12.45/6.49 WORST_CASE(Omega(n^1), O(n^3)) 12.45/6.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 12.45/6.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.45/6.50 12.45/6.50 12.45/6.50 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^3). 12.45/6.50 12.45/6.50 (0) CpxIntTrs 12.45/6.50 (1) Koat Proof [FINISHED, 809 ms] 12.45/6.50 (2) BOUNDS(1, n^3) 12.45/6.50 (3) Loat Proof [FINISHED, 3144 ms] 12.45/6.50 (4) BOUNDS(n^1, INF) 12.45/6.50 12.45/6.50 12.45/6.50 ---------------------------------------- 12.45/6.50 12.45/6.50 (0) 12.45/6.50 Obligation: 12.45/6.50 Complexity Int TRS consisting of the following rules: 12.45/6.50 evalrealshellsortstart(A, B, C, D, E) -> Com_1(evalrealshellsortentryin(A, B, C, D, E)) :|: TRUE 12.45/6.50 evalrealshellsortentryin(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, 0, C, D, E)) :|: A >= 0 && A <= 0 12.45/6.50 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 12.45/6.50 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 12.45/6.50 evalrealshellsortbb8in(A, B, C, D, E) -> Com_1(evalrealshellsortbb6in(A, B, 0, D, E)) :|: B >= 1 12.45/6.50 evalrealshellsortbb8in(A, B, C, D, E) -> Com_1(evalrealshellsortreturnin(A, B, C, D, E)) :|: 0 >= B 12.45/6.50 evalrealshellsortbb6in(A, B, C, D, E) -> Com_1(evalrealshellsortbb1in(A, B, C, D, E)) :|: A >= C + 1 12.45/6.50 evalrealshellsortbb6in(A, B, C, D, E) -> Com_1(evalrealshellsortbb7in(A, B, C, D, E)) :|: C >= A 12.45/6.50 evalrealshellsortbb1in(A, B, C, D, E) -> Com_1(evalrealshellsortbb3in(A, B, C, F, C)) :|: TRUE 12.45/6.50 evalrealshellsortbb3in(A, B, C, D, E) -> Com_1(evalrealshellsortbb5in(A, B, C, D, E)) :|: B >= E + 1 12.45/6.50 evalrealshellsortbb3in(A, B, C, D, E) -> Com_1(evalrealshellsortbb4in(A, B, C, D, E)) :|: E >= B 12.45/6.50 evalrealshellsortbb4in(A, B, C, D, E) -> Com_1(evalrealshellsortbb2in(A, B, C, D, E)) :|: F >= D + 1 12.45/6.50 evalrealshellsortbb4in(A, B, C, D, E) -> Com_1(evalrealshellsortbb5in(A, B, C, D, E)) :|: D >= F 12.45/6.50 evalrealshellsortbb2in(A, B, C, D, E) -> Com_1(evalrealshellsortbb3in(A, B, C, D, E - B)) :|: TRUE 12.45/6.50 evalrealshellsortbb5in(A, B, C, D, E) -> Com_1(evalrealshellsortbb6in(A, B, C + 1, D, E)) :|: TRUE 12.45/6.50 evalrealshellsortbb7in(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, 0, C, D, E)) :|: B >= 0 && B <= 0 12.45/6.50 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 12.45/6.50 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 12.45/6.50 evalrealshellsortreturnin(A, B, C, D, E) -> Com_1(evalrealshellsortstop(A, B, C, D, E)) :|: TRUE 12.45/6.50 12.45/6.50 The start-symbols are:[evalrealshellsortstart_5] 12.45/6.50 12.45/6.50 12.45/6.50 ---------------------------------------- 12.45/6.50 12.45/6.50 (1) Koat Proof (FINISHED) 12.45/6.50 YES(?, 82*ar_0 + 68*ar_0^2 + 18*ar_0^3 + 43) 12.45/6.50 12.45/6.50 12.45/6.50 12.45/6.50 Initial complexity problem: 12.45/6.50 12.45/6.50 1: T: 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 start location: koat_start 12.45/6.50 12.45/6.50 leaf cost: 0 12.45/6.50 12.45/6.50 12.45/6.50 12.45/6.50 Repeatedly propagating knowledge in problem 1 produces the following problem: 12.45/6.50 12.45/6.50 2: T: 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 start location: koat_start 12.45/6.50 12.45/6.50 leaf cost: 0 12.45/6.50 12.45/6.50 12.45/6.50 12.45/6.50 A polynomial rank function with 12.45/6.50 12.45/6.50 Pol(evalrealshellsortstart) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortentryin) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb8in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb6in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortreturnin) = 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb1in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb7in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb3in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb5in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb4in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb2in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortstop) = 0 12.45/6.50 12.45/6.50 Pol(koat_start) = 2 12.45/6.50 12.45/6.50 orients all transitions weakly and the transitions 12.45/6.50 12.45/6.50 evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 strictly and produces the following problem: 12.45/6.50 12.45/6.50 3: T: 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 start location: koat_start 12.45/6.50 12.45/6.50 leaf cost: 0 12.45/6.50 12.45/6.50 12.45/6.50 12.45/6.50 A polynomial rank function with 12.45/6.50 12.45/6.50 Pol(evalrealshellsortstart) = V_1 + 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortentryin) = V_1 + 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb8in) = 