/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^4), O(n^8)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^4, n^8). (0) CpxIntTrs (1) Koat Proof [FINISHED, 208 ms] (2) BOUNDS(1, n^8) (3) Loat Proof [FINISHED, 1218 ms] (4) BOUNDS(n^4, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalfstart(A, B, C, D, E) -> Com_1(evalfentryin(A, B, C, D, E)) :|: TRUE evalfentryin(A, B, C, D, E) -> Com_1(evalfbb10in(B, A, C, D, E)) :|: TRUE evalfbb10in(A, B, C, D, E) -> Com_1(evalfbb8in(A, B, 1, D, E)) :|: B >= 1 evalfbb10in(A, B, C, D, E) -> Com_1(evalfreturnin(A, B, C, D, E)) :|: 0 >= B evalfbb8in(A, B, C, D, E) -> Com_1(evalfbb6in(A, B, C, B, E)) :|: A >= C evalfbb8in(A, B, C, D, E) -> Com_1(evalfbb9in(A, B, C, D, E)) :|: C >= A + 1 evalfbb6in(A, B, C, D, E) -> Com_1(evalfbb4in(A, B, C, D, 1)) :|: B + C >= D evalfbb6in(A, B, C, D, E) -> Com_1(evalfbb7in(A, B, C, D, E)) :|: D >= B + C + 1 evalfbb4in(A, B, C, D, E) -> Com_1(evalfbb3in(A, B, C, D, E)) :|: D >= E evalfbb4in(A, B, C, D, E) -> Com_1(evalfbb5in(A, B, C, D, E)) :|: E >= D + 1 evalfbb3in(A, B, C, D, E) -> Com_1(evalfbb4in(A, B, C, D, E + 1)) :|: TRUE evalfbb5in(A, B, C, D, E) -> Com_1(evalfbb6in(A, B, C, D + 1, E)) :|: TRUE evalfbb7in(A, B, C, D, E) -> Com_1(evalfbb8in(A, B, C + 1, D, E)) :|: TRUE evalfbb9in(A, B, C, D, E) -> Com_1(evalfbb10in(A, B - 1, C, D, E)) :|: TRUE evalfreturnin(A, B, C, D, E) -> Com_1(evalfstop(A, B, C, D, E)) :|: TRUE The start-symbols are:[evalfstart_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 227895*Ar_0 + 239753*Ar_0*Ar_1 + 106031*Ar_1 + 166582*Ar_0^2*Ar_1 + 150116*Ar_0^2 + 54594*Ar_0^2*Ar_1^2 + 70968*Ar_0*Ar_1^2 + 29482*Ar_1^2 + 35100*Ar_0^3*Ar_1 + 28200*Ar_0^3 + 14212*Ar_0^3*Ar_1^2 + 1104*Ar_0^4*Ar_1^2 + 2240*Ar_0^4*Ar_1 + 224*Ar_0^4*Ar_1^3 + 1984*Ar_0^3*Ar_1^3 + 4608*Ar_0^2*Ar_1^3 + 4160*Ar_0*Ar_1^3 + 1600*Ar_0^4 + 16*Ar_0^4*Ar_1^4 + 64*Ar_0^3*Ar_1^4 + 96*Ar_0^2*Ar_1^4 + 64*Ar_0*Ar_1^4 + 16*Ar_1^4 + 1312*Ar_1^3 + 104385) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfstart) = 2 Pol(evalfentryin) = 2 Pol(evalfbb10in) = 2 Pol(evalfbb8in) = 2 Pol(evalfreturnin) = 1 Pol(evalfbb6in) = 2 Pol(evalfbb9in) = 2 Pol(evalfbb4in) = 2 Pol(evalfbb7in) = 2 Pol(evalfbb3in) = 2 Pol(evalfbb5in) = 2 Pol(evalfstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfstart) = V_1 + 1 Pol(evalfentryin) = V_1 + 1 Pol(evalfbb10in) = V_2 + 1 Pol(evalfbb8in) = V_2 Pol(evalfreturnin) = V_2 Pol(evalfbb6in) = V_2 Pol(evalfbb9in) = V_2 Pol(evalfbb4in) = V_2 Pol(evalfbb7in) = V_2 Pol(evalfbb3in) = V_2 Pol(evalfbb5in) = V_2 Pol(evalfstop) = V_2 Pol(koat_start) = V_1 + 1 orients all transitions weakly and the transition evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4)) (Comp: Ar_0 + 1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb9in) = 1 Pol(evalfbb10in) = 0 Pol(evalfbb8in) = 2 Pol(evalfbb6in) = 2 Pol(evalfbb7in) = 2 Pol(evalfbb4in) = 2 Pol(evalfbb5in) = 2 Pol(evalfbb3in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-1) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-1) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-1) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-0) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-1) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-2) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-0) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-1) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_0 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transitions evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4)) (Comp: Ar_0 + 1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb8in) = V_1 - V_3 + 1 Pol(evalfbb6in) = V_1 - V_3 Pol(evalfbb7in) = V_1 - V_3 Pol(evalfbb4in) = V_1 - V_3 Pol(evalfbb5in) = V_1 - V_3 Pol(evalfbb3in) = V_1 - V_3 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 