/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^3), O(n^4)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^3, n^4). (0) CpxIntTrs (1) Koat Proof [FINISHED, 221 ms] (2) BOUNDS(1, n^4) (3) Loat Proof [FINISHED, 1048 ms] (4) BOUNDS(n^3, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalfstart(A, B, C, D, E, F) -> Com_1(evalfentryin(A, B, C, D, E, F)) :|: TRUE evalfentryin(A, B, C, D, E, F) -> Com_1(evalfbb7in(B, C, D, A, E, F)) :|: TRUE evalfbb7in(A, B, C, D, E, F) -> Com_1(evalfbb5in(A, B, C, D, B, F)) :|: A >= D evalfbb7in(A, B, C, D, E, F) -> Com_1(evalfreturnin(A, B, C, D, E, F)) :|: D >= A + 1 evalfbb5in(A, B, C, D, E, F) -> Com_1(evalfbb1in(A, B, C, D, E, F)) :|: C >= E evalfbb5in(A, B, C, D, E, F) -> Com_1(evalfbb6in(A, B, C, D, E, F)) :|: E >= C + 1 evalfbb1in(A, B, C, D, E, F) -> Com_1(evalfbb3in(A, B, C, D, E, D - E)) :|: TRUE evalfbb3in(A, B, C, D, E, F) -> Com_1(evalfbb2in(A, B, C, D, E, F)) :|: D + E >= F evalfbb3in(A, B, C, D, E, F) -> Com_1(evalfbb4in(A, B, C, D, E, F)) :|: F >= D + E + 1 evalfbb2in(A, B, C, D, E, F) -> Com_1(evalfbb3in(A, B, C, D, E, F + 1)) :|: TRUE evalfbb4in(A, B, C, D, E, F) -> Com_1(evalfbb5in(A, B, C, D, E + 1, F)) :|: TRUE evalfbb6in(A, B, C, D, E, F) -> Com_1(evalfbb7in(A, B, C, D + 1, E, F)) :|: TRUE evalfreturnin(A, B, C, D, E, F) -> Com_1(evalfstop(A, B, C, D, E, F)) :|: TRUE The start-symbols are:[evalfstart_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 113*Ar_0 + 113*Ar_1 + 124*Ar_0*Ar_3 + 124*Ar_1*Ar_3 + 128*Ar_0*Ar_2 + 128*Ar_1*Ar_2 + 96*Ar_3 + 100*Ar_2 + 28*Ar_0^2*Ar_3 + 56*Ar_0*Ar_1*Ar_3 + 28*Ar_0^2*Ar_2 + 56*Ar_0*Ar_1*Ar_2 + 20*Ar_0^2 + 40*Ar_0*Ar_1 + 28*Ar_1^2*Ar_3 + 28*Ar_1^2*Ar_2 + 20*Ar_1^2 + 36*Ar_0*Ar_2*Ar_3 + 36*Ar_1*Ar_2*Ar_3 + 20*Ar_0*Ar_2^2 + 20*Ar_1*Ar_2^2 + 20*Ar_2*Ar_3 + 12*Ar_2^2 + 8*Ar_0^2*Ar_3^2 + 16*Ar_0*Ar_1*Ar_3^2 + 16*Ar_0^2*Ar_2*Ar_3 + 32*Ar_0*Ar_1*Ar_2*Ar_3 + 16*Ar_0*Ar_3^2 + 8*Ar_1^2*Ar_3^2 + 16*Ar_1^2*Ar_2*Ar_3 + 16*Ar_1*Ar_3^2 + 8*Ar_0^2*Ar_2^2 + 16*Ar_0*Ar_1*Ar_2^2 + 8*Ar_1^2*Ar_2^2 + 8*Ar_3^2 + 99) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 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, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfstart) = 2 Pol(evalfentryin) = 2 Pol(evalfbb7in) = 2 Pol(evalfbb5in) = 2 Pol(evalfreturnin) = 1 Pol(evalfbb1in) = 2 Pol(evalfbb6in) = 2 Pol(evalfbb3in) = 2 Pol(evalfbb2in) = 2 Pol(evalfbb4in) = 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, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfstart) = -V_1 + V_2 + 1 Pol(evalfentryin) = -V_1 + V_2 + 1 Pol(evalfbb7in) = V_1 - V_4 + 1 Pol(evalfbb5in) = V_1 - V_4 Pol(evalfreturnin) = V_1 - V_4 Pol(evalfbb1in) = V_1 - V_4 Pol(evalfbb6in) = V_1 - V_4 Pol(evalfbb3in) = V_1 - V_4 Pol(evalfbb2in) = V_1 - V_4 Pol(evalfbb4in) = V_1 - V_4 Pol(evalfstop) = V_1 - V_4 Pol(koat_start) = -V_1 + V_2 + 1 orients all transitions weakly and the transition evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5)) (Comp: Ar_0 + Ar_1 + 1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) (Comp: ?, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb6in) = 1 Pol(evalfbb7in) = 0 Pol(evalfbb5in) = 2 Pol(evalfbb1in) = 2 Pol(evalfbb4in) = 2 Pol(evalfbb3in) = 2 Pol(evalfbb2in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_2 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-1) = Ar_2 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-3) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-5) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-1) = Ar_2 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-2) = Ar_3 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-3) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-5) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-0) = Ar_1 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-1) = Ar_2 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-2) = Ar_3 