/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 139 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 1025 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_sipmabubble_start(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb0_in(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_bb0_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_0(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_0(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_1(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_1(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_2(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_2(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_3(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_3(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_4(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_4(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_5(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_5(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_6(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_6(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb1_in(v_24, v_n, v_j_0, v_n)) :|: TRUE eval_sipmabubble_bb1_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb2_in(v_24, v_i_0, 0, v_n)) :|: v_i_0 >= 0 eval_sipmabubble_bb1_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb7_in(v_24, v_i_0, v_j_0, v_n)) :|: v_i_0 < 0 eval_sipmabubble_bb2_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb3_in(v_24, v_i_0, v_j_0, v_n)) :|: v_j_0 <= v_i_0 - 1 eval_sipmabubble_bb2_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb6_in(v_24, v_i_0, v_j_0, v_n)) :|: v_j_0 > v_i_0 - 1 eval_sipmabubble_bb3_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb4_in(v_24, v_i_0, v_j_0, v_n)) :|: nondef_0 > nondef_1 eval_sipmabubble_bb3_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb5_in(v_24, v_i_0, v_j_0, v_n)) :|: nondef_0 <= nondef_1 eval_sipmabubble_bb4_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb5_in(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_bb5_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb2_in(v_24, v_i_0, v_j_0 + 1, v_n)) :|: TRUE eval_sipmabubble_bb6_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_29(v_i_0 - 1, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_29(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_30(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_30(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb1_in(v_24, v_24, v_j_0, v_n)) :|: TRUE eval_sipmabubble_bb7_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_stop(v_24, v_i_0, v_j_0, v_n)) :|: TRUE The start-symbols are:[eval_sipmabubble_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 1283*Ar_1 + 30*Ar_1^2 + 2459) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1)) (Comp: ?, Cost: 1) evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1)) (Comp: ?, Cost: 1) evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalsipmabubblestart) = 2 Pol(evalsipmabubblebb0in) = 2 Pol(evalsipmabubble0) = 2 Pol(evalsipmabubble1) = 2 Pol(evalsipmabubble2) = 2 Pol(evalsipmabubble3) = 2 Pol(evalsipmabubble4) = 2 Pol(evalsipmabubble5) = 2 Pol(evalsipmabubble6) = 2 Pol(evalsipmabubblebb1in) = 2 Pol(evalsipmabubblebb2in) = 2 Pol(evalsipmabubblebb7in) = 1 Pol(evalsipmabubblebb3in) = 2 Pol(evalsipmabubblebb6in) = 2 Pol(evalsipmabubblebb4in) = 2 Pol(evalsipmabubblebb5in) = 2 Pol(evalsipmabubble29) = 2 Pol(evalsipmabubble30) = 2 Pol(evalsipmabubblestop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3)) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1)) (Comp: ?, Cost: 1) evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalsipmabubblestart) = V_2 + 2 Pol(evalsipmabubblebb0in) = V_2 + 2 Pol(evalsipmabubble0) = V_2 + 2 Pol(evalsipmabubble1) = V_2 + 2 Pol(evalsipmabubble2) = V_2 + 2 Pol(evalsipmabubble3) = V_2 + 2 Pol(evalsipmabubble4) = V_2 + 2 Pol(evalsipmabubble5) = V_2 + 2 Pol(evalsipmabubble6) = V_2 + 2 Pol(evalsipmabubblebb1in) = V_1 + 1 Pol(evalsipmabubblebb2in) = V_1 Pol(evalsipmabubblebb7in) = V_1 + 1 Pol(evalsipmabubblebb3in) = V_1 Pol(evalsipmabubblebb6in) = V_1 Pol(evalsipmabubblebb4in) = V_1 Pol(evalsipmabubblebb5in) = V_1 Pol(evalsipmabubble29) = V_4 + 1 Pol(evalsipmabubble30) = V_4 + 1 Pol(evalsipmabubblestop) = V_1 + 1 Pol(koat_start) = V_2 + 2 orients all transitions weakly and the transition evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1)) (Comp: ?, Cost: 1) evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalsipmabubblebb6in) = 3 Pol(evalsipmabubble29) = 2 Pol(evalsipmabubblebb5in) = 4 