2*V_2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb6in) = V_2 + 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortreturnin) = 2*V_2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb1in) = V_2 + 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb7in) = V_2 + 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb3in) = V_2 + 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb5in) = V_2 + 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb4in) = V_2 + 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb2in) = V_2 + 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortstop) = 2*V_2 12.45/6.50 12.45/6.50 Pol(koat_start) = V_1 + 1 12.45/6.50 12.45/6.50 orients all transitions weakly and the transitions 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 strictly and produces the following problem: 12.45/6.50 12.45/6.50 4: T: 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 start location: koat_start 12.45/6.50 12.45/6.50 leaf cost: 0 12.45/6.50 12.45/6.50 12.45/6.50 12.45/6.50 Repeatedly propagating knowledge in problem 4 produces the following problem: 12.45/6.50 12.45/6.50 5: T: 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 start location: koat_start 12.45/6.50 12.45/6.50 leaf cost: 0 12.45/6.50 12.45/6.50 12.45/6.50 12.45/6.50 A polynomial rank function with 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb7in) = 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb8in) = 0 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb6in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb1in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb5in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb4in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb2in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb3in) = 2 12.45/6.50 12.45/6.50 and size complexities 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 orients the transitions 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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)) 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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)) 12.45/6.50 12.45/6.50 evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) 12.45/6.50 12.45/6.50 weakly and the transitions 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 strictly and produces the following problem: 12.45/6.50 12.45/6.50 6: T: 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 start location: koat_start 12.45/6.50 12.45/6.50 leaf cost: 0 12.45/6.50 12.45/6.50 12.45/6.50 12.45/6.50 A polynomial rank function with 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb6in) = V_1 - V_3 + 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb1in) = V_1 - V_3 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb5in) = V_1 - V_3 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb4in) = V_1 - V_3 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb2in) = V_1 - V_3 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb3in) = V_1 - V_3 12.45/6.50 12.45/6.50 and size complexities 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 orients the transitions 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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)) 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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)) 12.45/6.50 12.45/6.50 evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) 12.45/6.50 12.45/6.50 weakly and the transition 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 strictly and produces the following problem: 12.45/6.50 12.45/6.50 7: T: 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 start location: koat_start 12.45/6.50 12.45/6.50 leaf cost: 0 12.45/6.50 12.45/6.50 12.45/6.50 12.45/6.50 Repeatedly propagating knowledge in problem 7 produces the following problem: 12.45/6.50 12.45/6.50 8: T: 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 start location: koat_start 12.45/6.50 12.45/6.50 leaf cost: 0 12.45/6.50 12.45/6.50 12.45/6.50 12.45/6.50 A polynomial rank function with 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb5in) = 1 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb6in) = 0 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb4in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb2in) = 2 12.45/6.50 12.45/6.50 Pol(evalrealshellsortbb3in) = 2 12.45/6.50 12.45/6.50 and size complexities 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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) = ? 