5.16/2.50 WORST_CASE(Omega(n^2), O(n^2)) 5.40/2.50 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 5.40/2.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.40/2.50 5.40/2.50 5.40/2.50 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). 5.40/2.50 5.40/2.50 (0) CpxIntTrs 5.40/2.50 (1) Koat Proof [FINISHED, 310 ms] 5.40/2.50 (2) BOUNDS(1, n^2) 5.40/2.50 (3) Loat Proof [FINISHED, 705 ms] 5.40/2.50 (4) BOUNDS(n^2, INF) 5.40/2.50 5.40/2.50 5.40/2.50 ---------------------------------------- 5.40/2.50 5.40/2.50 (0) 5.40/2.50 Obligation: 5.40/2.50 Complexity Int TRS consisting of the following rules: 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 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 5.40/2.50 5.40/2.50 The start-symbols are:[eval_realselect_start_5] 5.40/2.50 5.40/2.50 5.40/2.50 ---------------------------------------- 5.40/2.50 5.40/2.50 (1) Koat Proof (FINISHED) 5.40/2.50 YES(?, 37*ar_1 + 21*ar_1^2 + 13) 5.40/2.50 5.40/2.50 5.40/2.50 5.40/2.50 Initial complexity problem: 5.40/2.50 5.40/2.50 1: T: 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 start location: koat_start 5.40/2.50 5.40/2.50 leaf cost: 0 5.40/2.50 5.40/2.50 5.40/2.50 5.40/2.50 Repeatedly propagating knowledge in problem 1 produces the following problem: 5.40/2.50 5.40/2.50 2: T: 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 start location: koat_start 5.40/2.50 5.40/2.50 leaf cost: 0 5.40/2.50 5.40/2.50 5.40/2.50 5.40/2.50 A polynomial rank function with 5.40/2.50 5.40/2.50 Pol(evalrealselectstart) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselectbb0in) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselect0) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselect1) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselect2) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselect3) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselect4) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselect5) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselect6) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselectbb1in) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselectbb2in) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselectbb5in) = 1 5.40/2.50 5.40/2.50 Pol(evalrealselectbb3in) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselectbb4in) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselect19) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselect20) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselect27) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselect28) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselectstop) = 0 5.40/2.50 5.40/2.50 Pol(koat_start) = 2 5.40/2.50 5.40/2.50 orients all transitions weakly and the transitions 5.40/2.50 5.40/2.50 evalrealselectbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealselectstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 5.40/2.50 5.40/2.50 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 ] 5.40/2.50 5.40/2.50 strictly and produces the following problem: 5.40/2.50 5.40/2.50 3: T: 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 start location: koat_start 5.40/2.50 5.40/2.50 leaf cost: 0 5.40/2.50 5.40/2.50 5.40/2.50 5.40/2.50 A polynomial rank function with 5.40/2.50 5.40/2.50 Pol(evalrealselectstart) = V_2 5.40/2.50 5.40/2.50 Pol(evalrealselectbb0in) = V_2 5.40/2.50 5.40/2.50 Pol(evalrealselect0) = V_2 5.40/2.50 5.40/2.50 Pol(evalrealselect1) = V_2 5.40/2.50 