/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 222 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 828 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_realselect_start(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_bb0_in(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE eval_realselect_bb0_in(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_0(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE eval_realselect_0(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_1(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE eval_realselect_1(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_2(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE eval_realselect_2(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_3(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE eval_realselect_3(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_4(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE eval_realselect_4(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_5(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE eval_realselect_5(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_6(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE eval_realselect_6(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_bb1_in(v_2, v_21, v_array_size, 0, v_j_0_sink)) :|: TRUE eval_realselect_bb1_in(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_bb2_in(v_2, v_21, v_array_size, v_i_0, v_i_0)) :|: v_i_0 < v_array_size - 1 eval_realselect_bb1_in(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_bb5_in(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: v_i_0 >= v_array_size - 1 eval_realselect_bb2_in(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_bb3_in(v_j_0_sink + 1, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: v_j_0_sink + 1 < v_array_size eval_realselect_bb2_in(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_bb4_in(v_j_0_sink + 1, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: v_j_0_sink + 1 >= v_array_size eval_realselect_bb3_in(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_bb2_in(v_2, v_21, v_array_size, v_i_0, v_2)) :|: nondef_0 < nondef_1 eval_realselect_bb3_in(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_bb2_in(v_2, v_21, v_array_size, v_i_0, v_2)) :|: nondef_0 >= nondef_1 eval_realselect_bb4_in(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_19(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE eval_realselect_19(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_20(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE eval_realselect_20(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_27(v_2, v_i_0 + 1, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE eval_realselect_27(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_28(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE eval_realselect_28(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_bb1_in(v_2, v_21, v_array_size, v_21, v_j_0_sink)) :|: TRUE eval_realselect_bb5_in(v_2, v_21, v_array_size, v_i_0, v_j_0_sink) -> Com_1(eval_realselect_stop(v_2, v_21, v_array_size, v_i_0, v_j_0_sink)) :|: TRUE The start-symbols are:[eval_realselect_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 37*Ar_1 + 21*Ar_1^2 + 13) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ] (Comp: ?, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ] (Comp: ?, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1)) (Comp: ?, Cost: 1) evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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) evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ] (Comp: ?, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ] (Comp: ?, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1)) (Comp: ?, Cost: 1) evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealselectstart) = 2 Pol(evalrealselectbb0in) = 2 Pol(evalrealselect0) = 2 Pol(evalrealselect1) = 2 Pol(evalrealselect2) = 2 Pol(evalrealselect3) = 2 Pol(evalrealselect4) = 2 Pol(evalrealselect5) = 2 Pol(evalrealselect6) = 2 Pol(evalrealselectbb1in) = 2 Pol(evalrealselectbb2in) = 2 Pol(evalrealselectbb5in) = 1 Pol(evalrealselectbb3in) = 2 Pol(evalrealselectbb4in) = 2 Pol(evalrealselect19) = 2 Pol(evalrealselect20) = 2 Pol(evalrealselect27) = 2 Pol(evalrealselect28) = 2 Pol(evalrealselectstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ] (Comp: 2, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ] (Comp: ?, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1)) (Comp: ?, Cost: 1) evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealselectstart) = V_2 Pol(evalrealselectbb0in) = V_2 