/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).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, 76 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_jama_ex4_start(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb0_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0)) :|: TRUE eval_jama_ex4_bb0_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb1_in(v_a, v_b, v_c, v_d, v_a, v_j.0)) :|: TRUE eval_jama_ex4_bb1_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb2_in(v_a, v_b, v_c, v_d, v_i.0, v_c)) :|: v_i.0 <= v_b eval_jama_ex4_bb1_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb5_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0)) :|: v_i.0 > v_b eval_jama_ex4_bb2_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb3_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0)) :|: v_j.0 <= v_d eval_jama_ex4_bb2_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb4_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0)) :|: v_j.0 > v_d eval_jama_ex4_bb3_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb2_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0 + 1)) :|: TRUE eval_jama_ex4_bb4_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_bb1_in(v_a, v_b, v_c, v_d, v_i.0 + 1, v_j.0)) :|: TRUE eval_jama_ex4_bb5_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0) -> Com_1(eval_jama_ex4_stop(v_a, v_b, v_c, v_d, v_i.0, v_j.0)) :|: TRUE The start-symbols are:[eval_jama_ex4_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 7*Ar_1 + 7*Ar_2 + 2*Ar_1*Ar_4 + 2*Ar_2*Ar_4 + 2*Ar_1*Ar_5 + 2*Ar_2*Ar_5 + 2*Ar_4 + 2*Ar_5 + 13) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ] (Comp: ?, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(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(evaljamaex4start(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) evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ] (Comp: ?, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(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(evaljamaex4start(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(evaljamaex4start) = 2 Pol(evaljamaex4bb0in) = 2 Pol(evaljamaex4bb1in) = 2 Pol(evaljamaex4bb2in) = 2 Pol(evaljamaex4bb5in) = 1 Pol(evaljamaex4bb3in) = 2 Pol(evaljamaex4bb4in) = 2 Pol(evaljamaex4stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ] (Comp: 2, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ] (Comp: ?, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(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(evaljamaex4start(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(evaljamaex4start) = -V_2 + V_3 + 1 Pol(evaljamaex4bb0in) = -V_2 + V_3 + 1 Pol(evaljamaex4bb1in) = -V_1 + V_3 + 1 Pol(evaljamaex4bb2in) = -V_1 + V_3 Pol(evaljamaex4bb5in) = -V_1 + V_3 Pol(evaljamaex4bb3in) = -V_1 + V_3 Pol(evaljamaex4bb4in) = -V_1 + V_3 Pol(evaljamaex4stop) = -V_1 + V_3 Pol(koat_start) = -V_2 + V_3 + 1 orients all transitions weakly and the transition evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1 + Ar_2 + 1, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ] (Comp: 2, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ] (Comp: ?, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: ?, Cost: 1) evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(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(evaljamaex4start(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(evaljamaex4bb4in) = 1 Pol(evaljamaex4bb1in) = 0 Pol(evaljamaex4bb3in) = 2 Pol(evaljamaex4bb2in) = 2 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4start(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(evaljamaex4start(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(evaljamaex4start(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(evaljamaex4start(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(evaljamaex4start(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(evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5 S("evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = ? S("evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = ? S("evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = ? S("evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = ? S("evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-0) = ? S("evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-1) = Ar_1 S("evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-2) = Ar_2 S("evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-3) = ? S("evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-4) = Ar_4 S("evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-5) = Ar_5 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ]", 0-0) = ? S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ]", 0-1) = Ar_1 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ]", 0-2) = Ar_2 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ]", 0-3) = ? S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ]", 0-4) = Ar_4 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ]", 0-5) = Ar_5 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ]", 0-0) = ? S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ]", 0-1) = Ar_1 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ]", 0-2) = Ar_2 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ]", 0-3) = ? S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ]", 0-4) = Ar_4 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ]", 0-5) = Ar_5 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ]", 0-0) = ? S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ]", 0-2) = Ar_2 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ]", 0-3) = ? S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ]", 0-4) = Ar_4 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ]", 0-5) = Ar_5 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ]", 0-0) = ? S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ]", 0-1) = Ar_1 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ]", 0-2) = Ar_2 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ]", 0-3) = Ar_4 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ]", 0-4) = Ar_4 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ]", 0-5) = Ar_5 S("evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_1 