> evalperfectbb8in : B'=-C+B, C'=-1+C, D'=A, [ C>=1 && C>=1+A && A==0 ], cost: 3 23: evalperfectbb8in -> evalperfectbb8in : C'=-1+C, D'=A, [ C>=1 && C>=1+A && 0>=1+A ], cost: 3 24: evalperfectbb8in -> evalperfectbb8in : C'=-1+C, D'=A, [ C>=1 && C>=1+A && A>=1 ], cost: 3 25: evalperfectbb8in -> evalperfectbb8in : B'=-C+B, C'=-1+C, D'=-C+A, [ C>=1 && C>=1-C+A && -C+A==0 ], cost: 5 26: evalperfectbb8in -> evalperfectbb8in : C'=-1+C, D'=-C+A, [ C>=1 && C>=1-C+A && -C+A>=1 ], cost: 5 Accelerated rule 22 with metering function C-A, yielding the new rule 27. Accelerated rule 23 with metering function C, yielding the new rule 28. Accelerated rule 24 with metering function C-A, yielding the new rule 29. Accelerated rule 25 with metering function C-A, yielding the new rule 30. Accelerated rule 26 with metering function meter (where 2*meter==2*C-A), yielding the new rule 31. During metering: Instantiating temporary variables by {meter==1} Removing the simple loops: 22 23 24 25 26. Accelerated all simple loops using metering functions (where possible): Start location: evalperfectstart 17: evalperfectstart -> evalperfectbb8in : B'=A, C'=-1+A, [ A>=2 ], cost: 3 27: evalperfectbb8in -> evalperfectbb8in : B'=-1/2*C+1/2*A+1/2*(C-A)^2+B-C*(C-A), C'=A, D'=A, [ C>=1 && C>=1+A && A==0 ], cost: 3*C-3*A 28: evalperfectbb8in -> evalperfectbb8in : C'=0, D'=A, [ C>=1 && C>=1+A && 0>=1+A ], cost: 3*C 29: evalperfectbb8in -> evalperfectbb8in : C'=A, D'=A, [ C>=1 && C>=1+A && A>=1 ], cost: 3*C-3*A 30: evalperfectbb8in -> evalperfectbb8in : B'=-1/2*C+1/2*A+1/2*(C-A)^2+B-C*(C-A), C'=A, D'=-1, [ C>=1 && C>=1-C+A && -C+A==0 && C-A>=1 ], cost: 5*C-5*A 31: evalperfectbb8in -> evalperfectbb8in : C'=C-meter, D'=-1-C+meter+A, [ C>=1 && C>=1-C+A && -C+A>=1 && 2*meter==2*C-A && meter>=1 ], cost: 5*meter Chained accelerated rules (with incoming rules): Start location: evalperfectstart 17: evalperfectstart -> evalperfectbb8in : B'=A, C'=-1+A, [ A>=2 ], cost: 3 32: evalperfectstart -> evalperfectbb8in : B'=A, C'=-1-meter+A, D'=meter, [ -1+A>=2 && 2*meter==-2+A && meter>=1 ], cost: 3+5*meter Removed unreachable locations (and leaf rules with constant cost): Start location: evalperfectstart 32: evalperfectstart -> evalperfectbb8in : B'=A, C'=-1-meter+A, D'=meter, [ -1+A>=2 && 2*meter==-2+A && meter>=1 ], cost: 3+5*meter ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalperfectstart 32: evalperfectstart -> evalperfectbb8in : B'=A, C'=-1-meter+A, D'=meter, [ -1+A>=2 && 2*meter==-2+A && meter>=1 ], cost: 3+5*meter Computing asymptotic complexity for rule 32 Solved the limit problem by the following transformations: Created initial limit problem: -1-2*meter+A (+/+!), 3+5*meter (+), 3+2*meter-A (+/+!), -2+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {meter==n,A==2+2*n} resulting limit problem: [solved] Solution: meter / n A / 2+2*n Resulting cost 3+5*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 3+5*n Rule cost: 3+5*meter Rule guard: [ -1+A>=2 && 2*meter==-2+A ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)