/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 543 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 2750 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalrealheapsortstep2start(A, B, C, D) -> Com_1(evalrealheapsortstep2entryin(A, B, C, D)) :|: TRUE evalrealheapsortstep2entryin(A, B, C, D) -> Com_1(evalrealheapsortstep2bbin(A, B, C, D)) :|: A >= 3 evalrealheapsortstep2entryin(A, B, C, D) -> Com_1(evalrealheapsortstep2returnin(A, B, C, D)) :|: 2 >= A evalrealheapsortstep2bbin(A, B, C, D) -> Com_1(evalrealheapsortstep2bb11in(A, 0, C, D)) :|: TRUE evalrealheapsortstep2bb11in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb1in(A, B, C, D)) :|: A >= 2 + B evalrealheapsortstep2bb11in(A, B, C, D) -> Com_1(evalrealheapsortstep2returnin(A, B, C, D)) :|: B + 1 >= A evalrealheapsortstep2bb1in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb9in(A, B, 0, D)) :|: TRUE evalrealheapsortstep2bb9in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb2in(A, B, C, D)) :|: A >= B + 3 + 2 * C evalrealheapsortstep2bb9in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb10in(A, B, C, D)) :|: 2 * C + 2 + B >= A evalrealheapsortstep2bb2in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb4in(A, B, C, D)) :|: A >= 2 * C + 3 + B && A <= 2 * C + 3 + B evalrealheapsortstep2bb2in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb3in(A, B, C, D)) :|: A >= B + 4 + 2 * C evalrealheapsortstep2bb2in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb3in(A, B, C, D)) :|: 2 * C + 2 + B >= A evalrealheapsortstep2bb3in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb4in(A, B, C, D)) :|: TRUE evalrealheapsortstep2bb3in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb5in(A, B, C, D)) :|: TRUE evalrealheapsortstep2bb4in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb6in(A, B, C, 2 * C + 1)) :|: TRUE evalrealheapsortstep2bb5in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb6in(A, B, C, 2 * C + 2)) :|: TRUE evalrealheapsortstep2bb6in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb7in(A, B, C, D)) :|: TRUE evalrealheapsortstep2bb6in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb9in(A, B, A, D)) :|: TRUE evalrealheapsortstep2bb7in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb9in(A, B, D, D)) :|: TRUE evalrealheapsortstep2bb10in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb11in(A, B + 1, C, D)) :|: TRUE evalrealheapsortstep2returnin(A, B, C, D) -> Com_1(evalrealheapsortstep2stop(A, B, C, D)) :|: TRUE The start-symbols are:[evalrealheapsortstep2start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 86*Ar_0 + 60*Ar_0^2 + 34) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 1: evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: ?, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: ?, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealheapsortstep2bb7in) = 2 Pol(evalrealheapsortstep2bb9in) = 2 Pol(evalrealheapsortstep2bb6in) = 2 Pol(evalrealheapsortstep2bb5in) = 2 Pol(evalrealheapsortstep2bb3in) = 2 Pol(evalrealheapsortstep2bb4in) = 2 Pol(evalrealheapsortstep2bb10in) = 2 Pol(evalrealheapsortstep2bb11in) = 2 Pol(evalrealheapsortstep2bb2in) = 2 Pol(evalrealheapsortstep2bb1in) = 2 Pol(evalrealheapsortstep2returnin) = 1 Pol(evalrealheapsortstep2stop) = 0 Pol(evalrealheapsortstep2bbin) = 2 Pol(evalrealheapsortstep2entryin) = 2 Pol(evalrealheapsortstep2start) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealheapsortstep2bb9in) = V_1 - V_2 Pol(evalrealheapsortstep2bb2in) = V_1 - V_2 Pol(evalrealheapsortstep2bb10in) = V_1 - V_2 Pol(evalrealheapsortstep2bb7in) = V_1 - V_2 Pol(evalrealheapsortstep2bb6in) = V_1 - V_2 Pol(evalrealheapsortstep2bb5in) = V_1 - V_2 Pol(evalrealheapsortstep2bb4in) = V_1 - V_2 Pol(evalrealheapsortstep2bb3in) = V_1 - V_2 Pol(evalrealheapsortstep2bb1in) = V_1 - V_2 Pol(evalrealheapsortstep2bb11in) = V_1 - V_2 + 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-1) = Ar_1 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-2) = Ar_2 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-3) = Ar_3 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-1) = Ar_1 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-2) = Ar_2 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-3) = Ar_3 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-1) = 0 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-1) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-2) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-3) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-1) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-2) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-3) = ? S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-2) = 0 