Pol(evalrealselect0) = V_2 Pol(evalrealselect1) = V_2 Pol(evalrealselect2) = V_2 Pol(evalrealselect3) = V_2 Pol(evalrealselect4) = V_2 Pol(evalrealselect5) = V_2 Pol(evalrealselect6) = V_2 Pol(evalrealselectbb1in) = -V_1 + V_2 Pol(evalrealselectbb2in) = -V_1 + V_2 - 1 Pol(evalrealselectbb5in) = -V_1 + V_2 Pol(evalrealselectbb3in) = -V_1 + V_2 - 1 Pol(evalrealselectbb4in) = -V_1 + V_2 - 1 Pol(evalrealselect19) = -V_1 + V_2 - 1 Pol(evalrealselect20) = -V_1 + V_2 - 1 Pol(evalrealselect27) = V_2 - V_5 Pol(evalrealselect28) = V_2 - V_5 Pol(evalrealselectstop) = -V_1 + V_2 Pol(koat_start) = V_2 orients all transitions weakly and the transition evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ] (Comp: 2, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ] (Comp: ?, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1)) (Comp: ?, Cost: 1) evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealselectbb4in) = 5 Pol(evalrealselect19) = 4 Pol(evalrealselectbb3in) = 6 Pol(evalrealselectbb2in) = 6 Pol(evalrealselect28) = 1 Pol(evalrealselectbb1in) = 0 Pol(evalrealselect27) = 2 Pol(evalrealselect20) = 3 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = ? S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = ? S("evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = ? S("evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1))", 0-0) = ? S("evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1))", 0-1) = Ar_1 S("evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1))", 0-2) = ? S("evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1))", 0-3) = ? S("evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1))", 0-4) = ? S("evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = ? S("evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = ? S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = ? S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ]", 0-0) = ? S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ]", 0-1) = Ar_1 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ]", 0-2) = ? S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ]", 0-3) = ? S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ]", 0-4) = ? S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ]", 0-0) = ? S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ]", 0-1) = Ar_1 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ]", 0-2) = ? S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ]", 0-3) = ? S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ]", 0-4) = ? S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ]", 0-0) = ? S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ]", 0-1) = Ar_1 S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ]", 0-2) = ? S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ]", 0-3) = ? S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ]", 0-4) = ? S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ]", 0-0) = ? S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ]", 0-1) = Ar_1 S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ]", 0-2) = ? S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ]", 0-3) = ? S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ]", 0-4) = ? S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ]", 0-0) = ? S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ]", 0-1) = Ar_1 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ]", 0-2) = ? S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ]", 0-3) = ? S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ]", 0-4) = ? S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ]", 0-0) = ? S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ]", 0-1) = Ar_1 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ]", 0-2) = ? S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ]", 0-3) = ? S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ]", 0-4) = ? S("evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 0 S("evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ] evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ] evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ] evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ] evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4)) evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1)) evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) weakly and the transitions evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ] evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4)) evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1)) evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ] (Comp: 2, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ] (Comp: 