/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 611 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 1436 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalfstart(A, B, C, D, E, F) -> Com_1(evalfentryin(A, B, C, D, E, F)) :|: TRUE evalfentryin(A, B, C, D, E, F) -> Com_1(evalfbb9in(B, B, C, D, E, F)) :|: TRUE evalfbb9in(A, B, C, D, E, F) -> Com_1(evalfbbin(A, B, C, D, E, F)) :|: B >= 2 evalfbb9in(A, B, C, D, E, F) -> Com_1(evalfreturnin(A, B, C, D, E, F)) :|: 1 >= B evalfbbin(A, B, C, D, E, F) -> Com_1(evalfbb6in(A, B, B - 1, A + B - 1, E, F)) :|: TRUE evalfbb6in(A, B, C, D, E, F) -> Com_1(evalfbb8in(A, B, C, D, E, F)) :|: C >= D evalfbb6in(A, B, C, D, E, F) -> Com_1(evalfbb7in(A, B, C, D, E, F)) :|: D >= C + 1 evalfbb7in(A, B, C, D, E, F) -> Com_1(evalfbb1in(A, B, C, D, E, F)) :|: 0 >= G + 1 evalfbb7in(A, B, C, D, E, F) -> Com_1(evalfbb1in(A, B, C, D, E, F)) :|: G >= 1 evalfbb7in(A, B, C, D, E, F) -> Com_1(evalfbb8in(A, B, C, D, E, F)) :|: TRUE evalfbb1in(A, B, C, D, E, F) -> Com_1(evalfbb3in(A, B, C, D, C, D - 1)) :|: TRUE evalfbb3in(A, B, C, D, E, F) -> Com_1(evalfbb5in(A, B, C, D, E, F)) :|: TRUE evalfbb3in(A, B, C, D, E, F) -> Com_1(evalfbb4in(A, B, C, D, E, F)) :|: 0 >= 3 evalfbb4in(A, B, C, D, E, F) -> Com_1(evalfbb2in(A, B, C, D, E, F)) :|: 0 >= G + 1 evalfbb4in(A, B, C, D, E, F) -> Com_1(evalfbb2in(A, B, C, D, E, F)) :|: G >= 1 evalfbb4in(A, B, C, D, E, F) -> Com_1(evalfbb5in(A, B, C, D, E, F)) :|: TRUE evalfbb2in(A, B, C, D, E, F) -> Com_1(evalfbb3in(A, B, C, D, E + 1, F - 2)) :|: TRUE evalfbb5in(A, B, C, D, E, F) -> Com_1(evalfbb6in(A, B, E, F - 1, E, F)) :|: TRUE evalfbb8in(A, B, C, D, E, F) -> Com_1(evalfbb9in(D - C + 1, C - 1, C, D, E, F)) :|: TRUE evalfreturnin(A, B, C, D, E, F) -> Com_1(evalfstop(A, B, C, D, E, F)) :|: TRUE The start-symbols are:[evalfstart_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 110*Ar_1 + 14) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ] (Comp: ?, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= 3 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 - 2)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= 3 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5 - 2)) We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ] (Comp: ?, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ] (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb5in) = 2 Pol(evalfbb6in) = 2 Pol(evalfbb3in) = 2 Pol(evalfbb1in) = 2 Pol(evalfbb7in) = 2 Pol(evalfbb8in) = 2 Pol(evalfbb9in) = 2 Pol(evalfreturnin) = 1 Pol(evalfstop) = 0 Pol(evalfbbin) = 2 Pol(evalfentryin) = 2 Pol(evalfstart) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ] strictly and produces the following problem: 4: T: (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ] (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb5in) = V_5 Pol(evalfbb6in) = V_3 Pol(evalfbb3in) = V_5 Pol(evalfbb1in) = V_3 Pol(evalfbb7in) = V_3 Pol(evalfbb8in) = V_3 Pol(evalfbb9in) = V_2 + 1 Pol(evalfreturnin) = V_2 + 1 Pol(evalfstop) = V_2 + 1 Pol(evalfbbin) = V_2 - 1 Pol(evalfentryin) = V_2 + 1 Pol(evalfstart) = V_2 + 1 Pol(koat_start) = V_2 + 1 orients all transitions weakly and the transition evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ] strictly and produces the following problem: 5: T: (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ] (Comp: Ar_1 + 1, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ] (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1 + 1, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ] (Comp: Ar_1 + 1, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ] (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb8in) = 1 Pol(evalfbb9in) = 0 Pol(evalfbb7in) = 2 Pol(evalfbb1in) = 2 Pol(evalfbb6in) = 2 Pol(evalfbb5in) = 2 Pol(evalfbb3in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ]", 0-0) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ]", 0-1) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ]", 0-2) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ]", 0-3) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ]", 0-4) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ]", 0-5) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ]", 0-0) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ]", 0-1) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ]", 0-2) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ]", 0-3) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ]", 0-4) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ]", 0-5) = ? S("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5))", 0-0) = ? S("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5))", 0-1) = ? S("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5))", 0-2) = ? S("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5))", 0-3) = ? S("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5))", 0-4) = ? S("evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5))", 0-5) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ]", 0-0) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ]", 0-1) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ]", 0-5) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ]", 0-0) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ]", 0-1) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ]", 0-5) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ]", 0-0) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ]", 0-1) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ]", 0-2) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ]", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ]", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ]", 0-5) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ]", 0-0) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ]", 0-1) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ]", 0-2) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ]", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ]", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ]", 0-5) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1))", 0-0) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1))", 0-1) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1))", 0-2) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1))", 0-3) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1))", 0-4) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1))", 0-5) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5))", 0-0) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5))", 0-1) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5))", 0-2) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5))", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5))", 