/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 186 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_peed_pldi09_fig4_4_start(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb0_in(v_i.0, v_m, v_n)) :|: TRUE eval_peed_pldi09_fig4_4_bb0_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb3_in(v_i.0, v_m, v_n)) :|: 0 >= v_m eval_peed_pldi09_fig4_4_bb0_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb1_in(v_n, v_m, v_n)) :|: 0 < v_m eval_peed_pldi09_fig4_4_bb1_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb2_in(v_i.0, v_m, v_n)) :|: v_i.0 > 0 eval_peed_pldi09_fig4_4_bb1_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb3_in(v_i.0, v_m, v_n)) :|: v_i.0 <= 0 eval_peed_pldi09_fig4_4_bb2_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb1_in(v_i.0 - 1, v_m, v_n)) :|: v_i.0 < v_m eval_peed_pldi09_fig4_4_bb2_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb1_in(v_i.0 - v_m, v_m, v_n)) :|: v_i.0 >= v_m eval_peed_pldi09_fig4_4_bb3_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_stop(v_i.0, v_m, v_n)) :|: TRUE The start-symbols are:[eval_peed_pldi09_fig4_4_start_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 6*Ar_2 + 7) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_2, Ar_2)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - Ar_0, Ar_2)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44start(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) evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_2, Ar_2)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - Ar_0, Ar_2)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalpeedpldi09fig44start) = 2 Pol(evalpeedpldi09fig44bb0in) = 2 Pol(evalpeedpldi09fig44bb3in) = 1 Pol(evalpeedpldi09fig44bb1in) = 2 Pol(evalpeedpldi09fig44bb2in) = 2 Pol(evalpeedpldi09fig44stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44stop(Ar_0, Ar_1, Ar_2)) evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_2, Ar_2)) [ Ar_0 >= 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= 1 ] (Comp: 2, Cost: 1) evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - Ar_0, Ar_2)) [ Ar_1 >= Ar_0 ] (Comp: 2, Cost: 1) evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalpeedpldi09fig44bb1in: -X_2 + X_3 >= 0 /\ X_1 - 1 >= 0 For symbol evalpeedpldi09fig44bb2in: X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44stop(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - Ar_0, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_1 ] (Comp: ?, Cost: 1) evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_2, Ar_2)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalpeedpldi09fig44bb2in) = 2*V_2 - 1 Pol(evalpeedpldi09fig44bb1in) = 2*V_2 and size complexities S("evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ]", 0-0) = Ar_0 S("evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ]", 0-1) = Ar_1 S("evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ]", 0-2) = Ar_2 S("evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_2, Ar_2)) [ Ar_0 >= 1 ]", 0-0) = Ar_0 S("evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_2, Ar_2)) [ Ar_0 >= 1 ]", 0-1) = Ar_2 S("evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_2, Ar_2)) [ Ar_0 >= 1 ]", 0-2) = Ar_2 S("evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0 S("evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = Ar_2 S("evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= 1 ]", 0-2) = Ar_2 S("evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ 0 >= Ar_1 ]", 0-0) = Ar_0 S("evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ 0 >= Ar_1 ]", 0-1) = Ar_2 S("evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ 0 >= Ar_1 ]", 0-2) = Ar_2 S("evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-1) = Ar_2 S("evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_1 + 1 ]", 0-2) = Ar_2 S("evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - Ar_0, Ar_2)) [ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-0) = Ar_0 S("evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - Ar_0, Ar_2)) [ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-1) = Ar_2 S("evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - Ar_0, Ar_2)) [ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-2) = Ar_2 S("evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44stop(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44stop(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 + Ar_2 S("evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44stop(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 orients the transitions evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - Ar_0, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_0 ] evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ] evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ] weakly and the transitions evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - Ar_0, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_0 ] evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ] evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44stop(Ar_0, Ar_1, Ar_2)) (Comp: 2*Ar_2, Cost: 1) evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - Ar_0, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 2*Ar_2, Cost: 1) evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_1 + 1 ] (Comp: 2, Cost: 1) evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - 1 >= 0 /\ 0 >= Ar_1 ] (Comp: 2*Ar_2, Cost: 1) evalpeedpldi09fig44bb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb2in(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= 1 ] (Comp: 1, Cost: 1) evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb1in(Ar_0, Ar_2, Ar_2)) [ Ar_0 >= 1 ] (Comp: 1, Cost: 1) evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb3in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ] (Comp: 1, Cost: 1) evalpeedpldi09fig44start(Ar_0, Ar_1, Ar_2) -> Com_1(evalpeedpldi09fig44bb0in(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 Complexity upper bound 6*Ar_2 + 7 Time: 0.149 sec (SMT: 0.125 sec) ---------------------------------------- (2) BOUNDS(1, n^1)