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-3) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-4) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-5) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-1) = Ar_2 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-2) = Ar_3 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-5) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-1) = Ar_2 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-2) = Ar_3 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-3) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-5) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-0) = Ar_1 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-1) = Ar_2 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-2) = Ar_3 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-3) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-4) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-5) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-1) = Ar_2 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-2) = Ar_3 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-5) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-1) = Ar_2 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-2) = Ar_3 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-3) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-5) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-1) = Ar_2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-2) = Ar_3 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-5) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-1) = Ar_2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-2) = Ar_3 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-3) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-4) = Ar_2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-5) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-1) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-3) = Ar_0 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 orients the transitions evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ] evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4)) weakly and the transitions evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5)) (Comp: Ar_0 + Ar_1 + 1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb5in) = V_3 - V_5 + 1 Pol(evalfbb1in) = V_3 - V_5 Pol(evalfbb4in) = V_3 - V_5 Pol(evalfbb3in) = V_3 - V_5 Pol(evalfbb2in) = V_3 - V_5 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_2 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = 3*Ar_0 + 3*Ar_1 + 162 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-1) = Ar_2 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-5) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-1) = Ar_2 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-2) = Ar_3 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-5) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-0) = Ar_1 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-1) = Ar_2 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-2) = Ar_3 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-4) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-5) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-1) = Ar_2 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-2) = Ar_3 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-5) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-1) = Ar_2 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-2) = Ar_3 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-5) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-0) = Ar_1 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-1) = Ar_2 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-2) = Ar_3 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-4) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-5) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-1) = Ar_2 