/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 287 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_t27_start(v_.0, v_.01, v_.1, v_1, v_n, v_y) -> Com_1(eval_t27_bb0_in(v_.0, v_.01, v_.1, v_1, v_n, v_y)) :|: TRUE eval_t27_bb0_in(v_.0, v_.01, v_.1, v_1, v_n, v_y) -> Com_1(eval_t27_bb1_in(v_n, v_y, v_.1, v_1, v_n, v_y)) :|: TRUE eval_t27_bb1_in(v_.0, v_.01, v_.1, v_1, v_n, v_y) -> Com_1(eval_t27_bb2_in(v_.0, v_.01, v_.1, v_1, v_n, v_y)) :|: v_.0 < 0 eval_t27_bb1_in(v_.0, v_.01, v_.1, v_1, v_n, v_y) -> Com_1(eval_t27_bb5_in(v_.0, v_.01, v_.1, v_1, v_n, v_y)) :|: v_.0 >= 0 eval_t27_bb2_in(v_.0, v_.01, v_.1, v_1, v_n, v_y) -> Com_1(eval_t27_bb3_in(v_.0, v_.01, v_.01 + 1000, v_.0 + 1, v_n, v_y)) :|: TRUE eval_t27_bb3_in(v_.0, v_.01, v_.1, v_1, v_n, v_y) -> Com_1(eval_t27_bb4_in(v_.0, v_.01, v_.1, v_1, v_n, v_y)) :|: v_.1 >= 100 eval_t27_bb3_in(v_.0, v_.01, v_.1, v_1, v_n, v_y) -> Com_1(eval_t27_bb1_in(v_1, v_.1, v_.1, v_1, v_n, v_y)) :|: v_.1 < 100 eval_t27_bb4_in(v_.0, v_.01, v_.1, v_1, v_n, v_y) -> Com_1(eval_t27_bb3_in(v_.0, v_.01, v_.1 - 100, v_1, v_n, v_y)) :|: TRUE eval_t27_bb5_in(v_.0, v_.01, v_.1, v_1, v_n, v_y) -> Com_1(eval_t27_stop(v_.0, v_.01, v_.1, v_1, v_n, v_y)) :|: TRUE The start-symbols are:[eval_t27_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 4003*Ar_1 + 4*Ar_3 + 6) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1)) (Comp: ?, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ] (Comp: ?, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ] (Comp: ?, Cost: 1) evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) (Comp: ?, Cost: 1) evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(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(evalt27start(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) evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1)) (Comp: ?, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ] (Comp: ?, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ] (Comp: ?, Cost: 1) evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) (Comp: ?, Cost: 1) evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(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(evalt27start(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(evalt27start) = 2 Pol(evalt27bb0in) = 2 Pol(evalt27bb1in) = 2 Pol(evalt27bb2in) = 2 Pol(evalt27bb5in) = 1 Pol(evalt27bb3in) = 2 Pol(evalt27bb4in) = 2 Pol(evalt27stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1)) (Comp: ?, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ] (Comp: ?, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ] (Comp: ?, Cost: 1) evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) (Comp: 2, Cost: 1) evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(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(evalt27start(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(evalt27start) = -V_2 Pol(evalt27bb0in) = -V_2 Pol(evalt27bb1in) = -V_1 Pol(evalt27bb2in) = -V_1 - 1 Pol(evalt27bb5in) = -V_1 Pol(evalt27bb3in) = -V_6 Pol(evalt27bb4in) = -V_6 Pol(evalt27stop) = -V_1 Pol(koat_start) = -V_2 orients all transitions weakly and the transition evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1)) (Comp: ?, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ] (Comp: ?, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ] (Comp: ?, Cost: 1) evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) (Comp: 2, Cost: 1) evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(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(evalt27start(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 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ] (Comp: Ar_1, Cost: 1) evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1)) (Comp: ?, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ] (Comp: ?, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ] (Comp: ?, Cost: 1) evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) (Comp: 2, Cost: 1) evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(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(evalt27start(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(evalt27bb4in) = 1 Pol(evalt27bb3in) = 1 