6*Ar_1, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ] (Comp: 6*Ar_1, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 6*Ar_1, Cost: 1) evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 6*Ar_1, Cost: 1) evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1)) (Comp: 6*Ar_1, Cost: 1) evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 6*Ar_1, Cost: 1) evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealselectbb3in) = V_2 - V_4 Pol(evalrealselectbb2in) = V_2 - V_3 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]", 0-4) = Ar_4 S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 6*Ar_1 S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = 6*Ar_1 + 6*Ar_4 S("evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 6*Ar_1 S("evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = 6*Ar_1 S("evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 6*Ar_1 S("evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = 6*Ar_1 S("evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1))", 0-0) = 6*Ar_1 S("evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1))", 0-1) = Ar_1 S("evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1))", 0-2) = ? S("evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1))", 0-3) = ? S("evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1))", 0-4) = 6*Ar_1 S("evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 6*Ar_1 S("evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = 6*Ar_1 + 6*Ar_4 S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 6*Ar_1 S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = ? S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = ? S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = 6*Ar_1 + 6*Ar_4 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ]", 0-0) = 6*Ar_1 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ]", 0-1) = Ar_1 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ]", 0-2) = ? S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ]", 0-3) = ? S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ]", 0-4) = 6*Ar_1 + 6*Ar_4 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ]", 0-0) = 6*Ar_1 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ]", 0-1) = Ar_1 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ]", 0-2) = ? S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ]", 0-3) = ? S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ]", 0-4) = 6*Ar_1 + 6*Ar_4 S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ]", 0-0) = 6*Ar_1 S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ]", 0-1) = Ar_1 S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ]", 0-2) = ? S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ]", 0-3) = ? S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ]", 0-4) = 6*Ar_1 + 6*Ar_4 S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ]", 0-0) = 6*Ar_1 S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ]", 0-1) = Ar_1 S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ]", 0-2) = ? S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ]", 0-3) = ? S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ]", 0-4) = 6*Ar_1 + 6*Ar_4 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ]", 0-0) = 6*Ar_1 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ]", 0-1) = Ar_1 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ]", 0-2) = ? S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ]", 0-3) = ? S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ]", 0-4) = 6*Ar_1 + 6*Ar_4 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ]", 0-0) = 6*Ar_1 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ]", 0-1) = Ar_1 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ]", 0-2) = 6*Ar_1 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ]", 0-3) = ? S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ]", 0-4) = 6*Ar_1 + 6*Ar_4 S("evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = 0 S("evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-0) = Ar_0 S("evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-1) = Ar_1 S("evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-2) = Ar_2 S("evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-3) = Ar_3 S("evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 orients the transitions evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ] evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ] evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ] weakly and the transition evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ] (Comp: 2, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ] (Comp: 