/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^3). (0) CpxIntTrs (1) Koat Proof [FINISHED, 779 ms] (2) BOUNDS(1, n^3) (3) Loat Proof [FINISHED, 3149 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalrealshellsortstart(A, B, C, D, E) -> Com_1(evalrealshellsortentryin(A, B, C, D, E)) :|: TRUE evalrealshellsortentryin(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, 0, C, D, E)) :|: A >= 0 && A <= 0 evalrealshellsortentryin(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, F, C, D, E)) :|: A >= 1 && F >= 0 && A >= 2 * F && 1 + 2 * F >= A evalrealshellsortentryin(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, F, C, D, E)) :|: 0 >= A + 1 && 0 >= F && 2 * F >= A && 1 + A >= 2 * F evalrealshellsortbb8in(A, B, C, D, E) -> Com_1(evalrealshellsortbb6in(A, B, 0, D, E)) :|: B >= 1 evalrealshellsortbb8in(A, B, C, D, E) -> Com_1(evalrealshellsortreturnin(A, B, C, D, E)) :|: 0 >= B evalrealshellsortbb6in(A, B, C, D, E) -> Com_1(evalrealshellsortbb1in(A, B, C, D, E)) :|: A >= C + 1 evalrealshellsortbb6in(A, B, C, D, E) -> Com_1(evalrealshellsortbb7in(A, B, C, D, E)) :|: C >= A evalrealshellsortbb1in(A, B, C, D, E) -> Com_1(evalrealshellsortbb3in(A, B, C, F, C)) :|: TRUE evalrealshellsortbb3in(A, B, C, D, E) -> Com_1(evalrealshellsortbb5in(A, B, C, D, E)) :|: B >= E + 1 evalrealshellsortbb3in(A, B, C, D, E) -> Com_1(evalrealshellsortbb4in(A, B, C, D, E)) :|: E >= B evalrealshellsortbb4in(A, B, C, D, E) -> Com_1(evalrealshellsortbb2in(A, B, C, D, E)) :|: F >= D + 1 evalrealshellsortbb4in(A, B, C, D, E) -> Com_1(evalrealshellsortbb5in(A, B, C, D, E)) :|: D >= F evalrealshellsortbb2in(A, B, C, D, E) -> Com_1(evalrealshellsortbb3in(A, B, C, D, E - B)) :|: TRUE evalrealshellsortbb5in(A, B, C, D, E) -> Com_1(evalrealshellsortbb6in(A, B, C + 1, D, E)) :|: TRUE evalrealshellsortbb7in(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, 0, C, D, E)) :|: B >= 0 && B <= 0 evalrealshellsortbb7in(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, F, C, D, E)) :|: B >= 1 && F >= 0 && B >= 2 * F && 1 + 2 * F >= B evalrealshellsortbb7in(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, F, C, D, E)) :|: 0 >= B + 1 && 0 >= F && 2 * F >= B && 1 + B >= 2 * F evalrealshellsortreturnin(A, B, C, D, E) -> Com_1(evalrealshellsortstop(A, B, C, D, E)) :|: TRUE The start-symbols are:[evalrealshellsortstart_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 73*ar_0 + 65*ar_0^2 + 18*ar_0^3 + 37) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: ?, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: ?, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: ?, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) (Comp: ?, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ] (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] (Comp: ?, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: ?, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) (Comp: ?, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ] (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] (Comp: ?, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealshellsortstart) = 2 Pol(evalrealshellsortentryin) = 2 Pol(evalrealshellsortbb8in) = 2 Pol(evalrealshellsortbb6in) = 2 Pol(evalrealshellsortreturnin) = 1 Pol(evalrealshellsortbb1in) = 2 Pol(evalrealshellsortbb7in) = 2 Pol(evalrealshellsortbb3in) = 2 Pol(evalrealshellsortbb5in) = 2 Pol(evalrealshellsortbb4in) = 2 Pol(evalrealshellsortbb2in) = 2 Pol(evalrealshellsortstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: ?, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) (Comp: ?, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ] (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] (Comp: 2, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealshellsortstart) = V_1 + 1 Pol(evalrealshellsortentryin) = V_1 + 1 Pol(evalrealshellsortbb8in) = 2*V_2 Pol(evalrealshellsortbb6in) = V_2 + 1 Pol(evalrealshellsortreturnin) = 2*V_2 Pol(evalrealshellsortbb1in) = V_2 + 1 Pol(evalrealshellsortbb7in) = V_2 + 1 Pol(evalrealshellsortbb3in) = V_2 + 1 Pol(evalrealshellsortbb5in) = V_2 + 1 Pol(evalrealshellsortbb4in) = V_2 + 1 Pol(evalrealshellsortbb2in) = V_2 + 1 Pol(evalrealshellsortstop) = 2*V_2 Pol(koat_start) = V_1 + 1 orients all transitions weakly and the transitions evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: ?, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) (Comp: ?, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ] (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] (Comp: 2, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: ar_0 + 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) (Comp: ?, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ] (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] (Comp: 2, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealshellsortbb7in) = 1 Pol(evalrealshellsortbb8in) = 0 Pol(evalrealshellsortbb6in) = 2 Pol(evalrealshellsortbb1in) = 2 Pol(evalrealshellsortbb5in) = 2 Pol(evalrealshellsortbb4in) = 2 Pol(evalrealshellsortbb2in) = 2 Pol(evalrealshellsortbb3in) = 2 and size complexities S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_0 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ? S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ? S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-0) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-1) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-2) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-3) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-4) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-0) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-1) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-2) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-3) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-4) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-0) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-1) = 0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-2) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-3) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-4) = ? S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-0) = ar_0 S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-1) = ar_0 S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-2) = ? S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-3) = ? S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-4) = ? S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-0) = ar_0 