/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).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, 336 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 726 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalfstart(A, B, C, D) -> Com_1(evalfentryin(A, B, C, D)) :|: TRUE evalfentryin(A, B, C, D) -> Com_1(evalfbb3in(A, B, 0, 0)) :|: A >= 1 && B >= A + 1 evalfbb3in(A, B, C, D) -> Com_1(evalfreturnin(A, B, C, D)) :|: D >= B evalfbb3in(A, B, C, D) -> Com_1(evalfbb4in(A, B, C, D)) :|: B >= D + 1 evalfbb4in(A, B, C, D) -> Com_1(evalfbbin(A, B, C, D)) :|: 0 >= E + 1 evalfbb4in(A, B, C, D) -> Com_1(evalfbbin(A, B, C, D)) :|: E >= 1 evalfbb4in(A, B, C, D) -> Com_1(evalfreturnin(A, B, C, D)) :|: TRUE evalfbbin(A, B, C, D) -> Com_1(evalfbb1in(A, B, C, D)) :|: A >= C + 1 evalfbbin(A, B, C, D) -> Com_1(evalfbb2in(A, B, C, D)) :|: C >= A evalfbb1in(A, B, C, D) -> Com_1(evalfbb3in(A, B, C + 1, D)) :|: TRUE evalfbb2in(A, B, C, D) -> Com_1(evalfbb3in(A, B, 0, D + 1)) :|: TRUE evalfreturnin(A, B, C, D) -> Com_1(evalfstop(A, B, C, D)) :|: TRUE The start-symbols are:[evalfstart_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 20*Ar_1 + 10*Ar_0 + 20*Ar_0*Ar_1 + 16) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, Ar_3 + 1)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstart(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) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, Ar_3 + 1)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfstart) = 2 Pol(evalfentryin) = 2 Pol(evalfbb3in) = 2 Pol(evalfreturnin) = 1 Pol(evalfbb4in) = 2 Pol(evalfbbin) = 2 Pol(evalfbb1in) = 2 Pol(evalfbb2in) = 2 Pol(evalfstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ] (Comp: 2, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, Ar_3 + 1)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstart(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 evalfbb1in: 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 evalfbb2in: 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 evalfbb3in: 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 evalfbb4in: 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 evalfbbin: 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 evalfreturnin: 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(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstop(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 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb2in(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) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(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) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\ E >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb4in(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: 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 2*V_2 Pol(evalfstart) = 2*V_2 Pol(evalfreturnin) = 2*V_2 - 2*V_4 Pol(evalfstop) = 2*V_2 - 2*V_4 Pol(evalfbb2in) = 2*V_2 - 2*V_4 - 1 Pol(evalfbb3in) = 2*V_2 - 2*V_4 Pol(evalfbb1in) = 2*V_2 - 2*V_4 Pol(evalfbbin) = 2*V_2 - 2*V_4 Pol(evalfbb4in) = 2*V_2 - 2*V_4 Pol(evalfentryin) = 2*V_2 orients all transitions weakly and the transitions evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb2in(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 ] evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstop(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 ] (Comp: 2*Ar_1, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb2in(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) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(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) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\ E >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb4in(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: 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbbin) = 2*V_1 - 2*V_3 + 1 Pol(evalfbb1in) = 2*V_1 - 2*V_3 Pol(evalfbb4in) = 2*V_1 - 2*V_3 + 1 Pol(evalfbb3in) = 2*V_1 - 2*V_3 + 1 and size complexities S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\\ Ar_1 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\\ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\\ Ar_1 >= Ar_0 + 1 ]", 0-2) = 0 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\\ Ar_1 >= Ar_0 + 1 ]", 0-3) = 0 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb4in(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("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb4in(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("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb4in(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("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb4in(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("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\\ 0 >= E + 1 ]", 0-0) = Ar_0 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\\ 0 >= E + 1 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\\ 0 >= E + 1 ]", 0-2) = Ar_0 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\\ 0 >= E + 1 ]", 0-3) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\\ E >= 1 ]", 0-0) = Ar_0 