5.40/2.50 Pol(evalrealselect2) = V_2 5.40/2.50 5.40/2.50 Pol(evalrealselect3) = V_2 5.40/2.50 5.40/2.50 Pol(evalrealselect4) = V_2 5.40/2.50 5.40/2.50 Pol(evalrealselect5) = V_2 5.40/2.50 5.40/2.50 Pol(evalrealselect6) = V_2 5.40/2.50 5.40/2.50 Pol(evalrealselectbb1in) = -V_1 + V_2 5.40/2.50 5.40/2.50 Pol(evalrealselectbb2in) = -V_1 + V_2 - 1 5.40/2.50 5.40/2.50 Pol(evalrealselectbb5in) = -V_1 + V_2 5.40/2.50 5.40/2.50 Pol(evalrealselectbb3in) = -V_1 + V_2 - 1 5.40/2.50 5.40/2.50 Pol(evalrealselectbb4in) = -V_1 + V_2 - 1 5.40/2.50 5.40/2.50 Pol(evalrealselect19) = -V_1 + V_2 - 1 5.40/2.50 5.40/2.50 Pol(evalrealselect20) = -V_1 + V_2 - 1 5.40/2.50 5.40/2.50 Pol(evalrealselect27) = V_2 - V_5 5.40/2.50 5.40/2.50 Pol(evalrealselect28) = V_2 - V_5 5.40/2.50 5.40/2.50 Pol(evalrealselectstop) = -V_1 + V_2 5.40/2.50 5.40/2.50 Pol(koat_start) = V_2 5.40/2.50 5.40/2.50 orients all transitions weakly and the transition 5.40/2.50 5.40/2.50 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 ] 5.40/2.50 5.40/2.50 strictly and produces the following problem: 5.40/2.50 5.40/2.50 4: T: 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 start location: koat_start 5.40/2.50 5.40/2.50 leaf cost: 0 5.40/2.50 5.40/2.50 5.40/2.50 5.40/2.50 A polynomial rank function with 5.40/2.50 5.40/2.50 Pol(evalrealselectbb4in) = 5 5.40/2.50 5.40/2.50 Pol(evalrealselect19) = 4 5.40/2.50 5.40/2.50 Pol(evalrealselectbb3in) = 6 5.40/2.50 5.40/2.50 Pol(evalrealselectbb2in) = 6 5.40/2.50 5.40/2.50 Pol(evalrealselect28) = 1 5.40/2.50 5.40/2.50 Pol(evalrealselectbb1in) = 0 5.40/2.50 5.40/2.50 Pol(evalrealselect27) = 2 5.40/2.50 5.40/2.50 Pol(evalrealselect20) = 3 5.40/2.50 5.40/2.50 and size complexities 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 orients the transitions 5.40/2.50 5.40/2.50 evalrealselectbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealselect19(ar_0, ar_1, ar_2, ar_3, ar_4)) 5.40/2.50 5.40/2.50 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 ] 5.40/2.50 5.40/2.50 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 ] 5.40/2.50 5.40/2.50 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 ] 5.40/2.50 5.40/2.50 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 ] 5.40/2.50 5.40/2.50 evalrealselect28(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealselectbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 5.40/2.50 5.40/2.50 evalrealselect27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealselect28(ar_0, ar_1, ar_2, ar_3, ar_4)) 5.40/2.50 5.40/2.50 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)) 5.40/2.50 5.40/2.50 evalrealselect19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealselect20(ar_0, ar_1, ar_2, ar_3, ar_4)) 5.40/2.50 5.40/2.50 weakly and the transitions 5.40/2.50 5.40/2.50 evalrealselectbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealselect19(ar_0, ar_1, ar_2, ar_3, ar_4)) 5.40/2.50 5.40/2.50 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 ] 5.40/2.50 5.40/2.50 evalrealselect28(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealselectbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 5.40/2.50 5.40/2.50 evalrealselect27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealselect28(ar_0, ar_1, ar_2, ar_3, ar_4)) 5.40/2.50 5.40/2.50 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)) 5.40/2.50 5.40/2.50 evalrealselect19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealselect20(ar_0, ar_1, ar_2, ar_3, ar_4)) 5.40/2.50 5.40/2.50 