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-1) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-2) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-3) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-1) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-2) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-3) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-1) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-2) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-3) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-1) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-2) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-3) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-0) = Ar_0 S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-1) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-2) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-3) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-0) = Ar_0 S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-1) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-2) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-3) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-2) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-3) = ? orients the transitions evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) weakly and the transition evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] strictly and produces the following problem: 5: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: Ar_0 + 1, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: Ar_0 + 1, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: Ar_0 + 1, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealheapsortstep2bb9in) = 2 Pol(evalrealheapsortstep2bb2in) = 2 Pol(evalrealheapsortstep2bb10in) = 1 Pol(evalrealheapsortstep2bb7in) = 2 Pol(evalrealheapsortstep2bb6in) = 2 Pol(evalrealheapsortstep2bb5in) = 2 Pol(evalrealheapsortstep2bb4in) = 2 Pol(evalrealheapsortstep2bb3in) = 2 Pol(evalrealheapsortstep2bb11in) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-1) = Ar_1 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-2) = Ar_2 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-3) = Ar_3 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-1) = Ar_1 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-2) = Ar_2 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-3) = Ar_3 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-1) = 0 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-1) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-2) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ]", 0-3) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-1) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-2) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ]", 0-3) = ? S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-2) = 0 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-1) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-2) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-3) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-1) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-2) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-3) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-1) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-2) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-3) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-1) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-2) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-3) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-0) = Ar_0 S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-1) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-2) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1))", 0-3) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-0) = Ar_0 S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-1) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-2) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2))", 0-3) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-2) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-1) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-2) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3))", 0-3) = ? orients the transitions evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) weakly and the transitions evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) strictly and produces the following problem: 7: T: (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) (Comp: 2*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: Ar_0 + 1, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 + 1 >= Ar_0 ] (Comp: Ar_0 + 1, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 7 to obtain the following invariants: For symbol evalrealheapsortstep2bb10in: