0.92/0.95 WORST_CASE(?,O(n^2)) 0.92/0.95 0.92/0.95 Preprocessing Cost Relations 0.92/0.95 ===================================== 0.92/0.95 0.92/0.95 #### Computed strongly connected components 0.92/0.95 0. recursive : [eval_SingleLinkCluster_6/8,eval_SingleLinkCluster_7/9,eval_SingleLinkCluster_bb5_in/8,eval_SingleLinkCluster_bb6_in/8,eval_SingleLinkCluster_bb7_in/8,eval_SingleLinkCluster_bb8_in/9,eval_SingleLinkCluster_bb9_in/10] 0.92/0.95 1. recursive : [eval_SingleLinkCluster_bb3_in/8,eval_SingleLinkCluster_bb4_in/8,eval_SingleLinkCluster_bb5_in_loop_cont/9] 0.92/0.95 2. recursive : [eval_SingleLinkCluster_bb1_in/4,eval_SingleLinkCluster_bb2_in/4,eval_SingleLinkCluster_bb3_in_loop_cont/5] 0.92/0.95 3. non_recursive : [eval_SingleLinkCluster_stop/1] 0.92/0.95 4. non_recursive : [eval_SingleLinkCluster_bb10_in/1] 0.92/0.95 5. non_recursive : [eval_SingleLinkCluster_bb1_in_loop_cont/2] 0.92/0.95 6. non_recursive : [eval_SingleLinkCluster_bb0_in/2] 0.92/0.95 7. non_recursive : [eval_SingleLinkCluster_start/2] 0.92/0.95 0.92/0.95 #### Obtained direct recursion through partial evaluation 0.92/0.95 0. SCC is partially evaluated into eval_SingleLinkCluster_bb5_in/8 0.92/0.95 1. SCC is partially evaluated into eval_SingleLinkCluster_bb3_in/8 0.92/0.95 2. SCC is partially evaluated into eval_SingleLinkCluster_bb1_in/4 0.92/0.95 3. SCC is completely evaluated into other SCCs 0.92/0.95 4. SCC is completely evaluated into other SCCs 0.92/0.95 5. SCC is completely evaluated into other SCCs 0.92/0.95 6. SCC is partially evaluated into eval_SingleLinkCluster_bb0_in/2 0.92/0.95 7. SCC is partially evaluated into eval_SingleLinkCluster_start/2 0.92/0.95 0.92/0.95 Control-Flow Refinement of Cost Relations 0.92/0.95 ===================================== 0.92/0.95 0.92/0.95 ### Specialization of cost equations eval_SingleLinkCluster_bb5_in/8 0.92/0.95 * CE 10 is refined into CE [11] 0.92/0.95 * CE 7 is refined into CE [12] 0.92/0.95 * CE 9 is refined into CE [13] 0.92/0.95 * CE 8 is refined into CE [14] 0.92/0.95 0.92/0.95 0.92/0.95 ### Cost equations --> "Loop" of eval_SingleLinkCluster_bb5_in/8 0.92/0.95 * CEs [12] --> Loop 11 0.92/0.95 * CEs [13] --> Loop 12 0.92/0.95 * CEs [14] --> Loop 13 0.92/0.95 * CEs [11] --> Loop 14 0.92/0.95 0.92/0.95 ### Ranking functions of CR eval_SingleLinkCluster_bb5_in(V_b_1,V_a_1,V_i_0,V_b_2,V_a_2,B,C,D) 0.92/0.95 * RF of phase [11,13]: [V_i_0] 0.92/0.95 * RF of phase [12]: [V_i_0] 0.92/0.95 0.92/0.95 #### Partial ranking functions of