7*Ar_1^2, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ] (Comp: 6*Ar_1, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ] (Comp: 6*Ar_1, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 6*Ar_1, Cost: 1) evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 6*Ar_1, Cost: 1) evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1)) (Comp: 6*Ar_1, Cost: 1) evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 6*Ar_1, Cost: 1) evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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) evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: Ar_1, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 2 ] (Comp: 2, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 + 1 >= Ar_1 ] (Comp: 7*Ar_1^2, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_1 >= Ar_2 + 2 ] (Comp: 6*Ar_1, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_2 + 1, Ar_4)) [ Ar_2 + 1 >= Ar_1 ] (Comp: 7*Ar_1^2, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ F >= G + 1 ] (Comp: 7*Ar_1^2, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_3, Ar_3, Ar_4)) [ G >= F ] (Comp: 6*Ar_1, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 6*Ar_1, Cost: 1) evalrealselect19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 6*Ar_1, Cost: 1) evalrealselect20(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 + 1)) (Comp: 6*Ar_1, Cost: 1) evalrealselect27(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 6*Ar_1, Cost: 1) evalrealselect28(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectbb1in(Ar_4, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 37*Ar_1 + 21*Ar_1^2 + 13 Time: 0.232 sec (SMT: 0.145 sec) ---------------------------------------- (2) BOUNDS(1, n^2) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalrealselectstart 0: evalrealselectstart -> evalrealselectbb0in : [], cost: 1 1: evalrealselectbb0in -> evalrealselect0 : [], cost: 1 2: evalrealselect0 -> evalrealselect1 : [], cost: 1 3: evalrealselect1 -> evalrealselect2 : [], cost: 1 4: evalrealselect2 -> evalrealselect3 : [], cost: 1 5: evalrealselect3 -> evalrealselect4 : [], cost: 1 6: evalrealselect4 -> evalrealselect5 : [], cost: 1 7: evalrealselect5 -> evalrealselect6 : [], cost: 1 8: evalrealselect6 -> evalrealselectbb1in : A'=0, [], cost: 1 9: evalrealselectbb1in -> evalrealselectbb2in : C'=A, [ B>=2+A ], cost: 1 10: evalrealselectbb1in -> evalrealselectbb5in : [ 1+A>=B ], cost: 1 11: evalrealselectbb2in -> evalrealselectbb3in : D'=1+C, [ B>=2+C ], cost: 1 12: evalrealselectbb2in -> evalrealselectbb4in : D'=1+C, [ 1+C>=B ], cost: 1 13: evalrealselectbb3in -> evalrealselectbb2in : C'=D, [ free>=1+free_1 ], cost: 1 14: evalrealselectbb3in -> evalrealselectbb2in : C'=D, [ free_3>=free_2 ], cost: 1 15: evalrealselectbb4in -> evalrealselect19 : [], cost: 1 16: evalrealselect19 -> evalrealselect20 : [], cost: 1 17: evalrealselect20 -> evalrealselect27 : E'=1+A, [], cost: 1 18: evalrealselect27 -> evalrealselect28 : [], cost: 1 19: evalrealselect28 -> evalrealselectbb1in : A'=E, [], cost: 1 20: evalrealselectbb5in -> evalrealselectstop : [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: evalrealselectstart -> evalrealselectbb0in : [], cost: 1 Removed unreachable and leaf rules: Start location: evalrealselectstart 0: evalrealselectstart -> evalrealselectbb0in : [], cost: 1 1: evalrealselectbb0in -> evalrealselect0 : [], cost: 1 2: evalrealselect0 -> evalrealselect1 : [], cost: 1 3: evalrealselect1 -> evalrealselect2 : [], cost: 1 4: evalrealselect2 -> evalrealselect3 : [], cost: 1 5: evalrealselect3 -> evalrealselect4 : [], cost: 1 6: evalrealselect4 -> evalrealselect5 : [], cost: 1 7: evalrealselect5 -> evalrealselect6 : [], cost: 1 8: evalrealselect6 -> evalrealselectbb1in : A'=0, [], cost: 1 9: evalrealselectbb1in -> evalrealselectbb2in : C'=A, [ B>=2+A ], cost: 1 11: evalrealselectbb2in -> evalrealselectbb3in : D'=1+C, [ B>=2+C ], cost: 1 12: evalrealselectbb2in -> evalrealselectbb4in : D'=1+C, [ 1+C>=B ], cost: 1 13: evalrealselectbb3in -> evalrealselectbb2in : C'=D, [ free>=1+free_1 ], cost: 1 14: evalrealselectbb3in -> evalrealselectbb2in : C'=D, [ free_3>=free_2 ], cost: 1 15: evalrealselectbb4in -> evalrealselect19 : [], cost: 1 16: evalrealselect19 -> evalrealselect20 : [], cost: 1 17: evalrealselect20 -> evalrealselect27 : E'=1+A, [], cost: 1 18: evalrealselect27 -> evalrealselect28 : [], cost: 1 19: evalrealselect28 -> evalrealselectbb1in : A'=E, [], cost: 1 Simplified all rules, resulting in: Start location: evalrealselectstart 0: evalrealselectstart -> evalrealselectbb0in : [], cost: 1 1: evalrealselectbb0in -> evalrealselect0 : [], cost: 1 2: evalrealselect0 -> evalrealselect1 : [], cost: 1 3: evalrealselect1 -> evalrealselect2 : [], cost: 1 4: evalrealselect2 -> evalrealselect3 : [], cost: 1 5: evalrealselect3 -> evalrealselect4 : [], cost: 1 6: evalrealselect4 -> evalrealselect5 : [], cost: 1 7: evalrealselect5 -> evalrealselect6 : [], cost: 1 8: evalrealselect6 -> evalrealselectbb1in : A'=0, [], cost: 1 9: evalrealselectbb1in -> evalrealselectbb2in : C'=A, [ B>=2+A ], cost: 1 11: evalrealselectbb2in -> evalrealselectbb3in : D'=1+C, [ B>=2+C ], cost: 1 12: evalrealselectbb2in -> evalrealselectbb4in : D'=1+C, [ 1+C>=B ], cost: 1 14: evalrealselectbb3in -> evalrealselectbb2in : C'=D, [], cost: 1 15: evalrealselectbb4in -> evalrealselect19 : [], cost: 1 16: evalrealselect19 -> evalrealselect20 : [], cost: 1 17: evalrealselect20 -> evalrealselect27 : E'=1+A, [], cost: 1 18: evalrealselect27 -> evalrealselect28 : [], cost: 1 19: evalrealselect28 -> evalrealselectbb1in : A'=E, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalrealselectstart 28: evalrealselectstart -> evalrealselectbb1in : A'=0, [], cost: 9 9: evalrealselectbb1in -> evalrealselectbb2in : C'=A, [ B>=2+A ], cost: 1 29: evalrealselectbb2in -> evalrealselectbb2in : C'=1+C, D'=1+C, [ B>=2+C ], cost: 2 34: evalrealselectbb2in -> evalrealselectbb1in : A'=1+A, D'=1+C, E'=1+A, [ 1+C>=B ], cost: 6 Accelerating simple loops of location 10. Accelerating the following rules: 29: evalrealselectbb2in -> evalrealselectbb2in : C'=1+C, D'=1+C, [ B>=2+C ], cost: 2 Accelerated rule 29 with metering function -1-C+B, yielding the new rule 35. Removing the simple loops: 29. Accelerated all simple loops using metering functions (where possible): Start location: evalrealselectstart 28: evalrealselectstart -> evalrealselectbb1in : A'=0, [], cost: 9 9: evalrealselectbb1in -> evalrealselectbb2in : C'=A, [ B>=2+A ], cost: 1 34: evalrealselectbb2in -> evalrealselectbb1in : A'=1+A, D'=1+C, E'=1+A, [ 1+C>=B ], cost: 6 35: evalrealselectbb2in -> evalrealselectbb2in : C'=-1+B, D'=-1+B, [ B>=2+C ], cost: -2-2*C+2*B Chained accelerated rules (with incoming rules): Start location: evalrealselectstart 28: evalrealselectstart -> evalrealselectbb1in : A'=0, [], cost: 9 9: evalrealselectbb1in -> evalrealselectbb2in : C'=A, [ B>=2+A ], cost: 1 36: evalrealselectbb1in -> evalrealselectbb2in : C'=-1+B, D'=-1+B, [ B>=2+A ], cost: -1-2*A+2*B 34: evalrealselectbb2in -> evalrealselectbb1in : A'=1+A, D'=1+C, E'=1+A, [ 1+C>=B ], cost: 6 Eliminated locations (on tree-shaped paths): Start location: evalrealselectstart 28: evalrealselectstart -> evalrealselectbb1in : A'=0, [], cost: 9 37: evalrealselectbb1in -> evalrealselectbb1in : A'=1+A, C'=-1+B, D'=B, E'=1+A, [ B>=2+A ], cost: 5-2*A+2*B Accelerating simple loops of location 9. Accelerating the following rules: 37: evalrealselectbb1in -> evalrealselectbb1in : A'=1+A, C'=-1+B, D'=B, E'=1+A, [ B>=2+A ], cost: 5-2*A+2*B Accelerated rule 37 with metering function -1-A+B, yielding the new rule 38. Removing the simple loops: 37. Accelerated all simple loops using metering functions (where possible): Start location: evalrealselectstart 28: evalrealselectstart -> evalrealselectbb1in : A'=0, [], cost: 9 38: evalrealselectbb1in -> evalrealselectbb1in : A'=-1+B, C'=-1+B, D'=B, E'=-1+B, [ B>=2+A ], cost: -6-(1+A-B)^2-6*A+2*A*(1+A-B)-2*(1+A-B)*B+6*B Chained accelerated rules (with incoming rules): Start location: evalrealselectstart 28: evalrealselectstart -> evalrealselectbb1in : A'=0, [], cost: 9 39: evalrealselectstart -> evalrealselectbb1in : A'=-1+B, C'=-1+B, D'=B, E'=-1+B, [ B>=2 ], cost: 3+2*(-1+B)*B+6*B-(-1+B)^2 Removed unreachable locations (and leaf rules with constant cost): Start location: evalrealselectstart 39: evalrealselectstart -> evalrealselectbb1in : A'=-1+B, C'=-1+B, D'=B, E'=-1+B, [ B>=2 ], cost: 3+2*(-1+B)*B+6*B-(-1+B)^2 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalrealselectstart 39: evalrealselectstart -> evalrealselectbb1in : A'=-1+B, C'=-1+B, D'=B, E'=-1+B, [ B>=2 ], cost: 3+2*(-1+B)*B+6*B-(-1+B)^2 Computing asymptotic complexity for rule 39 Solved the limit problem by the following transformations: Created initial limit problem: -1+B (+/+!), 2+6*B+B^2 (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {B==n} resulting limit problem: [solved] Solution: B / n Resulting cost 2+6*n+n^2 has complexity: Poly(n^2) Found new complexity Poly(n^2). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^2) Cpx degree: 2 Solved cost: 2+6*n+n^2 Rule cost: 3+2*(-1+B)*B+6*B-(-1+B)^2 Rule guard: [ B>=2 ] WORST_CASE(Omega(n^2),?) ---------------------------------------- (4) BOUNDS(n^2, INF)