/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^2)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 85 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_textbook_ex2_start(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb0_in(v_i.0, v_j.0, v_n)) :|: TRUE eval_textbook_ex2_bb0_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb1_in(0, v_j.0, v_n)) :|: TRUE eval_textbook_ex2_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb2_in(v_i.0, 0, v_n)) :|: v_i.0 <= v_n - 1 eval_textbook_ex2_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb5_in(v_i.0, v_j.0, v_n)) :|: v_i.0 > v_n - 1 eval_textbook_ex2_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb3_in(v_i.0, v_j.0, v_n)) :|: v_j.0 <= v_i.0 eval_textbook_ex2_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb4_in(v_i.0, v_j.0, v_n)) :|: v_j.0 > v_i.0 eval_textbook_ex2_bb3_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb2_in(v_i.0, v_j.0 + 1, v_n)) :|: TRUE eval_textbook_ex2_bb4_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_bb1_in(v_i.0 + 1, v_j.0, v_n)) :|: TRUE eval_textbook_ex2_bb5_in(v_i.0, v_j.0, v_n) -> Com_1(eval_textbook_ex2_stop(v_i.0, v_j.0, v_n)) :|: TRUE The start-symbols are:[eval_textbook_ex2_start_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 27*Ar_1 + 4*Ar_1^2 + 29) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 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) evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaltextbookex2start) = 2 Pol(evaltextbookex2bb0in) = 2 Pol(evaltextbookex2bb1in) = 2 Pol(evaltextbookex2bb2in) = 2 Pol(evaltextbookex2bb5in) = 1 Pol(evaltextbookex2bb3in) = 2 Pol(evaltextbookex2bb4in) = 2 Pol(evaltextbookex2stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2)) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaltextbookex2start) = V_2 + 1 Pol(evaltextbookex2bb0in) = V_2 + 1 Pol(evaltextbookex2bb1in) = -V_1 + V_2 + 1 Pol(evaltextbookex2bb2in) = -V_1 + V_2 Pol(evaltextbookex2bb5in) = -V_1 + V_2 Pol(evaltextbookex2bb3in) = -V_1 + V_2 Pol(evaltextbookex2bb4in) = -V_1 + V_2 Pol(evaltextbookex2stop) = -V_1 + V_2 Pol(koat_start) = V_2 + 1 orients all transitions weakly and the transition evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2)) (Comp: Ar_1 + 1, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaltextbookex2bb4in) = 1 Pol(evaltextbookex2bb1in) = 0 Pol(evaltextbookex2bb3in) = 2 Pol(evaltextbookex2bb2in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 S("evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2))", 0-0) = ? S("evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2))", 0-2) = ? S("evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2))", 0-0) = ? S("evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2))", 0-1) = Ar_1 S("evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2))", 0-2) = ? S("evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1))", 0-0) = ? S("evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1))", 0-1) = Ar_1 S("evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1))", 0-2) = ? S("evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = ? S("evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = ? S("evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ]", 0-0) = ? S("evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ]", 0-1) = Ar_1 S("evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ]", 0-2) = ? S("evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ]", 0-0) = ? S("evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ]", 0-2) = ? S("evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = ? S("evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = 0 S("evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2))", 0-0) = 0 S("evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2))", 0-2) = Ar_2 S("evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 orients the transitions evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2)) evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1)) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ] weakly and the transitions evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2)) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2)) (Comp: Ar_1 + 1, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_1 + 2, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: 2*Ar_1 + 2, Cost: 1) evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaltextbookex2bb3in) = V_1 - V_3 Pol(evaltextbookex2bb2in) = V_1 - V_3 + 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 S("evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2))", 0-0) = 2*Ar_1 + 32 S("evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2))", 0-2) = ? S("evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2))", 0-0) = 2*Ar_1 + 8 S("evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2))", 0-1) = Ar_1 S("evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2))", 0-2) = ? S("evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1))", 0-0) = 2*Ar_1 + 8 S("evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1))", 0-1) = Ar_1 S("evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1))", 0-2) = ? S("evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = 2*Ar_1 + 8 S("evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = ? S("evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ]", 0-0) = 2*Ar_1 + 8 S("evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ]", 0-1) = Ar_1 S("evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ]", 0-2) = ? S("evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ]", 0-0) = 2*Ar_1 + 16 S("evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ]", 0-1) = Ar_1 S("evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ]", 0-2) = ? S("evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ]", 0-0) = 2*Ar_1 + 8 S("evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ]", 0-2) = 0 S("evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2))", 0-0) = 0 S("evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2))", 0-2) = Ar_2 S("evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 orients the transitions evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1)) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ] weakly and the transition evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2)) (Comp: Ar_1 + 1, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] (Comp: 2*Ar_1^2 + 11*Ar_1 + 9, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_1 + 2, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: 2*Ar_1 + 2, Cost: 1) evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 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) evaltextbookex2start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evaltextbookex2bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(0, Ar_1, Ar_2)) (Comp: Ar_1 + 1, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, 0)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evaltextbookex2bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 ] (Comp: 2*Ar_1^2 + 11*Ar_1 + 9, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: 2*Ar_1 + 2, Cost: 1) evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 2*Ar_1^2 + 11*Ar_1 + 9, Cost: 1) evaltextbookex2bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: 2*Ar_1 + 2, Cost: 1) evaltextbookex2bb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2bb1in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evaltextbookex2bb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evaltextbookex2start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 27*Ar_1 + 4*Ar_1^2 + 29 Time: 0.069 sec (SMT: 0.055 sec) ---------------------------------------- (2) BOUNDS(1, n^2)