Pol(evalsipmabubblebb2in) = 4 Pol(evalsipmabubblebb4in) = 4 Pol(evalsipmabubblebb3in) = 4 Pol(evalsipmabubble30) = 1 Pol(evalsipmabubblebb1in) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1))", 0-0) = ? S("evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1))", 0-1) = Ar_1 S("evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1))", 0-2) = ? S("evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1))", 0-3) = ? S("evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-0) = ? S("evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-1) = Ar_1 S("evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-2) = ? S("evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-3) = ? S("evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = ? S("evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ? S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ]", 0-0) = ? S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ]", 0-1) = Ar_1 S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ]", 0-2) = ? S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ]", 0-3) = ? S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ]", 0-0) = ? S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ]", 0-1) = Ar_1 S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ]", 0-2) = ? S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ]", 0-3) = ? S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ]", 0-0) = ? S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ]", 0-1) = Ar_1 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ]", 0-2) = ? S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ]", 0-3) = ? S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ]", 0-0) = ? S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ]", 0-2) = ? S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ]", 0-3) = ? S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-0) = ? S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-2) = ? S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-3) = ? S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ]", 0-0) = ? S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ]", 0-2) = 0 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ]", 0-3) = ? S("evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_1 S("evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1)) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ] evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ] evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3)) evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3)) weakly and the transitions evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1)) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3)) evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3)) strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: 4*Ar_1 + 8, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 4*Ar_1 + 8, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1)) (Comp: 4*Ar_1 + 8, Cost: 1) evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1 + 8, Cost: 1) evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalsipmabubblebb5in) = V_1 - V_3 Pol(evalsipmabubblebb2in) = V_1 - V_3 + 1 Pol(evalsipmabubblebb4in) = V_1 - V_3 Pol(evalsipmabubblebb3in) = V_1 - V_3 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 S("evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 5*Ar_1 + 5000 S("evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = 5*Ar_1 + 5*Ar_3 + 25000 S("evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-0) = 5*Ar_1 + 200 S("evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3))", 0-3) = 5*Ar_1 + 1000 S("evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 5*Ar_1 + 5000 S("evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = 5*Ar_1 + 200 S("evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1))", 0-0) = 5*Ar_1 + 1000 S("evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1))", 0-1) = Ar_1 S("evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1))", 0-2) = ? S("evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1))", 0-3) = 5*Ar_1 + 200 S("evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-0) = 5*Ar_1 + 200 S("evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-1) = Ar_1 S("evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-2) = ? S("evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))", 0-3) = 5*Ar_1 + 5*Ar_3 + 25000 S("evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = 5*Ar_1 + 200 S("evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = ? S("evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = 5*Ar_1 + 5*Ar_3 + 25000 S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ]", 0-0) = 5*Ar_1 + 200 S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ]", 0-1) = Ar_1 S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ]", 0-2) = ? S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ]", 0-3) = 5*Ar_1 + 5*Ar_3 + 25000 S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ]", 0-0) = 5*Ar_1 + 200 S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ]", 0-1) = Ar_1 S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ]", 0-2) = ? S("evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ]", 0-3) = 5*Ar_1 + 5*Ar_3 + 25000 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ]", 0-0) = 5*Ar_1 + 200 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ]", 0-1) = Ar_1 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ]", 0-2) = ? S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ]", 0-3) = 5*Ar_1 + 5*Ar_3 + 125000 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ]", 0-0) = 5*Ar_1 + 200 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ]", 0-1) = Ar_1 S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ]", 0-2) = ? S("evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ]", 0-3) = 5*Ar_1 + 5*Ar_3 + 25000 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-0) = 5*Ar_1 + 1000 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-1) = Ar_1 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-2) = ? S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]", 0-3) = 5*Ar_1 + 5*Ar_3 + 5000 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ]", 0-0) = 5*Ar_1 + 200 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ]", 0-1) = Ar_1 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ]", 0-2) = 0 S("evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ]", 0-3) = 5*Ar_1 + 5*Ar_3 + 5000 S("evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_1 S("evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0 S("evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 orients the transitions evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ] evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ] evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] weakly and the transition evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 5*Ar_1^2 + 211*Ar_1 + 402, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: 4*Ar_1 + 8, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 4*Ar_1 + 8, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1)) (Comp: 4*Ar_1 + 8, Cost: 1) evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1 + 8, Cost: 1) evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (Comp: 1, Cost: 1) evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubblebb0in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) evalsipmabubble6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_1, Ar_1, Ar_2, Ar_3)) (Comp: Ar_1 + 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalsipmabubblebb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ] (Comp: 5*Ar_1^2 + 211*Ar_1 + 402, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 ] (Comp: 4*Ar_1 + 8, Cost: 1) evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 ] (Comp: 5*Ar_1^2 + 211*Ar_1 + 402, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= F + 1 ] (Comp: 5*Ar_1^2 + 211*Ar_1 + 402, Cost: 1) evalsipmabubblebb3in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ F >= E ] (Comp: 5*Ar_1^2 + 211*Ar_1 + 402, Cost: 1) evalsipmabubblebb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 10*Ar_1^2 + 422*Ar_1 + 804, Cost: 1) evalsipmabubblebb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb2in(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 4*Ar_1 + 8, Cost: 1) evalsipmabubblebb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_0 - 1)) (Comp: 4*Ar_1 + 8, Cost: 1) evalsipmabubble29(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 4*Ar_1 + 8, Cost: 1) evalsipmabubble30(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblebb1in(Ar_3, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) evalsipmabubblebb7in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestop(Ar_0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalsipmabubblestart(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 1283*Ar_1 + 30*Ar_1^2 + 2459 Time: 0.177 sec (SMT: 0.118 sec) ---------------------------------------- (2) BOUNDS(1, n^2) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: evalsipmabubblestart 0: evalsipmabubblestart -> evalsipmabubblebb0in : [], cost: 1 1: evalsipmabubblebb0in -> evalsipmabubble0 : [], cost: 