/export/starexec/sandbox/solver/bin/starexec_run_C /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^1)) Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [eval_xdr3dfcoord_10/12,eval_xdr3dfcoord_11/13,eval_xdr3dfcoord_bb5_in/10,eval_xdr3dfcoord_bb6_in/10,eval_xdr3dfcoord_bb7_in/12] 1. recursive : [eval_xdr3dfcoord_bb8_in/6,eval_xdr3dfcoord_bb9_in/6] 2. recursive : [eval_xdr3dfcoord_2/4,eval_xdr3dfcoord_3/5,eval_xdr3dfcoord_bb1_in/4,eval_xdr3dfcoord_bb2_in/4,eval_xdr3dfcoord_bb3_in/4,eval_xdr3dfcoord_bb4_in/5,eval_xdr3dfcoord_bb5_in_loop_cont/10,eval_xdr3dfcoord_bb8_in_loop_cont/5] 3. non_recursive : [eval_xdr3dfcoord_stop/1] 4. non_recursive : [eval_xdr3dfcoord_bb10_in/1] 5. non_recursive : [eval_xdr3dfcoord_bb1_in_loop_cont/2] 6. non_recursive : [eval_xdr3dfcoord_bb0_in/3] 7. non_recursive : [eval_xdr3dfcoord_start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into eval_xdr3dfcoord_bb5_in/10 1. SCC is partially evaluated into eval_xdr3dfcoord_bb8_in/6 2. SCC is partially evaluated into eval_xdr3dfcoord_bb1_in/4 3. SCC is completely evaluated into other SCCs 4. SCC is completely evaluated into other SCCs 5. SCC is completely evaluated into other SCCs 6. SCC is partially evaluated into eval_xdr3dfcoord_bb0_in/3 7. SCC is partially evaluated into eval_xdr3dfcoord_start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations eval_xdr3dfcoord_bb5_in/10 * CE 14 is refined into CE [17] * CE 13 is refined into CE [18] * CE 9 is refined into CE [19] * CE 10 is discarded (unfeasible) * CE 7 is refined into CE [20] * CE 11 is refined into CE [21] * CE 8 is discarded (unfeasible) * CE 12 is discarded (unfeasible) ### Cost equations --> "Loop" of eval_xdr3dfcoord_bb5_in/10 * CEs [19] --> Loop 16 * CEs [20] --> Loop 17 * CEs [21] --> Loop 18 * CEs [17] --> Loop 19 * CEs [18] --> Loop 20 ### Ranking functions of CR eval_xdr3dfcoord_bb5_in(V_size,V_limit,V_run_0,V_is_small_2,V_i_1,B,C,D,E,F) * RF of phase [16]: [V_limit-V_run_0,V_size-V_i_1-1] #### Partial ranking functions of CR eval_xdr3dfcoord_bb5_in(V_size,V_limit,V_run_0,V_is_small_2,V_i_1,B,C,D,E,F) * Partial RF of phase [16]: - RF of loop [16:1]: V_limit-V_run_0 V_size-V_i_1-1 ### Specialization of cost equations eval_xdr3dfcoord_bb8_in/6 * CE 16 is refined into CE [22] * CE 15 is refined into CE [23] ### Cost equations --> "Loop" of eval_xdr3dfcoord_bb8_in/6 * CEs [23] --> Loop 21 * CEs [22] --> Loop 22 ### Ranking functions of CR eval_xdr3dfcoord_bb8_in(V_i_0,V_is_small_1,V_run_0,V_is_small_2,V_k_0,B) * RF of phase [21]: [V_run_0/3-V_k_0/3] #### Partial ranking functions of CR eval_xdr3dfcoord_bb8_in(V_i_0,V_is_small_1,V_run_0,V_is_small_2,V_k_0,B) * Partial