CR eval_SingleLinkCluster_bb5_in(V_b_1,V_a_1,V_i_0,V_b_2,V_a_2,B,C,D) 0.92/0.95 * Partial RF of phase [11,13]: 0.92/0.95 - RF of loop [11:1,13:1]: 0.92/0.95 V_i_0 0.92/0.95 - RF of loop [13:1]: 0.92/0.95 V_a_2 0.92/0.95 V_b_1+V_a_1-V_b_2-1 0.92/0.95 * Partial RF of phase [12]: 0.92/0.95 - RF of loop [12:1]: 0.92/0.95 V_i_0 0.92/0.95 0.92/0.95 0.92/0.95 ### Specialization of cost equations eval_SingleLinkCluster_bb3_in/8 0.92/0.95 * CE 6 is refined into CE [15] 0.92/0.95 * CE 5 is refined into CE [16,17,18,19] 0.92/0.95 0.92/0.95 0.92/0.95 ### Cost equations --> "Loop" of eval_SingleLinkCluster_bb3_in/8 0.92/0.95 * CEs [19] --> Loop 15 0.92/0.95 * CEs [18] --> Loop 16 0.92/0.95 * CEs [17] --> Loop 17 0.92/0.95 * CEs [16] --> Loop 18 0.92/0.95 * CEs [15] --> Loop 19 0.92/0.95 0.92/0.95 ### Ranking functions of CR eval_SingleLinkCluster_bb3_in(V_n,V_b_0,V_a_0,V_b_1,V_a_1,B,C,D) 0.92/0.95 * RF of phase [15]: [V_b_1+V_a_1-1] 0.92/0.95 * RF of phase [16]: [V_b_1] 0.92/0.95 * RF of phase [17]: [V_b_1] 0.92/0.95 0.92/0.95 #### Partial ranking functions of CR eval_SingleLinkCluster_bb3_in(V_n,V_b_0,V_a_0,V_b_1,V_a_1,B,C,D) 0.92/0.95 * Partial RF of phase [15]: 0.92/0.95 - RF of loop [15:1]: 0.92/0.95 V_b_1+V_a_1-1 0.92/0.95 * Partial RF of phase [16]: 0.92/0.95 - RF of loop [16:1]: 0.92/0.95 V_b_1 0.92/0.95 * Partial RF of phase [17]: 0.92/0.95 - RF of loop [17:1]: 0.92/0.95 V_b_1 0.92/0.95 0.92/0.95 0.92/0.95 ### Specialization of cost equations eval_SingleLinkCluster_bb1_in/4 0.92/0.95 * CE 4 is refined into CE [20] 0.92/0.95 * CE 3 is refined into CE [21,22,23,24,25,26,27] 0.92/0.95 0.92/0.95 0.92/0.95 ### Cost equations --> "Loop" of eval_SingleLinkCluster_bb1_in/4 0.92/0.95 * CEs [27] --> Loop 20 0.92/0.95 * CEs [26] --> Loop 21 0.92/0.95 * CEs [25] --> Loop 22 0.92/0.95 * CEs [24] --> Loop 23 0.92/0.95 * CEs [23] --> Loop 24 0.92/0.95 * CEs [22] --> Loop 25 0.92/0.95 * CEs [21] --> Loop 26 0.92/0.95 * CEs [20] --> Loop 27 0.92/0.95 0.92/0.95 ### Ranking functions of CR eval_SingleLinkCluster_bb1_in(V_n,V_b_0,V_a_0,B) 0.92/0.95 * RF of phase [21]: [V_a_0-1] 0.92/0.95 * RF of phase [22]: [V_a_0] 0.92/0.95 0.92/0.95 #### Partial ranking functions of CR eval_SingleLinkCluster_bb1_in(V_n,V_b_0,V_a_0,B) 0.92/0.95 * Partial RF of phase [21]: 0.92/0.95 - RF of loop [21:1]: 0.92/0.95 V_a_0-1 0.92/0.95 * Partial RF of phase [22]: 0.92/0.95 - RF of loop [22:1]: 0.92/0.95 V_a_0 0.92/0.95 0.92/0.95 0.92/0.95 ### Specialization of cost equations eval_SingleLinkCluster_bb0_in/2 