Pol(evalt27bb1in) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27start(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(evalt27start(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(evalt27start(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(evalt27start(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(evalt27start(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(evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5 S("evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = 2*Ar_1 S("evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = ? S("evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = ? S("evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = 2*Ar_1 + 2*Ar_5 S("evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))", 0-0) = 2*Ar_1 S("evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))", 0-1) = Ar_1 S("evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))", 0-2) = ? S("evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))", 0-3) = Ar_3 S("evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))", 0-4) = ? S("evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5))", 0-5) = 2*Ar_1 S("evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]", 0-0) = 2*Ar_1 S("evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]", 0-1) = Ar_1 S("evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]", 0-2) = ? S("evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]", 0-3) = Ar_3 S("evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]", 0-4) = ? S("evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ]", 0-5) = 2*Ar_1 S("evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]", 0-0) = 2*Ar_1 S("evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]", 0-1) = Ar_1 S("evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]", 0-2) = ? S("evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]", 0-3) = Ar_3 S("evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]", 0-4) = ? S("evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ]", 0-5) = 2*Ar_1 S("evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))", 0-0) = 2*Ar_1 S("evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))", 0-1) = Ar_1 S("evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))", 0-2) = ? S("evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))", 0-3) = Ar_3 S("evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))", 0-4) = ? S("evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1))", 0-5) = 2*Ar_1 S("evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]", 0-0) = 2*Ar_1 S("evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]", 0-2) = ? S("evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]", 0-3) = Ar_3 S("evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]", 0-4) = ? S("evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ]", 0-5) = 2*Ar_1 + 2*Ar_5 S("evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]", 0-0) = 2*Ar_1 S("evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]", 0-2) = ? S("evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]", 0-4) = ? S("evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ]", 0-5) = 2*Ar_1 + 2*Ar_5 S("evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_1 S("evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_3 S("evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 orients the transitions evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ] evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ] weakly and the transition evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 0 ] (Comp: Ar_1, Cost: 1) evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1)) (Comp: ?, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 100 ] (Comp: Ar_1, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_4 ] (Comp: ?, Cost: 1) evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) (Comp: 2, Cost: 1) evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(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(evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 6 to obtain the following invariants: For symbol evalt27bb1in: X_1 - X_2 >= 0 For symbol evalt27bb2in: -X_2 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 - 2 >= 0 /\ -X_1 - 1 >= 0 For symbol evalt27bb3in: -X_6 >= 0 /\ -X_2 - X_6 - 1 >= 0 /\ X_1 - X_6 + 1 >= 0 /\ -X_1 - X_6 - 1 >= 0 /\ -X_2 + X_6 - 1 >= 0 /\ -X_1 + X_6 - 1 >= 0 /\ X_3 - X_5 + 1000 >= 0 /\ -X_2 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 - 2 >= 0 /\ -X_1 - 1 >= 0 For symbol evalt27bb4in: -X_6 >= 0 /\ X_5 - X_6 - 100 >= 0 /\ X_3 - X_6 + 900 >= 0 /\ -X_2 - X_6 - 1 >= 0 /\ X_1 - X_6 + 1 >= 0 /\ -X_1 - X_6 - 1 >= 0 /\ -X_2 + X_6 - 1 >= 0 /\ -X_1 + X_6 - 1 >= 0 /\ X_3 - X_5 + 1000 >= 0 /\ X_5 - 100 >= 0 /\ X_3 + X_5 + 800 >= 0 /\ -X_2 + X_5 - 101 >= 0 /\ -X_1 + X_5 - 101 >= 0 /\ X_3 + 900 >= 0 /\ -X_2 + X_3 + 899 >= 0 /\ -X_1 + X_3 + 899 >= 0 /\ -X_2 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 - 2 >= 0 /\ -X_1 - 1 >= 0 For symbol evalt27bb5in: X_1 - X_2 >= 0 /\ X_1 >= 0 This yielded the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) [ -Ar_5 >= 0 /\ Ar_4 - Ar_5 - 100 >= 0 /\ Ar_2 - Ar_5 + 900 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ Ar_4 - 100 >= 0 /\ Ar_2 + Ar_4 + 800 >= 0 /\ -Ar_1 + Ar_4 - 101 >= 0 /\ -Ar_0 + Ar_4 - 101 >= 0 /\ Ar_2 + 900 >= 0 /\ -Ar_1 + Ar_2 + 899 >= 0 /\ -Ar_0 + Ar_2 + 899 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 ] (Comp: Ar_1, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ -Ar_5 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 /\ 99 >= Ar_4 ] (Comp: ?, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_5 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 /\ Ar_4 >= 100 ] (Comp: Ar_1, Cost: 1) evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1)) [ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: Ar_1, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = -2000*V_2 + 2*V_4 Pol(evalt27start) = -2000*V_2 + 2*V_4 Pol(evalt27bb5in) = -2000*V_1 + 2*V_3 Pol(evalt27stop) = -2000*V_1 + 2*V_3 Pol(evalt27bb4in) = 2*V_5 - 2000*V_6 - 100 Pol(evalt27bb3in) = 2*V_5 - 2000*V_6 Pol(evalt27bb1in) = -2000*V_1 + 2*V_3 Pol(evalt27bb2in) = -2000*V_1 + 2*V_3 Pol(evalt27bb0in) = -2000*V_2 + 2*V_4 orients all transitions weakly and the transitions evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) [ -Ar_5 >= 0 /\ Ar_4 - Ar_5 - 100 >= 0 /\ Ar_2 - Ar_5 + 900 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ Ar_4 - 100 >= 0 /\ Ar_2 + Ar_4 + 800 >= 0 /\ -Ar_1 + Ar_4 - 101 >= 0 /\ -Ar_0 + Ar_4 - 101 >= 0 /\ Ar_2 + 900 >= 0 /\ -Ar_1 + Ar_2 + 899 >= 0 /\ -Ar_0 + Ar_2 + 899 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 ] evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_5 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 /\ Ar_4 >= 100 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2000*Ar_1 + 2*Ar_3, Cost: 1) evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 100, Ar_5)) [ -Ar_5 >= 0 /\ Ar_4 - Ar_5 - 100 >= 0 /\ Ar_2 - Ar_5 + 900 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ Ar_4 - 100 >= 0 /\ Ar_2 + Ar_4 + 800 >= 0 /\ -Ar_1 + Ar_4 - 101 >= 0 /\ -Ar_0 + Ar_4 - 101 >= 0 /\ Ar_2 + 900 >= 0 /\ -Ar_1 + Ar_2 + 899 >= 0 /\ -Ar_0 + Ar_2 + 899 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 ] (Comp: Ar_1, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_5, Ar_1, Ar_4, Ar_3, Ar_4, Ar_5)) [ -Ar_5 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 /\ 99 >= Ar_4 ] (Comp: 2000*Ar_1 + 2*Ar_3, Cost: 1) evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ -Ar_5 >= 0 /\ -Ar_1 - Ar_5 - 1 >= 0 /\ Ar_0 - Ar_5 + 1 >= 0 /\ -Ar_0 - Ar_5 - 1 >= 0 /\ -Ar_1 + Ar_5 - 1 >= 0 /\ -Ar_0 + Ar_5 - 1 >= 0 /\ Ar_2 - Ar_4 + 1000 >= 0 /\ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 /\ Ar_4 >= 100 ] (Comp: Ar_1, Cost: 1) evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_2 + 1000, Ar_0 + 1)) [ -Ar_1 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 - 2 >= 0 /\ -Ar_0 - 1 >= 0 ] (Comp: 2, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: Ar_1, Cost: 1) evalt27bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 - Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evalt27start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evalt27bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 Complexity upper bound 4003*Ar_1 + 4*Ar_3 + 6 Time: 0.274 sec (SMT: 0.213 sec) ---------------------------------------- (2) BOUNDS(1, n^1)