/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 377 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_realselect_start(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb0_in(v_array_size, v_i.0, v_j.0)) :|: TRUE eval_realselect_bb0_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb1_in(v_array_size, 0, v_j.0)) :|: TRUE eval_realselect_bb1_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb2_in(v_array_size, v_i.0, v_j.0)) :|: v_i.0 < v_array_size - 1 eval_realselect_bb1_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb6_in(v_array_size, v_i.0, v_j.0)) :|: v_i.0 >= v_array_size - 1 eval_realselect_bb2_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb3_in(v_array_size, v_i.0, v_i.0 + 1)) :|: TRUE eval_realselect_bb3_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb4_in(v_array_size, v_i.0, v_j.0)) :|: v_j.0 < v_array_size eval_realselect_bb3_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb5_in(v_array_size, v_i.0, v_j.0)) :|: v_j.0 >= v_array_size eval_realselect_bb4_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_4(v_array_size, v_i.0, v_j.0)) :|: TRUE eval_realselect_4(v_array_size, v_i.0, v_j.0) -> Com_2(eval_nondet_start(v_array_size, v_i.0, v_j.0), eval_realselect_5(v_array_size, v_i.0, v_j.0)) :|: TRUE eval_realselect_5(v_array_size, v_i.0, v_j.0) -> Com_2(eval_nondet_start(v_array_size, v_i.0, v_j.0), eval_realselect_6(v_array_size, v_i.0, v_j.0)) :|: TRUE eval_realselect_6(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb3_in(v_array_size, v_i.0, v_j.0 + 1)) :|: TRUE eval_realselect_bb5_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_bb1_in(v_array_size, v_i.0 + 1, v_j.0)) :|: TRUE eval_realselect_bb6_in(v_array_size, v_i.0, v_j.0) -> Com_1(eval_realselect_stop(v_array_size, v_i.0, v_j.0)) :|: TRUE The start-symbols are:[eval_realselect_start_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 76*Ar_1 + 200*Ar_1^2 + 6) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealselectstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_0 + 2 ] (Comp: ?, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb6in(Ar_0, Ar_1, Ar_2)) [ Ar_0 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_0 + 1)) (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselectbb6in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalrealselectstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_0 + 2 ] (Comp: ?, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb6in(Ar_0, Ar_1, Ar_2)) [ Ar_0 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_0 + 1)) (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselectbb6in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealselectstart) = 2 Pol(evalrealselectbb0in) = 2 Pol(evalrealselectbb1in) = 2 Pol(evalrealselectbb2in) = 2 Pol(evalrealselectbb6in) = 1 Pol(evalrealselectbb3in) = 2 Pol(evalrealselectbb4in) = 2 Pol(evalrealselectbb5in) = 2 Pol(evalrealselect4) = 2 Pol(evalnondetstart) = 0 Pol(evalrealselect5) = 2 Pol(evalrealselect6) = 2 Pol(evalrealselectstop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalrealselectbb6in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2)) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb6in(Ar_0, Ar_1, Ar_2)) [ Ar_0 + 1 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalrealselectstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_0 + 2 ] (Comp: 2, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb6in(Ar_0, Ar_1, Ar_2)) [ Ar_0 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_0 + 1)) (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(Ar_0 + 1, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evalrealselectbb6in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalrealselect4: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalrealselect5: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalrealselect6: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalrealselectbb1in: X_1 >= 0 For symbol evalrealselectbb2in: X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalrealselectbb3in: X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalrealselectbb4in: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalrealselectbb5in: X_3 - 2 >= 0 /\ X_2 + X_3 - 4 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ -X_1 + X_3 - 2 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0 For symbol evalrealselectbb6in: X_1 - X_2 + 1 >= 0 /\ X_1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalrealselectbb6in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_1 + 1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_2 - 2 >= 0 /\ Ar_1 + Ar_2 - 4 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ -Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb6in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ Ar_0 + 1 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 2 ] (Comp: 1, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalrealselectstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 4*V_2 Pol(evalrealselectstart) = 4*V_2 - 4 Pol(evalrealselectbb6in) = -4*V_1 + 4*V_2 - 4 Pol(evalrealselectstop) = -4*V_1 + 4*V_2 - 4 Pol(evalrealselectbb5in) = -4*V_1 + 4*V_2 - 7 Pol(evalrealselectbb1in) = -4*V_1 + 4*V_2 - 4 Pol(evalrealselect6) = -4*V_1 + 4*V_2 - 6 Pol(evalrealselectbb3in) = -4*V_1 + 4*V_2 - 6 Pol(evalrealselect5) = -4*V_1 + 4*V_2 - 6 Pol(evalnondetstart) = 0 Pol(evalrealselect4) = -4*V_1 + 4*V_2 - 6 Pol(evalrealselectbb4in) = -4*V_1 + 4*V_2 - 6 Pol(evalrealselectbb2in) = -4*V_1 + 4*V_2 - 5 Pol(evalrealselectbb0in) = 4*V_2 - 4 orients all transitions weakly and the transitions evalrealselectbb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_2 - 2 >= 0 /\ Ar_1 + Ar_2 - 4 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ -Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 ] evalrealselectbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 2 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalrealselectbb6in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_1 + 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 4*Ar_1, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_2 - 2 >= 0 /\ Ar_1 + Ar_2 - 4 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ -Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 4*Ar_1, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: 4*Ar_1, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb6in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ Ar_0 + 1 >= Ar_1 ] (Comp: 4*Ar_1, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 2 ] (Comp: 1, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalrealselectstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealselectbb4in) = 5*V_2 - 5*V_3 + 2 Pol(evalrealselect4) = 5*V_2 - 5*V_3 + 1 Pol(evalrealselectbb3in) = 5*V_2 - 5*V_3 + 3 Pol(evalrealselect6) = 5*V_2 - 5*V_3 - 1 Pol(evalrealselect5) = 5*V_2 - 5*V_3 Pol(evalnondetstart) = 0 and size complexities S("evalrealselectstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("evalrealselectstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalrealselectstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2))", 0-0) = 0 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalrealselectbb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2))", 0-2) = Ar_2 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 2 ]", 0-0) = Ar_1 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 2 ]", 0-1) = Ar_1 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 2 ]", 0-2) = Ar_1 + Ar_2 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb6in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\\ Ar_0 + 1 >= Ar_1 ]", 0-0) = Ar_1 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb6in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\\ Ar_0 + 1 >= Ar_1 ]", 0-1) = Ar_1 S("evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb6in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\\ Ar_0 + 1 >= Ar_1 ]", 0-2) = Ar_1 + Ar_2 S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_1 S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalrealselectbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_1 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 ]", 0-0) = Ar_1 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_1 >= Ar_2 + 1 ]", 0-2) = Ar_1 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-0) = Ar_1 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-1) = Ar_1 S("evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_1 ]", 0-2) = Ar_1 S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_1 S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalrealselectbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_1 S("evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_1 S("evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_1 S("evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 1-0) = Ar_1 S("evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 1-1) = Ar_1 S("evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 1-2) = Ar_1 S("evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_1 S("evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_1 S("evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 1-0) = Ar_1 S("evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 1-1) = Ar_1 S("evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 1-2) = Ar_1 S("evalrealselect6(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_1 S("evalrealselect6(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalrealselect6(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 3 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ -Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_1 S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_2 - 2 >= 0 /\\ Ar_1 + Ar_2 - 4 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ -Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_1 S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_2 - 2 >= 0 /\\ Ar_1 + Ar_2 - 4 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ -Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalrealselectbb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_2 - 2 >= 0 /\\ Ar_1 + Ar_2 - 4 >= 0 /\\ -Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 2 >= 0 /\\ -Ar_0 + Ar_2 - 2 >= 0 /\\ Ar_1 - 2 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_1 S("evalrealselectbb6in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_1 + 1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_1 S("evalrealselectbb6in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_1 + 1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalrealselectbb6in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_1 + 1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_1 + Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 orients the transitions evalrealselectbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] evalrealselect6(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] weakly and the transitions evalrealselectbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] evalrealselect6(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalrealselectbb6in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectstop(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_1 + 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 4*Ar_1, Cost: 1) evalrealselectbb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_2 - 2 >= 0 /\ Ar_1 + Ar_2 - 4 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 2 >= 0 /\ -Ar_0 + Ar_2 - 2 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 40*Ar_1^2 + 12*Ar_1, Cost: 1) evalrealselect6(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 40*Ar_1^2 + 12*Ar_1, Cost: 1) evalrealselect5(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect6(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 40*Ar_1^2 + 12*Ar_1, Cost: 1) evalrealselect4(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalrealselect5(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 40*Ar_1^2 + 12*Ar_1, Cost: 1) evalrealselectbb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselect4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 4*Ar_1, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb5in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: 40*Ar_1^2 + 12*Ar_1, Cost: 1) evalrealselectbb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: 4*Ar_1, Cost: 1) evalrealselectbb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb3in(Ar_0, Ar_1, Ar_0 + 1)) [ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb6in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ Ar_0 + 1 >= Ar_1 ] (Comp: 4*Ar_1, Cost: 1) evalrealselectbb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb2in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 2 ] (Comp: 1, Cost: 1) evalrealselectbb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb1in(0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalrealselectstart(Ar_0, Ar_1, Ar_2) -> Com_1(evalrealselectbb0in(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 Complexity upper bound 76*Ar_1 + 200*Ar_1^2 + 6 Time: 0.349 sec (SMT: 0.283 sec) ---------------------------------------- (2) BOUNDS(1, n^2)