162 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = 3*Ar_0 + 18 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = 3*Ar_0 + 54 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-0) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-1) = 3*Ar_0 + 54 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-2) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-0) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_0 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transition evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4)) (Comp: Ar_0 + 1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ] (Comp: Ar_0*Ar_1 + Ar_1 + 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb7in) = 1 Pol(evalfbb8in) = 0 Pol(evalfbb6in) = 2 Pol(evalfbb4in) = 2 Pol(evalfbb5in) = 2 Pol(evalfbb3in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 162 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = 3*Ar_0 + 18 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-2) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = 3*Ar_0 + 54 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-0) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-1) = 3*Ar_0 + 54 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-2) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-0) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_0 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transitions evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4)) (Comp: Ar_0 + 1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ] (Comp: Ar_0*Ar_1 + Ar_1 + 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] (Comp: 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 4, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 4, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb6in) = V_2 + V_3 - V_4 + 1 Pol(evalfbb4in) = V_2 + V_3 - V_4 Pol(evalfbb5in) = V_2 + V_3 - V_4 Pol(evalfbb3in) = V_2 + V_3 - V_4 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 162 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 + 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = 3*Ar_0 + 18 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = 3*Ar_0 + 54 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-0) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-1) = 3*Ar_0 + 54 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-2) = Ar_2 + 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-0) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_0 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transition evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4)) (Comp: Ar_0 + 1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ] (Comp: Ar_0*Ar_1 + Ar_1 + 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 14*Ar_0^2*Ar_1 + 96*Ar_0*Ar_1 + 20*Ar_0^2 + 2*Ar_0^2*Ar_1^2 + 4*Ar_0*Ar_1^2 + 2*Ar_1^2 + 176*Ar_0 + 82*Ar_1 + 156, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] (Comp: 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 4, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 4, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb5in) = 1 Pol(evalfbb6in) = 0 Pol(evalfbb4in) = 2 Pol(evalfbb3in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 162 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 + 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = 3*Ar_0 + 18 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = 3*Ar_0 + 54 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-0) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-1) = 3*Ar_0 + 54 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-2) = Ar_2 + 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-0) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-3) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_0 