/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).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, 288 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_sipmabubble_start(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb0_in(v_i.0, v_j.0, v_n)) :|: TRUE eval_sipmabubble_bb0_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb1_in(v_n, v_j.0, v_n)) :|: TRUE eval_sipmabubble_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb2_in(v_i.0, 0, v_n)) :|: v_i.0 >= 0 eval_sipmabubble_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb5_in(v_i.0, v_j.0, v_n)) :|: v_i.0 < 0 eval_sipmabubble_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb3_in(v_i.0, v_j.0, v_n)) :|: v_j.0 <= v_i.0 - 1 eval_sipmabubble_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb4_in(v_i.0, v_j.0, v_n)) :|: v_j.0 > v_i.0 - 1 eval_sipmabubble_bb3_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_2(v_i.0, v_j.0, v_n)) :|: TRUE eval_sipmabubble_2(v_i.0, v_j.0, v_n) -> Com_2(eval_nondet_start(v_i.0, v_j.0, v_n), eval_sipmabubble_3(v_i.0, v_j.0, v_n)) :|: TRUE eval_sipmabubble_3(v_i.0, v_j.0, v_n) -> Com_2(eval_nondet_start(v_i.0, v_j.0, v_n), eval_sipmabubble_4(v_i.0, v_j.0, v_n)) :|: TRUE eval_sipmabubble_4(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb2_in(v_i.0, v_j.0 + 1, v_n)) :|: TRUE eval_sipmabubble_bb4_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb1_in(v_i.0 - 1, v_j.0, v_n)) :|: TRUE eval_sipmabubble_bb5_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_stop(v_i.0, v_j.0, v_n)) :|: TRUE The start-symbols are:[eval_sipmabubble_start_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 159*Ar_1 + 75*Ar_1^2 + 90) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_0 - 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestart(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) evalsipmabubblestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_0 - 1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalsipmabubblestart) = 2 Pol(evalsipmabubblebb0in) = 2 Pol(evalsipmabubblebb1in) = 2 Pol(evalsipmabubblebb2in) = 2 Pol(evalsipmabubblebb5in) = 1 Pol(evalsipmabubblebb3in) = 2 Pol(evalsipmabubblebb4in) = 2 Pol(evalsipmabubble2) = 2 Pol(evalnondetstart) = 0 Pol(evalsipmabubble3) = 2 Pol(evalsipmabubble4) = 2 Pol(evalsipmabubblestop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2)) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_0 - 1, Ar_1, Ar_2)) (Comp: 2, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestart(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 evalsipmabubble2: X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalsipmabubble3: X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalsipmabubble4: X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalsipmabubblebb1in: -X_1 + X_2 >= 0 For symbol evalsipmabubblebb2in: X_2 - X_3 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalsipmabubblebb3in: X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0 For symbol evalsipmabubblebb4in: X_2 - X_3 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalsipmabubblebb5in: -X_1 + X_2 >= 0 /\ -X_1 - 1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_1 >= 0 /\ -Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0)) [ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 3*V_2 + 3 Pol(evalsipmabubblestart) = 3*V_2 + 3 Pol(evalsipmabubblebb5in) = 3*V_1 Pol(evalsipmabubblestop) = 3*V_1 Pol(evalsipmabubblebb4in) = 3*V_1 + 1 Pol(evalsipmabubblebb1in) = 3*V_1 + 3 Pol(evalsipmabubble4) = 3*V_1 + 2 Pol(evalsipmabubblebb2in) = 3*V_1 + 2 Pol(evalsipmabubble3) = 3*V_1 + 2 Pol(evalnondetstart) = 0 Pol(evalsipmabubble2) = 3*V_1 + 2 Pol(evalsipmabubblebb3in) = 3*V_1 + 2 Pol(evalsipmabubblebb0in) = 3*V_2 + 3 orients all transitions weakly and the transitions evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 ] evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0)) [ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_1 >= 0 /\ -Ar_0 - 1 >= 0 ] (Comp: 3*Ar_1 + 3, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 3*Ar_1 + 3, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 3*Ar_1 + 3, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0)) [ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalsipmabubblebb3in) = 5*V_1 - 5*V_3 - 1 Pol(evalsipmabubble2) = 5*V_1 - 5*V_3 - 2 Pol(evalsipmabubblebb2in) = 5*V_1 - 5*V_3 Pol(evalsipmabubble4) = 5*V_1 - 5*V_3 - 4 Pol(evalsipmabubble3) = 5*V_1 - 5*V_3 - 3 Pol(evalnondetstart) = 0 and size complexities S("evalsipmabubblestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("evalsipmabubblestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalsipmabubblestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2))", 0-0) = Ar_1 S("evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2))", 0-1) = Ar_1 S("evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2))", 0-2) = Ar_2 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0)) [ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_1 + 1 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0)) [ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0)) [ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = 0 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 ]", 0-0) = Ar_1 + 1 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 ]", 0-2) = Ar_1 + Ar_2 + 1 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_2 + 1 ]", 0-0) = Ar_1 + 1 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_0 >= Ar_2 + 1 ]", 0-2) = Ar_1 + 1 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_0 ]", 0-0) = Ar_1 + 1 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_0 ]", 0-1) = Ar_1 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= Ar_0 ]", 0-2) = Ar_1 + 1 S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_1 + 1 S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = Ar_1 S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = Ar_1 + 1 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_1 + 1 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = Ar_1 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = Ar_1 + 1 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 1-0) = Ar_1 + 1 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 1-1) = Ar_1 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 1-2) = Ar_1 + 1 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_1 + 1 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = Ar_1 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = Ar_1 + 1 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 1-0) = Ar_1 + 1 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 1-1) = Ar_1 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 1-2) = Ar_1 + 1 S("evalsipmabubble4(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_1 + 1 S("evalsipmabubble4(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = Ar_1 S("evalsipmabubble4(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 - 1 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = Ar_1 + 1 S("evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-0) = Ar_1 + 1 S("evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_0 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 >= 0 /\\ -Ar_0 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 ]", 0-2) = Ar_1 + 1 S("evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_1 >= 0 /\\ -Ar_0 - 1 >= 0 ]", 0-0) = Ar_1 + 1 S("evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_1 >= 0 /\\ -Ar_0 - 1 >= 0 ]", 0-1) = Ar_1 S("evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_1 >= 0 /\\ -Ar_0 - 1 >= 0 ]", 0-2) = Ar_1 + Ar_2 + 1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 orients the transitions evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ] evalsipmabubble4(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] weakly and the transitions evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ] evalsipmabubble4(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_1 >= 0 /\ -Ar_0 - 1 >= 0 ] (Comp: 3*Ar_1 + 3, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 15*Ar_1^2 + 30*Ar_1 + 15, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 15*Ar_1^2 + 30*Ar_1 + 15, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble4(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 15*Ar_1^2 + 30*Ar_1 + 15, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2) -> Com_2(evalnondetstart(Ar_0, Ar_1, Ar_2), evalsipmabubble3(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 15*Ar_1^2 + 30*Ar_1 + 15, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 3*Ar_1 + 3, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_0 ] (Comp: 15*Ar_1^2 + 30*Ar_1 + 15, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_2 + 1 ] (Comp: 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 3*Ar_1 + 3, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0)) [ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 1, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2)) (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1, Ar_2) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 Complexity upper bound 159*Ar_1 + 75*Ar_1^2 + 90 Time: 0.269 sec (SMT: 0.218 sec) ---------------------------------------- (2) BOUNDS(1, n^2)