X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb11in: X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb1in: X_1 - X_2 - 2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb2in: X_1 - X_3 - 3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 - 3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb3in: X_1 - X_3 - 4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 4 >= 0 /\ X_1 - X_2 - 4 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ X_1 - 4 >= 0 For symbol evalrealheapsortstep2bb4in: X_1 - X_3 - 3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 - 3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb5in: X_1 - X_3 - 4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 4 >= 0 /\ X_1 - X_2 - 4 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ X_1 - 4 >= 0 For symbol evalrealheapsortstep2bb6in: X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 4 >= 0 /\ X_1 - X_3 - 3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 - 3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb7in: X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 4 >= 0 /\ X_1 - X_3 - 3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 - 3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bb9in: X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 3 >= 0 For symbol evalrealheapsortstep2bbin: X_1 - 3 >= 0 This yielded the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) [ Ar_0 - 3 >= 0 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: Ar_0 + 1, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_1 + 1 >= Ar_0 ] (Comp: Ar_0 + 1, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 - Ar_1 - 2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealheapsortstep2bb9in) = 6*V_1 - 6*V_3 + 2 Pol(evalrealheapsortstep2bb2in) = 6*V_1 - 6*V_3 + 1 Pol(evalrealheapsortstep2bb7in) = 6*V_1 - 6*V_3 - 3 Pol(evalrealheapsortstep2bb6in) = 6*V_1 - 6*V_3 - 2 Pol(evalrealheapsortstep2bb5in) = 6*V_1 - 6*V_3 - 1 Pol(evalrealheapsortstep2bb4in) = 6*V_1 - 6*V_3 - 1 Pol(evalrealheapsortstep2bb3in) = 6*V_1 - 6*V_3 and size complexities S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-2) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ -Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 1 >= 0 /\\ Ar_0 + Ar_3 - 4 >= 0 /\\ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 4 >= 0 /\\ Ar_0 - Ar_1 - 4 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 4 >= 0 /\\ Ar_0 - 4 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-2) = ? S("evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-2) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ]", 0-3) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-2) = ? S("evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_0 - Ar_1 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ]", 0-3) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-2) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ]", 0-3) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-2) = ? S("evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 3 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ]", 0-3) = ? S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-2) = 0 S("evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 - Ar_1 - 2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 ]", 0-3) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_1 + 1 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_1 + 1 >= Ar_0 ]", 0-1) = 2*Ar_0 + 16 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_1 + 1 >= Ar_0 ]", 0-2) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_1 + 1 >= Ar_0 ]", 0-3) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2 ]", 0-1) = 2*Ar_0 + 8 S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2 ]", 0-2) = ? S("evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ Ar_0 - 3 >= 0 /\\ Ar_0 >= Ar_1 + 2 ]", 0-3) = ? S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = 2*Ar_0 + 2*Ar_1 + 32 S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) [ Ar_0 - 3 >= 0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) [ Ar_0 - 3 >= 0 ]", 0-1) = 0 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) [ Ar_0 - 3 >= 0 ]", 0-2) = Ar_2 S("evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) [ Ar_0 - 3 >= 0 ]", 0-3) = Ar_3 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-0) = Ar_0 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-1) = Ar_1 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-2) = Ar_2 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ]", 0-3) = Ar_3 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-0) = Ar_0 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-1) = Ar_1 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-2) = Ar_2 S("evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ]", 0-3) = Ar_3 