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 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 12.45/6.50 12.45/6.50 orients the transitions 12.45/6.50 12.45/6.50 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)) 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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)) 12.45/6.50 12.45/6.50 weakly and the transitions 12.45/6.50 12.45/6.50 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)) 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 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 ] 12.45/6.50 12.45/6.50 strictly and produces the following problem: 12.45/6.50 12.45/6.50 9: T: 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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)) 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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)) 12.45/6.51 12.45/6.51 (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)) 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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)) 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 start location: koat_start 12.45/6.51 12.45/6.51 leaf cost: 0 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Applied AI with 'oct' on problem 9 to obtain the following invariants: 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 For symbol evalrealshellsortbb6in: X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 12.45/6.51 12.45/6.51 For symbol evalrealshellsortbb7in: X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 - 1 >= 0 12.45/6.51 12.45/6.51 For symbol evalrealshellsortreturnin: -X_2 >= 0 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 This yielded the following problem: 12.45/6.51 12.45/6.51 10: T: 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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)) 12.45/6.51 12.45/6.51 start location: koat_start 12.45/6.51 12.45/6.51 leaf cost: 0 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Testing for unsatisfiable constraints removes the following transitions from problem 10: 12.45/6.51 12.45/6.51 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 ] 12.45/6.51 12.45/6.51 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 ] 12.45/6.51 12.45/6.51 We thus obtain the following problem: 12.45/6.51 12.45/6.51 11: T: 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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)) 12.45/6.51 12.45/6.51 start location: koat_start 12.45/6.51 12.45/6.51 leaf cost: 0 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 A polynomial rank function with 12.45/6.51 12.45/6.51 Pol(evalrealshellsortbb4in) = 3*V_1 + 3*V_5 - 3 12.45/6.51 12.45/6.51 Pol(evalrealshellsortbb2in) = 3*V_1 + 3*V_5 - 4 12.45/6.51 12.45/6.51 Pol(evalrealshellsortbb3in) = 3*V_1 + 3*V_5 - 2 12.45/6.51 12.45/6.51 and size complexities 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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) = ? 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 orients the transitions 12.45/6.51 12.45/6.51 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 ] 12.45/6.51 12.45/6.51 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 ] 12.45/6.51 12.45/6.51 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 ] 12.45/6.51 12.45/6.51 weakly and the transitions 12.45/6.51 12.45/6.51 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 ] 12.45/6.51 12.45/6.51 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 ] 12.45/6.51 12.45/6.51 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 ] 12.45/6.51 12.45/6.51 strictly and produces the following problem: 12.45/6.51 12.45/6.51 12: T: 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (Comp: 6*ar_0^3 + 20*ar_0^2 + 18*ar_0 + 4, 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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (Comp: 6*ar_0^3 + 20*ar_0^2 + 18*ar_0 + 4, 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 ] 12.45/6.51 12.45/6.51 (Comp: 6*ar_0^3 + 20*ar_0^2 + 18*ar_0 + 4, 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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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 ] 12.45/6.51 12.45/6.51 (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)) 12.45/6.51 12.45/6.51 start location: koat_start 12.45/6.51 12.45/6.51 leaf cost: 0 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Complexity upper bound 82*ar_0 + 68*ar_0^2 + 18*ar_0^3 + 43 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Time: 0.826 sec (SMT: 0.613 sec) 12.45/6.51 12.45/6.51 12.45/6.51 ---------------------------------------- 12.45/6.51 12.45/6.51 (2) 12.45/6.51 BOUNDS(1, n^3) 12.45/6.51 12.45/6.51 ---------------------------------------- 12.45/6.51 12.45/6.51 (3) Loat Proof (FINISHED) 12.45/6.51 12.45/6.51 12.45/6.51 ### Pre-processing the ITS problem ### 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Initial