1 2: evalsipmabubble0 -> evalsipmabubble1 : [], cost: 1 3: evalsipmabubble1 -> evalsipmabubble2 : [], cost: 1 4: evalsipmabubble2 -> evalsipmabubble3 : [], cost: 1 5: evalsipmabubble3 -> evalsipmabubble4 : [], cost: 1 6: evalsipmabubble4 -> evalsipmabubble5 : [], cost: 1 7: evalsipmabubble5 -> evalsipmabubble6 : [], cost: 1 8: evalsipmabubble6 -> evalsipmabubblebb1in : A'=B, [], cost: 1 9: evalsipmabubblebb1in -> evalsipmabubblebb2in : C'=0, [ A>=0 ], cost: 1 10: evalsipmabubblebb1in -> evalsipmabubblebb7in : [ 0>=1+A ], cost: 1 11: evalsipmabubblebb2in -> evalsipmabubblebb3in : [ A>=1+C ], cost: 1 12: evalsipmabubblebb2in -> evalsipmabubblebb6in : [ C>=A ], cost: 1 13: evalsipmabubblebb3in -> evalsipmabubblebb4in : [ free_1>=1+free ], cost: 1 14: evalsipmabubblebb3in -> evalsipmabubblebb5in : [ free_2>=free_3 ], cost: 1 15: evalsipmabubblebb4in -> evalsipmabubblebb5in : [], cost: 1 16: evalsipmabubblebb5in -> evalsipmabubblebb2in : C'=1+C, [], cost: 1 17: evalsipmabubblebb6in -> evalsipmabubble29 : D'=-1+A, [], cost: 1 18: evalsipmabubble29 -> evalsipmabubble30 : [], cost: 1 19: evalsipmabubble30 -> evalsipmabubblebb1in : A'=D, [], cost: 1 20: evalsipmabubblebb7in -> evalsipmabubblestop : [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: evalsipmabubblestart -> evalsipmabubblebb0in : [], cost: 1 Removed unreachable and leaf rules: Start location: evalsipmabubblestart 0: evalsipmabubblestart -> evalsipmabubblebb0in : [], cost: 1 1: evalsipmabubblebb0in -> evalsipmabubble0 : [], cost: 1 2: evalsipmabubble0 -> evalsipmabubble1 : [], cost: 1 3: evalsipmabubble1 -> evalsipmabubble2 : [], cost: 1 4: evalsipmabubble2 -> evalsipmabubble3 : [], cost: 1 5: evalsipmabubble3 -> evalsipmabubble4 : [], cost: 1 6: evalsipmabubble4 -> evalsipmabubble5 : [], cost: 1 7: evalsipmabubble5 -> evalsipmabubble6 : [], cost: 1 8: evalsipmabubble6 -> evalsipmabubblebb1in : A'=B, [], cost: 1 9: evalsipmabubblebb1in -> evalsipmabubblebb2in : C'=0, [ A>=0 ], cost: 1 11: evalsipmabubblebb2in -> evalsipmabubblebb3in : [ A>=1+C ], cost: 1 12: evalsipmabubblebb2in -> evalsipmabubblebb6in : [ C>=A ], cost: 1 13: evalsipmabubblebb3in -> evalsipmabubblebb4in : [ free_1>=1+free ], cost: 1 14: evalsipmabubblebb3in -> evalsipmabubblebb5in : [ free_2>=free_3 ], cost: 1 15: evalsipmabubblebb4in -> evalsipmabubblebb5in : [], cost: 1 16: evalsipmabubblebb5in -> evalsipmabubblebb2in : C'=1+C, [], cost: 1 17: evalsipmabubblebb6in -> evalsipmabubble29 : D'=-1+A, [], cost: 1 18: evalsipmabubble29 -> evalsipmabubble30 : [], cost: 1 19: evalsipmabubble30 -> evalsipmabubblebb1in : A'=D, [], cost: 1 Simplified all rules, resulting in: Start location: evalsipmabubblestart 0: evalsipmabubblestart -> evalsipmabubblebb0in : [], cost: 1 1: evalsipmabubblebb0in -> evalsipmabubble0 : [], cost: 1 2: evalsipmabubble0 -> evalsipmabubble1 : [], cost: 1 3: evalsipmabubble1 -> evalsipmabubble2 : [], cost: 1 4: evalsipmabubble2 -> evalsipmabubble3 : [], cost: 1 5: evalsipmabubble3 -> evalsipmabubble4 : [], cost: 1 6: evalsipmabubble4 -> evalsipmabubble5 : [], cost: 1 7: evalsipmabubble5 -> evalsipmabubble6 : [], cost: 1 8: evalsipmabubble6 -> evalsipmabubblebb1in : A'=B, [], cost: 1 9: evalsipmabubblebb1in -> evalsipmabubblebb2in : C'=0, [ A>=0 ], cost: 1 11: evalsipmabubblebb2in -> evalsipmabubblebb3in : [ A>=1+C ], cost: 1 12: evalsipmabubblebb2in -> evalsipmabubblebb6in : [ C>=A ], cost: 1 13: evalsipmabubblebb3in -> evalsipmabubblebb4in : [], cost: 1 14: evalsipmabubblebb3in -> evalsipmabubblebb5in : [], cost: 1 15: evalsipmabubblebb4in -> evalsipmabubblebb5in : [], cost: 1 16: evalsipmabubblebb5in -> evalsipmabubblebb2in : C'=1+C, [], cost: 1 17: evalsipmabubblebb6in -> evalsipmabubble29 : D'=-1+A, [], cost: 1 18: evalsipmabubble29 -> evalsipmabubble30 : [], cost: 1 19: evalsipmabubble30 -> evalsipmabubblebb1in : A'=D, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: evalsipmabubblestart 28: evalsipmabubblestart -> evalsipmabubblebb1in : A'=B, [], cost: 9 9: evalsipmabubblebb1in -> evalsipmabubblebb2in : C'=0, [ A>=0 ], cost: 1 11: evalsipmabubblebb2in -> evalsipmabubblebb3in : [ A>=1+C ], cost: 1 31: evalsipmabubblebb2in -> evalsipmabubblebb1in : A'=-1+A, D'=-1+A, [ C>=A ], cost: 4 14: evalsipmabubblebb3in -> evalsipmabubblebb5in : [], cost: 1 32: evalsipmabubblebb3in -> evalsipmabubblebb5in : [], cost: 2 16: evalsipmabubblebb5in -> evalsipmabubblebb2in : C'=1+C, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalsipmabubblestart 28: evalsipmabubblestart -> evalsipmabubblebb1in : A'=B, [], cost: 9 9: evalsipmabubblebb1in -> evalsipmabubblebb2in : C'=0, [ A>=0 ], cost: 1 31: evalsipmabubblebb2in -> evalsipmabubblebb1in : A'=-1+A, D'=-1+A, [ C>=A ], cost: 4 33: evalsipmabubblebb2in -> evalsipmabubblebb5in : [ A>=1+C ], cost: 2 34: evalsipmabubblebb2in -> evalsipmabubblebb5in : [ A>=1+C ], cost: 3 16: evalsipmabubblebb5in -> evalsipmabubblebb2in : C'=1+C, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: evalsipmabubblestart 28: evalsipmabubblestart -> evalsipmabubblebb1in : A'=B, [], cost: 9 9: evalsipmabubblebb1in -> evalsipmabubblebb2in : C'=0, [ A>=0 ], cost: 1 31: evalsipmabubblebb2in -> evalsipmabubblebb1in : A'=-1+A, D'=-1+A, [ C>=A ], cost: 4 35: evalsipmabubblebb2in -> evalsipmabubblebb2in : C'=1+C, [ A>=1+C ], cost: 3 36: evalsipmabubblebb2in -> evalsipmabubblebb2in : C'=1+C, [ A>=1+C ], cost: 4 Accelerating simple loops of location 10. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 36: evalsipmabubblebb2in -> evalsipmabubblebb2in : C'=1+C, [ A>=1+C ], cost: 4 Accelerated rule 36 with metering function -C+A, yielding the new rule 37. Removing the simple loops: 36. Accelerated all simple loops using metering functions (where possible): Start location: evalsipmabubblestart 28: evalsipmabubblestart -> evalsipmabubblebb1in : A'=B, [], cost: 9 9: evalsipmabubblebb1in -> evalsipmabubblebb2in : C'=0, [ A>=0 ], cost: 1 31: evalsipmabubblebb2in -> evalsipmabubblebb1in : A'=-1+A, D'=-1+A, [ C>=A ], cost: 4 37: evalsipmabubblebb2in -> evalsipmabubblebb2in : C'=A, [ A>=1+C ], cost: -4*C+4*A Chained accelerated rules (with incoming rules): Start location: evalsipmabubblestart 28: evalsipmabubblestart -> evalsipmabubblebb1in : A'=B, [], cost: 9 9: evalsipmabubblebb1in -> evalsipmabubblebb2in : C'=0, [ A>=0 ], cost: 1 38: evalsipmabubblebb1in -> evalsipmabubblebb2in : C'=A, [ A>=1 ], cost: 1+4*A 31: evalsipmabubblebb2in -> evalsipmabubblebb1in : A'=-1+A, D'=-1+A, [ C>=A ], cost: 4 Eliminated locations (on tree-shaped paths): Start location: evalsipmabubblestart 28: evalsipmabubblestart -> evalsipmabubblebb1in : A'=B, [], cost: 9 39: evalsipmabubblebb1in -> evalsipmabubblebb1in : A'=-1+A, C'=0, D'=-1+A, [ A>=0 && 0>=A ], cost: 5 40: evalsipmabubblebb1in -> evalsipmabubblebb1in : A'=-1+A, C'=A, D'=-1+A, [ A>=1 ], cost: 5+4*A Accelerating simple loops of location 9. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 39: evalsipmabubblebb1in -> evalsipmabubblebb1in : A'=-1+A, C'=0, D'=-1+A, [ -A==0 ], cost: 5 40: evalsipmabubblebb1in -> evalsipmabubblebb1in : A'=-1+A, C'=A, D'=-1+A, [ A>=1 ], cost: 5+4*A Accelerated rule 39 with metering function 1+A, yielding the new rule 41. Accelerated rule 40 with metering function A, yielding the new rule 42. Removing the simple loops: 39 40. Accelerated all simple loops using metering functions (where possible): Start location: evalsipmabubblestart 28: evalsipmabubblestart -> evalsipmabubblebb1in : A'=B, [], cost: 9 41: evalsipmabubblebb1in -> evalsipmabubblebb1in : A'=-1, C'=0, D'=-1, [ -A==0 ], cost: 5+5*A 42: evalsipmabubblebb1in -> evalsipmabubblebb1in : A'=0, C'=1, D'=0, [ A>=1 ], cost: 7*A+2*A^2 Chained accelerated rules (with incoming rules): Start location: evalsipmabubblestart 28: evalsipmabubblestart -> evalsipmabubblebb1in : A'=B, [], cost: 9 43: evalsipmabubblestart -> evalsipmabubblebb1in : A'=-1, C'=0, D'=-1, [ -B==0 ], cost: 14+5*B 44: evalsipmabubblestart -> evalsipmabubblebb1in : A'=0, C'=1, D'=0, [ B>=1 ], cost: 9+7*B+2*B^2 Removed unreachable locations (and leaf rules with constant cost): Start location: evalsipmabubblestart 43: evalsipmabubblestart -> evalsipmabubblebb1in : A'=-1, C'=0, D'=-1, [ -B==0 ], cost: 14+5*B 44: evalsipmabubblestart -> evalsipmabubblebb1in : A'=0, C'=1, D'=0, [ B>=1 ], cost: 9+7*B+2*B^2 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: evalsipmabubblestart 43: evalsipmabubblestart -> evalsipmabubblebb1in : A'=-1, C'=0, D'=-1, [ -B==0 ], cost: 14+5*B 44: evalsipmabubblestart -> evalsipmabubblebb1in : A'=0, C'=1, D'=0, [ B>=1 ], cost: 9+7*B+2*B^2 Computing asymptotic complexity for rule 43 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 44 Solved the limit problem by the following transformations: Created initial limit problem: B (+/+!), 9+7*B+2*B^2 (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {B==n} resulting limit problem: [solved] Solution: B / n Resulting cost 9+2*n^2+7*n has complexity: Poly(n^2) Found new complexity Poly(n^2). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^2) Cpx degree: 2 Solved cost: 9+2*n^2+7*n Rule cost: 9+7*B+2*B^2 Rule guard: [ B>=1 ] WORST_CASE(Omega(n^2),?) ---------------------------------------- (4) BOUNDS(n^2, INF)