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transitions evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] strictly and produces the following problem: 9: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4)) (Comp: Ar_0 + 1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ] (Comp: Ar_0*Ar_1 + Ar_1 + 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 14*Ar_0^2*Ar_1 + 96*Ar_0*Ar_1 + 20*Ar_0^2 + 2*Ar_0^2*Ar_1^2 + 4*Ar_0*Ar_1^2 + 2*Ar_1^2 + 176*Ar_0 + 82*Ar_1 + 156, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] (Comp: 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 4, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 352*Ar_0 + 164*Ar_1 + 312, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 352*Ar_0 + 164*Ar_1 + 312, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 4, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb4in) = V_4 - V_5 + 1 Pol(evalfbb3in) = V_4 - V_5 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 162 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 + 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 + 353*Ar_0 + 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 164*Ar_1 + 330 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 + 353*Ar_0 + 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 164*Ar_1 + 330 S("evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-3) = 353*Ar_0 + 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 164*Ar_1 + 330 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4))", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-1) = 3*Ar_0 + 18 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-3) = 353*Ar_0 + 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 164*Ar_1 + 330 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4))", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-1) = 3*Ar_0 + 18 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-3) = 353*Ar_0 + 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 164*Ar_1 + 330 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-3) = 353*Ar_0 + 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 164*Ar_1 + 330 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ]", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-3) = 353*Ar_0 + 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 164*Ar_1 + 330 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-3) = 353*Ar_0 + 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 164*Ar_1 + 330 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ]", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-3) = 353*Ar_0 + 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 164*Ar_1 + 330 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ]", 0-4) = 1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = Ar_3 + 353*Ar_0 + 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 164*Ar_1 + 330 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-0) = Ar_1 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-2) = 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-3) = 3*Ar_0 + 54 S("evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-0) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-1) = 3*Ar_0 + 54 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-2) = Ar_2 + 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 5 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-3) = Ar_3 + 353*Ar_0 + 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 164*Ar_1 + 330 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ]", 0-4) = ? S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-0) = Ar_1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-1) = 3*Ar_0 + 18 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-2) = 1 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-3) = Ar_3 + 353*Ar_0 + 