linear ITS problem 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 0: evalrealshellsortstart -> evalrealshellsortentryin : [], cost: 1 12.45/6.51 12.45/6.51 1: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 1 12.45/6.51 12.45/6.51 2: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 1 12.45/6.51 12.45/6.51 3: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 1 12.45/6.51 12.45/6.51 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 12.45/6.51 12.45/6.51 5: evalrealshellsortbb8in -> evalrealshellsortreturnin : [ 0>=B ], cost: 1 12.45/6.51 12.45/6.51 6: evalrealshellsortbb6in -> evalrealshellsortbb1in : [ A>=1+C ], cost: 1 12.45/6.51 12.45/6.51 7: evalrealshellsortbb6in -> evalrealshellsortbb7in : [ C>=A ], cost: 1 12.45/6.51 12.45/6.51 8: evalrealshellsortbb1in -> evalrealshellsortbb3in : D'=free_2, E'=C, [], cost: 1 12.45/6.51 12.45/6.51 9: evalrealshellsortbb3in -> evalrealshellsortbb5in : [ B>=1+E ], cost: 1 12.45/6.51 12.45/6.51 10: evalrealshellsortbb3in -> evalrealshellsortbb4in : [ E>=B ], cost: 1 12.45/6.51 12.45/6.51 11: evalrealshellsortbb4in -> evalrealshellsortbb2in : [ free_3>=1+D ], cost: 1 12.45/6.51 12.45/6.51 12: evalrealshellsortbb4in -> evalrealshellsortbb5in : [ D>=free_4 ], cost: 1 12.45/6.51 12.45/6.51 13: evalrealshellsortbb2in -> evalrealshellsortbb3in : E'=E-B, [], cost: 1 12.45/6.51 12.45/6.51 14: evalrealshellsortbb5in -> evalrealshellsortbb6in : C'=1+C, [], cost: 1 12.45/6.51 12.45/6.51 15: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=0, [ B==0 ], cost: 1 12.45/6.51 12.45/6.51 16: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_5, [ B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 1 12.45/6.51 12.45/6.51 17: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_6, [ 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 1 12.45/6.51 12.45/6.51 18: evalrealshellsortreturnin -> evalrealshellsortstop : [], cost: 1 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Removed unreachable and leaf rules: 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 0: evalrealshellsortstart -> evalrealshellsortentryin : [], cost: 1 12.45/6.51 12.45/6.51 1: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 1 12.45/6.51 12.45/6.51 2: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 1 12.45/6.51 12.45/6.51 3: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 1 12.45/6.51 12.45/6.51 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 12.45/6.51 12.45/6.51 6: evalrealshellsortbb6in -> evalrealshellsortbb1in : [ A>=1+C ], cost: 1 12.45/6.51 12.45/6.51 7: evalrealshellsortbb6in -> evalrealshellsortbb7in : [ C>=A ], cost: 1 12.45/6.51 12.45/6.51 8: evalrealshellsortbb1in -> evalrealshellsortbb3in : D'=free_2, E'=C, [], cost: 1 12.45/6.51 12.45/6.51 9: evalrealshellsortbb3in -> evalrealshellsortbb5in : [ B>=1+E ], cost: 1 12.45/6.51 12.45/6.51 10: evalrealshellsortbb3in -> evalrealshellsortbb4in : [ E>=B ], cost: 1 12.45/6.51 12.45/6.51 11: evalrealshellsortbb4in -> evalrealshellsortbb2in : [ free_3>=1+D ], cost: 1 12.45/6.51 12.45/6.51 12: evalrealshellsortbb4in -> evalrealshellsortbb5in : [ D>=free_4 ], cost: 1 12.45/6.51 12.45/6.51 13: evalrealshellsortbb2in -> evalrealshellsortbb3in : E'=E-B, [], cost: 1 12.45/6.51 12.45/6.51 14: evalrealshellsortbb5in -> evalrealshellsortbb6in : C'=1+C, [], cost: 1 12.45/6.51 12.45/6.51 15: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=0, [ B==0 ], cost: 1 12.45/6.51 12.45/6.51 16: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_5, [ B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 1 12.45/6.51 12.45/6.51 17: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_6, [ 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 1 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Simplified all rules, resulting in: 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 0: evalrealshellsortstart -> evalrealshellsortentryin : [], cost: 1 12.45/6.51 12.45/6.51 1: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 1 12.45/6.51 12.45/6.51 2: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 1 12.45/6.51 12.45/6.51 3: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 1 12.45/6.51 12.45/6.51 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 12.45/6.51 12.45/6.51 6: evalrealshellsortbb6in -> evalrealshellsortbb1in : [ A>=1+C ], cost: 1 12.45/6.51 12.45/6.51 7: evalrealshellsortbb6in -> evalrealshellsortbb7in : [ C>=A ], cost: 1 12.45/6.51 12.45/6.51 8: evalrealshellsortbb1in -> evalrealshellsortbb3in : D'=free_2, E'=C, [], cost: 1 12.45/6.51 12.45/6.51 9: evalrealshellsortbb3in -> evalrealshellsortbb5in : [ B>=1+E ], cost: 1 12.45/6.51 12.45/6.51 10: evalrealshellsortbb3in -> evalrealshellsortbb4in : [ E>=B ], cost: 1 12.45/6.51 12.45/6.51 