strictly and produces the following problem: 5.40/2.50 5.40/2.50 5: T: 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 start location: koat_start 5.40/2.50 5.40/2.50 leaf cost: 0 5.40/2.50 5.40/2.50 5.40/2.50 5.40/2.50 A polynomial rank function with 5.40/2.50 5.40/2.50 Pol(evalrealselectbb3in) = V_2 - V_4 5.40/2.50 5.40/2.50 Pol(evalrealselectbb2in) = V_2 - V_3 5.40/2.50 5.40/2.50 and size complexities 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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) = ? 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 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 5.40/2.50 5.40/2.50 orients the transitions 5.40/2.50 5.40/2.50 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 ] 5.40/2.50 5.40/2.50 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 ] 5.40/2.50 5.40/2.50 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 ] 5.40/2.50 5.40/2.50 weakly and the transition 5.40/2.50 5.40/2.50 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 ] 5.40/2.50 5.40/2.50 strictly and produces the following problem: 5.40/2.50 5.40/2.50 6: T: 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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)) 5.40/2.50 5.40/2.50 (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 ] 5.40/2.50 5.40/2.50 start location: koat_start 5.40/2.50 5.40/2.50 leaf cost: 0 5.40/2.50 5.40/2.50 5.40/2.50 5.40/2.50 Repeatedly propagating knowledge in problem 6 produces the following problem: 5.40/2.50 5.40/2.50 7: T: 5.40/2.50 5.40/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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 ] 5.41/2.50 5.41/2.50 (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 ] 5.41/2.50 5.41/2.50 (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 ] 5.41/2.50 5.41/2.50 (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 ] 5.41/2.50 5.41/2.50 (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 ] 5.41/2.50 5.41/2.50 (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 ] 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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)) 5.41/2.50 5.41/2.50 (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 ] 5.41/2.51 5.41/2.51 start location: koat_start 5.41/2.51 5.41/2.51 leaf cost: 0 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Complexity upper bound 37*ar_1 + 21*ar_1^2 + 13 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Time: 0.289 sec (SMT: 0.200 sec) 5.41/2.51 5.41/2.51 5.41/2.51 ---------------------------------------- 5.41/2.51 5.41/2.51 (2) 5.41/2.51 BOUNDS(1, n^2) 5.41/2.51 5.41/2.51 ---------------------------------------- 5.41/2.51 5.41/2.51 (3) Loat Proof (FINISHED) 5.41/2.51 5.41/2.51 5.41/2.51 ### Pre-processing the ITS problem ### 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Initial linear ITS problem 5.41/2.51 5.41/2.51 Start location: evalrealselectstart 5.41/2.51 5.41/2.51 0: evalrealselectstart -> evalrealselectbb0in : [], cost: 1 5.41/2.51 5.41/2.51 1: evalrealselectbb0in -> evalrealselect0 : [], cost: 1 5.41/2.51 5.41/2.51 2: evalrealselect0 -> evalrealselect1 : [], cost: 1 5.41/2.51 5.41/2.51 3: evalrealselect1 -> evalrealselect2 : [], cost: 1 5.41/2.51 5.41/2.51 4: evalrealselect2 -> evalrealselect3 : [], cost: 1 5.41/2.51 5.41/2.51 5: evalrealselect3 -> evalrealselect4 : [], cost: 1 5.41/2.51 5.41/2.51 6: evalrealselect4 -> evalrealselect5 : [], cost: 1 5.41/2.51 5.41/2.51 7: evalrealselect5 -> evalrealselect6 : [], cost: 1 5.41/2.51 5.41/2.51 8: evalrealselect6 -> evalrealselectbb1in : A'=0, [], cost: 1 5.41/2.51 5.41/2.51 9: evalrealselectbb1in -> evalrealselectbb2in : C'=A, [ B>=2+A ], cost: 1 5.41/2.51 5.41/2.51 10: evalrealselectbb1in -> evalrealselectbb5in : [ 1+A>=B ], cost: 1 5.41/2.51 5.41/2.51 11: evalrealselectbb2in -> evalrealselectbb3in : D'=1+C, [ B>=2+C ], cost: 1 5.41/2.51 5.41/2.51 12: evalrealselectbb2in -> evalrealselectbb4in : D'=1+C, [ 1+C>=B ], cost: 1 5.41/2.51 5.41/2.51 13: evalrealselectbb3in -> evalrealselectbb2in : C'=D, [ free>=1+free_1 ], cost: 1 5.41/2.51 5.41/2.51 14: evalrealselectbb3in -> evalrealselectbb2in : C'=D, [ free_3>=free_2 ], cost: 1 5.41/2.51 5.41/2.51 15: evalrealselectbb4in -> evalrealselect19 : [], cost: 1 5.41/2.51 5.41/2.51 16: evalrealselect19 -> evalrealselect20 : [], cost: 1 5.41/2.51 5.41/2.51 17: evalrealselect20 -> evalrealselect27 : E'=1+A, [], cost: 1 5.41/2.51 5.41/2.51 18: evalrealselect27 -> evalrealselect28 : [], cost: 1 5.41/2.51 5.41/2.51 19: evalrealselect28 -> evalrealselectbb1in : A'=E, [], cost: 1 5.41/2.51 5.41/2.51 20: evalrealselectbb5in -> evalrealselectstop : [], cost: 1 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Removed unreachable and leaf rules: 5.41/2.51 5.41/2.51 Start location: evalrealselectstart 5.41/2.51 5.41/2.51 0: evalrealselectstart -> evalrealselectbb0in : [], cost: 1 5.41/2.51 5.41/2.51 1: evalrealselectbb0in -> evalrealselect0 : [], cost: 1 5.41/2.51 5.41/2.51 2: evalrealselect0 -> evalrealselect1 : [], cost: 1 5.41/2.51 5.41/2.51 3: evalrealselect1 -> evalrealselect2 : [], cost: 1 5.41/2.51 5.41/2.51 4: evalrealselect2 -> evalrealselect3 : [], cost: 1 5.41/2.51 5.41/2.51 5: evalrealselect3 -> evalrealselect4 : [], cost: 1 5.41/2.51 5.41/2.51 6: evalrealselect4 -> evalrealselect5 : [], cost: 1 5.41/2.51 5.41/2.51 7: evalrealselect5 -> evalrealselect6 : [], cost: 1 5.41/2.51 5.41/2.51 8: evalrealselect6 -> evalrealselectbb1in : A'=0, [], cost: 1 5.41/2.51 5.41/2.51 9: evalrealselectbb1in -> evalrealselectbb2in : C'=A, [ B>=2+A ], cost: 1 5.41/2.51 5.41/2.51 11: evalrealselectbb2in -> evalrealselectbb3in : D'=1+C, [ B>=2+C ], cost: 1 5.41/2.51 5.41/2.51 12: evalrealselectbb2in -> evalrealselectbb4in : D'=1+C, [ 1+C>=B ], cost: 1 5.41/2.51 5.41/2.51 13: evalrealselectbb3in -> evalrealselectbb2in : C'=D, [ free>=1+free_1 ], cost: 1 5.41/2.51 5.41/2.51 14: evalrealselectbb3in -> evalrealselectbb2in : C'=D, [ free_3>=free_2 ], cost: 1 5.41/2.51 5.41/2.51 15: evalrealselectbb4in -> evalrealselect19 : [], cost: 1 5.41/2.51 5.41/2.51 16: evalrealselect19 -> evalrealselect20 : [], cost: 1 5.41/2.51 5.41/2.51 17: evalrealselect20 -> evalrealselect27 : E'=1+A, [], cost: 1 5.41/2.51 5.41/2.51 18: evalrealselect27 -> evalrealselect28 : [], cost: 1 5.41/2.51 5.41/2.51 19: evalrealselect28 -> evalrealselectbb1in : A'=E, [], cost: 1 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Simplified all rules, resulting in: 5.41/2.51 5.41/2.51 Start location: evalrealselectstart 5.41/2.51 5.41/2.51 0: evalrealselectstart -> evalrealselectbb0in : [], cost: 1 5.41/2.51 5.41/2.51 1: evalrealselectbb0in -> evalrealselect0 : [], cost: 1 5.41/2.51 5.41/2.51 2: evalrealselect0 -> evalrealselect1 : [], cost: 1 5.41/2.51 5.41/2.51 3: evalrealselect1 -> evalrealselect2 : [], cost: 1 5.41/2.51 5.41/2.51 4: evalrealselect2 -> evalrealselect3 : [], cost: 1 5.41/2.51 5.41/2.51 5: evalrealselect3 -> evalrealselect4 : [], cost: 