S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-1) = ar_0 S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-2) = ? S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-3) = ? S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-4) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-0) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-1) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-2) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-3) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-4) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-0) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-1) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-2) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-3) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-4) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-0) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-1) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-2) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-0) = ar_0 S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-1) = ar_0 S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-2) = ? S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-3) = ? S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-4) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-0) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-1) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-2) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-3) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-4) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-0) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-3) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-4) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-0) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-1) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-2) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-3) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-4) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-0) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-1) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-2) = 0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-3) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-4) = ? S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-0) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-1) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-2) = ar_2 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-3) = ar_3 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-4) = ar_4 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-0) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-1) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-2) = ar_2 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-3) = ar_3 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-4) = ar_4 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-0) = 0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-1) = 0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-2) = ar_2 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-3) = ar_3 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-4) = ar_4 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 orients the transitions evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ] evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) weakly and the transitions evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: ar_0 + 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] (Comp: 2*ar_0 + 4, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) (Comp: ?, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ] (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: 2*ar_0 + 4, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] (Comp: 2, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealshellsortbb6in) = V_1 - V_3 + 1 Pol(evalrealshellsortbb1in) = V_1 - V_3 Pol(evalrealshellsortbb5in) = V_1 - V_3 Pol(evalrealshellsortbb4in) = V_1 - V_3 Pol(evalrealshellsortbb2in) = V_1 - V_3 Pol(evalrealshellsortbb3in) = V_1 - V_3 and size complexities S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_0 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ? S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ? S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-0) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-1) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-2) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-3) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-4) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-0) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-1) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-2) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-3) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-4) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-0) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-1) = 0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-2) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-3) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-4) = ? S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-0) = ar_0 S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-1) = ar_0 S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-2) = ? S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-3) = ? S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-4) = ? S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-0) = ar_0 S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-1) = ar_0 S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-2) = ? S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-3) = ? S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-4) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-0) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-1) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-2) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-3) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-4) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-0) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-1) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-2) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-3) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-4) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-0) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-1) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-2) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-0) = ar_0 