0.92/0.95 * CE 2 is refined into CE [28,29,30,31,32] 0.92/0.95 0.92/0.95 0.92/0.95 ### Cost equations --> "Loop" of eval_SingleLinkCluster_bb0_in/2 0.92/0.95 * CEs [32] --> Loop 28 0.92/0.95 * CEs [31] --> Loop 29 0.92/0.95 * CEs [30] --> Loop 30 0.92/0.95 * CEs [29] --> Loop 31 0.92/0.95 * CEs [28] --> Loop 32 0.92/0.95 0.92/0.95 ### Ranking functions of CR eval_SingleLinkCluster_bb0_in(V_n,B) 0.92/0.95 0.92/0.95 #### Partial ranking functions of CR eval_SingleLinkCluster_bb0_in(V_n,B) 0.92/0.95 0.92/0.95 0.92/0.95 ### Specialization of cost equations eval_SingleLinkCluster_start/2 0.92/0.95 * CE 1 is refined into CE [33,34,35,36,37] 0.92/0.95 0.92/0.95 0.92/0.95 ### Cost equations --> "Loop" of eval_SingleLinkCluster_start/2 0.92/0.95 * CEs [37] --> Loop 33 0.92/0.95 * CEs [36] --> Loop 34 0.92/0.95 * CEs [35] --> Loop 35 0.92/0.95 * CEs [34] --> Loop 36 0.92/0.95 * CEs [33] --> Loop 37 0.92/0.95 0.92/0.95 ### Ranking functions of CR eval_SingleLinkCluster_start(V_n,B) 0.92/0.95 0.92/0.95 #### Partial ranking functions of CR eval_SingleLinkCluster_start(V_n,B) 0.92/0.95 0.92/0.95 0.92/0.95 Computing Bounds 0.92/0.95 ===================================== 0.92/0.95 0.92/0.95 #### Cost of chains of eval_SingleLinkCluster_bb5_in(V_b_1,V_a_1,V_i_0,V_b_2,V_a_2,B,C,D): 0.92/0.95 * Chain [[12],14]: 1*it(12)+0 0.92/0.95 Such that:it(12) =< V_i_0 0.92/0.95 0.92/0.95 with precondition: [B=2,V_b_2=C,V_a_1+V_b_1=V_a_2+V_b_2+1,V_a_1+V_b_1=V_b_2+D+1,V_b_1>=1,V_i_0>=1,V_b_2+1>=V_b_1,V_b_2+1>=V_a_1+V_b_1] 0.92/0.95 0.92/0.95 * Chain [[11,13],[12],14]: 1*it(11)+1*it(12)+1*it(13)+0 0.92/0.95 Such that:it(12) =< V_i_0+V_b_2-C 0.92/0.95 it(13) =< -V_b_2+C 0.92/0.95 aux(3) =< V_i_0 0.92/0.95 it(12) =< aux(3) 0.92/0.95 it(11) =< aux(3) 0.92/0.95 it(13) =< aux(3) 0.92/0.95 0.92/0.95 with precondition: [B=2,D=0,V_a_1+V_b_1=C+1,V_a_1+V_b_1=V_a_2+V_b_2+1,V_b_1>=1,V_a_2>=1,V_a_1>=V_a_2,V_i_0>=V_a_2+1] 0.92/0.95 0.92/0.95 * Chain [[11,13],14]: 1*it(11)+1*it(13)+0 0.92/0.95 Such that:it(13) =< V_a_2-D 0.92/0.95 aux(4) =< V_i_0 0.92/0.95 it(11) =< aux(4) 0.92/0.95 it(13) =< aux(4) 0.92/0.95 0.92/0.95 with precondition: [B=2,V_a_1+V_b_1=V_a_2+V_b_2+1,V_a_1+V_b_1=C+D+1,V_b_1>=1,V_i_0>=1,V_a_2>=1,V_a_1>=V_a_2,V_a_1+V_b_1>=C+1,V_a_2+C+1>=V_a_1+V_b_1,V_a_1+V_b_1+V_i_0>=V_a_2+C+1] 0.92/0.95 0.92/0.95 * Chain [14]: 0 0.92/0.95 with precondition: [B=2,V_b_2=C,V_a_2=D,V_a_2+V_b_2+1=V_a_1+V_b_1,0>=V_i_0,V_b_1>=1,V_b_2+1>=V_b_1] 0.92/0.95 0.92/0.95 0.92/0.95 #### Cost of chains