1 5.41/2.51 5.41/2.51 6: evalrealselect4 -> evalrealselect5 : [], cost: 1 5.41/2.51 5.41/2.51 7: evalrealselect5 -> evalrealselect6 : [], cost: 1 5.41/2.51 5.41/2.51 8: evalrealselect6 -> evalrealselectbb1in : A'=0, [], cost: 1 5.41/2.51 5.41/2.51 9: evalrealselectbb1in -> evalrealselectbb2in : C'=A, [ B>=2+A ], cost: 1 5.41/2.51 5.41/2.51 11: evalrealselectbb2in -> evalrealselectbb3in : D'=1+C, [ B>=2+C ], cost: 1 5.41/2.51 5.41/2.51 12: evalrealselectbb2in -> evalrealselectbb4in : D'=1+C, [ 1+C>=B ], cost: 1 5.41/2.51 5.41/2.51 14: evalrealselectbb3in -> evalrealselectbb2in : C'=D, [], cost: 1 5.41/2.51 5.41/2.51 15: evalrealselectbb4in -> evalrealselect19 : [], cost: 1 5.41/2.51 5.41/2.51 16: evalrealselect19 -> evalrealselect20 : [], cost: 1 5.41/2.51 5.41/2.51 17: evalrealselect20 -> evalrealselect27 : E'=1+A, [], cost: 1 5.41/2.51 5.41/2.51 18: evalrealselect27 -> evalrealselect28 : [], cost: 1 5.41/2.51 5.41/2.51 19: evalrealselect28 -> evalrealselectbb1in : A'=E, [], cost: 1 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 ### Simplification by acceleration and chaining ### 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Eliminated locations (on linear paths): 5.41/2.51 5.41/2.51 Start location: evalrealselectstart 5.41/2.51 5.41/2.51 28: evalrealselectstart -> evalrealselectbb1in : A'=0, [], cost: 9 5.41/2.51 5.41/2.51 9: evalrealselectbb1in -> evalrealselectbb2in : C'=A, [ B>=2+A ], cost: 1 5.41/2.51 5.41/2.51 29: evalrealselectbb2in -> evalrealselectbb2in : C'=1+C, D'=1+C, [ B>=2+C ], cost: 2 5.41/2.51 5.41/2.51 34: evalrealselectbb2in -> evalrealselectbb1in : A'=1+A, D'=1+C, E'=1+A, [ 1+C>=B ], cost: 6 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Accelerating simple loops of location 10. 5.41/2.51 5.41/2.51 Accelerating the following rules: 5.41/2.51 5.41/2.51 29: evalrealselectbb2in -> evalrealselectbb2in : C'=1+C, D'=1+C, [ B>=2+C ], cost: 2 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Accelerated rule 29 with metering function -1-C+B, yielding the new rule 35. 5.41/2.51 5.41/2.51 Removing the simple loops: 29. 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Accelerated all simple loops using metering functions (where possible): 5.41/2.51 5.41/2.51 Start location: evalrealselectstart 5.41/2.51 5.41/2.51 28: evalrealselectstart -> evalrealselectbb1in : A'=0, [], cost: 9 5.41/2.51 5.41/2.51 9: evalrealselectbb1in -> evalrealselectbb2in : C'=A, [ B>=2+A ], cost: 1 5.41/2.51 5.41/2.51 34: evalrealselectbb2in -> evalrealselectbb1in : A'=1+A, D'=1+C, E'=1+A, [ 1+C>=B ], cost: 6 5.41/2.51 5.41/2.51 35: evalrealselectbb2in -> evalrealselectbb2in : C'=-1+B, D'=-1+B, [ B>=2+C ], cost: -2-2*C+2*B 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Chained accelerated rules (with incoming rules): 5.41/2.51 5.41/2.51 Start location: evalrealselectstart 5.41/2.51 5.41/2.51 28: evalrealselectstart -> evalrealselectbb1in : A'=0, [], cost: 9 5.41/2.51 5.41/2.51 9: evalrealselectbb1in -> evalrealselectbb2in : C'=A, [ B>=2+A ], cost: 1 5.41/2.51 5.41/2.51 36: evalrealselectbb1in -> evalrealselectbb2in : C'=-1+B, D'=-1+B, [ B>=2+A ], cost: -1-2*A+2*B 5.41/2.51 5.41/2.51 34: evalrealselectbb2in -> evalrealselectbb1in : A'=1+A, D'=1+C, E'=1+A, [ 1+C>=B ], cost: 6 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Eliminated locations (on tree-shaped paths): 5.41/2.51 5.41/2.51 Start location: evalrealselectstart 5.41/2.51 5.41/2.51 28: evalrealselectstart -> evalrealselectbb1in : A'=0, [], cost: 9 5.41/2.51 5.41/2.51 37: evalrealselectbb1in -> evalrealselectbb1in : A'=1+A, C'=-1+B, D'=B, E'=1+A, [ B>=2+A ], cost: 5-2*A+2*B 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Accelerating simple loops of location 9. 