/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 76 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_t08_start(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb0_in(v_.0, v_.1, v_y, v_z)) :|: TRUE eval_t08_bb0_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb1_in(v_y, v_.1, v_y, v_z)) :|: TRUE eval_t08_bb1_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb2_in(v_.0, v_.1, v_y, v_z)) :|: v_z > v_.0 eval_t08_bb1_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb3_in(v_.0, v_.0, v_y, v_z)) :|: v_z <= v_.0 eval_t08_bb2_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb1_in(v_.0 + 1, v_.1, v_y, v_z)) :|: TRUE eval_t08_bb3_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb4_in(v_.0, v_.1, v_y, v_z)) :|: v_.1 > 2 eval_t08_bb3_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb5_in(v_.0, v_.1, v_y, v_z)) :|: v_.1 <= 2 eval_t08_bb4_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_bb3_in(v_.0, v_.1 - 3, v_y, v_z)) :|: TRUE eval_t08_bb5_in(v_.0, v_.1, v_y, v_z) -> Com_1(eval_t08_stop(v_.0, v_.1, v_y, v_z)) :|: TRUE The start-symbols are:[eval_t08_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 14*Ar_1 + 14*Ar_2 + 11) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalt08start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ] (Comp: ?, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - 3)) (Comp: ?, Cost: 1) evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalt08start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ] (Comp: ?, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - 3)) (Comp: ?, Cost: 1) evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalt08start) = 3 Pol(evalt08bb0in) = 3 Pol(evalt08bb1in) = 3 Pol(evalt08bb2in) = 3 Pol(evalt08bb3in) = 2 Pol(evalt08bb4in) = 2 Pol(evalt08bb5in) = 1 Pol(evalt08stop) = 0 Pol(koat_start) = 3 orients all transitions weakly and the transitions evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08stop(Ar_0, Ar_1, Ar_2, Ar_3)) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_3 ] evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 >= Ar_2 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalt08start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ] (Comp: 3, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - 3)) (Comp: 3, Cost: 1) evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalt08start) = -V_2 + V_3 Pol(evalt08bb0in) = -V_2 + V_3 Pol(evalt08bb1in) = -V_1 + V_3 Pol(evalt08bb2in) = -V_1 + V_3 - 1 Pol(evalt08bb3in) = -2*V_1 + V_3 + V_4 Pol(evalt08bb4in) = -2*V_1 + V_3 + V_4 Pol(evalt08bb5in) = -2*V_1 + V_3 + V_4 Pol(evalt08stop) = -2*V_1 + V_3 + V_4 Pol(koat_start) = -V_2 + V_3 orients all transitions weakly and the transition evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalt08start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + Ar_2, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ] (Comp: 3, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - 3)) (Comp: 3, Cost: 1) evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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) evalt08start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + Ar_2, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 >= Ar_2 ] (Comp: Ar_1 + Ar_2, Cost: 1) evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ] (Comp: 3, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - 3)) (Comp: 3, Cost: 1) evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalt08bb4in) = V_4 - 3 Pol(evalt08bb3in) = V_4 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - 3))", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - 3))", 0-1) = Ar_1 S("evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - 3))", 0-2) = Ar_2 S("evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - 3))", 0-3) = ? S("evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_3 ]", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_3 ]", 0-1) = Ar_1 S("evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_3 ]", 0-2) = Ar_2 S("evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_3 ]", 0-3) = ? S("evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ]", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ]", 0-1) = Ar_1 S("evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ]", 0-2) = Ar_2 S("evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ]", 0-3) = ? S("evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 >= Ar_2 ]", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 >= Ar_2 ]", 0-1) = Ar_1 S("evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 >= Ar_2 ]", 0-2) = Ar_2 S("evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 >= Ar_2 ]", 0-3) = 2*Ar_1 + 2*Ar_2 S("evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = Ar_2 S("evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_1 S("evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalt08start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalt08start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalt08start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalt08start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - 3)) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ] weakly and the transition evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalt08start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + Ar_2, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 >= Ar_2 ] (Comp: Ar_1 + Ar_2, Cost: 1) evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 6*Ar_1 + 6*Ar_2, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ] (Comp: 3, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_3 ] (Comp: ?, Cost: 1) evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - 3)) (Comp: 3, Cost: 1) evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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) evalt08start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalt08bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + Ar_2, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalt08bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_0)) [ Ar_0 >= Ar_2 ] (Comp: Ar_1 + Ar_2, Cost: 1) evalt08bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 6*Ar_1 + 6*Ar_2, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 3 ] (Comp: 3, Cost: 1) evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_3 ] (Comp: 6*Ar_1 + 6*Ar_2, Cost: 1) evalt08bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08bb3in(Ar_0, Ar_1, Ar_2, Ar_3 - 3)) (Comp: 3, Cost: 1) evalt08bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt08start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 14*Ar_1 + 14*Ar_2 + 11 Time: 0.080 sec (SMT: 0.062 sec) ---------------------------------------- (2) BOUNDS(1, n^1)