of eval_SingleLinkCluster_bb3_in(V_n,V_b_0,V_a_0,V_b_1,V_a_1,B,C,D): 0.92/0.95 * Chain [[17],19]: 1*it(17)+0 0.92/0.95 Such that:it(17) =< V_b_1 0.92/0.95 0.92/0.95 with precondition: [B=3,C=0,V_a_0=V_a_1+1,V_a_0=D+1,1>=V_n,V_a_0>=1,V_b_1>=1,V_b_0+1>=V_b_1] 0.92/0.95 0.92/0.95 * Chain [[16],19]: 1*it(16)+1*s(3)+0 0.92/0.95 Such that:aux(5) =< V_n 0.92/0.95 it(16) =< V_b_1 0.92/0.95 s(3) =< it(16)*aux(5) 0.92/0.95 0.92/0.95 with precondition: [V_a_1=0,B=3,C=0,D=0,V_n>=2,V_a_0>=1,V_b_1>=1,V_a_0+V_b_0>=V_b_1] 0.92/0.95 0.92/0.95 * Chain [[15],[16],19]: 2*it(15)+1*s(3)+1*s(10)+1*s(11)+0 0.92/0.95 Such that:s(10) =< V_a_1 0.92/0.95 aux(7) =< V_n 0.92/0.95 aux(8) =< V_b_1+V_a_1 0.92/0.95 it(15) =< aux(8) 0.92/0.95 s(3) =< it(15)*aux(7) 0.92/0.95 s(12) =< it(15)*aux(7) 0.92/0.95 s(11) =< s(12) 0.92/0.95 s(10) =< s(12) 0.92/0.95 0.92/0.95 with precondition: [B=3,C=0,D=0,V_n>=2,V_b_1>=1,V_a_1>=1,V_a_0>=V_a_1+1,V_a_0+V_b_0>=V_a_1+V_b_1] 0.92/0.95 0.92/0.95 * Chain [[15],19]: 1*it(15)+1*s(10)+1*s(11)+0 0.92/0.95 Such that:aux(6) =< V_n 0.92/0.95 it(15) =< V_b_1+V_a_1-D 0.92/0.95 s(10) =< V_a_1-D 0.92/0.95 s(12) =< it(15)*aux(6) 0.92/0.95 s(11) =< s(12) 0.92/0.95 s(10) =< s(12) 0.92/0.95 0.92/0.95 with precondition: [B=3,C=0,V_n>=2,V_b_1>=1,D>=1,V_a_0>=V_a_1+1,V_a_1>=D,V_a_0+V_b_0>=V_a_1+V_b_1] 0.92/0.95 0.92/0.95 * Chain [[15],18,[16],19]: 2*it(15)+1*s(3)+1*s(10)+1*s(11)+2*s(13)+1*s(14)+1 0.92/0.95 Such that:aux(10) =< V_n 0.92/0.95 aux(11) =< V_b_1+V_a_1 0.92/0.95 aux(12) =< V_a_1 0.92/0.95 s(13) =< aux(10) 0.92/0.95 s(14) =< aux(10) 0.92/0.95 it(15) =< aux(11) 0.92/0.95 s(10) =< aux(12) 0.92/0.95 s(14) =< aux(12) 0.92/0.95 s(3) =< it(15)*aux(10) 0.92/0.95 s(12) =< it(15)*aux(10) 0.92/0.95 s(11) =< s(12) 0.92/0.95 s(10) =< s(12) 0.92/0.95 0.92/0.95 with precondition: [B=3,C=0,D=0,V_n>=3,V_b_1>=1,V_a_1>=1,V_a_0>=V_a_1+1,V_a_1+V_b_1>=3,V_a_0+V_b_0>=V_a_1+V_b_1] 0.92/0.95 0.92/0.95 * Chain [19]: 0 0.92/0.95 with precondition: [B=3,V_b_1=C,V_a_1=D,0>=V_b_1,V_a_1>=0,V_a_0>=V_a_1+1,V_a_0+V_b_0>=V_a_1+V_b_1] 0.92/0.95 0.92/0.95 * Chain [18,[16],19]: 1*it(16)+1*s(3)+1*s(13)+1*s(14)+1*s(16)+1 0.92/0.95 Such that:s(13) =< V_n-V_a_1 0.92/0.95 it(16) =< V_b_1+V_a_1 0.92/0.95 s(14) =< V_a_1 0.92/0.95 aux(9) =< V_n 0.92/0.95 s(3) =< it(16)*aux(9) 0.92/0.95 s(13) =< aux(9) 0.92/0.95 s(16) =< aux(9) 0.92/0.95 s(14) =< aux(9) 0.92/0.95 0.92/0.95 with precondition: [B=3,C=0,D=0,V_b_1>=1,V_a_1>=1,V_n>=V_a_1+2,V_a_0>=V_a_1+1,V_a_0+V_b_0>=V_a_1+V_b_1] 0.92/0.95 0.92/0.95 0.92/0.95 #### Cost of chains of eval_SingleLinkCluster_bb1_in(V_n,V_b_0,V_a_0,B): 0.92/0.95 * Chain [[22],27]: 2*it(22)+0 0.92/0.95 Such that:aux(16) =< 1 0.92/0.95 it(22) =< aux(16) 0.92/0.95 0.92/0.95 with precondition: [V_n=1,V_b_0=0,V_a_0=1,B=4] 0.92/0.95 0.92/0.95 * Chain [[21],26,27]: 2*it(21)+1*s(21)+1*s(22)+1*s(35)+1*s(36)+1 0.92/0.95 Such that:s(21) =< 1 0.92/0.95 aux(20) =< V_n 0.92/0.95 aux(21) =< V_a_0 0.92/0.95 s(22) =< s(21)*aux(20) 0.92/0.95 it(21) =< aux(21) 0.92/0.95 s(35) =< aux(21) 0.92/0.95 s(37) =< it(21)*aux(20) 0.92/0.95 s(36) =< s(37) 0.92/0.95 s(35) =< s(37) 0.92/0.95 0.92/0.95 with precondition: [V_b_0=0,B=4,V_a_0>=2,V_n>=V_a_0] 0.92/0.95 0.92/0.95 * Chain [[21],25,27]: 4*it(21)+2*s(35)+2*s(36)+1*s(43)+1 0.92/0.95 Such that:aux(23) =< V_n 0.92/0.95 aux(24) =< V_a_0 0.92/0.95 s(35) =< aux(24) 0.92/0.95 it(21) =< aux(24) 0.92/0.95 s(43) =< it(21)*aux(23) 0.92/0.95 s(37) =< it(21)*aux(23) 0.92/0.95 s(36) =< s(37) 0.92/0.95 s(35) =< s(37) 0.92/0.95 0.92/0.95 with precondition: [V_b_0=0,B=4,V_a_0>=3,V_n>=V_a_0] 0.92/0.95 0.92/0.95 * Chain [[21],24,27]: 4*it(21)+2*s(35)+2*s(36)+2*s(49)+1*s(50)+1*s(53)+2 0.92/0.95 Such that:aux(26) =< V_n 0.92/0.95 aux(27) =< V_a_0 0.92/0.95 s(49) =< aux(26) 0.92/0.95 s(50) =< aux(26) 0.92/0.95 it(21) =< aux(27) 0.92/0.95 s(35) =< aux(27) 0.92/0.95 s(50) =< aux(27) 0.92/0.95 s(53) =< it(21)*aux(26) 0.92/0.95 s(37) =< it(21)*aux(26) 0.92/0.95 s(36) =< s(37) 0.92/0.95 s(35) =< s(37) 0.92/0.95 0.92/0.95 with precondition: [V_b_0=0,B=4,V_a_0>=4,V_n>=V_a_0] 0.92/0.95 0.92/0.95 * Chain [[21],23,27]: 2*it(21)+1*s(35)+1*s(36)+1*s(56)+1*s(57)+1*s(58)+1*s(60)+1*s(61)+2 0.92/0.95 Such that:aux(29) =< V_n 0.92/0.95 aux(30) =< V_n+1 0.92/0.95 aux(31) =< V_a_0 0.92/0.95 s(56) =< aux(29) 0.92/0.95 aux(28) =< aux(30) 0.92/0.95 s(56) =< aux(30) 0.92/0.95 aux(28) =< aux(31) 0.92/0.95 s(57) =< aux(28) 0.92/0.95 s(58) =< aux(28) 0.92/0.95 s(60) =< s(57)*aux(29) 0.92/0.95 s(61) =< aux(29) 0.92/0.95 s(58) =< aux(29) 0.92/0.95 it(21) =< aux(31) 0.92/0.95 s(35) =< aux(31) 0.92/0.95 s(37) =< it(21)*aux(29) 0.92/0.95 s(36) =< s(37) 0.92/0.95 s(35) =< s(37) 0.92/0.95 0.92/0.95 with precondition: [V_b_0=0,B=4,V_a_0>=3,V_n>=V_a_0] 0.92/0.95 0.92/0.95 * Chain [27]: 0 0.92/0.95 with precondition: [V_b_0=0,B=4,0>=V_a_0,V_n>=V_a_0] 0.92/0.95 0.92/0.95 * Chain [25,27]: 1*s(39)+2*s(42)+1*s(43)+1*s(45)+1 0.92/0.95 Such that:s(40) =< V_n 0.92/0.95 aux(22) =< V_a_0 0.92/0.95 s(39) =< aux(22) 0.92/0.95 s(42) =< aux(22) 0.92/0.95 s(43) =< s(42)*s(40) 