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 164*Ar_1 + 330 S("evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ]", 0-4) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_0 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) weakly and the transition evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] strictly and produces the following problem: 10: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4)) (Comp: Ar_0 + 1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ] (Comp: Ar_0*Ar_1 + Ar_1 + 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 14*Ar_0^2*Ar_1 + 96*Ar_0*Ar_1 + 20*Ar_0^2 + 2*Ar_0^2*Ar_1^2 + 4*Ar_0*Ar_1^2 + 2*Ar_1^2 + 176*Ar_0 + 82*Ar_1 + 156, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] (Comp: 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 4, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] (Comp: 17550*Ar_0^3*Ar_1 + 83256*Ar_0^2*Ar_1 + 14100*Ar_0^3 + 7106*Ar_0^3*Ar_1^2 + 27292*Ar_0^2*Ar_1^2 + 35474*Ar_0*Ar_1^2 + 75008*Ar_0^2 + 119634*Ar_0*Ar_1 + 552*Ar_0^4*Ar_1^2 + 1120*Ar_0^4*Ar_1 + 112*Ar_0^4*Ar_1^3 + 992*Ar_0^3*Ar_1^3 + 2304*Ar_0^2*Ar_1^3 + 2080*Ar_0*Ar_1^3 + 800*Ar_0^4 + 8*Ar_0^4*Ar_1^4 + 32*Ar_0^3*Ar_1^4 + 48*Ar_0^2*Ar_1^4 + 32*Ar_0*Ar_1^4 + 8*Ar_1^4 + 656*Ar_1^3 + 14736*Ar_1^2 + 113500*Ar_0 + 52808*Ar_1 + 51792, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 352*Ar_0 + 164*Ar_1 + 312, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 352*Ar_0 + 164*Ar_1 + 312, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 4, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 10 produces the following problem: 11: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_1, Ar_0, Ar_2, Ar_3, Ar_4)) (Comp: Ar_0 + 1, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, 1, Ar_3, Ar_4)) [ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalfbb10in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_1 ] (Comp: Ar_0*Ar_1 + Ar_1 + 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb8in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 14*Ar_0^2*Ar_1 + 96*Ar_0*Ar_1 + 20*Ar_0^2 + 2*Ar_0^2*Ar_1^2 + 4*Ar_0*Ar_1^2 + 2*Ar_1^2 + 176*Ar_0 + 82*Ar_1 + 156, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, 1)) [ Ar_1 + Ar_2 >= Ar_3 ] (Comp: 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 4, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + Ar_2 + 1 ] (Comp: 17550*Ar_0^3*Ar_1 + 83256*Ar_0^2*Ar_1 + 14100*Ar_0^3 + 7106*Ar_0^3*Ar_1^2 + 27292*Ar_0^2*Ar_1^2 + 35474*Ar_0*Ar_1^2 + 75008*Ar_0^2 + 119634*Ar_0*Ar_1 + 552*Ar_0^4*Ar_1^2 + 1120*Ar_0^4*Ar_1 + 112*Ar_0^4*Ar_1^3 + 992*Ar_0^3*Ar_1^3 + 2304*Ar_0^2*Ar_1^3 + 2080*Ar_0*Ar_1^3 + 800*Ar_0^4 + 8*Ar_0^4*Ar_1^4 + 32*Ar_0^3*Ar_1^4 + 48*Ar_0^2*Ar_1^4 + 32*Ar_0*Ar_1^4 + 8*Ar_1^4 + 656*Ar_1^3 + 14736*Ar_1^2 + 113500*Ar_0 + 52808*Ar_1 + 51792, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_4 ] (Comp: 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 352*Ar_0 + 164*Ar_1 + 312, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_3 + 1 ] (Comp: 17550*Ar_0^3*Ar_1 + 83256*Ar_0^2*Ar_1 + 14100*Ar_0^3 + 7106*Ar_0^3*Ar_1^2 + 27292*Ar_0^2*Ar_1^2 + 35474*Ar_0*Ar_1^2 + 75008*Ar_0^2 + 119634*Ar_0*Ar_1 + 552*Ar_0^4*Ar_1^2 + 1120*Ar_0^4*Ar_1 + 112*Ar_0^4*Ar_1^3 + 992*Ar_0^3*Ar_1^3 + 2304*Ar_0^2*Ar_1^3 + 2080*Ar_0*Ar_1^3 + 800*Ar_0^4 + 8*Ar_0^4*Ar_1^4 + 32*Ar_0^3*Ar_1^4 + 48*Ar_0^2*Ar_1^4 + 32*Ar_0*Ar_1^4 + 8*Ar_1^4 + 656*Ar_1^3 + 14736*Ar_1^2 + 113500*Ar_0 + 52808*Ar_1 + 51792, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) (Comp: 28*Ar_0^2*Ar_1 + 192*Ar_0*Ar_1 + 40*Ar_0^2 + 4*Ar_0^2*Ar_1^2 + 8*Ar_0*Ar_1^2 + 4*Ar_1^2 + 352*Ar_0 + 164*Ar_1 + 312, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) (Comp: 2*Ar_0*Ar_1 + 2*Ar_1 + 4*Ar_0 + 4, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb8in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 