5.41/2.51 5.41/2.51 Accelerating the following rules: 5.41/2.51 5.41/2.51 37: evalrealselectbb1in -> evalrealselectbb1in : A'=1+A, C'=-1+B, D'=B, E'=1+A, [ B>=2+A ], cost: 5-2*A+2*B 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Accelerated rule 37 with metering function -1-A+B, yielding the new rule 38. 5.41/2.51 5.41/2.51 Removing the simple loops: 37. 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Accelerated all simple loops using metering functions (where possible): 5.41/2.51 5.41/2.51 Start location: evalrealselectstart 5.41/2.51 5.41/2.51 28: evalrealselectstart -> evalrealselectbb1in : A'=0, [], cost: 9 5.41/2.51 5.41/2.51 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*(1+A-B)*B+2*A*(1+A-B)+6*B 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Chained accelerated rules (with incoming rules): 5.41/2.51 5.41/2.51 Start location: evalrealselectstart 5.41/2.51 5.41/2.51 28: evalrealselectstart -> evalrealselectbb1in : A'=0, [], cost: 9 5.41/2.51 5.41/2.51 39: evalrealselectstart -> evalrealselectbb1in : A'=-1+B, C'=-1+B, D'=B, E'=-1+B, [ B>=2 ], cost: 3+2*(-1+B)*B-(-1+B)^2+6*B 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Removed unreachable locations (and leaf rules with constant cost): 5.41/2.51 5.41/2.51 Start location: evalrealselectstart 5.41/2.51 5.41/2.51 39: evalrealselectstart -> evalrealselectbb1in : A'=-1+B, C'=-1+B, D'=B, E'=-1+B, [ B>=2 ], cost: 3+2*(-1+B)*B-(-1+B)^2+6*B 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 ### Computing asymptotic complexity ### 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Fully simplified ITS problem 5.41/2.51 5.41/2.51 Start location: evalrealselectstart 5.41/2.51 5.41/2.51 39: evalrealselectstart -> evalrealselectbb1in : A'=-1+B, C'=-1+B, D'=B, E'=-1+B, [ B>=2 ], cost: 3+2*(-1+B)*B-(-1+B)^2+6*B 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Computing asymptotic complexity for rule 39 5.41/2.51 5.41/2.51 Solved the limit problem by the following transformations: 5.41/2.51 5.41/2.51 Created initial limit problem: 5.41/2.51 5.41/2.51 -1+B (+/+!), 2+B^2+6*B (+) [not solved] 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 removing all constraints (solved by SMT) 5.41/2.51 5.41/2.51 resulting limit problem: [solved] 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 applying transformation rule (C) using substitution {B==n} 5.41/2.51 5.41/2.51 resulting limit problem: 5.41/2.51 5.41/2.51 [solved] 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Solution: 5.41/2.51 5.41/2.51 B / n 5.41/2.51 5.41/2.51 Resulting cost 2+n^2+6*n has complexity: Poly(n^2) 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Found new complexity Poly(n^2). 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 Obtained the following overall complexity (w.r.t. the length of the input n): 5.41/2.51 5.41/2.51 Complexity: Poly(n^2) 5.41/2.51 5.41/2.51 Cpx degree: 2 5.41/2.51 5.41/2.51 Solved cost: 2+n^2+6*n 5.41/2.51 5.41/2.51 Rule cost: 3+2*(-1+B)*B-(-1+B)^2+6*B 5.41/2.51 5.41/2.51 Rule guard: [ B>=2 ] 5.41/2.51 5.41/2.51 5.41/2.51 5.41/2.51 WORST_CASE(Omega(n^2),?) 5.41/2.51 5.41/2.51 5.41/2.51 ---------------------------------------- 5.41/2.51 5.41/2.51 (4) 5.41/2.51 BOUNDS(n^2, INF) 5.41/2.54 EOF