S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-1) = ar_0 S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-2) = ? S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-3) = ? S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-4) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-0) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-1) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-2) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-3) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-4) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-0) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-3) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-4) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-0) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-1) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-2) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-3) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-4) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-0) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-1) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-2) = 0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-3) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-4) = ? S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-0) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-1) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-2) = ar_2 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-3) = ar_3 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-4) = ar_4 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-0) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-1) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-2) = ar_2 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-3) = ar_3 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-4) = ar_4 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-0) = 0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-1) = 0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-2) = ar_2 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-3) = ar_3 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-4) = ar_4 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 orients the transitions evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) weakly and the transition evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: ar_0 + 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ar_0^2 + 3*ar_0 + 2, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] (Comp: 2*ar_0 + 4, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) (Comp: ?, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ] (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: 2*ar_0 + 4, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] (Comp: 2, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 7 produces the following problem: 8: T: (Comp: 1, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: ar_0 + 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ar_0^2 + 3*ar_0 + 2, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] (Comp: 2*ar_0 + 4, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ] (Comp: ar_0^2 + 3*ar_0 + 2, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) (Comp: ?, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ] (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: 2*ar_0 + 4, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] (Comp: 2, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealshellsortbb5in) = 1 Pol(evalrealshellsortbb6in) = 0 Pol(evalrealshellsortbb4in) = 2 Pol(evalrealshellsortbb2in) = 2 Pol(evalrealshellsortbb3in) = 2 and size complexities S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_0 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ? S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ? S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-0) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-1) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-2) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-3) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\\ 0 >= f /\\ 2*f >= ar_1 /\\ ar_1 + 1 >= 2*f ]", 0-4) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-0) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-1) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-2) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-3) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-4) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-0) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-1) = 0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-2) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-3) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ]", 0-4) = ? S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-0) = ar_0 S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-1) = ar_0 S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-2) = ? S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-3) = ? S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4))", 0-4) = ? S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-0) = ar_0 S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-1) = ar_0 S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-2) = ? S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-3) = ? S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1))", 0-4) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-0) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-1) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-2) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-3) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ]", 0-4) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-0) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-1) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-2) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-3) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ]", 0-4) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-0) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-1) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-2) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-0) = ar_0 S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-1) = ar_0 S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-2) = ? S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-3) = ? S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2))", 