/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 75 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_t20_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE eval_t20_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb1_in(v_x, v_.01, v_x, v_y)) :|: TRUE eval_t20_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 < v_y eval_t20_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb3_in(v_.0, v_y, v_x, v_y)) :|: v_.0 >= v_y eval_t20_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb1_in(v_.0 + 1, v_.01, v_x, v_y)) :|: TRUE eval_t20_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb4_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 < v_.0 eval_t20_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb5_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 >= v_.0 eval_t20_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb3_in(v_.0, v_.01 + 1, v_x, v_y)) :|: TRUE eval_t20_bb5_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE The start-symbols are:[eval_t20_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 14*Ar_1 + 20*Ar_2 + 17) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalt20start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) (Comp: ?, Cost: 1) evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20start(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) evalt20start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) (Comp: ?, Cost: 1) evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalt20start) = 3 Pol(evalt20bb0in) = 3 Pol(evalt20bb1in) = 3 Pol(evalt20bb2in) = 3 Pol(evalt20bb3in) = 2 Pol(evalt20bb4in) = 2 Pol(evalt20bb5in) = 1 Pol(evalt20stop) = 0 Pol(koat_start) = 3 orients all transitions weakly and the transitions evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20stop(Ar_0, Ar_1, Ar_2, Ar_3)) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 >= Ar_2 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalt20start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 3, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) (Comp: 3, Cost: 1) evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalt20start) = -V_2 + V_3 Pol(evalt20bb0in) = -V_2 + V_3 Pol(evalt20bb1in) = -V_1 + V_3 Pol(evalt20bb2in) = -V_1 + V_3 - 1 Pol(evalt20bb3in) = -V_1 + 2*V_3 - V_4 Pol(evalt20bb4in) = -V_1 + 2*V_3 - V_4 Pol(evalt20bb5in) = -V_1 + 2*V_3 - V_4 Pol(evalt20stop) = -V_1 + 2*V_3 - V_4 Pol(koat_start) = -V_2 + V_3 orients all transitions weakly and the transition evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb2in(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) evalt20start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + Ar_2, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 3, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) (Comp: 3, Cost: 1) evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20start(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) evalt20start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + Ar_2, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: Ar_1 + Ar_2, Cost: 1) evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 3, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) (Comp: 3, Cost: 1) evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalt20bb4in) = V_1 - V_4 Pol(evalt20bb3in) = V_1 - V_4 + 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20start(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(evalt20start(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(evalt20start(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(evalt20start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1))", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1))", 0-1) = Ar_1 S("evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1))", 0-2) = Ar_2 S("evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1))", 0-3) = ? S("evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ]", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ]", 0-1) = Ar_1 S("evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ]", 0-2) = Ar_2 S("evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ]", 0-3) = ? S("evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ]", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ]", 0-1) = Ar_1 S("evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ]", 0-2) = Ar_2 S("evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ]", 0-3) = ? S("evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 >= Ar_2 ]", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 >= Ar_2 ]", 0-1) = Ar_1 S("evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 >= Ar_2 ]", 0-2) = Ar_2 S("evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 >= Ar_2 ]", 0-3) = Ar_2 S("evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ]", 0-0) = 2*Ar_1 + 2*Ar_2 S("evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ]", 0-2) = Ar_2 S("evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ]", 0-3) = Ar_3 S("evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_1 S("evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalt20start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalt20start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalt20start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalt20start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ] weakly and the transition evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalt20start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + Ar_2, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: Ar_1 + Ar_2, Cost: 1) evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 6*Ar_1 + 9*Ar_2 + 3, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 3, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) (Comp: 3, Cost: 1) evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20start(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) evalt20start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalt20bb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + Ar_2, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalt20bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 >= Ar_2 ] (Comp: Ar_1 + Ar_2, Cost: 1) evalt20bb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) (Comp: 6*Ar_1 + 9*Ar_2 + 3, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 3, Cost: 1) evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_0 ] (Comp: 6*Ar_1 + 9*Ar_2 + 3, Cost: 1) evalt20bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20bb3in(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) (Comp: 3, Cost: 1) evalt20bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20stop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalt20start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 14*Ar_1 + 20*Ar_2 + 17 Time: 0.079 sec (SMT: 0.062 sec) ---------------------------------------- (2) BOUNDS(1, n^1)