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-2) = Ar_3 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-5) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-1) = Ar_2 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-2) = Ar_3 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-5) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-1) = Ar_2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-2) = Ar_3 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 54 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-5) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-1) = Ar_2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-2) = Ar_3 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-4) = Ar_2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-5) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-1) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-3) = Ar_0 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 orients the transitions evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4)) weakly and the transition evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5)) (Comp: Ar_0 + Ar_1 + 1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0*Ar_3 + Ar_1*Ar_3 + Ar_0*Ar_2 + Ar_1*Ar_2 + Ar_3 + Ar_2 + Ar_0 + Ar_1 + 1, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5)) (Comp: Ar_0 + Ar_1 + 1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0*Ar_3 + Ar_1*Ar_3 + Ar_0*Ar_2 + Ar_1*Ar_2 + Ar_3 + Ar_2 + Ar_0 + Ar_1 + 1, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ] (Comp: Ar_0*Ar_3 + Ar_1*Ar_3 + Ar_0*Ar_2 + Ar_1*Ar_2 + Ar_3 + Ar_2 + Ar_0 + Ar_1 + 1, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) (Comp: ?, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb4in) = 1 Pol(evalfbb5in) = 0 Pol(evalfbb3in) = 2 Pol(evalfbb2in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_2 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = 3*Ar_0 + 3*Ar_1 + 162 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-1) = Ar_2 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-4) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-5) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-1) = Ar_2 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-2) = Ar_3 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-4) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-5) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-0) = Ar_1 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-1) = Ar_2 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-2) = Ar_3 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-4) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-5) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-1) = Ar_2 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-2) = Ar_3 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-5) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-1) = Ar_2 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-2) = Ar_3 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-4) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-5) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-0) = Ar_1 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-1) = Ar_2 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-2) = Ar_3 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-4) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-5) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-1) = Ar_2 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-2) = Ar_3 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-5) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-1) = Ar_2 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-2) = Ar_3 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-4) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-5) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-1) = Ar_2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-2) = Ar_3 