0-5) = ? orients the transitions evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ] evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ] evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ] evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5)) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1)) weakly and the transitions evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ] strictly and produces the following problem: 7: T: (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1)) (Comp: 2*Ar_1 + 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ G >= 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= G + 1 ] (Comp: 2*Ar_1 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 ] (Comp: 2*Ar_1 + 2, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_3 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1 + 1, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ] (Comp: Ar_1 + 1, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ] (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 7 to obtain the following invariants: For symbol evalfbb1in: X_4 - 2 >= 0 /\ X_3 + X_4 - 3 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 4 >= 0 /\ -X_2 + X_4 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ -X_2 + X_3 + 1 >= 0 /\ X_2 - 2 >= 0 For symbol evalfbb3in: X_4 - X_6 - 1 >= 0 /\ X_6 - 1 >= 0 /\ X_5 + X_6 - 2 >= 0 /\ -X_5 + X_6 >= 0 /\ X_4 + X_6 - 3 >= 0 /\ -X_4 + X_6 + 1 >= 0 /\ X_3 + X_6 - 2 >= 0 /\ -X_3 + X_6 >= 0 /\ X_2 + X_6 - 3 >= 0 /\ -X_2 + X_6 + 1 >= 0 /\ X_4 - X_5 - 1 >= 0 /\ X_3 - X_5 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_5 - 1 >= 0 /\ X_4 + X_5 - 3 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ -X_3 + X_5 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ -X_2 + X_5 + 1 >= 0 /\ X_4 - 2 >= 0 /\ X_3 + X_4 - 3 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 4 >= 0 /\ -X_2 + X_4 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ -X_2 + X_3 + 1 >= 0 /\ X_2 - 2 >= 0 For symbol evalfbb5in: X_4 - X_6 - 1 >= 0 /\ X_6 - 1 >= 0 /\ X_5 + X_6 - 2 >= 0 /\ -X_5 + X_6 >= 0 /\ X_4 + X_6 - 3 >= 0 /\ -X_4 + X_6 + 1 >= 0 /\ X_3 + X_6 - 2 >= 0 /\ -X_3 + X_6 >= 0 /\ X_2 + X_6 - 3 >= 0 /\ -X_2 + X_6 + 1 >= 0 /\ X_4 - X_5 - 1 >= 0 /\ X_3 - X_5 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_5 - 1 >= 0 /\ X_4 + X_5 - 3 >= 0 /\ X_3 + X_5 - 2 >= 0 /\ -X_3 + X_5 >= 0 /\ X_2 + X_5 - 3 >= 0 /\ -X_2 + X_5 + 1 >= 0 /\ X_4 - 2 >= 0 /\ X_3 + X_4 - 3 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 4 >= 0 /\ -X_2 + X_4 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ -X_2 + X_3 + 1 >= 0 /\ X_2 - 2 >= 0 For symbol evalfbb6in: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ -X_2 + X_3 + 1 >= 0 /\ X_2 - 2 >= 0 For symbol evalfbb7in: X_4 - 2 >= 0 /\ X_3 + X_4 - 3 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 4 >= 0 /\ -X_2 + X_4 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ -X_2 + X_3 + 1 >= 0 /\ X_2 - 2 >= 0 For symbol evalfbb8in: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ -X_2 + X_3 + 1 >= 0 /\ X_2 - 2 >= 0 For symbol evalfbbin: X_2 - 2 >= 0 For symbol evalfreturnin: -X_2 + 1 >= 0 This yielded the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1 + 1, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ] (Comp: 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ] (Comp: Ar_1 + 1, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5)) [ Ar_1 - 2 >= 0 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_1 + 1 >= 0 ] (Comp: 2*Ar_1 + 2, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_3 >= Ar_2 + 1 ] (Comp: 2*Ar_1 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 /\ 0 >= G + 1 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 /\ G >= 1 ] (Comp: 2*Ar_1 + 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - Ar_5 - 1 >= 0 /\ Ar_5 - 1 >= 0 /\ Ar_4 + Ar_5 - 2 >= 0 /\ -Ar_4 + Ar_5 >= 0 /\ Ar_3 + Ar_5 - 3 >= 0 /\ -Ar_3 + Ar_5 + 1 >= 0 /\ Ar_2 + Ar_5 - 2 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ Ar_1 + Ar_5 - 3 >= 0 /\ -Ar_1 + Ar_5 + 1 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_3 + Ar_4 - 3 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 - 3 >= 0 /\ -Ar_1 + Ar_4 + 1 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5)) [ Ar_3 - Ar_5 - 1 >= 0 /\ Ar_5 - 1 >= 0 /\ Ar_4 + Ar_5 - 2 >= 0 /\ -Ar_4 + Ar_5 >= 0 /\ Ar_3 + Ar_5 - 3 >= 0 /\ -Ar_3 + Ar_5 + 1 >= 0 /\ Ar_2 + Ar_5 - 2 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ Ar_1 + Ar_5 - 3 >= 0 /\ -Ar_1 + Ar_5 + 1 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_3 + Ar_4 - 3 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 - 3 >= 0 /\ -Ar_1 + Ar_4 + 1 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 17*V_2 Pol(evalfstart) = 17*V_2 Pol(evalfentryin) = 17*V_2 Pol(evalfbb9in) = 10*V_1 + 7*V_2 - 7 Pol(evalfbbin) = 10*V_1 + 7*V_2 - 7 Pol(evalfreturnin) = 10*V_1 + 7*V_2 - 7 Pol(evalfbb6in) = -3*V_2 + 10*V_4 + 3 Pol(evalfstop) = 10*V_1 + 7*V_2 - 7 Pol(evalfbb8in) = -3*V_3 + 10*V_4 - 4 Pol(evalfbb7in) = -3*V_3 + 10*V_4 - 4 Pol(evalfbb1in) = -3*V_3 + 10*V_4 - 8 Pol(evalfbb3in) = -3*V_2 + 10*V_6 + 1 Pol(evalfbb5in) = -3*V_2 + 10*V_6 - 3 orients all transitions weakly and the transitions evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 /\ G >= 1 ] evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 /\ 0 >= G + 1 ] evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_3 >= Ar_2 + 1 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5)) [ Ar_3 - Ar_5 - 1 >= 0 /\ Ar_5 - 1 >= 0 /\ Ar_4 + Ar_5 - 2 >= 0 /\ -Ar_4 + Ar_5 >= 0 /\ Ar_3 + Ar_5 - 3 >= 0 /\ -Ar_3 + Ar_5 + 1 >= 0 /\ Ar_2 + Ar_5 - 2 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ Ar_1 + Ar_5 - 3 >= 0 /\ -Ar_1 + Ar_5 + 1 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_3 + Ar_4 - 3 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 - 3 >= 0 /\ -Ar_1 + Ar_4 + 1 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - Ar_5 - 1 >= 0 /\ Ar_5 - 1 >= 0 /\ Ar_4 + Ar_5 - 2 >= 0 /\ -Ar_4 + Ar_5 >= 0 /\ Ar_3 + Ar_5 - 3 >= 0 /\ -Ar_3 + Ar_5 + 1 >= 0 /\ Ar_2 + Ar_5 - 2 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ Ar_1 + Ar_5 - 3 >= 0 /\ -Ar_1 + Ar_5 + 1 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_3 + Ar_4 - 3 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 - 3 >= 0 /\ -Ar_1 + Ar_4 + 1 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] strictly and produces the following problem: 9: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1 + 1, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 2 ] (Comp: 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 1 >= Ar_1 ] (Comp: Ar_1 + 1, Cost: 1) evalfbbin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_1 - 1, Ar_0 + Ar_1 - 1, Ar_4, Ar_5)) [ Ar_1 - 2 >= 0 ] (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_1 + 1 >= 0 ] (Comp: 2*Ar_1 + 2, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_2 >= Ar_3 ] (Comp: 17*Ar_1, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_3 >= Ar_2 + 1 ] (Comp: 2*Ar_1 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb9in(Ar_3 - Ar_2 + 1, Ar_2 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] (Comp: 17*Ar_1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 /\ 0 >= G + 1 ] (Comp: 17*Ar_1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 /\ G >= 1 ] (Comp: 2*Ar_1 + 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] (Comp: 17*Ar_1, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2, Ar_3 - 1)) [ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] (Comp: 17*Ar_1, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 - Ar_5 - 1 >= 0 /\ Ar_5 - 1 >= 0 /\ Ar_4 + Ar_5 - 2 >= 0 /\ -Ar_4 + Ar_5 >= 0 /\ Ar_3 + Ar_5 - 3 >= 0 /\ -Ar_3 + Ar_5 + 1 >= 0 /\ Ar_2 + Ar_5 - 2 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ Ar_1 + Ar_5 - 3 >= 0 /\ -Ar_1 + Ar_5 + 1 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_3 + Ar_4 - 3 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 - 3 >= 0 /\ -Ar_1 + Ar_4 + 1 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] (Comp: 17*Ar_1, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_4, Ar_5 - 1, Ar_4, Ar_5)) [ Ar_3 - Ar_5 - 1 >= 0 /\ Ar_5 - 1 >= 0 /\ Ar_4 + Ar_5 - 2 >= 0 /\ -Ar_4 + Ar_5 >= 0 /\ Ar_3 + Ar_5 - 3 >= 0 /\ -Ar_3 + Ar_5 + 1 >= 0 /\ Ar_2 + Ar_5 - 2 >= 0 /\ -Ar_2 + Ar_5 >= 0 /\ Ar_1 + Ar_5 - 3 >= 0 /\ -Ar_1 + Ar_5 + 1 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_2 - Ar_4 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_4 - 1 >= 0 /\ Ar_3 + Ar_4 - 3 >= 0 /\ Ar_2 + Ar_4 - 2 >= 0 /\ -Ar_2 + Ar_4 >= 0 /\ Ar_1 + Ar_4 - 3 >= 0 /\ -Ar_1 + Ar_4 + 1 >= 0 /\ Ar_3 - 2 >= 0 /\ Ar_2 + Ar_3 - 3 >= 0 /\ -Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 - 4 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 + 1 >= 0 /\ Ar_1 - 2 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 110*Ar_1 + 14 Time: 0.603 sec (SMT: 0.454 sec) ---------------------------------------- (2) BOUNDS(1, n^1) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalfstart 0: evalfstart -> evalfentryin : [], cost: 1 1: evalfentryin -> evalfbb9in : A'=B, [], cost: 1 2: evalfbb9in -> evalfbbin : [ B>=2 ], cost: 1 3: evalfbb9in -> evalfreturnin : [ 1>=B ], cost: 1 4: evalfbbin -> evalfbb6in : C'=-1+B, D'=-1+A+B, [], cost: 1 5: evalfbb6in -> evalfbb8in : [ C>=D ], cost: 1 6: evalfbb6in -> evalfbb7in : [ D>=1+C ], cost: 1 7: evalfbb7in -> evalfbb1in : [ 0>=1+free ], cost: 1 8: evalfbb7in -> evalfbb1in : [ free_1>=1 ], cost: 1 9: evalfbb7in -> evalfbb8in : [], cost: 1 10: evalfbb1in -> evalfbb3in : E'=C, F'=-1+D, [], cost: 1 11: evalfbb3in -> evalfbb5in : [], cost: 1 12: evalfbb3in -> evalfbb4in : [ 0>=3 ], cost: 1 13: evalfbb4in -> evalfbb2in : [ 0>=1+free_2 ], cost: 1 14: evalfbb4in -> evalfbb2in : [ free_3>=1 ], cost: 1 15: evalfbb4in -> evalfbb5in : [], cost: 1 16: evalfbb2in -> evalfbb3in : E'=1+E, F'=-2+F, [], cost: 1 17: evalfbb5in -> evalfbb6in : C'=E, D'=-1+F, [], cost: 1 18: evalfbb8in -> evalfbb9in : A'=1-C+D, B'=-1+C, [], cost: 1 19: 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 -> evalfbb9in : A'=B, [], cost: 1 2: evalfbb9in -> evalfbbin : [ B>=2 ], cost: 1 4: evalfbbin -> evalfbb6in : C'=-1+B, D'=-1+A+B, [], cost: 1 5: evalfbb6in -> evalfbb8in : [ C>=D ], cost: 1 6: evalfbb6in -> evalfbb7in : [ D>=1+C ], cost: 1 7: evalfbb7in -> evalfbb1in : [ 0>=1+free ], cost: 1 8: evalfbb7in -> evalfbb1in : [ free_1>=1 ], cost: 1 9: evalfbb7in -> evalfbb8in : [], cost: 1 10: evalfbb1in -> evalfbb3in : E'=C, F'=-1+D, [], cost: 1 11: evalfbb3in -> evalfbb5in : [], cost: 1 12: evalfbb3in -> evalfbb4in : [ 0>=3 ], cost: 1 13: evalfbb4in -> evalfbb2in : [ 0>=1+free_2 ], cost: 1 14: evalfbb4in -> evalfbb2in : [ free_3>=1 ], cost: 1 15: evalfbb4in -> evalfbb5in : [], cost: 1 16: evalfbb2in -> evalfbb3in : E'=1+E, F'=-2+F, [], cost: 1 17: evalfbb5in -> evalfbb6in : C'=E, D'=-1+F, [], cost: 1 18: evalfbb8in -> evalfbb9in : A'=1-C+D, B'=-1+C, [], cost: 1 Removed rules with unsatisfiable guard: Start location: evalfstart 0: evalfstart -> evalfentryin : [], cost: 1 1: evalfentryin -> evalfbb9in : A'=B, [], cost: 1 2: evalfbb9in -> evalfbbin : [ B>=2 ], cost: 1 4: evalfbbin -> evalfbb6in : C'=-1+B, D'=-1+A+B, [], cost: 1 5: evalfbb6in -> evalfbb8in : [ C>=D ], cost: 1 6: evalfbb6in -> evalfbb7in : [ D>=1+C ], cost: 1 7: evalfbb7in -> evalfbb1in : [ 0>=1+free ], cost: 1 8: evalfbb7in -> evalfbb1in : [ free_1>=1 ], cost: 1 9: evalfbb7in -> evalfbb8in : [], cost: 1 10: evalfbb1in -> evalfbb3in : E'=C, F'=-1+D, [], cost: 1 11: evalfbb3in -> evalfbb5in : [], cost: 1 13: evalfbb4in -> evalfbb2in : [ 0>=1+free_2 ], cost: 1 14: evalfbb4in -> evalfbb2in : [ free_3>=1 ], cost: 1 15: evalfbb4in -> evalfbb5in : [], cost: 1 16: evalfbb2in -> evalfbb3in : E'=1+E, F'=-2+F, [], cost: 1 17: evalfbb5in -> evalfbb6in : C'=E, D'=-1+F, [], cost: 1 18: evalfbb8in -> evalfbb9in : A'=1-C+D, B'=-1+C, [], cost: 1 Removed unreachable and leaf rules: Start location: evalfstart 0: evalfstart -> evalfentryin : [], cost: 1 1: evalfentryin -> evalfbb9in : A'=B, [], cost: 1 2: evalfbb9in -> evalfbbin : [ B>=2 ], cost: 1 4: evalfbbin -> evalfbb6in : C'=-1+B, D'=-1+A+B, [], cost: 1 5: evalfbb6in -> evalfbb8in : [ C>=D ], cost: 1 6: evalfbb6in -> evalfbb7in : [ D>=1+C ], cost: 1 7: evalfbb7in -> evalfbb1in : [ 0>=1+free ], cost: 1 8: evalfbb7in -> evalfbb1in : [ free_1>=1 ], cost: 1 9: evalfbb7in -> evalfbb8in : [], cost: 1 10: evalfbb1in -> evalfbb3in : E'=C, F'=-1+D, [], cost: 1 11: evalfbb3in -> evalfbb5in : [], cost: 1 17: evalfbb5in -> evalfbb6in : C'=E, D'=-1+F, [], cost: 1 18: evalfbb8in -> evalfbb9in : A'=1-C+D, B'=-1+C, [], cost: 1 Simplified all rules, resulting in: Start location: evalfstart 0: evalfstart -> evalfentryin : [], cost: 1 1: evalfentryin -> evalfbb9in : A'=B, [], cost: 1 2: evalfbb9in -> evalfbbin : [ B>=2 ], cost: 1 4: evalfbbin -> evalfbb6in : C'=-1+B, D'=-1+A+B, [], cost: 1 5: evalfbb6in -> evalfbb8in : [ C>=D ], cost: 1 6: evalfbb6in -> evalfbb7in : [ D>=1+C ], cost: 1 8: evalfbb7in -> evalfbb1in : [], cost: 1 9: evalfbb7in -> evalfbb8in : [], cost: 1 10: evalfbb1in -> evalfbb3in : E'=C, F'=-1+D, [], cost: 1 11: evalfbb3in -> evalfbb5in : [], cost: 1 17: evalfbb5in -> evalfbb6in : C'=E, D'=-1+F, [], cost: 1 18: evalfbb8in -> evalfbb9in : A'=1-C+D, B'=-1+C, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalfstart 20: evalfstart -> evalfbb9in : A'=B, [], cost: 