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] weakly and the transitions evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] strictly and produces the following problem: 9: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep2entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep2bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, 0, Ar_2, Ar_3)) [ Ar_0 - 3 >= 0 ] (Comp: 2, Cost: 1) evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: Ar_0 + 1, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2 ] (Comp: 2, Cost: 1) evalrealheapsortstep2bb11in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_1 + 1 >= Ar_0 ] (Comp: Ar_0 + 1, Cost: 1) evalrealheapsortstep2bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 - Ar_1 - 2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: 6*Ar_0^2 + 8*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 3 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ 2*Ar_2 + Ar_1 + 2 >= Ar_0 ] (Comp: 6*Ar_0^2 + 8*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 = 2*Ar_2 + Ar_1 + 3 ] (Comp: 6*Ar_0^2 + 8*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 /\ Ar_0 >= Ar_1 + 2*Ar_2 + 4 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb10in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb11in(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: 6*Ar_0^2 + 8*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 1)) [ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: 6*Ar_0^2 + 8*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] (Comp: 6*Ar_0^2 + 8*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] (Comp: 6*Ar_0^2 + 8*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, 2*Ar_2 + 2)) [ Ar_0 - Ar_2 - 4 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - Ar_1 - 4 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 4 >= 0 ] (Comp: 6*Ar_0^2 + 8*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: 6*Ar_0^2 + 8*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_0, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] (Comp: 6*Ar_0^2 + 8*Ar_0 + 2, Cost: 1) evalrealheapsortstep2bb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep2bb9in(Ar_0, Ar_1, Ar_3, Ar_3)) [ Ar_3 - 1 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 1 >= 0 /\ Ar_0 + Ar_3 - 4 >= 0 /\ Ar_0 - Ar_2 - 3 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 3 >= 0 /\ Ar_0 - Ar_1 - 3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 3 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 86*Ar_0 + 60*Ar_0^2 + 34 Time: 0.553 sec (SMT: 0.426 sec) ---------------------------------------- (2) BOUNDS(1, n^2) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalrealheapsortstep2start 0: evalrealheapsortstep2start -> evalrealheapsortstep2entryin : [], cost: 1 1: evalrealheapsortstep2entryin -> evalrealheapsortstep2bbin : [ A>=3 ], cost: 1 2: evalrealheapsortstep2entryin -> evalrealheapsortstep2returnin : [ 2>=A ], cost: 1 3: evalrealheapsortstep2bbin -> evalrealheapsortstep2bb11in : B'=0, [], cost: 1 4: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb1in : [ A>=2+B ], cost: 1 5: evalrealheapsortstep2bb11in -> evalrealheapsortstep2returnin : [ 1+B>=A ], cost: 1 6: evalrealheapsortstep2bb1in -> evalrealheapsortstep2bb9in : C'=0, [], cost: 1 7: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb2in : [ A>=3+2*C+B ], cost: 1 8: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb10in : [ 2+2*C+B>=A ], cost: 1 9: evalrealheapsortstep2bb2in -> evalrealheapsortstep2bb4in : [ A==3+2*C+B ], cost: 1 10: evalrealheapsortstep2bb2in -> evalrealheapsortstep2bb3in : [ A>=4+2*C+B ], cost: 1 11: evalrealheapsortstep2bb2in -> evalrealheapsortstep2bb3in : [ 2+2*C+B>=A ], cost: 1 12: evalrealheapsortstep2bb3in -> evalrealheapsortstep2bb4in : [], cost: 1 13: evalrealheapsortstep2bb3in -> evalrealheapsortstep2bb5in : [], cost: 1 14: evalrealheapsortstep2bb4in -> evalrealheapsortstep2bb6in : D'=1+2*C, [], cost: 1 15: evalrealheapsortstep2bb5in -> evalrealheapsortstep2bb6in : D'=2+2*C, [], cost: 1 16: evalrealheapsortstep2bb6in -> evalrealheapsortstep2bb7in : [], cost: 1 17: evalrealheapsortstep2bb6in -> evalrealheapsortstep2bb9in : C'=A, [], cost: 1 18: evalrealheapsortstep2bb7in -> evalrealheapsortstep2bb9in : C'=D, [], cost: 1 19: evalrealheapsortstep2bb10in -> evalrealheapsortstep2bb11in : B'=1+B, [], cost: 1 20: evalrealheapsortstep2returnin -> evalrealheapsortstep2stop : [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: evalrealheapsortstep2start -> evalrealheapsortstep2entryin : [], cost: 1 Removed unreachable and leaf rules: Start location: evalrealheapsortstep2start 0: evalrealheapsortstep2start -> evalrealheapsortstep2entryin : [], cost: 1 1: evalrealheapsortstep2entryin -> evalrealheapsortstep2bbin : [ A>=3 ], cost: 1 3: evalrealheapsortstep2bbin -> evalrealheapsortstep2bb11in : B'=0, [], cost: 1 4: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb1in : [ A>=2+B ], cost: 1 6: evalrealheapsortstep2bb1in -> evalrealheapsortstep2bb9in : C'=0, [], cost: 1 7: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb2in : [ A>=3+2*C+B ], cost: 1 8: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb10in : [ 2+2*C+B>=A ], cost: 1 9: evalrealheapsortstep2bb2in -> evalrealheapsortstep2bb4in : [ A==3+2*C+B ], cost: 1 10: evalrealheapsortstep2bb2in -> evalrealheapsortstep2bb3in : [ A>=4+2*C+B ], cost: 1 11: evalrealheapsortstep2bb2in -> evalrealheapsortstep2bb3in : [ 2+2*C+B>=A ], cost: 1 12: evalrealheapsortstep2bb3in -> evalrealheapsortstep2bb4in : [], cost: 1 13: evalrealheapsortstep2bb3in -> evalrealheapsortstep2bb5in : [], cost: 1 14: evalrealheapsortstep2bb4in -> evalrealheapsortstep2bb6in : D'=1+2*C, [], cost: 1 15: evalrealheapsortstep2bb5in -> evalrealheapsortstep2bb6in : D'=2+2*C, [], cost: 1 16: evalrealheapsortstep2bb6in -> evalrealheapsortstep2bb7in : [], cost: 1 17: evalrealheapsortstep2bb6in -> evalrealheapsortstep2bb9in : C'=A, [], cost: 1 18: evalrealheapsortstep2bb7in -> evalrealheapsortstep2bb9in : C'=D, [], cost: 1 19: evalrealheapsortstep2bb10in -> evalrealheapsortstep2bb11in : B'=1+B, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalrealheapsortstep2start 22: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=0, [ A>=3 ], cost: 3 23: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb9in : C'=0, [ A>=2+B ], cost: 2 7: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb2in : [ A>=3+2*C+B ], cost: 1 24: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb11in : B'=1+B, [ 2+2*C+B>=A ], cost: 2 9: evalrealheapsortstep2bb2in -> evalrealheapsortstep2bb4in : [ A==3+2*C+B ], cost: 1 10: evalrealheapsortstep2bb2in -> evalrealheapsortstep2bb3in : [ A>=4+2*C+B ], cost: 1 11: evalrealheapsortstep2bb2in -> evalrealheapsortstep2bb3in : [ 2+2*C+B>=A ], cost: 1 12: evalrealheapsortstep2bb3in -> evalrealheapsortstep2bb4in : [], cost: 1 25: evalrealheapsortstep2bb3in -> evalrealheapsortstep2bb6in : D'=2+2*C, [], cost: 2 14: evalrealheapsortstep2bb4in -> evalrealheapsortstep2bb6in : D'=1+2*C, [], cost: 1 17: evalrealheapsortstep2bb6in -> evalrealheapsortstep2bb9in : C'=A, [], cost: 1 26: evalrealheapsortstep2bb6in -> evalrealheapsortstep2bb9in : C'=D, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: evalrealheapsortstep2start 22: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=0, [ A>=3 ], cost: 3 23: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb9in : C'=0, [ A>=2+B ], cost: 2 24: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb11in : B'=1+B, [ 2+2*C+B>=A ], cost: 2 27: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb4in : [ A==3+2*C+B ], cost: 2 28: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb3in : [ A>=4+2*C+B ], cost: 2 12: evalrealheapsortstep2bb3in -> evalrealheapsortstep2bb4in : [], cost: 1 25: evalrealheapsortstep2bb3in -> evalrealheapsortstep2bb6in : D'=2+2*C, [], cost: 2 14: evalrealheapsortstep2bb4in -> evalrealheapsortstep2bb6in : D'=1+2*C, [], cost: 1 17: evalrealheapsortstep2bb6in -> evalrealheapsortstep2bb9in : C'=A, [], cost: 1 26: evalrealheapsortstep2bb6in -> evalrealheapsortstep2bb9in : C'=D, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: evalrealheapsortstep2start 22: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=0, [ A>=3 ], cost: 3 23: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb9in : C'=0, [ A>=2+B ], cost: 2 24: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb11in : B'=1+B, [ 2+2*C+B>=A ], cost: 2 30: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb6in : D'=2+2*C, [ A>=4+2*C+B ], cost: 4 31: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb6in : D'=1+2*C, [ A==3+2*C+B ], cost: 3 32: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb6in : D'=1+2*C, [ A>=4+2*C+B ], cost: 4 17: evalrealheapsortstep2bb6in -> evalrealheapsortstep2bb9in : C'=A, [], cost: 1 26: evalrealheapsortstep2bb6in -> evalrealheapsortstep2bb9in : C'=D, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: evalrealheapsortstep2start 22: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=0, [ A>=3 ], cost: 3 23: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb9in : C'=0, [ A>=2+B ], cost: 2 24: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb11in : B'=1+B, [ 2+2*C+B>=A ], cost: 2 33: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=A, D'=2+2*C, [ A>=4+2*C+B ], cost: 5 34: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=2+2*C, D'=2+2*C, [ A>=4+2*C+B ], cost: 6 35: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=A, D'=1+2*C, [ A==3+2*C+B ], cost: 4 36: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=1+2*C, D'=1+2*C, [ A==3+2*C+B ], cost: 5 37: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=A, D'=1+2*C, [ A>=4+2*C+B ], cost: 5 38: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=1+2*C, D'=1+2*C, [ A>=4+2*C+B ], cost: 6 Accelerating simple loops of location 5. Accelerating the following rules: 33: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=A, D'=2+2*C, [ A>=4+2*C+B ], cost: 5 34: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=2+2*C, D'=2+2*C, [ A>=4+2*C+B ], cost: 6 35: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=A, D'=1+2*C, [ A==3+2*C+B ], cost: 4 36: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=1+2*C, D'=1+2*C, [ A==3+2*C+B ], cost: 5 37: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=A, D'=1+2*C, [ A>=4+2*C+B ], cost: 5 38: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=1+2*C, D'=1+2*C, [ A>=4+2*C+B ], cost: 6 Accelerated rule 33 with NONTERM (after strengthening guard), yielding the new rule 39. Found no metering function for rule 34. Accelerated rule 35 with NONTERM (after strengthening guard), yielding the new rule 40. Found no metering function for rule 36. Accelerated rule 37 with NONTERM (after strengthening guard), yielding the new rule 41. Found no metering function for rule 38. Removing the simple loops:. Also removing duplicate rules: 39. Accelerated all simple loops using metering functions (where possible): Start location: evalrealheapsortstep2start 22: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=0, [ A>=3 ], cost: 3 23: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb9in : C'=0, [ A>=2+B ], cost: 2 24: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb11in : B'=1+B, [ 2+2*C+B>=A ], cost: 2 33: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=A, D'=2+2*C, [ A>=4+2*C+B ], cost: 5 34: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=2+2*C, D'=2+2*C, [ A>=4+2*C+B ], cost: 6 35: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=A, D'=1+2*C, [ A==3+2*C+B ], cost: 4 36: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=1+2*C, D'=1+2*C, [ A==3+2*C+B ], cost: 5 37: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=A, D'=1+2*C, [ A>=4+2*C+B ], cost: 5 38: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb9in : C'=1+2*C, D'=1+2*C, [ A>=4+2*C+B ], cost: 6 40: evalrealheapsortstep2bb9in -> [15] : [ A==3+2*C+B && A==3+2*A+B ], cost: NONTERM 41: evalrealheapsortstep2bb9in -> [15] : [ A>=4+2*C+B && A>=4+2*A+B ], cost: NONTERM Chained accelerated rules (with incoming rules): Start location: evalrealheapsortstep2start 22: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=0, [ A>=3 ], cost: 3 23: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb9in : C'=0, [ A>=2+B ], cost: 2 42: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb9in : C'=A, D'=2, [ A>=4+B ], cost: 7 43: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb9in : C'=2, D'=2, [ A>=4+B ], cost: 8 44: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb9in : C'=A, D'=1, [ A==3+B ], cost: 6 45: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb9in : C'=1, D'=1, [ A==3+B ], cost: 7 46: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb9in : C'=A, D'=1, [ A>=4+B ], cost: 7 47: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb9in : C'=1, D'=1, [ A>=4+B ], cost: 8 48: evalrealheapsortstep2bb11in -> [15] : C'=0, [ A==3+B && A==3+2*A+B ], cost: NONTERM 49: evalrealheapsortstep2bb11in -> [15] : C'=0, [ A>=4+B && A>=4+2*A+B ], cost: NONTERM 24: evalrealheapsortstep2bb9in -> evalrealheapsortstep2bb11in : B'=1+B, [ 2+2*C+B>=A ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: evalrealheapsortstep2start 22: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=0, [ A>=3 ], cost: 3 48: evalrealheapsortstep2bb11in -> [15] : C'=0, [ A==3+B && A==3+2*A+B ], cost: NONTERM 49: evalrealheapsortstep2bb11in -> [15] : C'=0, [ A>=4+B && A>=4+2*A+B ], cost: NONTERM 50: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=0, [ A>=2+B && 2+B>=A ], cost: 4 51: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=A, D'=2, [ A>=4+B && 2+2*A+B>=A ], cost: 9 52: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=2, D'=2, [ A>=4+B && 6+B>=A ], cost: 10 53: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=A, D'=1, [ A==3+B && 2+2*A+B>=A ], cost: 8 54: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=1, D'=1, [ A==3+B ], cost: 9 55: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=A, D'=1, [ A>=4+B && 2+2*A+B>=A ], cost: 9 56: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=1, D'=1, [ A>=4+B && 4+B>=A ], cost: 10 Applied pruning (of leafs and parallel rules): Start location: evalrealheapsortstep2start 22: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=0, [ A>=3 ], cost: 3 48: evalrealheapsortstep2bb11in -> [15] : C'=0, [ A==3+B && A==3+2*A+B ], cost: NONTERM 49: evalrealheapsortstep2bb11in -> [15] : C'=0, [ A>=4+B && A>=4+2*A+B ], cost: NONTERM 50: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=0, [ A>=2+B && 2+B>=A ], cost: 4 51: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=A, D'=2, [ A>=4+B && 2+2*A+B>=A ], cost: 9 52: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=2, D'=2, [ A>=4+B && 6+B>=A ], cost: 10 53: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=A, D'=1, [ A==3+B && 2+2*A+B>=A ], cost: 8 54: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=1, D'=1, [ A==3+B ], cost: 9 Accelerating simple loops of location 3. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 50: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=0, [ 2-A+B==0 ], cost: 4 51: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=A, D'=2, [ A>=4+B && 2+2*A+B>=A ], cost: 9 52: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=2, D'=2, [ A>=4+B && 6+B>=A ], cost: 10 53: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=A, D'=1, [ A==3+B && 2+2*A+B>=A ], cost: 8 54: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=1+B, C'=1, D'=1, [ A==3+B ], cost: 9 Accelerated rule 50 with metering function -1+A-B, yielding the new rule 57. Accelerated rule 51 with metering function -3+A-B, yielding the new rule 58. Accelerated rule 52 with metering function -3+A-B, yielding the new rule 59. Accelerated rule 53 with metering function -2+A-B, yielding the new rule 60. Accelerated rule 54 with metering function -2+A-B, yielding the new rule 61. Removing the simple loops: 50 51 52 53 54. Accelerated all simple loops using metering functions (where possible): Start location: evalrealheapsortstep2start 22: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=0, [ A>=3 ], cost: 3 48: evalrealheapsortstep2bb11in -> [15] : C'=0, [ A==3+B && A==3+2*A+B ], cost: NONTERM 49: evalrealheapsortstep2bb11in -> [15] : C'=0, [ A>=4+B && A>=4+2*A+B ], cost: NONTERM 57: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=-1+A, C'=0, [ 2-A+B==0 ], cost: -4+4*A-4*B 58: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=-3+A, C'=A, D'=2, [ A>=4+B && 2+2*A+B>=A ], cost: -27+9*A-9*B 59: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=-3+A, C'=2, D'=2, [ A>=4+B && 6+B>=A ], cost: -30+10*A-10*B 60: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=-2+A, C'=A, D'=1, [ A==3+B && 2+2*A+B>=A ], cost: -16+8*A-8*B 61: evalrealheapsortstep2bb11in -> evalrealheapsortstep2bb11in : B'=-2+A, C'=1, D'=1, [ A==3+B ], cost: -18+9*A-9*B Chained accelerated rules (with incoming rules): Start location: evalrealheapsortstep2start 22: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=0, [ A>=3 ], cost: 3 62: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=-3+A, C'=A, D'=2, [ A>=4 ], cost: -24+9*A 63: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=-3+A, C'=2, D'=2, [ A>=4 && 6>=A ], cost: -27+10*A 64: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=-2+A, C'=A, D'=1, [ A==3 ], cost: -13+8*A 65: evalrealheapsortstep2start -> evalrealheapsortstep2bb11in : B'=-2+A, C'=1, D'=1, [ A==3 ], cost: -15+9*A 48: evalrealheapsortstep2bb11in -> [15] : C'=0, [ A==3+B && A==3+2*A+B ], cost: NONTERM 49: evalrealheapsortstep2bb11in -> [15] : C'=0, [ A>=4+B && A>=4+2*A+B ], cost: NONTERM Eliminated locations (on tree-shaped paths): Start location: evalrealheapsortstep2start 66: evalrealheapsortstep2start -> [17] : [ A>=4 ], cost: -24+9*A 67: evalrealheapsortstep2start -> [17] : [ A>=4 && 6>=A ], cost: -27+10*A 68: evalrealheapsortstep2start -> [17] : [ A==3 ], cost: -13+8*A 69: evalrealheapsortstep2start -> [17] : [ A==3 ], cost: -15+9*A Applied pruning (of leafs and parallel rules): Start location: evalrealheapsortstep2start 66: evalrealheapsortstep2start -> [17] : [ A>=4 ], cost: -24+9*A 67: evalrealheapsortstep2start -> [17] : [ A>=4 && 6>=A ], cost: -27+10*A 68: evalrealheapsortstep2start -> [17] : [ A==3 ], cost: -13+8*A 69: evalrealheapsortstep2start -> [17] : [ A==3 ], cost: -15+9*A ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalrealheapsortstep2start 66: evalrealheapsortstep2start -> [17] : [ A>=4 ], cost: -24+9*A 67: evalrealheapsortstep2start -> [17] : [ A>=4 && 6>=A ], cost: -27+10*A 68: evalrealheapsortstep2start -> [17] : [ A==3 ], cost: -13+8*A 69: evalrealheapsortstep2start -> [17] : [ A==3 ], cost: -15+9*A Computing asymptotic complexity for rule 66 Solved the limit problem by the following transformations: Created initial limit problem: -24+9*A (+), -3+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==n} resulting limit problem: [solved] Solution: A / n Resulting cost -24+9*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: -24+9*n Rule cost: -24+9*A Rule guard: [ A>=4 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)