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\\ E >= 1 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\\ E >= 1 ]", 0-2) = Ar_0 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\\ E >= 1 ]", 0-3) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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 ]", 0-0) = Ar_0 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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 ]", 0-1) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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 ]", 0-2) = Ar_0 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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 ]", 0-3) = Ar_1 S("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(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("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(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("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(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("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(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("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb2in(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("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb2in(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("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb2in(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("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb2in(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("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstop(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 ]", 0-0) = Ar_0 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstop(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 ]", 0-1) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstop(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 ]", 0-2) = Ar_0 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstop(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 ]", 0-3) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstart(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(evalfstart(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(evalfstart(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(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(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 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\ E >= 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\ 0 >= E + 1 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb4in(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 ] evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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 ] weakly and the transitions evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(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 ] evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstop(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 ] (Comp: 2*Ar_1, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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 + 2*Ar_1 + 1, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb2in(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 + 2*Ar_1 + 1, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(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) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\ E >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\ 0 >= E + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb4in(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: 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfentryin(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(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfstop(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 ] (Comp: 2*Ar_1, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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 + 2*Ar_1 + 1, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(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) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb2in(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 + 2*Ar_1 + 1, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb1in(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) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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 ] (Comp: 2*Ar_0 + 4*Ar_0*Ar_1 + 4*Ar_1 + 2, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\ E >= 1 ] (Comp: 2*Ar_0 + 4*Ar_0*Ar_1 + 4*Ar_1 + 2, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbbin(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 /\ 0 >= E + 1 ] (Comp: 2*Ar_0 + 4*Ar_0*Ar_1 + 4*Ar_1 + 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb4in(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: 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfreturnin(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: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfbb3in(Ar_0, Ar_1, 0, 0)) [ Ar_0 >= 1 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound 20*Ar_1 + 10*Ar_0 + 20*Ar_0*Ar_1 + 16 Time: 0.338 