0-4) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-0) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-1) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-2) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-3) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ]", 0-4) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-0) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-3) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ]", 0-4) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-0) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-1) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-2) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-3) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-4) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-0) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-1) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-2) = 0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-3) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-4) = ? S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-0) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-1) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-2) = ar_2 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-3) = ar_3 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-4) = ar_4 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-0) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-1) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-2) = ar_2 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-3) = ar_3 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-4) = ar_4 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-0) = 0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-1) = 0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-2) = ar_2 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-3) = ar_3 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-4) = ar_4 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 orients the transitions evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) weakly and the transitions evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] strictly and produces the following problem: 9: T: (Comp: 1, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: ar_0 + 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ar_0^2 + 3*ar_0 + 2, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] (Comp: 2*ar_0 + 4, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ] (Comp: ar_0^2 + 3*ar_0 + 2, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) (Comp: 2*ar_0^2 + 6*ar_0 + 4, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] (Comp: 2*ar_0^2 + 6*ar_0 + 4, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) (Comp: 2*ar_0^2 + 6*ar_0 + 4, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ] (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: 2*ar_0 + 4, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] (Comp: 2, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 9 to obtain the following invariants: For symbol evalrealshellsortbb1in: X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalrealshellsortbb2in: X_3 - X_5 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 - 1 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ X_2 + X_5 - 2 >= 0 /\ -X_2 + X_5 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 2 >= 0 For symbol evalrealshellsortbb3in: X_3 - X_5 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_3 + X_5 >= 0 /\ X_2 + X_5 - 1 >= 0 /\ X_1 + X_5 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalrealshellsortbb4in: X_3 - X_5 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_5 - 1 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ X_2 + X_5 - 2 >= 0 /\ -X_2 + X_5 >= 0 /\ X_1 + X_5 - 3 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 2 >= 0 For symbol evalrealshellsortbb5in: X_3 - X_5 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_3 + X_5 >= 0 /\ X_2 + X_5 - 1 >= 0 /\ X_1 + X_5 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 For symbol evalrealshellsortbb6in: X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 For symbol evalrealshellsortbb7in: X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 - 1 >= 0 For symbol evalrealshellsortreturnin: -X_2 >= 0 This yielded the following problem: 10: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 >= 0 ] (Comp: 2*ar_0 + 4, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_1 = 0 ] (Comp: 2*ar_0^2 + 6*ar_0 + 4, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: 2*ar_0^2 + 6*ar_0 + 4, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 /\ ar_3 >= f ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 /\ f >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_4 >= ar_1 ] (Comp: 2*ar_0^2 + 6*ar_0 + 4, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_4 + 1 ] (Comp: ar_0^2 + 3*ar_0 + 2, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) [ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 2*ar_0 + 4, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_2 >= ar_0 ] (Comp: ar_0^2 + 3*ar_0 + 2, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ] (Comp: 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ar_0 + 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: 1, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) start location: koat_start leaf cost: 0 Testing for unsatisfiable constraints removes the following transitions from problem 10: evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_1 = 0 ] We thus obtain the following problem: 11: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 >= 0 ] (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: 2*ar_0^2 + 6*ar_0 + 4, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: 2*ar_0^2 + 6*ar_0 + 4, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 /\ ar_3 >= f ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 /\ f >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_4 >= ar_1 ] (Comp: 2*ar_0^2 + 6*ar_0 + 4, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_4 + 1 ] (Comp: ar_0^2 + 3*ar_0 + 2, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) [ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 2*ar_0 + 4, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_2 >= ar_0 ] (Comp: ar_0^2 + 3*ar_0 + 2, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ] (Comp: 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ar_0 + 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: 1, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealshellsortbb4in) = 6*V_5 - 3 Pol(evalrealshellsortbb2in) = -6*V_2 + 6*V_5 + 1 Pol(evalrealshellsortbb3in) = 6*V_5 - 1 and size complexities S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-0) = 0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-1) = 0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-2) = ar_2 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-3) = ar_3 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ]", 0-4) = ar_4 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-0) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-1) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-2) = ar_2 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-3) = ar_3 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\\ f >= 0 /\\ ar_0 >= 2*f /\\ 2*f + 1 >= ar_0 ]", 0-4) = ar_4 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-0) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-1) = ar_0 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-2) = ar_2 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-3) = ar_3 S("evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\\ 0 >= f /\\ 2*f >= ar_0 /\\ ar_0 + 1 >= 2*f ]", 0-4) = ar_4 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-0) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-1) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-2) = 0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-3) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ]", 0-4) = ar_0 + ar_4 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-0) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-1) = ar_0 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-2) = ar_0 + ar_2 S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-3) = ? S("evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ]", 0-4) = ar_0 + ar_4 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-0) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-1) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-2) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-3) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-4) = ar_0 + ar_4 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_2 >= ar_0 ]", 0-0) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_2 >= ar_0 ]", 0-1) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_2 >= ar_0 ]", 0-2) = ar_0 S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_2 >= ar_0 ]", 0-3) = ? S("evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_2 >= ar_0 ]", 0-4) = ar_0 + ar_4 S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) [ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0 S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) [ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_0 S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) [ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_0 S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) [ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ? S("evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) [ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-4) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_4 + 1 ]", 0-0) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_4 + 1 ]", 0-1) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_4 + 1 ]", 0-2) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_4 + 1 ]", 0-3) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_4 + 1 ]", 0-4) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_4 >= ar_1 ]", 0-0) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_4 >= ar_1 ]", 0-1) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_4 >= ar_1 ]", 0-2) = ar_0 S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_4 >= ar_1 ]", 0-3) = ? S("evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_4 >= ar_1 ]", 0-4) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 /\\ f >= ar_3 + 1 ]", 0-0) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 /\\ f >= ar_3 + 1 ]", 0-1) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 /\\ f >= ar_3 + 1 ]", 0-2) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 /\\ f >= ar_3 + 1 ]", 0-3) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 /\\ f >= ar_3 + 1 ]", 0-4) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_3 >= f ]", 0-0) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_3 >= f ]", 0-1) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_3 >= f ]", 0-2) = ar_0 S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_3 >= f ]", 0-3) = ? S("evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_3 >= f ]", 0-4) = ar_0 S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-0) = ar_0 S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-1) = ar_0 S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-2) = ar_0 S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-3) = ? S("evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_4 - 1 >= 0 /\\ ar_2 + ar_4 - 2 >= 0 /\\ ar_1 + ar_4 - 2 >= 0 /\\ -ar_1 + ar_4 >= 0 /\\ ar_0 + ar_4 - 3 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-4) = ar_0 S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0 S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_0 S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_0 S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ? S("evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\\ ar_0 - ar_4 - 1 >= 0 /\\ ar_2 + ar_4 >= 0 /\\ ar_1 + ar_4 - 1 >= 0 /\\ ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-4) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-0) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-1) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-2) = ar_0 S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-3) = ? S("evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_1 >= 1 /\\ f >= 0 /\\ ar_1 >= 2*f /\\ 2*f + 1 >= ar_1 ]", 0-4) = ar_0 + ar_4 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 >= 0 ]", 0-0) = ar_0 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 >= 0 ]", 0-1) = ar_0 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 >= 0 ]", 0-2) = ar_0 + ar_2 S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 >= 0 ]", 0-3) = ? S("evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 >= 0 ]", 0-4) = ar_0 + ar_4 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 orients the transitions evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 /\ f >= ar_3 + 1 ] evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_4 >= ar_1 ] evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 ] weakly and the transitions evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 /\ f >= ar_3 + 1 ] evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_4 >= ar_1 ] evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 ] strictly and produces the following problem: 12: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 >= 0 ] (Comp: ar_0 + 1, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: 2*ar_0^2 + 6*ar_0 + 4, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 6*ar_0^3 + 19*ar_0^2 + 15*ar_0 + 2, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 ] (Comp: 2*ar_0^2 + 6*ar_0 + 4, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 /\ ar_3 >= f ] (Comp: 6*ar_0^3 + 19*ar_0^2 + 15*ar_0 + 2, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_4 - 1 >= 0 /\ ar_2 + ar_4 - 2 >= 0 /\ ar_1 + ar_4 - 2 >= 0 /\ -ar_1 + ar_4 >= 0 /\ ar_0 + ar_4 - 3 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 /\ f >= ar_3 + 1 ] (Comp: 6*ar_0^3 + 19*ar_0^2 + 15*ar_0 + 2, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_4 >= ar_1 ] (Comp: 2*ar_0^2 + 6*ar_0 + 4, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 >= 0 /\ ar_0 - ar_4 - 1 >= 0 /\ ar_2 + ar_4 >= 0 /\ ar_1 + ar_4 - 1 >= 0 /\ ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_4 + 1 ] (Comp: ar_0^2 + 3*ar_0 + 2, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) [ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 ] (Comp: 2*ar_0 + 4, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_2 >= ar_0 ] (Comp: ar_0^2 + 3*ar_0 + 2, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ] (Comp: 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ar_0 + 2, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: 1, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: 1, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) start location: koat_start leaf cost: 0 Complexity upper bound 73*ar_0 + 65*ar_0^2 + 18*ar_0^3 + 37 Time: 0.801 sec (SMT: 0.583 sec) ---------------------------------------- (2) BOUNDS(1, n^3) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalrealshellsortstart 0: evalrealshellsortstart -> evalrealshellsortentryin : [], cost: 1 1: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 1 2: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 1 3: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 1 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 5: evalrealshellsortbb8in -> evalrealshellsortreturnin : [ 0>=B ], cost: 1 6: evalrealshellsortbb6in -> evalrealshellsortbb1in : [ A>=1+C ], cost: 1 7: evalrealshellsortbb6in -> evalrealshellsortbb7in : [ C>=A ], cost: 1 8: evalrealshellsortbb1in -> evalrealshellsortbb3in : D'=free_2, E'=C, [], cost: 1 9: evalrealshellsortbb3in -> evalrealshellsortbb5in : [ B>=1+E ], cost: 1 10: evalrealshellsortbb3in -> evalrealshellsortbb4in : [ E>=B ], cost: 1 11: evalrealshellsortbb4in -> evalrealshellsortbb2in : [ free_3>=1+D ], cost: 1 12: evalrealshellsortbb4in -> evalrealshellsortbb5in : [ D>=free_4 ], cost: 1 13: evalrealshellsortbb2in -> evalrealshellsortbb3in : E'=E-B, [], cost: 1 14: evalrealshellsortbb5in -> evalrealshellsortbb6in : C'=1+C, [], cost: 1 15: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=0, [ B==0 ], cost: 1 16: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_5, [ B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 1 17: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_6, [ 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 1 18: evalrealshellsortreturnin -> evalrealshellsortstop : [], cost: 1 Removed unreachable and leaf rules: Start location: evalrealshellsortstart 0: evalrealshellsortstart -> evalrealshellsortentryin : [], cost: 1 1: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 1 2: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 1 3: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 1 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 6: evalrealshellsortbb6in -> evalrealshellsortbb1in : [ A>=1+C ], cost: 1 7: evalrealshellsortbb6in -> evalrealshellsortbb7in : [ C>=A ], cost: 1 8: evalrealshellsortbb1in -> evalrealshellsortbb3in : D'=free_2, E'=C, [], cost: 1 9: evalrealshellsortbb3in -> evalrealshellsortbb5in : [ B>=1+E ], cost: 1 10: evalrealshellsortbb3in -> evalrealshellsortbb4in : [ E>=B ], cost: 1 11: evalrealshellsortbb4in -> evalrealshellsortbb2in : [ free_3>=1+D ], cost: 1 12: evalrealshellsortbb4in -> evalrealshellsortbb5in : [ D>=free_4 ], cost: 1 13: evalrealshellsortbb2in -> evalrealshellsortbb3in : E'=E-B, [], cost: 1 14: evalrealshellsortbb5in -> evalrealshellsortbb6in : C'=1+C, [], cost: 1 15: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=0, [ B==0 ], cost: 1 16: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_5, [ B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 1 17: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_6, [ 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 1 Simplified all rules, resulting in: Start location: evalrealshellsortstart 0: evalrealshellsortstart -> evalrealshellsortentryin : [], cost: 1 1: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 1 2: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 1 3: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 1 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 6: evalrealshellsortbb6in -> evalrealshellsortbb1in : [ A>=1+C ], cost: 1 7: evalrealshellsortbb6in -> evalrealshellsortbb7in : [ C>=A ], cost: 1 8: evalrealshellsortbb1in -> evalrealshellsortbb3in : D'=free_2, E'=C, [], cost: 1 9: evalrealshellsortbb3in -> evalrealshellsortbb5in : [ B>=1+E ], cost: 1 10: evalrealshellsortbb3in -> evalrealshellsortbb4in : [ E>=B ], cost: 1 11: evalrealshellsortbb4in -> evalrealshellsortbb2in : [], cost: 1 12: evalrealshellsortbb4in -> evalrealshellsortbb5in : [], cost: 1 13: evalrealshellsortbb2in -> evalrealshellsortbb3in : E'=E-B, [], cost: 1 14: evalrealshellsortbb5in -> evalrealshellsortbb6in : C'=1+C, [], cost: 1 15: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=0, [ B==0 ], cost: 1 16: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_5, [ B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 1 17: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_6, [ 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalrealshellsortstart 0: evalrealshellsortstart -> evalrealshellsortentryin : [], cost: 1 1: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 1 2: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 