11: evalrealshellsortbb4in -> evalrealshellsortbb2in : [], cost: 1 12.45/6.51 12.45/6.51 12: evalrealshellsortbb4in -> evalrealshellsortbb5in : [], cost: 1 12.45/6.51 12.45/6.51 13: evalrealshellsortbb2in -> evalrealshellsortbb3in : E'=E-B, [], cost: 1 12.45/6.51 12.45/6.51 14: evalrealshellsortbb5in -> evalrealshellsortbb6in : C'=1+C, [], cost: 1 12.45/6.51 12.45/6.51 15: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=0, [ B==0 ], cost: 1 12.45/6.51 12.45/6.51 16: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_5, [ B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 1 12.45/6.51 12.45/6.51 17: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_6, [ 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 1 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 ### Simplification by acceleration and chaining ### 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Eliminated locations (on linear paths): 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 0: evalrealshellsortstart -> evalrealshellsortentryin : [], cost: 1 12.45/6.51 12.45/6.51 1: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 1 12.45/6.51 12.45/6.51 2: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 1 12.45/6.51 12.45/6.51 3: evalrealshellsortentryin -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 1 12.45/6.51 12.45/6.51 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 12.45/6.51 12.45/6.51 7: evalrealshellsortbb6in -> evalrealshellsortbb7in : [ C>=A ], cost: 1 12.45/6.51 12.45/6.51 19: evalrealshellsortbb6in -> evalrealshellsortbb3in : D'=free_2, E'=C, [ A>=1+C ], cost: 2 12.45/6.51 12.45/6.51 9: evalrealshellsortbb3in -> evalrealshellsortbb5in : [ B>=1+E ], cost: 1 12.45/6.51 12.45/6.51 10: evalrealshellsortbb3in -> evalrealshellsortbb4in : [ E>=B ], cost: 1 12.45/6.51 12.45/6.51 12: evalrealshellsortbb4in -> evalrealshellsortbb5in : [], cost: 1 12.45/6.51 12.45/6.51 20: evalrealshellsortbb4in -> evalrealshellsortbb3in : E'=E-B, [], cost: 2 12.45/6.51 12.45/6.51 14: evalrealshellsortbb5in -> evalrealshellsortbb6in : C'=1+C, [], cost: 1 12.45/6.51 12.45/6.51 15: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=0, [ B==0 ], cost: 1 12.45/6.51 12.45/6.51 16: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_5, [ B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 1 12.45/6.51 12.45/6.51 17: evalrealshellsortbb7in -> evalrealshellsortbb8in : B'=free_6, [ 0>=1+B && 0>=free_6 && 2*free_6>=B && 1+B>=2*free_6 ], cost: 1 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Eliminated locations (on tree-shaped paths): 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 12.45/6.51 12.45/6.51 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 12.45/6.51 12.45/6.51 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 12.45/6.51 12.45/6.51 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 12.45/6.51 12.45/6.51 19: evalrealshellsortbb6in -> evalrealshellsortbb3in : D'=free_2, E'=C, [ A>=1+C ], cost: 2 12.45/6.51 12.45/6.51 24: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=0, [ C>=A && B==0 ], cost: 2 12.45/6.51 12.45/6.51 25: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_5, [ C>=A && B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 2 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 28: evalrealshellsortbb3in -> evalrealshellsortbb3in : E'=E-B, [ E>=B ], cost: 3 12.45/6.51 12.45/6.51 29: evalrealshellsortbb3in -> evalrealshellsortbb6in : C'=1+C, [ B>=1+E ], cost: 2 12.45/6.51 12.45/6.51 30: evalrealshellsortbb3in -> evalrealshellsortbb6in : C'=1+C, [ E>=B ], cost: 3 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Accelerating simple loops of location 5. 12.45/6.51 12.45/6.51 Accelerating the following rules: 12.45/6.51 12.45/6.51 28: evalrealshellsortbb3in -> evalrealshellsortbb3in : E'=E-B, [ E>=B ], cost: 3 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Found no metering function for rule 28. 12.45/6.51 12.45/6.51 Removing the simple loops:. 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Accelerated all simple loops using metering functions (where possible): 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 12.45/6.51 12.45/6.51 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 12.45/6.51 12.45/6.51 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 12.45/6.51 12.45/6.51 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 12.45/6.51 12.45/6.51 19: evalrealshellsortbb6in -> evalrealshellsortbb3in : D'=free_2, E'=C, [ A>=1+C ], cost: 2 12.45/6.51 12.45/6.51 24: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=0, [ C>=A && B==0 ], cost: 2 12.45/6.51 12.45/6.51 25: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_5, [ C>=A && B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 