2*Ar_0 + 2, Cost: 1) evalfbb9in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfbb10in(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 227895*Ar_0 + 239753*Ar_0*Ar_1 + 106031*Ar_1 + 166582*Ar_0^2*Ar_1 + 150116*Ar_0^2 + 54594*Ar_0^2*Ar_1^2 + 70968*Ar_0*Ar_1^2 + 29482*Ar_1^2 + 35100*Ar_0^3*Ar_1 + 28200*Ar_0^3 + 14212*Ar_0^3*Ar_1^2 + 1104*Ar_0^4*Ar_1^2 + 2240*Ar_0^4*Ar_1 + 224*Ar_0^4*Ar_1^3 + 1984*Ar_0^3*Ar_1^3 + 4608*Ar_0^2*Ar_1^3 + 4160*Ar_0*Ar_1^3 + 1600*Ar_0^4 + 16*Ar_0^4*Ar_1^4 + 64*Ar_0^3*Ar_1^4 + 96*Ar_0^2*Ar_1^4 + 64*Ar_0*Ar_1^4 + 16*Ar_1^4 + 1312*Ar_1^3 + 104385 Time: 0.243 sec (SMT: 0.157 sec) ---------------------------------------- (2) BOUNDS(1, n^8) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalfstart 0: evalfstart -> evalfentryin : [], cost: 1 1: evalfentryin -> evalfbb10in : A'=B, B'=A, [], cost: 1 2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1 3: evalfbb10in -> evalfreturnin : [ 0>=B ], cost: 1 4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1 5: evalfbb8in -> evalfbb9in : [ C>=1+A ], cost: 1 6: evalfbb6in -> evalfbb4in : E'=1, [ C+B>=D ], cost: 1 7: evalfbb6in -> evalfbb7in : [ D>=1+C+B ], cost: 1 8: evalfbb4in -> evalfbb3in : [ D>=E ], cost: 1 9: evalfbb4in -> evalfbb5in : [ E>=1+D ], cost: 1 10: evalfbb3in -> evalfbb4in : E'=1+E, [], cost: 1 11: evalfbb5in -> evalfbb6in : D'=1+D, [], cost: 1 12: evalfbb7in -> evalfbb8in : C'=1+C, [], cost: 1 13: evalfbb9in -> evalfbb10in : B'=-1+B, [], cost: 1 14: 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 -> evalfbb10in : A'=B, B'=A, [], cost: 1 2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1 4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1 5: evalfbb8in -> evalfbb9in : [ C>=1+A ], cost: 1 6: evalfbb6in -> evalfbb4in : E'=1, [ C+B>=D ], cost: 1 7: evalfbb6in -> evalfbb7in : [ D>=1+C+B ], cost: 1 8: evalfbb4in -> evalfbb3in : [ D>=E ], cost: 1 9: evalfbb4in -> evalfbb5in : [ E>=1+D ], cost: 1 10: evalfbb3in -> evalfbb4in : E'=1+E, [], cost: 1 11: evalfbb5in -> evalfbb6in : D'=1+D, [], cost: 1 12: evalfbb7in -> evalfbb8in : C'=1+C, [], cost: 1 13: evalfbb9in -> evalfbb10in : B'=-1+B, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalfstart 15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2 2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1 4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1 16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2 6: evalfbb6in -> evalfbb4in : E'=1, [ C+B>=D ], cost: 1 17: evalfbb6in -> evalfbb8in : C'=1+C, [ D>=1+C+B ], cost: 2 18: evalfbb4in -> evalfbb4in : E'=1+E, [ D>=E ], cost: 2 19: evalfbb4in -> evalfbb6in : D'=1+D, [ E>=1+D ], cost: 2 Accelerating simple loops of location 5. Accelerating the following rules: 18: evalfbb4in -> evalfbb4in : E'=1+E, [ D>=E ], cost: 2 Accelerated rule 18 with metering function 1+D-E, yielding the new rule 20. Removing the simple loops: 18. Accelerated all simple loops using metering functions (where possible): Start location: evalfstart 15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2 2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1 4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1 16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2 6: evalfbb6in -> evalfbb4in : E'=1, [ C+B>=D ], cost: 1 17: evalfbb6in -> evalfbb8in : C'=1+C, [ D>=1+C+B ], cost: 2 19: evalfbb4in -> evalfbb6in : D'=1+D, [ E>=1+D ], cost: 2 20: evalfbb4in -> evalfbb4in : E'=1+D, [ D>=E ], cost: 2+2*D-2*E Chained accelerated rules (with incoming rules): Start location: evalfstart 15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2 2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1 4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1 16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2 6: evalfbb6in -> evalfbb4in : E'=1, [ C+B>=D ], cost: 1 17: evalfbb6in -> evalfbb8in : C'=1+C, [ D>=1+C+B ], cost: 2 21: evalfbb6in -> evalfbb4in : E'=1+D, [ C+B>=D && D>=1 ], cost: 1+2*D 19: evalfbb4in -> evalfbb6in : D'=1+D, [ E>=1+D ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: evalfstart 15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2 2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1 4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1 16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2 17: evalfbb6in -> evalfbb8in : C'=1+C, [ D>=1+C+B ], cost: 2 22: evalfbb6in -> evalfbb6in : D'=1+D, E'=1, [ C+B>=D && 1>=1+D ], cost: 3 23: evalfbb6in -> evalfbb6in : D'=1+D, E'=1+D, [ C+B>=D && D>=1 ], cost: 3+2*D Accelerating simple loops of location 4. Accelerating the following rules: 22: evalfbb6in -> evalfbb6in : D'=1+D, E'=1, [ C+B>=D && 1>=1+D ], cost: 3 23: evalfbb6in -> evalfbb6in : D'=1+D, E'=1+D, [ C+B>=D && D>=1 ], cost: 3+2*D Found no metering function for rule 22. Accelerated rule 23 with metering function 1+C-D+B, yielding the new rule 24. Removing the simple loops: 23. Accelerated all simple loops using metering functions (where possible): Start location: evalfstart 15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2 2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1 4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1 16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2 17: evalfbb6in -> evalfbb8in : C'=1+C, [ D>=1+C+B ], cost: 2 22: evalfbb6in -> evalfbb6in : D'=1+D, E'=1, [ C+B>=D && 1>=1+D ], cost: 3 24: evalfbb6in -> evalfbb6in : D'=1+C+B, E'=1+C+B, [ C+B>=D && D>=1 ], cost: 2+2*C+(1+C-D+B)^2-2*D+2*(1+C-D+B)*D+2*B Chained accelerated rules (with incoming rules): Start location: evalfstart 15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2 2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1 4: evalfbb8in -> evalfbb6in : D'=B, [ A>=C ], cost: 1 16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2 25: evalfbb8in -> evalfbb6in : D'=1+B, E'=1, [ A>=C && C+B>=B && 1>=1+B ], cost: 4 26: evalfbb8in -> evalfbb6in : D'=1+C+B, E'=1+C+B, [ A>=C && C+B>=B && B>=1 ], cost: 3+2*(1+C)*B+(1+C)^2+2*C 17: evalfbb6in -> evalfbb8in : C'=1+C, [ D>=1+C+B ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: evalfstart 15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2 2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1 16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2 27: evalfbb8in -> evalfbb8in : C'=1+C, D'=B, [ A>=C && B>=1+C+B ], cost: 3 28: evalfbb8in -> evalfbb8in : C'=1+C, D'=1+B, E'=1, [ A>=C && C+B>=B && 1>=1+B && 1+B>=1+C+B ], cost: 6 29: evalfbb8in -> evalfbb8in : C'=1+C, D'=1+C+B, E'=1+C+B, [ A>=C && C+B>=B && B>=1 ], cost: 5+2*(1+C)*B+(1+C)^2+2*C Accelerating simple loops of location 3. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 27: evalfbb8in -> evalfbb8in : C'=1+C, D'=B, [ A>=C && B>=1+C+B ], cost: 3 28: evalfbb8in -> evalfbb8in : C'=1+C, D'=1+B, E'=1, [ A>=C && -C==0 && 1>=1+B ], cost: 6 29: evalfbb8in -> evalfbb8in : C'=1+C, D'=1+C+B, E'=1+C+B, [ A>=C && C+B>=B && B>=1 ], cost: 5+2*(1+C)*B+(1+C)^2+2*C Found no metering function for rule 27. Accelerated rule 28 with metering function -C, yielding the new rule 30. Accelerated rule 29 with metering function 1-C+A, yielding the new rule 31. Removing the simple loops: 28 29. Accelerated all simple loops using metering functions (where possible): Start location: evalfstart 15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2 2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1 16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2 27: evalfbb8in -> evalfbb8in : C'=1+C, D'=B, [ A>=C && B>=1+C+B ], cost: 3 30: evalfbb8in -> evalfbb8in : C'=0, D'=1+B, E'=1, [ A>=C && -C==0 && 1>=1+B && -C>=1 ], cost: -6*C 31: evalfbb8in -> evalfbb8in : C'=1+A, D'=1+A+B, E'=1+A+B, [ A>=C && C+B>=B && B>=1 ], cost: 25/6+3/2*(-1+C-A)^2-(-1+C-A)*B-25/6*C+C*(-1+C-A)^2-2*C*(-1+C-A)*B-1/3*(-1+C-A)^3-3*C*(-1+C-A)+25/6*A-C^2*(-1+C-A)+(-1+C-A)^2*B Chained accelerated rules (with incoming rules): Start location: evalfstart 15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2 2: evalfbb10in -> evalfbb8in : C'=1, [ B>=1 ], cost: 1 32: evalfbb10in -> evalfbb8in : C'=1+A, D'=1+A+B, E'=1+A+B, [ B>=1 && A>=1 ], cost: 1+3*A*B+49/6*A+5/2*A^2+1/3*A^3+A^2*B 16: evalfbb8in -> evalfbb10in : B'=-1+B, [ C>=1+A ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: evalfstart 15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2 33: evalfbb10in -> evalfbb10in : B'=-1+B, C'=1, [ B>=1 && 1>=1+A ], cost: 3 34: evalfbb10in -> evalfbb10in : B'=-1+B, C'=1+A, D'=1+A+B, E'=1+A+B, [ B>=1 && A>=1 ], cost: 3+3*A*B+49/6*A+5/2*A^2+1/3*A^3+A^2*B Accelerating simple loops of location 2. Accelerating the following rules: 33: evalfbb10in -> evalfbb10in : B'=-1+B, C'=1, [ B>=1 && 1>=1+A ], cost: 3 34: evalfbb10in -> evalfbb10in : B'=-1+B, C'=1+A, D'=1+A+B, E'=1+A+B, [ B>=1 && A>=1 ], cost: 3+3*A*B+49/6*A+5/2*A^2+1/3*A^3+A^2*B Accelerated rule 33 with metering function B, yielding the new rule 35. Accelerated rule 34 with metering function B, yielding the new rule 36. Removing the simple loops: 33 34. Accelerated all simple loops using metering functions (where possible): Start location: evalfstart 15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2 35: evalfbb10in -> evalfbb10in : B'=0, C'=1, [ B>=1 && 1>=1+A ], cost: 3*B 36: evalfbb10in -> evalfbb10in : B'=0, C'=1+A, D'=2+A, E'=2+A, [ B>=1 && A>=1 ], cost: 29/3*A*B+3/2*A*B^2+1/3*A^3*B+1/2*A^2*B^2+3*B+3*A^2*B Chained accelerated rules (with incoming rules): Start location: evalfstart 15: evalfstart -> evalfbb10in : A'=B, B'=A, [], cost: 2 37: evalfstart -> evalfbb10in : A'=B, B'=0, C'=1, [ A>=1 && 1>=1+B ], cost: 2+3*A 38: evalfstart -> evalfbb10in : A'=B, B'=0, C'=1+B, D'=2+B, E'=2+B, [ A>=1 && B>=1 ], cost: 2+29/3*A*B+3*A*B^2+1/3*A*B^3+3*A+1/2*A^2*B^2+3/2*A^2*B Removed unreachable locations (and leaf rules with constant cost): Start location: evalfstart 37: evalfstart -> evalfbb10in : A'=B, B'=0, C'=1, [ A>=1 && 1>=1+B ], cost: 2+3*A 38: evalfstart -> evalfbb10in : A'=B, B'=0, C'=1+B, D'=2+B, E'=2+B, [ A>=1 && B>=1 ], cost: 2+29/3*A*B+3*A*B^2+1/3*A*B^3+3*A+1/2*A^2*B^2+3/2*A^2*B ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalfstart 37: evalfstart -> evalfbb10in : A'=B, B'=0, C'=1, [ A>=1 && 1>=1+B ], cost: 2+3*A 38: evalfstart -> evalfbb10in : A'=B, B'=0, C'=1+B, D'=2+B, E'=2+B, [ A>=1 && B>=1 ], cost: 2+29/3*A*B+3*A*B^2+1/3*A*B^3+3*A+1/2*A^2*B^2+3/2*A^2*B Computing asymptotic complexity for rule 37 Solved the limit problem by the following transformations: Created initial limit problem: 1-B (+/+!), A (+/+!), 2+3*A (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==n,B==0} resulting limit problem: [solved] Solution: A / n B / 0 Resulting cost 2+3*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Computing asymptotic complexity for rule 38 Solved the limit problem by the following transformations: Created initial limit problem: A (+/+!), 2+29/3*A*B+3*A*B^2+1/3*A*B^3+3*A+1/2*A^2*B^2+3/2*A^2*B (+), B (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {A==n,B==n} resulting limit problem: [solved] Solution: A / n B / n Resulting cost 2+5/6*n^4+3*n+29/3*n^2+9/2*n^3 has complexity: Poly(n^4) Found new complexity Poly(n^4). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^4) Cpx degree: 4 Solved cost: 2+5/6*n^4+3*n+29/3*n^2+9/2*n^3 Rule cost: 2+29/3*A*B+3*A*B^2+1/3*A*B^3+3*A+1/2*A^2*B^2+3/2*A^2*B Rule guard: [ A>=1 && B>=1 ] WORST_CASE(Omega(n^4),?) ---------------------------------------- (4) BOUNDS(n^4, INF)