0.92/0.95 s(44) =< s(42)*s(40) 0.92/0.95 s(45) =< s(44) 0.92/0.95 s(39) =< s(44) 0.92/0.95 0.92/0.95 with precondition: [V_b_0=0,B=4,V_a_0>=2,V_n>=V_a_0] 0.92/0.95 0.92/0.95 * Chain [24,27]: 2*s(49)+1*s(50)+2*s(51)+1*s(52)+1*s(53)+1*s(55)+2 0.92/0.95 Such that:s(46) =< V_n 0.92/0.95 aux(25) =< V_a_0 0.92/0.95 s(49) =< s(46) 0.92/0.95 s(50) =< s(46) 0.92/0.95 s(51) =< aux(25) 0.92/0.95 s(52) =< aux(25) 0.92/0.95 s(50) =< aux(25) 0.92/0.95 s(53) =< s(51)*s(46) 0.92/0.95 s(54) =< s(51)*s(46) 0.92/0.95 s(55) =< s(54) 0.92/0.95 s(52) =< s(54) 0.92/0.95 0.92/0.95 with precondition: [V_b_0=0,B=4,V_a_0>=3,V_n>=V_a_0] 0.92/0.95 0.92/0.95 0.92/0.95 #### Cost of chains of eval_SingleLinkCluster_bb0_in(V_n,B): 0.92/0.95 * Chain [32]: 2*s(107)+0 0.92/0.95 Such that:s(106) =< 1 0.92/0.95 s(107) =< s(106) 0.92/0.95 0.92/0.95 with precondition: [V_n=1] 0.92/0.95 0.92/0.95 * Chain [31]: 0 0.92/0.95 with precondition: [0>=V_n] 0.92/0.95 0.92/0.95 * Chain [30]: 1*s(108)+1*s(111)+4*s(112)+2*s(113)+2*s(115)+1*s(116)+1 0.92/0.95 Such that:s(108) =< 1 0.92/0.95 aux(36) =< V_n 0.92/0.95 s(111) =< s(108)*aux(36) 0.92/0.95 s(112) =< aux(36) 0.92/0.95 s(113) =< aux(36) 0.92/0.95 s(114) =< s(112)*aux(36) 0.92/0.95 s(115) =< s(114) 0.92/0.95 s(113) =< s(114) 0.92/0.95 s(116) =< s(112)*aux(36) 0.92/0.95 0.92/0.95 with precondition: [V_n>=2] 0.92/0.95 0.92/0.95 * Chain [29]: 12*s(120)+4*s(123)+2*s(124)+4*s(126)+1*s(127)+1*s(129)+1*s(130)+1*s(131)+2 0.92/0.95 Such that:s(117) =< V_n+1 0.92/0.95 aux(37) =< V_n 0.92/0.95 s(120) =< aux(37) 0.92/0.95 s(123) =< aux(37) 0.92/0.95 s(124) =< s(120)*aux(37) 0.92/0.95 s(125) =< s(120)*aux(37) 0.92/0.95 s(126) =< s(125) 0.92/0.95 s(123) =< s(125) 0.92/0.95 s(127) =< aux(37) 0.92/0.95 s(128) =< s(117) 0.92/0.95 s(127) =< s(117) 0.92/0.95 s(128) =< aux(37) 0.92/0.95 s(129) =< s(128) 0.92/0.95 s(130) =< s(128) 0.92/0.95 s(131) =< s(129)*aux(37) 0.92/0.95 s(130) =< aux(37) 0.92/0.95 0.92/0.95 with precondition: [V_n>=3] 0.92/0.95 0.92/0.95 * Chain [28]: 7*s(134)+2*s(137)+1*s(138)+2*s(140)+2 0.92/0.95 Such that:aux(38) =< V_n 0.92/0.95 s(134) =< aux(38) 0.92/0.95 s(137) =< aux(38) 0.92/0.95 s(138) =< s(134)*aux(38) 0.92/0.95 s(139) =< s(134)*aux(38) 0.92/0.95 s(140) =< s(139) 0.92/0.95 s(137) =< s(139) 0.92/0.95 0.92/0.95 with precondition: [V_n>=4] 0.92/0.95 0.92/0.95 0.92/0.95 #### Cost of chains of eval_SingleLinkCluster_start(V_n,B): 0.92/0.95 * Chain [37]: 2*s(142)+0 0.92/0.95 Such that:s(141) =< 1 0.92/0.95 s(142) =< s(141) 0.92/0.95 