2 21: evalfbb9in -> evalfbb6in : C'=-1+B, D'=-1+A+B, [ B>=2 ], cost: 2 5: evalfbb6in -> evalfbb8in : [ C>=D ], cost: 1 6: evalfbb6in -> evalfbb7in : [ D>=1+C ], cost: 1 9: evalfbb7in -> evalfbb8in : [], cost: 1 24: evalfbb7in -> evalfbb6in : C'=C, D'=-2+D, E'=C, F'=-1+D, [], cost: 4 18: evalfbb8in -> evalfbb9in : A'=1-C+D, B'=-1+C, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalfstart 20: evalfstart -> evalfbb9in : A'=B, [], cost: 2 21: evalfbb9in -> evalfbb6in : C'=-1+B, D'=-1+A+B, [ B>=2 ], cost: 2 26: evalfbb6in -> evalfbb6in : C'=C, D'=-2+D, E'=C, F'=-1+D, [ D>=1+C ], cost: 5 27: evalfbb6in -> evalfbb9in : A'=1-C+D, B'=-1+C, [ C>=D ], cost: 2 28: evalfbb6in -> evalfbb9in : A'=1-C+D, B'=-1+C, [ D>=1+C ], cost: 3 Accelerating simple loops of location 4. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 26: evalfbb6in -> evalfbb6in : D'=-2+D, E'=C, F'=-1+D, [ D>=1+C ], cost: 5 Accelerated rule 26 with metering function meter (where 2*meter==-C+D), yielding the new rule 29. Removing the simple loops: 26. Accelerated all simple loops using metering functions (where possible): Start location: evalfstart 20: evalfstart -> evalfbb9in : A'=B, [], cost: 2 21: evalfbb9in -> evalfbb6in : C'=-1+B, D'=-1+A+B, [ B>=2 ], cost: 2 27: evalfbb6in -> evalfbb9in : A'=1-C+D, B'=-1+C, [ C>=D ], cost: 2 28: evalfbb6in -> evalfbb9in : A'=1-C+D, B'=-1+C, [ D>=1+C ], cost: 3 29: evalfbb6in -> evalfbb6in : D'=-2*meter+D, E'=C, F'=1-2*meter+D, [ D>=1+C && 2*meter==-C+D && meter>=1 ], cost: 5*meter Chained accelerated rules (with incoming rules): Start location: evalfstart 20: evalfstart -> evalfbb9in : A'=B, [], cost: 2 21: evalfbb9in -> evalfbb6in : C'=-1+B, D'=-1+A+B, [ B>=2 ], cost: 2 30: evalfbb9in -> evalfbb6in : C'=-1+B, D'=-1-2*meter+A+B, E'=-1+B, F'=-2*meter+A+B, [ B>=2 && -1+A+B>=B && 2*meter==A && meter>=1 ], cost: 2+5*meter 27: evalfbb6in -> evalfbb9in : A'=1-C+D, B'=-1+C, [ C>=D ], cost: 2 28: evalfbb6in -> evalfbb9in : A'=1-C+D, B'=-1+C, [ D>=1+C ], cost: 3 Eliminated locations (on tree-shaped paths): Start location: evalfstart 20: evalfstart -> evalfbb9in : A'=B, [], cost: 2 31: evalfbb9in -> evalfbb9in : A'=1+A, B'=-2+B, C'=-1+B, D'=-1+A+B, [ B>=2 && -1+B>=-1+A+B ], cost: 4 32: evalfbb9in -> evalfbb9in : A'=1+A, B'=-2+B, C'=-1+B, D'=-1+A+B, [ B>=2 && -1+A+B>=B ], cost: 5 33: evalfbb9in -> evalfbb9in : A'=1-2*meter+A, B'=-2+B, C'=-1+B, D'=-1-2*meter+A+B, E'=-1+B, F'=-2*meter+A+B, [ B>=2 && -1+A+B>=B && 2*meter==A && meter>=1 ], cost: 4+5*meter 34: evalfbb9in -> [15] : [ B>=2 && -1+A+B>=B && 2*meter==A && meter>=1 ], cost: 2+5*meter Accelerating simple loops of location 2. Accelerating the following rules: 31: evalfbb9in -> evalfbb9in : A'=1+A, B'=-2+B, C'=-1+B, D'=-1+A+B, [ B>=2 && -1+B>=-1+A+B ], cost: 4 32: evalfbb9in -> evalfbb9in : A'=1+A, B'=-2+B, C'=-1+B, D'=-1+A+B, [ B>=2 && -1+A+B>=B ], cost: 5 33: evalfbb9in -> evalfbb9in : A'=1-2*meter+A, B'=-2+B, C'=-1+B, D'=-1-2*meter+A+B, E'=-1+B, F'=-2*meter+A+B, [ B>=2 && -1+A+B>=B && 2*meter==A && meter>=1 ], cost: 4+5*meter Found no metering function for rule 31. Accelerated rule 32 with metering function meter_1 (where 2*meter_1==-1+B), yielding the new rule 35. During metering: Instantiating temporary variables by {meter==1} Accelerated rule 33 with metering function -2+A, yielding the new rule 36. During metering: Instantiating temporary variables by {meter_1==1} During metering: Instantiating temporary variables by {meter==1,meter_1==1} Removing the simple loops: 32 33. Accelerated all simple loops using metering functions (where possible): Start location: evalfstart 20: evalfstart -> evalfbb9in : A'=B, [], cost: 2 31: evalfbb9in -> evalfbb9in : A'=1+A, B'=-2+B, C'=-1+B, D'=-1+A+B, [ B>=2 && -1+B>=-1+A+B ], cost: 4 34: evalfbb9in -> [15] : [ B>=2 && -1+A+B>=B && 2*meter==A && meter>=1 ], cost: 2+5*meter 35: evalfbb9in -> evalfbb9in : A'=meter_1+A, B'=-2*meter_1+B, C'=1-2*meter_1+B, D'=-meter_1+A+B, [ B>=2 && -1+A+B>=B && 2*meter_1==-1+B && meter_1>=1 ], cost: 5*meter_1 36: evalfbb9in -> evalfbb9in : A'=2, B'=4-2*A+B, C'=5-2*A+B, D'=6-2*A+B, E'=5-2*A+B, F'=7-2*A+B, [ B>=2 && 2==A && -2+A>=1 ], cost: -18+9*A Chained accelerated rules (with incoming rules): Start location: evalfstart 20: evalfstart -> evalfbb9in : A'=B, [], cost: 2 37: evalfstart -> evalfbb9in : A'=meter_1+B, B'=-2*meter_1+B, C'=1-2*meter_1+B, D'=-meter_1+2*B, [ B>=2 && 2*meter_1==-1+B && meter_1>=1 ], cost: 2+5*meter_1 34: evalfbb9in -> [15] : [ B>=2 && -1+A+B>=B && 2*meter==A && meter>=1 ], cost: 2+5*meter Eliminated locations (on tree-shaped paths): Start location: evalfstart 38: evalfstart -> [15] : A'=B, [ B>=2 && 2*meter==B && meter>=1 ], cost: 4+5*meter 39: evalfstart -> [17] : [ B>=2 && 2*meter_1==-1+B && meter_1>=1 ], cost: 2+5*meter_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalfstart 38: evalfstart -> [15] : A'=B, [ B>=2 && 2*meter==B && meter>=1 ], cost: 4+5*meter 39: evalfstart -> [17] : [ B>=2 && 2*meter_1==-1+B && meter_1>=1 ], cost: 2+5*meter_1 Computing asymptotic complexity for rule 38 Solved the limit problem by the following transformations: Created initial limit problem: 1-2*meter+B (+/+!), -1+B (+/+!), 1+2*meter-B (+/+!), 4+5*meter (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {meter==n,B==2*n} resulting limit problem: [solved] Solution: meter / n B / 2*n Resulting cost 4+5*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Computing asymptotic complexity for rule 39 Solved the limit problem by the following transformations: Created initial limit problem: 2+2*meter_1-B (+/+!), -2*meter_1+B (+/+!), -1+B (+/+!), 2+5*meter_1 (+) [not solved] applying transformation rule (C) using substitution {B==1+2*meter_1} resulting limit problem: 1 (+/+!), 2*meter_1 (+/+!), 2+5*meter_1 (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 2*meter_1 (+/+!), 2+5*meter_1 (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {meter_1==n} resulting limit problem: [solved] Solved the limit problem by the following transformations: Created initial limit problem: 2+2*meter_1-B (+/+!), -2*meter_1+B (+/+!), -1+B (+/+!), 2+5*meter_1 (+) [not solved] applying transformation rule (C) using substitution {B==1+2*meter_1} resulting limit problem: 1 (+/+!), 2*meter_1 (+/+!), 2+5*meter_1 (+) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 2*meter_1 (+/+!), 2+5*meter_1 (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {meter_1==n} resulting limit problem: [solved] Solution: meter_1 / n B / 1+2*n Resulting cost 2+5*n has complexity: Poly(n^1) Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 4+5*n Rule cost: 4+5*meter Rule guard: [ B>=2 && 2*meter==B ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)