S("evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 orients the transitions evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ] evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ] weakly and the transitions evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1 + Ar_2 + 1, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ] (Comp: 2, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ] (Comp: 2*Ar_1 + 2*Ar_2 + 2, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: 2*Ar_1 + 2*Ar_2 + 2, Cost: 1) evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(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(evaljamaex4start(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(evaljamaex4bb3in) = -V_4 + V_6 Pol(evaljamaex4bb2in) = -V_4 + V_6 + 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4start(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(evaljamaex4start(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(evaljamaex4start(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(evaljamaex4start(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(evaljamaex4start(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(evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-5) = Ar_5 S("evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = 3*Ar_1 + 3*Ar_2 + 162 S("evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = ? S("evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = 3*Ar_1 + 3*Ar_2 + 18 S("evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = ? S("evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-0) = 3*Ar_1 + 3*Ar_2 + 18 S("evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-1) = Ar_1 S("evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-2) = Ar_2 S("evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-3) = ? S("evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-4) = Ar_4 S("evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5))", 0-5) = Ar_5 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ]", 0-0) = 3*Ar_1 + 3*Ar_2 + 18 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ]", 0-1) = Ar_1 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ]", 0-2) = Ar_2 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ]", 0-3) = ? S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ]", 0-4) = Ar_4 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ]", 0-5) = Ar_5 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ]", 0-0) = 3*Ar_1 + 3*Ar_2 + 18 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ]", 0-1) = Ar_1 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ]", 0-2) = Ar_2 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ]", 0-3) = ? S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ]", 0-4) = Ar_4 S("evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ]", 0-5) = Ar_5 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ]", 0-0) = 3*Ar_1 + 3*Ar_2 + 54 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ]", 0-2) = Ar_2 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ]", 0-3) = ? S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ]", 0-4) = Ar_4 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ]", 0-5) = Ar_5 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ]", 0-0) = 3*Ar_1 + 3*Ar_2 + 18 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ]", 0-1) = Ar_1 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ]", 0-2) = Ar_2 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ]", 0-3) = Ar_4 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ]", 0-4) = Ar_4 S("evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ]", 0-5) = Ar_5 S("evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_1 S("evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 S("evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-0) = Ar_0 S("evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_1 S("evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_2 S("evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_3 S("evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-4) = Ar_4 S("evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5))", 0-5) = Ar_5 orients the transitions evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ] weakly and the transition evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1 + Ar_2 + 1, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ] (Comp: 2, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ] (Comp: Ar_1*Ar_4 + Ar_2*Ar_4 + Ar_1*Ar_5 + Ar_2*Ar_5 + Ar_4 + Ar_5 + Ar_1 + Ar_2 + 1, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ] (Comp: 2*Ar_1 + 2*Ar_2 + 2, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: 2*Ar_1 + 2*Ar_2 + 2, Cost: 1) evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(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(evaljamaex4start(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 6 produces the following problem: 7: T: (Comp: 1, Cost: 1) evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) evaljamaex4bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: Ar_1 + Ar_2 + 1, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4, Ar_5)) [ Ar_2 >= Ar_0 ] (Comp: 2, Cost: 1) evaljamaex4bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 1 ] (Comp: Ar_1*Ar_4 + Ar_2*Ar_4 + Ar_1*Ar_5 + Ar_2*Ar_5 + Ar_4 + Ar_5 + Ar_1 + Ar_2 + 1, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= Ar_3 ] (Comp: 2*Ar_1 + 2*Ar_2 + 2, Cost: 1) evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_5 + 1 ] (Comp: Ar_1*Ar_4 + Ar_2*Ar_4 + Ar_1*Ar_5 + Ar_2*Ar_5 + Ar_4 + Ar_5 + Ar_1 + Ar_2 + 1, Cost: 1) evaljamaex4bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb2in(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5)) (Comp: 2*Ar_1 + 2*Ar_2 + 2, Cost: 1) evaljamaex4bb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 2, Cost: 1) evaljamaex4bb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(evaljamaex4stop(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(evaljamaex4start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 7*Ar_1 + 7*Ar_2 + 2*Ar_1*Ar_4 + 2*Ar_2*Ar_4 + 2*Ar_1*Ar_5 + 2*Ar_2*Ar_5 + 2*Ar_4 + 2*Ar_5 + 13 Time: 0.109 sec (SMT: 0.078 sec) ---------------------------------------- (2) BOUNDS(1, n^2)