/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 235 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 621 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalspeedpldi3start(A, B, C, D) -> Com_1(evalspeedpldi3entryin(A, B, C, D)) :|: TRUE evalspeedpldi3entryin(A, B, C, D) -> Com_1(evalspeedpldi3returnin(A, B, C, D)) :|: 0 >= A evalspeedpldi3entryin(A, B, C, D) -> Com_1(evalspeedpldi3returnin(A, B, C, D)) :|: A >= B evalspeedpldi3entryin(A, B, C, D) -> Com_1(evalspeedpldi3bb5in(A, B, 0, 0)) :|: A >= 1 && B >= A + 1 evalspeedpldi3bb5in(A, B, C, D) -> Com_1(evalspeedpldi3bb2in(A, B, C, D)) :|: B >= D + 1 evalspeedpldi3bb5in(A, B, C, D) -> Com_1(evalspeedpldi3returnin(A, B, C, D)) :|: D >= B evalspeedpldi3bb2in(A, B, C, D) -> Com_1(evalspeedpldi3bb3in(A, B, C, D)) :|: A >= C + 1 evalspeedpldi3bb2in(A, B, C, D) -> Com_1(evalspeedpldi3bb4in(A, B, C, D)) :|: C >= A evalspeedpldi3bb3in(A, B, C, D) -> Com_1(evalspeedpldi3bb5in(A, B, C + 1, D)) :|: TRUE evalspeedpldi3bb4in(A, B, C, D) -> Com_1(evalspeedpldi3bb5in(A, B, 0, D + 1)) :|: TRUE evalspeedpldi3returnin(A, B, C, D) -> Com_1(evalspeedpldi3stop(A, B, C, D)) :|: TRUE The start-symbols are:[evalspeedpldi3start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 6*Ar_1 + 6*Ar_0 + 12*Ar_0*Ar_1 + 9) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) (Comp: ?, Cost: 1) evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) (Comp: ?, Cost: 1) evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalspeedpldi3start) = 2 Pol(evalspeedpldi3entryin) = 2 Pol(evalspeedpldi3returnin) = 1 Pol(evalspeedpldi3bb5in) = 2 Pol(evalspeedpldi3bb2in) = 2 Pol(evalspeedpldi3bb3in) = 2 Pol(evalspeedpldi3bb4in) = 2 Pol(evalspeedpldi3stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3)) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: 2, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) (Comp: 2, Cost: 1) evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalspeedpldi3bb2in: X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalspeedpldi3bb3in: X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_2 - X_3 - 2 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalspeedpldi3bb4in: X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol evalspeedpldi3bb5in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalspeedpldi3bb5in) = 2*V_2 - 2*V_4 Pol(evalspeedpldi3bb2in) = 2*V_2 - 2*V_4 Pol(evalspeedpldi3bb4in) = 2*V_2 - 2*V_4 - 1 Pol(evalspeedpldi3bb3in) = 2*V_2 - 2*V_4 and size complexities S("evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-0) = Ar_0 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-1) = Ar_1 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-2) = Ar_2 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-3) = Ar_3 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-0) = Ar_0 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-2) = Ar_2 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-3) = Ar_3 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\\ Ar_1 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\\ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\\ Ar_1 >= Ar_0 + 1 ]", 0-2) = 0 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\\ Ar_1 >= Ar_0 + 1 ]", 0-3) = 0 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-2) = Ar_0 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-3) = Ar_1 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-0) = Ar_0 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-1) = Ar_1 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-2) = 0 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-3) = Ar_1 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 + 1 ]", 0-2) = Ar_0 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 + 1 ]", 0-3) = Ar_1 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_0 ]", 0-0) = Ar_0 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_0 ]", 0-1) = Ar_1 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_0 ]", 0-2) = Ar_0 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_0 ]", 0-3) = Ar_1 S("evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 S("evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = Ar_1 S("evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = Ar_0 S("evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-3) = Ar_1 S("evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 S("evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = Ar_1 S("evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = 0 S("evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-3) = Ar_1 S("evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_1 + Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3start(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(evalspeedpldi3start(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(evalspeedpldi3start(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(evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_3 + 1 ] evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ] evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ] weakly and the transitions evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 2*Ar_1, Cost: 1) evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2*Ar_1, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalspeedpldi3bb5in) = 2*V_1 - 2*V_3 Pol(evalspeedpldi3bb2in) = 2*V_1 - 2*V_3 Pol(evalspeedpldi3bb3in) = 2*V_1 - 2*V_3 - 1 and size complexities S("evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-0) = Ar_0 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-1) = Ar_1 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-2) = Ar_2 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-3) = Ar_3 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-0) = Ar_0 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-2) = Ar_2 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ]", 0-3) = Ar_3 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\\ Ar_1 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\\ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\\ Ar_1 >= Ar_0 + 1 ]", 0-2) = 0 S("evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\\ Ar_1 >= Ar_0 + 1 ]", 0-3) = 0 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-0) = Ar_0 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-2) = Ar_0 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_3 + 1 ]", 0-3) = Ar_1 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-0) = Ar_0 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-1) = Ar_1 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-2) = 0 S("evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_3 >= Ar_1 ]", 0-3) = Ar_1 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 + 1 ]", 0-2) = Ar_0 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 + 1 ]", 0-3) = Ar_1 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_0 ]", 0-0) = Ar_0 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_0 ]", 0-1) = Ar_1 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_0 ]", 0-2) = Ar_0 S("evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_0 ]", 0-3) = Ar_1 S("evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 S("evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = Ar_1 S("evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = Ar_0 S("evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_1 - Ar_2 - 2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-3) = Ar_1 S("evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 S("evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = Ar_1 S("evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = 0 S("evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\\ Ar_3 >= 0 /\\ Ar_2 + Ar_3 - 1 >= 0 /\\ Ar_1 + Ar_3 - 2 >= 0 /\\ Ar_0 + Ar_3 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 3 >= 0 /\\ -Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-3) = Ar_1 S("evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_1 + Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3start(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(evalspeedpldi3start(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(evalspeedpldi3start(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(evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_3 + 1 ] evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ] weakly and the transitions evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 2*Ar_1, Cost: 1) evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2*Ar_0 + 4*Ar_0*Ar_1, Cost: 1) evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2*Ar_1, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ] (Comp: 2*Ar_0 + 4*Ar_0*Ar_1, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 2*Ar_1, Cost: 1) evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, Ar_3 + 1)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2*Ar_0 + 4*Ar_0*Ar_1, Cost: 1) evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 - Ar_2 - 2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 2*Ar_1, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_0 ] (Comp: 2*Ar_0 + 4*Ar_0*Ar_1, Cost: 1) evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_3 >= Ar_1 ] (Comp: 2*Ar_0 + 4*Ar_0*Ar_1 + 2*Ar_1 + 1, Cost: 1) evalspeedpldi3bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 0 /\ Ar_2 + Ar_3 >= 0 /\ Ar_1 + Ar_3 - 2 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3bb5in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 ] (Comp: 1, Cost: 1) evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalspeedpldi3start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalspeedpldi3entryin(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound 6*Ar_1 + 6*Ar_0 + 12*Ar_0*Ar_1 + 9 Time: 0.274 sec (SMT: 0.213 sec) ---------------------------------------- (2) BOUNDS(1, n^2) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalspeedpldi3start 0: evalspeedpldi3start -> evalspeedpldi3entryin : [], cost: 1 1: evalspeedpldi3entryin -> evalspeedpldi3returnin : [ 0>=A ], cost: 1 2: evalspeedpldi3entryin -> evalspeedpldi3returnin : [ A>=B ], cost: 1 3: evalspeedpldi3entryin -> evalspeedpldi3bb5in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 1 4: evalspeedpldi3bb5in -> evalspeedpldi3bb2in : [ B>=1+D ], cost: 1 5: evalspeedpldi3bb5in -> evalspeedpldi3returnin : [ D>=B ], cost: 1 6: evalspeedpldi3bb2in -> evalspeedpldi3bb3in : [ A>=1+C ], cost: 1 7: evalspeedpldi3bb2in -> evalspeedpldi3bb4in : [ C>=A ], cost: 1 8: evalspeedpldi3bb3in -> evalspeedpldi3bb5in : C'=1+C, [], cost: 1 9: evalspeedpldi3bb4in -> evalspeedpldi3bb5in : C'=0, D'=1+D, [], cost: 1 10: evalspeedpldi3returnin -> evalspeedpldi3stop : [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: evalspeedpldi3start -> evalspeedpldi3entryin : [], cost: 1 Removed unreachable and leaf rules: Start location: evalspeedpldi3start 0: evalspeedpldi3start -> evalspeedpldi3entryin : [], cost: 1 3: evalspeedpldi3entryin -> evalspeedpldi3bb5in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 1 4: evalspeedpldi3bb5in -> evalspeedpldi3bb2in : [ B>=1+D ], cost: 1 6: evalspeedpldi3bb2in -> evalspeedpldi3bb3in : [ A>=1+C ], cost: 1 7: evalspeedpldi3bb2in -> evalspeedpldi3bb4in : [ C>=A ], cost: 1 8: evalspeedpldi3bb3in -> evalspeedpldi3bb5in : C'=1+C, [], cost: 1 9: evalspeedpldi3bb4in -> evalspeedpldi3bb5in : C'=0, D'=1+D, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalspeedpldi3start 11: evalspeedpldi3start -> evalspeedpldi3bb5in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 2 4: evalspeedpldi3bb5in -> evalspeedpldi3bb2in : [ B>=1+D ], cost: 1 12: evalspeedpldi3bb2in -> evalspeedpldi3bb5in : C'=1+C, [ A>=1+C ], cost: 2 13: evalspeedpldi3bb2in -> evalspeedpldi3bb5in : C'=0, D'=1+D, [ C>=A ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: evalspeedpldi3start 11: evalspeedpldi3start -> evalspeedpldi3bb5in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 2 14: evalspeedpldi3bb5in -> evalspeedpldi3bb5in : C'=1+C, [ B>=1+D && A>=1+C ], cost: 3 15: evalspeedpldi3bb5in -> evalspeedpldi3bb5in : C'=0, D'=1+D, [ B>=1+D && C>=A ], cost: 3 Accelerating simple loops of location 2. Accelerating the following rules: 14: evalspeedpldi3bb5in -> evalspeedpldi3bb5in : C'=1+C, [ B>=1+D && A>=1+C ], cost: 3 15: evalspeedpldi3bb5in -> evalspeedpldi3bb5in : C'=0, D'=1+D, [ B>=1+D && C>=A ], cost: 3 Accelerated rule 14 with metering function -C+A, yielding the new rule 16. Accelerated rule 15 with metering function -D+B (after strengthening guard), yielding the new rule 17. Nested simple loops 15 (outer loop) and 16 (inner loop) with metering function -1-D+B, resulting in the new rules: 18, 19. Removing the simple loops: 14 15. Accelerated all simple loops using metering functions (where possible): Start location: evalspeedpldi3start 11: evalspeedpldi3start -> evalspeedpldi3bb5in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 2 16: evalspeedpldi3bb5in -> evalspeedpldi3bb5in : C'=A, [ B>=1+D && A>=1+C ], cost: -3*C+3*A 17: evalspeedpldi3bb5in -> evalspeedpldi3bb5in : C'=0, D'=B, [ B>=1+D && C>=A && 0>=A ], cost: -3*D+3*B 18: evalspeedpldi3bb5in -> evalspeedpldi3bb5in : C'=A, D'=-1+B, [ C>=A && B>=2+D && A>=1 ], cost: -3-3*A*(1+D-B)-3*D+3*B 19: evalspeedpldi3bb5in -> evalspeedpldi3bb5in : C'=A, D'=-1+B, [ A>=1+C && B>=2+D && A>=1 ], cost: -3-3*A*(1+D-B)-3*C-3*D+3*A+3*B Chained accelerated rules (with incoming rules): Start location: evalspeedpldi3start 11: evalspeedpldi3start -> evalspeedpldi3bb5in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 2 20: evalspeedpldi3start -> evalspeedpldi3bb5in : C'=A, D'=0, [ A>=1 && B>=1+A && B>=1 ], cost: 2+3*A 21: evalspeedpldi3start -> evalspeedpldi3bb5in : C'=A, D'=-1+B, [ A>=1 && B>=1+A && B>=2 ], cost: -1+3*A+3*B+3*(-1+B)*A Removed unreachable locations (and leaf rules with constant cost): Start location: evalspeedpldi3start 20: evalspeedpldi3start -> evalspeedpldi3bb5in : C'=A, D'=0, [ A>=1 && B>=1+A && B>=1 ], cost: 2+3*A 21: evalspeedpldi3start -> evalspeedpldi3bb5in : C'=A, D'=-1+B, [ A>=1 && B>=1+A && B>=2 ], cost: -1+3*A+3*B+3*(-1+B)*A ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalspeedpldi3start 20: evalspeedpldi3start -> evalspeedpldi3bb5in : C'=A, D'=0, [ A>=1 && B>=1+A && B>=1 ], cost: 2+3*A 21: evalspeedpldi3start -> evalspeedpldi3bb5in : C'=A, D'=-1+B, [ A>=1 && B>=1+A && B>=2 ], cost: -1+3*A+3*B+3*(-1+B)*A Computing asymptotic complexity for rule 20 Solved the limit problem by the following transformations: Created initial limit problem: A (+/+!), -A+B (+/+!), 2+3*A (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==n,B==1+n} resulting limit problem: [solved] Solution: A / n B / 1+n Resulting cost 2+3*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Computing asymptotic complexity for rule 21 Solved the limit problem by the following transformations: Created initial limit problem: -1+3*A*B+3*B (+), A (+/+!), -A+B (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==1+n,B==2+n} resulting limit problem: [solved] Solution: A / 1+n B / 2+n Resulting cost 11+12*n+3*n^2 has complexity: Poly(n^2) Found new complexity Poly(n^2). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^2) Cpx degree: 2 Solved cost: 11+12*n+3*n^2 Rule cost: -1+3*A+3*B+3*(-1+B)*A Rule guard: [ A>=1 && B>=1+A ] WORST_CASE(Omega(n^2),?) ---------------------------------------- (4) BOUNDS(n^2, INF)