0.92/0.95 with precondition: [V_n=1] 0.92/0.95 0.92/0.95 * Chain [36]: 0 0.92/0.95 with precondition: [0>=V_n] 0.92/0.95 0.92/0.95 * Chain [35]: 1*s(143)+1*s(145)+4*s(146)+2*s(147)+2*s(149)+1*s(150)+1 0.92/0.95 Such that:s(143) =< 1 0.92/0.95 s(144) =< V_n 0.92/0.95 s(145) =< s(143)*s(144) 0.92/0.95 s(146) =< s(144) 0.92/0.95 s(147) =< s(144) 0.92/0.95 s(148) =< s(146)*s(144) 0.92/0.95 s(149) =< s(148) 0.92/0.95 s(147) =< s(148) 0.92/0.95 s(150) =< s(146)*s(144) 0.92/0.95 0.92/0.95 with precondition: [V_n>=2] 0.92/0.95 0.92/0.95 * Chain [34]: 12*s(153)+4*s(154)+2*s(155)+4*s(157)+1*s(158)+1*s(160)+1*s(161)+1*s(162)+2 0.92/0.95 Such that:s(152) =< V_n 0.92/0.95 s(151) =< V_n+1 0.92/0.95 s(153) =< s(152) 0.92/0.95 s(154) =< s(152) 0.92/0.95 s(155) =< s(153)*s(152) 0.92/0.95 s(156) =< s(153)*s(152) 0.92/0.95 s(157) =< s(156) 0.92/0.95 s(154) =< s(156) 0.92/0.95 s(158) =< s(152) 0.92/0.95 s(159) =< s(151) 0.92/0.95 s(158) =< s(151) 0.92/0.95 s(159) =< s(152) 0.92/0.95 s(160) =< s(159) 0.92/0.95 s(161) =< s(159) 0.92/0.95 s(162) =< s(160)*s(152) 0.92/0.95 s(161) =< s(152) 0.92/0.95 0.92/0.95 with precondition: [V_n>=3] 0.92/0.95 0.92/0.95 * Chain [33]: 7*s(164)+2*s(165)+1*s(166)+2*s(168)+2 0.92/0.95 Such that:s(163) =< V_n 0.92/0.95 s(164) =< s(163) 0.92/0.95 s(165) =< s(163) 0.92/0.95 s(166) =< s(164)*s(163) 0.92/0.95 s(167) =< s(164)*s(163) 0.92/0.95 s(168) =< s(167) 0.92/0.95 s(165) =< s(167) 0.92/0.95 0.92/0.95 with precondition: [V_n>=4] 0.92/0.95 0.92/0.95 0.92/0.95 Closed-form bounds of eval_SingleLinkCluster_start(V_n,B): 0.92/0.95 ------------------------------------- 0.92/0.95 * Chain [37] with precondition: [V_n=1] 0.92/0.95 - Upper bound: 2 0.92/0.95 - Complexity: constant 0.92/0.95 * Chain [36] with precondition: [0>=V_n] 0.92/0.95 - Upper bound: 0 0.92/0.95 - Complexity: constant 0.92/0.95 * Chain [35] with precondition: [V_n>=2] 0.92/0.95 - Upper bound: 7*V_n+2+3*V_n*V_n 0.92/0.95 - Complexity: n^2 0.92/0.95 * Chain [34] with precondition: [V_n>=3] 0.92/0.95 - Upper bound: 17*V_n+2+6*V_n*V_n+(V_n+1)*V_n+(2*V_n+2) 0.92/0.95 - Complexity: n^2 0.92/0.95 * Chain [33] with precondition: [V_n>=4] 0.92/0.95 - Upper bound: 9*V_n+2+3*V_n*V_n 0.92/0.95 - Complexity: n^2 0.92/0.95 0.92/0.95 ### Maximum cost of eval_SingleLinkCluster_start(V_n,B): nat(V_n)*3*nat(V_n)+nat(V_n)*8+nat(V_n+1)*nat(V_n)+nat(V_n+1)*2+nat(V_n)*2+(nat(V_n)*3*nat(V_n)+nat(V_n)*7)+2 0.92/0.95 Asymptotic class: n^2 0.92/0.96 * Total analysis performed in 831 ms. 0.92/0.96 0.97/1.06 EOF