sec (SMT: 0.258 sec) ---------------------------------------- (2) BOUNDS(1, n^2) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalfstart 0: evalfstart -> evalfentryin : [], cost: 1 1: evalfentryin -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 1 2: evalfbb3in -> evalfreturnin : [ D>=B ], cost: 1 3: evalfbb3in -> evalfbb4in : [ B>=1+D ], cost: 1 4: evalfbb4in -> evalfbbin : [ 0>=1+free ], cost: 1 5: evalfbb4in -> evalfbbin : [ free_1>=1 ], cost: 1 6: evalfbb4in -> evalfreturnin : [], cost: 1 7: evalfbbin -> evalfbb1in : [ A>=1+C ], cost: 1 8: evalfbbin -> evalfbb2in : [ C>=A ], cost: 1 9: evalfbb1in -> evalfbb3in : C'=1+C, [], cost: 1 10: evalfbb2in -> evalfbb3in : C'=0, D'=1+D, [], cost: 1 11: evalfreturnin -> evalfstop : [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: evalfstart -> evalfentryin : [], cost: 1 Removed unreachable and leaf rules: Start location: evalfstart 0: evalfstart -> evalfentryin : [], cost: 1 1: evalfentryin -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 1 3: evalfbb3in -> evalfbb4in : [ B>=1+D ], cost: 1 4: evalfbb4in -> evalfbbin : [ 0>=1+free ], cost: 1 5: evalfbb4in -> evalfbbin : [ free_1>=1 ], cost: 1 7: evalfbbin -> evalfbb1in : [ A>=1+C ], cost: 1 8: evalfbbin -> evalfbb2in : [ C>=A ], cost: 1 9: evalfbb1in -> evalfbb3in : C'=1+C, [], cost: 1 10: evalfbb2in -> evalfbb3in : C'=0, D'=1+D, [], cost: 1 Simplified all rules, resulting in: Start location: evalfstart 0: evalfstart -> evalfentryin : [], cost: 1 1: evalfentryin -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 1 3: evalfbb3in -> evalfbb4in : [ B>=1+D ], cost: 1 5: evalfbb4in -> evalfbbin : [], cost: 1 7: evalfbbin -> evalfbb1in : [ A>=1+C ], cost: 1 8: evalfbbin -> evalfbb2in : [ C>=A ], cost: 1 9: evalfbb1in -> evalfbb3in : C'=1+C, [], cost: 1 10: evalfbb2in -> evalfbb3in : C'=0, D'=1+D, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalfstart 12: evalfstart -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 2 13: evalfbb3in -> evalfbbin : [ B>=1+D ], cost: 2 14: evalfbbin -> evalfbb3in : C'=1+C, [ A>=1+C ], cost: 2 15: evalfbbin -> evalfbb3in : C'=0, D'=1+D, [ C>=A ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: evalfstart 12: evalfstart -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 2 16: evalfbb3in -> evalfbb3in : C'=1+C, [ B>=1+D && A>=1+C ], cost: 4 17: evalfbb3in -> evalfbb3in : C'=0, D'=1+D, [ B>=1+D && C>=A ], cost: 4 Accelerating simple loops of location 2. Accelerating the following rules: 16: evalfbb3in -> evalfbb3in : C'=1+C, [ B>=1+D && A>=1+C ], cost: 4 17: evalfbb3in -> evalfbb3in : C'=0, D'=1+D, [ B>=1+D && C>=A ], cost: 4 Accelerated rule 16 with metering function -C+A, yielding the new rule 18. Accelerated rule 17 with metering function -D+B (after strengthening guard), yielding the new rule 19. Nested simple loops 17 (outer loop) and 18 (inner loop) with metering function -1-D+B, resulting in the new rules: 20, 21. Removing the simple loops: 16 17. Accelerated all simple loops using metering functions (where possible): Start location: evalfstart 12: evalfstart -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 2 18: evalfbb3in -> evalfbb3in : C'=A, [ B>=1+D && A>=1+C ], cost: -4*C+4*A 19: evalfbb3in -> evalfbb3in : C'=0, D'=B, [ B>=1+D && C>=A && 0>=A ], cost: -4*D+4*B 20: evalfbb3in -> evalfbb3in : C'=A, D'=-1+B, [ C>=A && B>=2+D && A>=1 ], cost: -4-4*A*(1+D-B)-4*D+4*B 21: evalfbb3in -> evalfbb3in : C'=A, D'=-1+B, [ A>=1+C && B>=2+D && A>=1 ], cost: -4-4*A*(1+D-B)-4*C-4*D+4*A+4*B Chained accelerated rules (with incoming rules): Start location: evalfstart 12: evalfstart -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 2 22: evalfstart -> evalfbb3in : C'=A, D'=0, [ A>=1 && B>=1+A && B>=1 ], cost: 2+4*A 23: evalfstart -> evalfbb3in : C'=A, D'=-1+B, [ A>=1 && B>=1+A && B>=2 ], cost: -2+4*A+4*B+4*(-1+B)*A Removed unreachable locations (and leaf rules with constant cost): Start location: evalfstart 22: evalfstart -> evalfbb3in : C'=A, D'=0, [ A>=1 && B>=1+A && B>=1 ], cost: 2+4*A 23: evalfstart -> evalfbb3in : C'=A, D'=-1+B, [ A>=1 && B>=1+A && B>=2 ], cost: -2+4*A+4*B+4*(-1+B)*A ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalfstart 22: evalfstart -> evalfbb3in : C'=A, D'=0, [ A>=1 && B>=1+A && B>=1 ], cost: 2+4*A 23: evalfstart -> evalfbb3in : C'=A, D'=-1+B, [ A>=1 && B>=1+A && B>=2 ], cost: -2+4*A+4*B+4*(-1+B)*A Computing asymptotic complexity for rule 22 Solved the limit problem by the following transformations: Created initial limit problem: 2+4*A (+), A (+/+!), -A+B (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==n,B==2*n} resulting limit problem: [solved] Solution: A / n B / 2*n Resulting cost 2+4*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Computing asymptotic complexity for rule 23 Solved the limit problem by the following transformations: Created initial limit problem: A (+/+!), -2+4*A*B+4*B (+), -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 14+4*n^2+16*n 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: 14+4*n^2+16*n Rule cost: -2+4*A+4*B+4*(-1+B)*A Rule guard: [ A>=1 && B>=1+A ] WORST_CASE(Omega(n^2),?) ---------------------------------------- (4) BOUNDS(n^2, INF)