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 54 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-4) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-5) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-1) = Ar_2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-2) = Ar_3 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-4) = Ar_2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-5) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-1) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-3) = Ar_0 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 orients the transitions evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) weakly and the transitions evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5)) (Comp: Ar_0 + Ar_1 + 1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0*Ar_3 + Ar_1*Ar_3 + Ar_0*Ar_2 + Ar_1*Ar_2 + Ar_3 + Ar_2 + Ar_0 + Ar_1 + 1, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ] (Comp: Ar_0*Ar_3 + Ar_1*Ar_3 + Ar_0*Ar_2 + Ar_1*Ar_2 + Ar_3 + Ar_2 + Ar_0 + Ar_1 + 1, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4)) (Comp: ?, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] (Comp: 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_2 + 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) (Comp: 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_2 + 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfbb3in) = V_4 + V_5 - V_6 + 1 Pol(evalfbb2in) = V_4 + V_5 - V_6 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_2 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = 3*Ar_0 + 3*Ar_1 + 162 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 + 3*Ar_2 + 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_0 + 2*Ar_1 + 2 S("evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = ? S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-1) = Ar_2 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-4) = 3*Ar_2 + 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_0 + 2*Ar_1 + 2 S("evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-5) = ? S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-0) = Ar_1 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-1) = Ar_2 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-2) = Ar_3 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-4) = 3*Ar_2 + 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_0 + 2*Ar_1 + 2 S("evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5))", 0-5) = ? S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-0) = Ar_1 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-1) = Ar_2 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-2) = Ar_3 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-4) = 3*Ar_2 + 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_0 + 2*Ar_1 + 2 S("evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1))", 0-5) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-1) = Ar_2 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-2) = Ar_3 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-4) = 3*Ar_2 + 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_0 + 2*Ar_1 + 2 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ]", 0-5) = ? S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-0) = Ar_1 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-1) = Ar_2 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-2) = Ar_3 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-4) = 3*Ar_2 + 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_0 + 2*Ar_1 + 2 S("evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ]", 0-5) = ? S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-0) = Ar_1 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-1) = Ar_2 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-2) = Ar_3 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-4) = 3*Ar_2 + 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_0 + 2*Ar_1 + 2 S("evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4))", 0-5) = 5*Ar_0 + 5*Ar_1 + 3*Ar_2 + 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 20 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-1) = Ar_2 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-2) = Ar_3 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-4) = 3*Ar_2 + 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_0 + 2*Ar_1 + 2 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ]", 0-5) = ? S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-0) = Ar_1 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-1) = Ar_2 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-2) = Ar_3 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-4) = 3*Ar_2 + 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_0 + 2*Ar_1 + 2 S("evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ]", 0-5) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-1) = Ar_2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-2) = Ar_3 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 54 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-4) = Ar_4 + 3*Ar_2 + 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_0 + 2*Ar_1 + 2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ]", 0-5) = ? S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-0) = Ar_1 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-1) = Ar_2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-2) = Ar_3 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-3) = 3*Ar_0 + 3*Ar_1 + 18 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-4) = Ar_2 S("evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ]", 0-5) = ? S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-1) = Ar_2 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-3) = Ar_0 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 orients the transitions evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) weakly and the transition evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] strictly and produces the following problem: 9: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5)) (Comp: Ar_0 + Ar_1 + 1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0*Ar_3 + Ar_1*Ar_3 + Ar_0*Ar_2 + Ar_1*Ar_2 + Ar_3 + Ar_2 + Ar_0 + Ar_1 + 1, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ] (Comp: Ar_0*Ar_3 + Ar_1*Ar_3 + Ar_0*Ar_2 + Ar_1*Ar_2 + Ar_3 + Ar_2 + Ar_0 + Ar_1 + 1, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4)) (Comp: 14*Ar_0^2*Ar_3 + 28*Ar_0*Ar_1*Ar_3 + 14*Ar_0^2*Ar_2 + 28*Ar_0*Ar_1*Ar_2 + 59*Ar_0*Ar_3 + 61*Ar_0*Ar_2 + 10*Ar_0^2 + 20*Ar_0*Ar_1 + 14*Ar_1^2*Ar_3 + 14*Ar_1^2*Ar_2 + 59*Ar_1*Ar_3 + 61*Ar_1*Ar_2 + 10*Ar_1^2 + 18*Ar_0*Ar_2*Ar_3 + 18*Ar_1*Ar_2*Ar_3 + 10*Ar_0*Ar_2^2 + 10*Ar_1*Ar_2^2 + 10*Ar_2*Ar_3 + 6*Ar_2^2 + 4*Ar_0^2*Ar_3^2 + 8*Ar_0*Ar_1*Ar_3^2 + 8*Ar_0^2*Ar_2*Ar_3 + 16*Ar_0*Ar_1*Ar_2*Ar_3 + 8*Ar_0*Ar_3^2 + 4*Ar_1^2*Ar_3^2 + 8*Ar_1^2*Ar_2*Ar_3 + 8*Ar_1*Ar_3^2 + 4*Ar_0^2*Ar_2^2 + 8*Ar_0*Ar_1*Ar_2^2 + 4*Ar_1^2*Ar_2^2 + 4*Ar_3^2 + 51*Ar_0 + 51*Ar_1 + 47*Ar_2 + 45*Ar_3 + 41, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] (Comp: 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_2 + 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] (Comp: ?, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) (Comp: 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_2 + 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 9 produces the following problem: 10: T: (Comp: 1, Cost: 1) evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalfentryin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_1, Ar_2, Ar_3, Ar_0, Ar_4, Ar_5)) (Comp: Ar_0 + Ar_1 + 1, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_1, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: 2, Cost: 1) evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0*Ar_3 + Ar_1*Ar_3 + Ar_0*Ar_2 + Ar_1*Ar_2 + Ar_3 + Ar_2 + Ar_0 + Ar_1 + 1, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_2 >= Ar_4 ] (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= Ar_2 + 1 ] (Comp: Ar_0*Ar_3 + Ar_1*Ar_3 + Ar_0*Ar_2 + Ar_1*Ar_2 + Ar_3 + Ar_2 + Ar_0 + Ar_1 + 1, Cost: 1) evalfbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_3 - Ar_4)) (Comp: 14*Ar_0^2*Ar_3 + 28*Ar_0*Ar_1*Ar_3 + 14*Ar_0^2*Ar_2 + 28*Ar_0*Ar_1*Ar_2 + 59*Ar_0*Ar_3 + 61*Ar_0*Ar_2 + 10*Ar_0^2 + 20*Ar_0*Ar_1 + 14*Ar_1^2*Ar_3 + 14*Ar_1^2*Ar_2 + 59*Ar_1*Ar_3 + 61*Ar_1*Ar_2 + 10*Ar_1^2 + 18*Ar_0*Ar_2*Ar_3 + 18*Ar_1*Ar_2*Ar_3 + 10*Ar_0*Ar_2^2 + 10*Ar_1*Ar_2^2 + 10*Ar_2*Ar_3 + 6*Ar_2^2 + 4*Ar_0^2*Ar_3^2 + 8*Ar_0*Ar_1*Ar_3^2 + 8*Ar_0^2*Ar_2*Ar_3 + 16*Ar_0*Ar_1*Ar_2*Ar_3 + 8*Ar_0*Ar_3^2 + 4*Ar_1^2*Ar_3^2 + 8*Ar_1^2*Ar_2*Ar_3 + 8*Ar_1*Ar_3^2 + 4*Ar_0^2*Ar_2^2 + 8*Ar_0*Ar_1*Ar_2^2 + 4*Ar_1^2*Ar_2^2 + 4*Ar_3^2 + 51*Ar_0 + 51*Ar_1 + 47*Ar_2 + 45*Ar_3 + 41, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 + Ar_4 >= Ar_5 ] (Comp: 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_2 + 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 + Ar_4 + 1 ] (Comp: 14*Ar_0^2*Ar_3 + 28*Ar_0*Ar_1*Ar_3 + 14*Ar_0^2*Ar_2 + 28*Ar_0*Ar_1*Ar_2 + 59*Ar_0*Ar_3 + 61*Ar_0*Ar_2 + 10*Ar_0^2 + 20*Ar_0*Ar_1 + 14*Ar_1^2*Ar_3 + 14*Ar_1^2*Ar_2 + 59*Ar_1*Ar_3 + 61*Ar_1*Ar_2 + 10*Ar_1^2 + 18*Ar_0*Ar_2*Ar_3 + 18*Ar_1*Ar_2*Ar_3 + 10*Ar_0*Ar_2^2 + 10*Ar_1*Ar_2^2 + 10*Ar_2*Ar_3 + 6*Ar_2^2 + 4*Ar_0^2*Ar_3^2 + 8*Ar_0*Ar_1*Ar_3^2 + 8*Ar_0^2*Ar_2*Ar_3 + 16*Ar_0*Ar_1*Ar_2*Ar_3 + 8*Ar_0*Ar_3^2 + 4*Ar_1^2*Ar_3^2 + 8*Ar_1^2*Ar_2*Ar_3 + 8*Ar_1*Ar_3^2 + 4*Ar_0^2*Ar_2^2 + 8*Ar_0*Ar_1*Ar_2^2 + 4*Ar_1^2*Ar_2^2 + 4*Ar_3^2 + 51*Ar_0 + 51*Ar_1 + 47*Ar_2 + 45*Ar_3 + 41, Cost: 1) evalfbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1)) (Comp: 2*Ar_0*Ar_3 + 2*Ar_1*Ar_3 + 2*Ar_0*Ar_2 + 2*Ar_1*Ar_2 + 2*Ar_3 + 2*Ar_2 + 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) (Comp: 2*Ar_0 + 2*Ar_1 + 2, Cost: 1) evalfbb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfbb7in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evalfreturnin(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalfstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 113*Ar_0 + 113*Ar_1 + 124*Ar_0*Ar_3 + 124*Ar_1*Ar_3 + 128*Ar_0*Ar_2 + 128*Ar_1*Ar_2 + 96*Ar_3 + 100*Ar_2 + 28*Ar_0^2*Ar_3 + 56*Ar_0*Ar_1*Ar_3 + 28*Ar_0^2*Ar_2 + 56*Ar_0*Ar_1*Ar_2 + 20*Ar_0^2 + 40*Ar_0*Ar_1 + 28*Ar_1^2*Ar_3 + 28*Ar_1^2*Ar_2 + 20*Ar_1^2 + 36*Ar_0*Ar_2*Ar_3 + 36*Ar_1*Ar_2*Ar_3 + 20*Ar_0*Ar_2^2 + 20*Ar_1*Ar_2^2 + 20*Ar_2*Ar_3 + 12*Ar_2^2 + 8*Ar_0^2*Ar_3^2 + 16*Ar_0*Ar_1*Ar_3^2 + 16*Ar_0^2*Ar_2*Ar_3 + 32*Ar_0*Ar_1*Ar_2*Ar_3 + 16*Ar_0*Ar_3^2 + 8*Ar_1^2*Ar_3^2 + 16*Ar_1^2*Ar_2*Ar_3 + 16*Ar_1*Ar_3^2 + 8*Ar_0^2*Ar_2^2 + 16*Ar_0*Ar_1*Ar_2^2 + 8*Ar_1^2*Ar_2^2 + 8*Ar_3^2 + 99 Time: 0.224 sec (SMT: 0.149 sec) ---------------------------------------- (2) BOUNDS(1, n^4) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalfstart 0: evalfstart -> evalfentryin : [], cost: 1 1: evalfentryin -> evalfbb7in : A'=B, B'=C, C'=D, D'=A, [], cost: 1 2: evalfbb7in -> evalfbb5in : E'=B, [ A>=D ], cost: 1 3: evalfbb7in -> evalfreturnin : [ D>=1+A ], cost: 1 4: evalfbb5in -> evalfbb1in : [ C>=E ], cost: 1 5: evalfbb5in -> evalfbb6in : [ E>=1+C ], cost: 1 6: evalfbb1in -> evalfbb3in : F'=D-E, [], cost: 1 7: evalfbb3in -> evalfbb2in : [ D+E>=F ], cost: 1 8: evalfbb3in -> evalfbb4in : [ F>=1+D+E ], cost: 1 9: evalfbb2in -> evalfbb3in : F'=1+F, [], cost: 1 10: evalfbb4in -> evalfbb5in : E'=1+E, [], cost: 1 11: evalfbb6in -> evalfbb7in : D'=1+D, [], cost: 1 12: 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 -> evalfbb7in : A'=B, B'=C, C'=D, D'=A, [], cost: 1 2: evalfbb7in -> evalfbb5in : E'=B, [ A>=D ], cost: 1 4: evalfbb5in -> evalfbb1in : [ C>=E ], cost: 1 5: evalfbb5in -> evalfbb6in : [ E>=1+C ], cost: 1 6: evalfbb1in -> evalfbb3in : F'=D-E, [], cost: 1 7: evalfbb3in -> evalfbb2in : [ D+E>=F ], cost: 1 8: evalfbb3in -> evalfbb4in : [ F>=1+D+E ], cost: 1 9: evalfbb2in -> evalfbb3in : F'=1+F, [], cost: 1 10: evalfbb4in -> evalfbb5in : E'=1+E, [], cost: 1 11: evalfbb6in -> evalfbb7in : D'=1+D, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalfstart 13: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=A, [], cost: 2 2: evalfbb7in -> evalfbb5in : E'=B, [ A>=D ], cost: 1 14: evalfbb5in -> evalfbb3in : F'=D-E, [ C>=E ], cost: 2 15: evalfbb5in -> evalfbb7in : D'=1+D, [ E>=1+C ], cost: 2 16: evalfbb3in -> evalfbb3in : F'=1+F, [ D+E>=F ], cost: 2 17: evalfbb3in -> evalfbb5in : E'=1+E, [ F>=1+D+E ], cost: 2 Accelerating simple loops of location 5. Accelerating the following rules: 16: evalfbb3in -> evalfbb3in : F'=1+F, [ D+E>=F ], cost: 2 Accelerated rule 16 with metering function 1-F+D+E, yielding the new rule 18. Removing the simple loops: 16. Accelerated all simple loops using metering functions (where possible): Start location: evalfstart 13: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=A, [], cost: 2 2: evalfbb7in -> evalfbb5in : E'=B, [ A>=D ], cost: 1 14: evalfbb5in -> evalfbb3in : F'=D-E, [ C>=E ], cost: 2 15: evalfbb5in -> evalfbb7in : D'=1+D, [ E>=1+C ], cost: 2 17: evalfbb3in -> evalfbb5in : E'=1+E, [ F>=1+D+E ], cost: 2 18: evalfbb3in -> evalfbb3in : F'=1+D+E, [ D+E>=F ], cost: 2-2*F+2*D+2*E Chained accelerated rules (with incoming rules): Start location: evalfstart 13: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=A, [], cost: 2 2: evalfbb7in -> evalfbb5in : E'=B, [ A>=D ], cost: 1 14: evalfbb5in -> evalfbb3in : F'=D-E, [ C>=E ], cost: 2 15: evalfbb5in -> evalfbb7in : D'=1+D, [ E>=1+C ], cost: 2 19: evalfbb5in -> evalfbb3in : F'=1+D+E, [ C>=E && D+E>=D-E ], cost: 4+4*E 17: evalfbb3in -> evalfbb5in : E'=1+E, [ F>=1+D+E ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: evalfstart 13: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=A, [], cost: 2 2: evalfbb7in -> evalfbb5in : E'=B, [ A>=D ], cost: 1 15: evalfbb5in -> evalfbb7in : D'=1+D, [ E>=1+C ], cost: 2 20: evalfbb5in -> evalfbb5in : E'=1+E, F'=D-E, [ C>=E && D-E>=1+D+E ], cost: 4 21: evalfbb5in -> evalfbb5in : E'=1+E, F'=1+D+E, [ C>=E && D+E>=D-E ], cost: 6+4*E Accelerating simple loops of location 3. Accelerating the following rules: 20: evalfbb5in -> evalfbb5in : E'=1+E, F'=D-E, [ C>=E && D-E>=1+D+E ], cost: 4 21: evalfbb5in -> evalfbb5in : E'=1+E, F'=1+D+E, [ C>=E && D+E>=D-E ], cost: 6+4*E Found no metering function for rule 20. Accelerated rule 21 with metering function 1+C-E, yielding the new rule 22. Removing the simple loops: 21. Accelerated all simple loops using metering functions (where possible): Start location: evalfstart 13: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=A, [], cost: 2 2: evalfbb7in -> evalfbb5in : E'=B, [ A>=D ], cost: 1 15: evalfbb5in -> evalfbb7in : D'=1+D, [ E>=1+C ], cost: 2 20: evalfbb5in -> evalfbb5in : E'=1+E, F'=D-E, [ C>=E && D-E>=1+D+E ], cost: 4 22: evalfbb5in -> evalfbb5in : E'=1+C, F'=1+C+D, [ C>=E && D+E>=D-E ], cost: 4+4*C+4*E*(1+C-E)+2*(1+C-E)^2-4*E Chained accelerated rules (with incoming rules): Start location: evalfstart 13: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=A, [], cost: 2 2: evalfbb7in -> evalfbb5in : E'=B, [ A>=D ], cost: 1 23: evalfbb7in -> evalfbb5in : E'=1+B, F'=D-B, [ A>=D && C>=B && D-B>=1+D+B ], cost: 5 24: evalfbb7in -> evalfbb5in : E'=1+C, F'=1+C+D, [ A>=D && C>=B && D+B>=D-B ], cost: 5+4*C+2*(1+C-B)^2+4*(1+C-B)*B-4*B 15: evalfbb5in -> evalfbb7in : D'=1+D, [ E>=1+C ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: evalfstart 13: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=A, [], cost: 2 25: evalfbb7in -> evalfbb7in : D'=1+D, E'=B, [ A>=D && B>=1+C ], cost: 3 26: evalfbb7in -> evalfbb7in : D'=1+D, E'=1+B, F'=D-B, [ A>=D && C>=B && D-B>=1+D+B && 1+B>=1+C ], cost: 7 27: evalfbb7in -> evalfbb7in : D'=1+D, E'=1+C, F'=1+C+D, [ A>=D && C>=B && D+B>=D-B ], cost: 7+4*C+2*(1+C-B)^2+4*(1+C-B)*B-4*B Accelerating simple loops of location 2. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 25: evalfbb7in -> evalfbb7in : D'=1+D, E'=B, [ A>=D && B>=1+C ], cost: 3 26: evalfbb7in -> evalfbb7in : D'=1+D, E'=1+B, F'=D-B, [ A>=D && -C+B==0 && D-B>=1+D+B ], cost: 7 27: evalfbb7in -> evalfbb7in : D'=1+D, E'=1+C, F'=1+C+D, [ A>=D && C>=B && D+B>=D-B ], cost: 7+4*C+2*(1+C-B)^2+4*(1+C-B)*B-4*B Accelerated rule 25 with metering function 1-D+A, yielding the new rule 28. Accelerated rule 26 with metering function 1-D+A, yielding the new rule 29. Accelerated rule 27 with metering function 1-D+A, yielding the new rule 30. Removing the simple loops: 25 26 27. Accelerated all simple loops using metering functions (where possible): Start location: evalfstart 13: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=A, [], cost: 2 28: evalfbb7in -> evalfbb7in : D'=1+A, E'=B, [ A>=D && B>=1+C ], cost: 3-3*D+3*A 29: evalfbb7in -> evalfbb7in : D'=1+A, E'=1+B, F'=A-B, [ A>=D && -C+B==0 && D-B>=1+D+B ], cost: 7-7*D+7*A 30: evalfbb7in -> evalfbb7in : D'=1+A, E'=1+C, F'=1+C+A, [ A>=D && C>=B && D+B>=D-B ], cost: 9+4*(-1+D-A)*B-2*C^2*(-1+D-A)-9*D+2*(-1+D-A)*B^2+9*A-8*C*(-1+D-A) Chained accelerated rules (with incoming rules): Start location: evalfstart 13: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=A, [], cost: 2 31: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=1+B, E'=C, [ B>=A && C>=1+D ], cost: 5-3*A+3*B 32: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=1+B, E'=1+C, F'=-C+B, [ B>=A && C-D==0 && -C+A>=1+C+A ], cost: 9-7*A+7*B 33: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=1+B, E'=1+D, F'=1+D+B, [ B>=A && D>=C && C+A>=-C+A ], cost: 11+2*C^2*(-1+A-B)-9*A-2*(-1+A-B)*D^2+4*C*(-1+A-B)+9*B-8*(-1+A-B)*D Removed unreachable locations (and leaf rules with constant cost): Start location: evalfstart 31: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=1+B, E'=C, [ B>=A && C>=1+D ], cost: 5-3*A+3*B 32: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=1+B, E'=1+C, F'=-C+B, [ B>=A && C-D==0 && -C+A>=1+C+A ], cost: 9-7*A+7*B 33: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=1+B, E'=1+D, F'=1+D+B, [ B>=A && D>=C && C+A>=-C+A ], cost: 11+2*C^2*(-1+A-B)-9*A-2*(-1+A-B)*D^2+4*C*(-1+A-B)+9*B-8*(-1+A-B)*D ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalfstart 31: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=1+B, E'=C, [ B>=A && C>=1+D ], cost: 5-3*A+3*B 32: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=1+B, E'=1+C, F'=-C+B, [ B>=A && C-D==0 && -C+A>=1+C+A ], cost: 9-7*A+7*B 33: evalfstart -> evalfbb7in : A'=B, B'=C, C'=D, D'=1+B, E'=1+D, F'=1+D+B, [ B>=A && D>=C && C+A>=-C+A ], cost: 11+2*C^2*(-1+A-B)-9*A-2*(-1+A-B)*D^2+4*C*(-1+A-B)+9*B-8*(-1+A-B)*D Computing asymptotic complexity for rule 31 Solved the limit problem by the following transformations: Created initial limit problem: C-D (+/+!), 5-3*A+3*B (+), 1-A+B (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==1,D==0,A==0,B==n} resulting limit problem: [solved] Solution: C / 1 D / 0 A / 0 B / n Resulting cost 5+3*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Computing asymptotic complexity for rule 33 Solved the limit problem by the following transformations: Created initial limit problem: 1-C+D (+/+!), 1+2*C (+/+!), 1-A+B (+/+!), 11-8*D*A-4*C+2*C^2*A-2*C^2-2*C^2*B+8*D+8*D*B-9*A+2*D^2*B+2*D^2-4*C*B+9*B+4*C*A-2*D^2*A (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==n,D==2*n,A==-n,B==0} resulting limit problem: [solved] Solution: C / n D / 2*n A / -n B / 0 Resulting cost 11+21*n+6*n^3+18*n^2 has complexity: Poly(n^3) Found new complexity Poly(n^3). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^3) Cpx degree: 3 Solved cost: 11+21*n+6*n^3+18*n^2 Rule cost: 11+2*C^2*(-1+A-B)-9*A-2*(-1+A-B)*D^2+4*C*(-1+A-B)+9*B-8*(-1+A-B)*D Rule guard: [ B>=A && D>=C && C+A>=-C+A ] WORST_CASE(Omega(n^3),?) ---------------------------------------- (4) BOUNDS(n^3, INF)