2 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 28: evalrealshellsortbb3in -> evalrealshellsortbb3in : E'=E-B, [ E>=B ], cost: 3 12.45/6.51 12.45/6.51 29: evalrealshellsortbb3in -> evalrealshellsortbb6in : C'=1+C, [ B>=1+E ], cost: 2 12.45/6.51 12.45/6.51 30: evalrealshellsortbb3in -> evalrealshellsortbb6in : C'=1+C, [ E>=B ], cost: 3 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Chained accelerated rules (with incoming rules): 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 12.45/6.51 12.45/6.51 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 12.45/6.51 12.45/6.51 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 12.45/6.51 12.45/6.51 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 12.45/6.51 12.45/6.51 19: evalrealshellsortbb6in -> evalrealshellsortbb3in : D'=free_2, E'=C, [ A>=1+C ], cost: 2 12.45/6.51 12.45/6.51 24: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=0, [ C>=A && B==0 ], cost: 2 12.45/6.51 12.45/6.51 25: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_5, [ C>=A && B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 2 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 31: evalrealshellsortbb6in -> evalrealshellsortbb3in : D'=free_2, E'=C-B, [ A>=1+C && C>=B ], cost: 5 12.45/6.51 12.45/6.51 29: evalrealshellsortbb3in -> evalrealshellsortbb6in : C'=1+C, [ B>=1+E ], cost: 2 12.45/6.51 12.45/6.51 30: evalrealshellsortbb3in -> evalrealshellsortbb6in : C'=1+C, [ E>=B ], cost: 3 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Eliminated locations (on tree-shaped paths): 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 12.45/6.51 12.45/6.51 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 12.45/6.51 12.45/6.51 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 12.45/6.51 12.45/6.51 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 12.45/6.51 12.45/6.51 24: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=0, [ C>=A && B==0 ], cost: 2 12.45/6.51 12.45/6.51 25: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_5, [ C>=A && B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 2 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 32: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C, [ A>=1+C && B>=1+C ], cost: 4 12.45/6.51 12.45/6.51 33: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C, [ A>=1+C && C>=B ], cost: 5 12.45/6.51 12.45/6.51 34: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C-B, [ A>=1+C && C>=B && B>=1+C-B ], cost: 7 12.45/6.51 12.45/6.51 35: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C-B, [ A>=1+C && C>=B && C-B>=B ], cost: 8 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Accelerating simple loops of location 3. 12.45/6.51 12.45/6.51 Accelerating the following rules: 12.45/6.51 12.45/6.51 32: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C, [ A>=1+C && B>=1+C ], cost: 4 12.45/6.51 12.45/6.51 33: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C, [ A>=1+C && C>=B ], cost: 5 12.45/6.51 12.45/6.51 34: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C-B, [ A>=1+C && C>=B && B>=1+C-B ], cost: 7 12.45/6.51 12.45/6.51 35: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=1+C, D'=free_2, E'=C-B, [ A>=1+C && C>=B && C-B>=B ], cost: 8 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Accelerated rule 32 with backward acceleration, yielding the new rule 36. 12.45/6.51 12.45/6.51 Accelerated rule 32 with backward acceleration, yielding the new rule 37. 12.45/6.51 12.45/6.51 Accelerated rule 33 with metering function -C+A, yielding the new rule 38. 12.45/6.51 12.45/6.51 Accelerated rule 34 with backward acceleration, yielding the new rule 39. 12.45/6.51 12.45/6.51 Accelerated rule 34 with backward acceleration, yielding the new rule 40. 12.45/6.51 12.45/6.51 Accelerated rule 35 with metering function -C+A, yielding the new rule 41. 12.45/6.51 12.45/6.51 Removing the simple loops: 32 33 34 35. 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Accelerated all simple loops using metering functions (where possible): 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 12.45/6.51 12.45/6.51 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 12.45/6.51 12.45/6.51 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 12.45/6.51 12.45/6.51 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 12.45/6.51 12.45/6.51 24: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=0, [ C>=A && B==0 ], cost: 2 12.45/6.51 12.45/6.51 25: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_5, [ C>=A && B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 2 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 36: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=A, D'=free_2, E'=-1+A, [ A>=1+C && B>=1+C && B>=A ], cost: -4*C+4*A 12.45/6.51 12.45/6.51 37: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=B, D'=free_2, E'=-1+B, [ A>=1+C && B>=1+C && A>=B ], cost: -4*C+4*B 12.45/6.51 12.45/6.51 38: evalrealshellsortbb6in -> evalrealshellsortbb6in : C'=A, D'=free_2, E'=-1+A, [ A>=1+C && C>=B ], cost: -5*C+5*A 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Chained accelerated rules (with incoming rules): 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 12.45/6.51 12.45/6.51 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 12.45/6.51 12.45/6.51 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 12.45/6.51 12.45/6.51 4: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=0, [ B>=1 ], cost: 1 12.45/6.51 12.45/6.51 42: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=A, D'=free_2, E'=-1+A, [ B>=1 && A>=1 && B>=A ], cost: 1+4*A 12.45/6.51 12.45/6.51 43: evalrealshellsortbb8in -> evalrealshellsortbb6in : C'=B, D'=free_2, E'=-1+B, [ B>=1 && A>=1 && A>=B ], cost: 1+4*B 12.45/6.51 12.45/6.51 24: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=0, [ C>=A && B==0 ], cost: 2 12.45/6.51 12.45/6.51 25: evalrealshellsortbb6in -> evalrealshellsortbb8in : B'=free_5, [ C>=A && B>=1 && free_5>=0 && B>=2*free_5 && 1+2*free_5>=B ], cost: 2 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Eliminated locations (on tree-shaped paths): 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 12.45/6.51 12.45/6.51 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 12.45/6.51 12.45/6.51 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 47: evalrealshellsortbb8in -> [14] : [ B>=1 && A>=1 && B>=A ], cost: 1+4*A 12.45/6.51 12.45/6.51 48: evalrealshellsortbb8in -> [14] : [ B>=1 && A>=1 && A>=B ], cost: 1+4*B 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Accelerating simple loops of location 2. 12.45/6.51 12.45/6.51 Simplified some of the simple loops (and removed duplicate rules). 12.45/6.51 12.45/6.51 Accelerating the following rules: 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 During metering: Instantiating temporary variables by {free_5==0} 12.45/6.51 12.45/6.51 Accelerated rule 44 with metering function B, yielding the new rule 49. 12.45/6.51 12.45/6.51 During metering: Instantiating temporary variables by {free_5==0} 12.45/6.51 12.45/6.51 Accelerated rule 45 with metering function 1-A+B, yielding the new rule 50. 12.45/6.51 12.45/6.51 During metering: Instantiating temporary variables by {free_5==0} 12.45/6.51 12.45/6.51 Accelerated rule 46 with metering function 1-A+B, yielding the new rule 51. 12.45/6.51 12.45/6.51 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. 12.45/6.51 12.45/6.51 Removing the simple loops: 44 45 46. 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Accelerated all simple loops using metering functions (where possible): 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 12.45/6.51 12.45/6.51 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 12.45/6.51 12.45/6.51 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 12.45/6.51 12.45/6.51 47: evalrealshellsortbb8in -> [14] : [ B>=1 && A>=1 && B>=A ], cost: 1+4*A 12.45/6.51 12.45/6.51 48: evalrealshellsortbb8in -> [14] : [ B>=1 && A>=1 && A>=B ], cost: 1+4*B 12.45/6.51 12.45/6.51 49: evalrealshellsortbb8in -> evalrealshellsortbb8in : B'=0, C'=0, [ B>=1 && 0>=A && 1>=B ], cost: 3*B 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 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 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Chained accelerated rules (with incoming rules): 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 21: evalrealshellsortstart -> evalrealshellsortbb8in : B'=0, [ A==0 ], cost: 2 12.45/6.51 12.45/6.51 22: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free, [ A>=1 && free>=0 && A>=2*free && 1+2*free>=A ], cost: 2 12.45/6.51 12.45/6.51 23: evalrealshellsortstart -> evalrealshellsortbb8in : B'=free_1, [ 0>=1+A && 0>=free_1 && 2*free_1>=A && 1+A>=2*free_1 ], cost: 2 12.45/6.51 12.45/6.51 47: evalrealshellsortbb8in -> [14] : [ B>=1 && A>=1 && B>=A ], cost: 1+4*A 12.45/6.51 12.45/6.51 48: evalrealshellsortbb8in -> [14] : [ B>=1 && A>=1 && A>=B ], cost: 1+4*B 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Eliminated locations (on tree-shaped paths): 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 53: evalrealshellsortstart -> [14] : B'=free, [ A>=1 && A>=2*free && 1+2*free>=A && free>=1 && A>=free ], cost: 3+4*free 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 ### Computing asymptotic complexity ### 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Fully simplified ITS problem 12.45/6.51 12.45/6.51 Start location: evalrealshellsortstart 12.45/6.51 12.45/6.51 53: evalrealshellsortstart -> [14] : B'=free, [ A>=1 && A>=2*free && 1+2*free>=A && free>=1 && A>=free ], cost: 3+4*free 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Computing asymptotic complexity for rule 53 12.45/6.51 12.45/6.51 Simplified the guard: 12.45/6.51 12.45/6.51 53: evalrealshellsortstart -> [14] : B'=free, [ A>=2*free && 1+2*free>=A && free>=1 ], cost: 3+4*free 12.45/6.51 12.45/6.51 Solved the limit problem by the following transformations: 12.45/6.51 12.45/6.51 Created initial limit problem: 12.45/6.51 12.45/6.51 3+4*free (+), 1-2*free+A (+/+!), 2+2*free-A (+/+!), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 removing all constraints (solved by SMT) 12.45/6.51 12.45/6.51 resulting limit problem: [solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (C) using substitution {free==n,A==2*n} 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 [solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Solved the limit problem by the following transformations: 12.45/6.51 12.45/6.51 Created initial limit problem: 12.45/6.51 12.45/6.51 3+4*free (+), 1-2*free+A (+/+!), 2+2*free-A (+/+!), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (C) using substitution {A==2*free} 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 1 (+/+!), 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (C) using substitution {A==1+2*free} 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 1 (+/+!), 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (B), deleting 1 (+/+!) 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (B), deleting 2 (+/+!) 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 3+4*free (+), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 removing all constraints (solved by SMT) 12.45/6.51 12.45/6.51 resulting limit problem: [solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (C) using substitution {free==n} 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 [solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Solved the limit problem by the following transformations: 12.45/6.51 12.45/6.51 Created initial limit problem: 12.45/6.51 12.45/6.51 3+4*free (+), 1-2*free+A (+/+!), 2+2*free-A (+/+!), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (C) using substitution {A==1+2*free} 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 1 (+/+!), 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (B), deleting 1 (+/+!) 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (B), deleting 2 (+/+!) 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 3+4*free (+), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 removing all constraints (solved by SMT) 12.45/6.51 12.45/6.51 resulting limit problem: [solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (C) using substitution {free==n} 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 [solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Solved the limit problem by the following transformations: 12.45/6.51 12.45/6.51 Created initial limit problem: 12.45/6.51 12.45/6.51 3+4*free (+), 1-2*free+A (+/+!), 2+2*free-A (+/+!), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (C) using substitution {A==2*free} 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 1 (+/+!), 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (B), deleting 1 (+/+!) 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 3+4*free (+), 2 (+/+!), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (B), deleting 2 (+/+!) 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 3+4*free (+), free (+/+!) [not solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 removing all constraints (solved by SMT) 12.45/6.51 12.45/6.51 resulting limit problem: [solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 applying transformation rule (C) using substitution {free==n} 12.45/6.51 12.45/6.51 resulting limit problem: 12.45/6.51 12.45/6.51 [solved] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Solution: 12.45/6.51 12.45/6.51 free / n 12.45/6.51 12.45/6.51 A / 2*n 12.45/6.51 12.45/6.51 Resulting cost 3+4*n has complexity: Poly(n^1) 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Found new complexity Poly(n^1). 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 Obtained the following overall complexity (w.r.t. the length of the input n): 12.45/6.51 12.45/6.51 Complexity: Poly(n^1) 12.45/6.51 12.45/6.51 Cpx degree: 1 12.45/6.51 12.45/6.51 Solved cost: 3+4*n 12.45/6.51 12.45/6.51 Rule cost: 3+4*free 12.45/6.51 12.45/6.51 Rule guard: [ A>=2*free && 1+2*free>=A && free>=1 ] 12.45/6.51 12.45/6.51 12.45/6.51 12.45/6.51 WORST_CASE(Omega(n^1),?) 12.45/6.51 12.45/6.51 12.45/6.51 ---------------------------------------- 12.45/6.51 12.45/6.51 (4) 12.45/6.51 BOUNDS(n^1, INF) 12.45/6.53 EOF