1 3: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 1 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 7: evalrealshellsortbb6in -> evalrealshellsortbb7in : [ C>=A ], cost: 1 19: evalrealshellsortbb6in -> evalrealshellsortbb3in : D'=free_2, E'=C, [ A>=1+C ], cost: 2 9: evalrealshellsortbb3in -> evalrealshellsortbb5in : [ B>=1+E ], cost: 1 10: evalrealshellsortbb3in -> evalrealshellsortbb4in : [ E>=B ], cost: 1 12: evalrealshellsortbb4in -> evalrealshellsortbb5in : [], cost: 1 20: evalrealshellsortbb4in -> evalrealshellsortbb3in : E'=E-B, [], cost: 2 14: evalrealshellsortbb5in -> evalrealshellsortbb6in : C'=1+C, [], cost: 1 15: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=0, [ B==0 ], cost: 1 16: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_5, [ B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 1 17: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_6, [ 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalrealshellsortstart 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 19: evalrealshellsortbb6in -> evalrealshellsortbb3in : D'=free_2, E'=C, [ A>=1+C ], cost: 2 24: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=0, [ C>=A && B==0 ], cost: 2 25: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_5, [ C>=A && B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 2 26: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_6, [ C>=A && 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 2 28: evalrealshellsortbb3in -> evalrealshellsortbb3in : E'=E-B, [ E>=B ], cost: 3 29: evalrealshellsortbb3in -> evalrealshellsortbb6in : C'=1+C, [ B>=1+E ], cost: 2 30: evalrealshellsortbb3in -> evalrealshellsortbb6in : C'=1+C, [ E>=B ], cost: 3 Accelerating simple loops of location 5. Accelerating the following rules: 28: evalrealshellsortbb3in -> evalrealshellsortbb3in : E'=E-B, [ E>=B ], cost: 3 Found no metering function for rule 28. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: evalrealshellsortstart 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 19: evalrealshellsortbb6in -> evalrealshellsortbb3in : D'=free_2, E'=C, [ A>=1+C ], cost: 2 24: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=0, [ C>=A && B==0 ], cost: 2 25: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_5, [ C>=A && B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 2 26: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_6, [ C>=A && 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 2 28: evalrealshellsortbb3in -> evalrealshellsortbb3in : E'=E-B, [ E>=B ], cost: 3 29: evalrealshellsortbb3in -> evalrealshellsortbb6in : C'=1+C, [ B>=1+E ], cost: 2 30: evalrealshellsortbb3in -> evalrealshellsortbb6in : C'=1+C, [ E>=B ], cost: 3 Chained accelerated rules (with incoming rules): Start location: evalrealshellsortstart 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 19: evalrealshellsortbb6in -> evalrealshellsortbb3in : D'=free_2, E'=C, [ A>=1+C ], cost: 2 24: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=0, [ C>=A && B==0 ], cost: 2 25: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_5, [ C>=A && B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 2 26: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_6, [ C>=A && 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 2 31: evalrealshellsortbb6in -> evalrealshellsortbb3in : D'=free_2, E'=C-B, [ A>=1+C && C>=B ], cost: 5 29: evalrealshellsortbb3in -> evalrealshellsortbb6in : C'=1+C, [ B>=1+E ], cost: 2 30: evalrealshellsortbb3in -> evalrealshellsortbb6in : C'=1+C, [ E>=B ], cost: 3 Eliminated locations (on tree-shaped paths): Start location: evalrealshellsortstart 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 24: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=0, [ C>=A && B==0 ], cost: 2 25: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_5, [ C>=A && B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 2 26: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_6, [ C>=A && 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 2 32: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C, [ A>=1+C && B>=1+C ], cost: 4 33: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C, [ A>=1+C && C>=B ], cost: 5 34: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C-B, [ A>=1+C && C>=B && B>=1+C-B ], cost: 7 35: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C-B, [ A>=1+C && C>=B && C-B>=B ], cost: 8 Accelerating simple loops of location 3. Accelerating the following rules: 32: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C, [ A>=1+C && B>=1+C ], cost: 4 33: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C, [ A>=1+C && C>=B ], cost: 5 34: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C-B, [ A>=1+C && C>=B && B>=1+C-B ], cost: 7 35: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C-B, [ A>=1+C && C>=B && C-B>=B ], cost: 8 Accelerated rule 32 with backward acceleration, yielding the new rule 36. Accelerated rule 32 with backward acceleration, yielding the new rule 37. Accelerated rule 33 with metering function -C+A, yielding the new rule 38. Accelerated rule 34 with backward acceleration, yielding the new rule 39. Accelerated rule 34 with backward acceleration, yielding the new rule 40. Accelerated rule 35 with metering function -C+A, yielding the new rule 41. Removing the simple loops: 32 33 34 35. Accelerated all simple loops using metering functions (where possible): Start location: evalrealshellsortstart 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 24: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=0, [ C>=A && B==0 ], cost: 2 25: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_5, [ C>=A && B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 2 26: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_6, [ C>=A && 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 2 36: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=A, D'=free_2, E'=-1+A, [ A>=1+C && B>=1+C && B>=A ], cost: -4*C+4*A 37: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=B, D'=free_2, E'=-1+B, [ A>=1+C && B>=1+C && A>=B ], cost: -4*C+4*B 38: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=A, D'=free_2, E'=-1+A, [ A>=1+C && C>=B ], cost: -5*C+5*A 39: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=A, D'=free_2, E'=-1+A-B, [ A>=1+C && C>=B && B>=1+C-B && -1+A>=B && B>=A-B ], cost: -7*C+7*A 40: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=2*B, D'=free_2, E'=-1+B, [ A>=1+C && C>=B && B>=1+C-B && A>=2*B && -1+2*B>=B ], cost: -7*C+14*B 41: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=A, D'=free_2, E'=-1+A-B, [ A>=1+C && C>=B && C-B>=B ], cost: -8*C+8*A Chained accelerated rules (with incoming rules): Start location: evalrealshellsortstart 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 42: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=A, D'=free_2, E'=-1+A, [ B>=1 && A>=1 && B>=A ], cost: 1+4*A 43: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=B, D'=free_2, E'=-1+B, [ B>=1 && A>=1 && A>=B ], cost: 1+4*B 24: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=0, [ C>=A && B==0 ], cost: 2 25: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_5, [ C>=A && B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 2 26: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_6, [ C>=A && 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: evalrealshellsortstart 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 44: evalrealshellsortbb8in -> evalrealshellsortbb8in : B'=free_5, C'=0, [ B>=1 && 0>=A && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 3 45: evalrealshellsortbb8in -> evalrealshellsortbb8in : B'=free_5, C'=A, D'=free_2, E'=-1+A, [ B>=1 && A>=1 && B>=A && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 3+4*A 46: evalrealshellsortbb8in -> evalrealshellsortbb8in : B'=free_5, C'=B, D'=free_2, E'=-1+B, [ B>=1 && A>=1 && A>=B && B>=A && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 3+4*B 47: evalrealshellsortbb8in -> [14] : [ B>=1 && A>=1 && B>=A ], cost: 1+4*A 48: evalrealshellsortbb8in -> [14] : [ B>=1 && A>=1 && A>=B ], cost: 1+4*B Accelerating simple loops of location 2. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 44: evalrealshellsortbb8in -> evalrealshellsortbb8in : B'=free_5, C'=0, [ B>=1 && 0>=A && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 3 45: evalrealshellsortbb8in -> evalrealshellsortbb8in : B'=free_5, C'=A, D'=free_2, E'=-1+A, [ B>=1 && A>=1 && B>=A && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 3+4*A 46: evalrealshellsortbb8in -> evalrealshellsortbb8in : B'=free_5, C'=B, D'=free_2, E'=-1+B, [ B>=1 && A>=1 && -A+B==0 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 3+4*B During metering: Instantiating temporary variables by {free_5==0} Accelerated rule 44 with metering function B, yielding the new rule 49. During metering: Instantiating temporary variables by {free_5==0} Accelerated rule 45 with metering function 1-A+B, yielding the new rule 50. During metering: Instantiating temporary variables by {free_5==0} Accelerated rule 46 with metering function 1-A+B, yielding the new rule 51. Nested simple loops 45 (outer loop) and 51 (inner loop) with metering function meter (where 3*meter==-2*A+B), resulting in the new rules: 52. Removing the simple loops: 44 45 46. Accelerated all simple loops using metering functions (where possible): Start location: evalrealshellsortstart 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 47: evalrealshellsortbb8in -> [14] : [ B>=1 && A>=1 && B>=A ], cost: 1+4*A 48: evalrealshellsortbb8in -> [14] : [ B>=1 && A>=1 && A>=B ], cost: 1+4*B 49: evalrealshellsortbb8in -> evalrealshellsortbb8in : B'=0, C'=0, [ B>=1 && 0>=A && 1>=B ], cost: 3*B 50: evalrealshellsortbb8in -> evalrealshellsortbb8in : B'=0, C'=A, D'=free_2, E'=-1+A, [ B>=1 && A>=1 && B>=A && 1>=B ], cost: 3-4*(-1+A-B)*A-3*A+3*B 51: evalrealshellsortbb8in -> evalrealshellsortbb8in : B'=0, C'=0, D'=free_2, E'=-1, [ B>=1 && A>=1 && -A+B==0 && 1>=B ], cost: 3-3*A+3*B 52: evalrealshellsortbb8in -> evalrealshellsortbb8in : B'=0, C'=0, D'=free_2, E'=-1, [ B>=A && B>=2 && 3>=B && 1-A==0 && 3*meter==-2*A+B && meter>=1 ], cost: 9*meter+A*meter Chained accelerated rules (with incoming rules): Start location: evalrealshellsortstart 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 47: evalrealshellsortbb8in -> [14] : [ B>=1 && A>=1 && B>=A ], cost: 1+4*A 48: evalrealshellsortbb8in -> [14] : [ B>=1 && A>=1 && A>=B ], cost: 1+4*B Eliminated locations (on tree-shaped paths): Start location: evalrealshellsortstart 53: evalrealshellsortstart -> [14] : B'=free, [ A>=1 && A>=2*free && 1+2*free>=A && free>=1 && A>=free ], cost: 3+4*free ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalrealshellsortstart 53: evalrealshellsortstart -> [14] : B'=free, [ A>=1 && A>=2*free && 1+2*free>=A && free>=1 && A>=free ], cost: 3+4*free Computing asymptotic complexity for rule 53 Simplified the guard: 53: evalrealshellsortstart -> [14] : B'=free, [ A>=2*free && 1+2*free>=A && free>=1 ], cost: 3+4*free Solved the limit problem by the following transformations: Created initial limit problem: 3+4*free (+), 1-2*free+A (+/+!), 2+2*free-A (+/+!), free (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {free==n,A==2*n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 3+4*free (+), 1-2*free+A (+/+!), 2+2*free-A (+/+!), free (+/+!) [not solved] applying transformation rule (C) using substitution {A==2*free} resulting limit problem: 1 (+/+!), 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] applying transformation rule (C) using substitution {A==1+2*free} resulting limit problem: 1 (+/+!), 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] applying transformation rule (B), deleting 2 (+/+!) resulting limit problem: 3+4*free (+), free (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {free==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 3+4*free (+), 1-2*free+A (+/+!), 2+2*free-A (+/+!), free (+/+!) [not solved] applying transformation rule (C) using substitution {A==1+2*free} resulting limit problem: 1 (+/+!), 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] applying transformation rule (B), deleting 2 (+/+!) resulting limit problem: 3+4*free (+), free (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {free==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 3+4*free (+), 1-2*free+A (+/+!), 2+2*free-A (+/+!), free (+/+!) [not solved] applying transformation rule (C) using substitution {A==2*free} resulting limit problem: 1 (+/+!), 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] applying transformation rule (B), deleting 2 (+/+!) resulting limit problem: 3+4*free (+), free (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {free==n} resulting limit problem: [solved] Solution: free / n A / 2*n Resulting cost 3+4*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+4*n Rule cost: 3+4*free Rule guard: [ A>=2*free && 1+2*free>=A && free>=1 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)