RF of phase [21]: - RF of loop [21:1]: V_run_0/3-V_k_0/3 ### Specialization of cost equations eval_xdr3dfcoord_bb1_in/4 * CE 6 is refined into CE [24] * CE 3 is refined into CE [25,26,27,28,29,30,31,32,33,34] * CE 4 is refined into CE [35,36] * CE 5 is refined into CE [37,38] ### Cost equations --> "Loop" of eval_xdr3dfcoord_bb1_in/4 * CEs [32] --> Loop 23 * CEs [29] --> Loop 24 * CEs [33] --> Loop 25 * CEs [35] --> Loop 26 * CEs [34,36] --> Loop 27 * CEs [30] --> Loop 28 * CEs [31] --> Loop 29 * CEs [28] --> Loop 30 * CEs [27] --> Loop 31 * CEs [38] --> Loop 32 * CEs [37] --> Loop 33 * CEs [26] --> Loop 34 * CEs [25] --> Loop 35 * CEs [24] --> Loop 36 ### Ranking functions of CR eval_xdr3dfcoord_bb1_in(V_size,V_limit,V_i_0,B) * RF of phase [23,24,25,26,27,28,34]: [V_size-V_i_0-1] #### Partial ranking functions of CR eval_xdr3dfcoord_bb1_in(V_size,V_limit,V_i_0,B) * Partial RF of phase [23,24,25,26,27,28,34]: - RF of loop [23:1,24:1]: V_size/3-V_i_0/3-1 - RF of loop [24:1]: V_size/3-V_limit/3-V_i_0/3-1/3 - RF of loop [25:1]: V_size/2-V_limit/2-V_i_0/2-1/2 - RF of loop [25:1,28:1,34:1]: V_size/2-V_i_0/2-1 - RF of loop [26:1,27:1]: V_size-V_i_0-1 ### Specialization of cost equations eval_xdr3dfcoord_bb0_in/3 * CE 2 is refined into CE [39,40,41,42,43,44,45,46,47,48,49,50,51] ### Cost equations --> "Loop" of eval_xdr3dfcoord_bb0_in/3 * CEs [48] --> Loop 37 * CEs [47] --> Loop 38 * CEs [51] --> Loop 39 * CEs [46] --> Loop 40 * CEs [50] --> Loop 41 * CEs [45] --> Loop 42 * CEs [49] --> Loop 43 * CEs [44] --> Loop 44 * CEs [40] --> Loop 45 * CEs [41] --> Loop 46 * CEs [39] --> Loop 47 * CEs [42] --> Loop 48 * CEs [43] --> Loop 49 ### Ranking functions of CR eval_xdr3dfcoord_bb0_in(V_size,V_limit,B) #### Partial ranking functions of CR eval_xdr3dfcoord_bb0_in(V_size,V_limit,B) ### Specialization of cost equations eval_xdr3dfcoord_start/3 * CE 1 is refined into CE [52,53,54,55,56,57,58,59,60,61,62,63,64] ### Cost equations --> "Loop" of eval_xdr3dfcoord_start/3 * CEs [64] --> Loop 50 * CEs [63] --> Loop 51 * CEs [62] --> Loop 52 * CEs [61] --> Loop 53 * CEs [60] --> Loop 54 * CEs [59] --> Loop 55 * CEs [58] --> Loop 56 * CEs [57] --> Loop 57 * CEs [56] --> Loop 58 * CEs [55] --> Loop 59 * CEs [54] --> Loop 60 * CEs [53] --> Loop 61 * CEs [52] --> Loop 62 ### Ranking functions of CR eval_xdr3dfcoord_start(V_size,V_limit,B) #### Partial ranking functions of CR eval_xdr3dfcoord_start(V_size,V_limit,B) Computing Bounds ===================================== #### Cost of chains of eval_xdr3dfcoord_bb5_in(V_size,V_limit,V_run_0,V_is_small_2,V_i_1,B,C,D,E,F): * Chain [[16],19]: 1*it(16)+0 Such that:it(16) =< V_limit-V_run_0 with precondition: [V_is_small_2=1,B=3,D=1,F=0,V_limit=C,V_i_1+V_limit=V_run_0+E,V_run_0>=0,V_limit>=V_run_0+1,V_run_0+V_size>=V_i_1+V_limit+1] * Chain [[16],18,20]: 1*it(16)+1 Such that:it(16) =< -V_run_0+C with precondition: [V_is_small_2=1,B=3,D=0,F=0,V_size=E,V_run_0+V_size=V_i_1+C,V_run_0>=0,V_size>=V_i_1+2,V_i_1+V_limit>=V_run_0+V_size] * Chain [[16],18,19]: 1*it(16)+1 Such that:it(16) =< V_limit-V_run_0 with precondition: [V_is_small_2=1,B=3,D=0,F=0,V_limit=C,V_size=E,V_run_0+V_size=V_i_1+V_limit,V_size>=V_i_1+2,V_i_1+V_limit>=V_size] * Chain [[16],17,20]: 1*it(16)+1 Such that:it(16) =< -V_run_0+C with precondition: [V_is_small_2=1,B=3,D=0,F=0,V_i_1+C=V_run_0+E,V_run_0>=0,C>=V_run_0+2,V_limit>=C,V_run_0+V_size>=V_i_1+C+1] * Chain [[16],17,19]: 1*it(16)+1 Such that:it(16) =< V_limit-V_run_0 with precondition: [V_is_small_2=1,B=3,D=0,F=0,V_limit=C,V_i_1+V_limit=V_run_0+E,V_run_0>=0,V_limit>=V_run_0+2,V_run_0+V_size>=V_i_1+V_limit+1] * Chain [20]: 0 with precondition: [V_is_small_2=0,B=3,D=0,F=0,V_run_0=C,V_i_1=E,V_run_0>=0,V_size>=V_i_1] * Chain [19]: 0 with precondition: [B=3,F=0,V_run_0=C,V_is_small_2=D,V_i_1=E,1>=V_is_small_2,V_run_0>=0,V_run_0>=V_limit,V_size>=V_i_1+V_is_small_2] * Chain [18,20]: 1 with precondition: [V_is_small_2=1,B=3,D=0,F=0,V_size=V_i_1+1,V_run_0+1=C,V_size=E,V_run_0>=0,V_limit>=V_run_0+1] * Chain [18,19]: 1 with precondition: [V_is_small_2=1,B=3,D=0,F=0,V_limit=V_run_0+1,V_size=V_i_1+1,V_limit=C,V_size=E,V_limit>=1] * Chain [17,20]: 1 with precondition: [V_is_small_2=1,B=3,D=0,F=0,V_run_0+1=C,V_i_1+1=E,V_run_0>=0,V_limit>=V_run_0+1,V_size>=V_i_1+2] * Chain [17,19]: 1 with precondition: [V_is_small_2=1,B=3,D=0,F=0,V_limit=V_run_0+1,E=V_i_1+1,V_limit=C,V_limit>=1,V_size>=E+1] #### Cost of chains of eval_xdr3dfcoord_bb8_in(V_i_0,V_is_small_1,V_run_0,V_is_small_2,V_k_0,B): * Chain [[21],22]: 1*it(21)+0 Such that:it(21) =< V_run_0/3-V_k_0/3 with precondition: [B=2,1>=V_is_small_1,V_is_small_1>=0,V_run_0>=V_k_0+1] * Chain [22]: 0 with precondition: [B=2,1>=V_is_small_1,V_is_small_1>=0,V_k_0>=V_run_0] #### Cost of chains of eval_xdr3dfcoord_bb1_in(V_size,V_limit,V_i_0,B): * Chain [[23,24,25,26,27,28,34],35,36]: 4*it(23)+5*it(25)+5*it(26)+1*s(1)+2*s(19)+1*s(23)+2*s(24)+2 Such that:s(1) =< 1/3 aux(16) =< V_size-V_i_0 aux(17) =< V_size/2-V_i_0/2 aux(18) =< V_size/3-V_i_0/3 aux(4) =< aux(16) it(23) =< aux(16) it(25) =< aux(16) it(26) =< aux(16) it(25) =< aux(17) s(24) =< aux(17) aux(4) =< aux(17) it(23) =< aux(18) s(24) =< aux(18) s(23) =< aux(18) s(24) =< aux(4)*(1/3) s(23) =< aux(16)*(1/3) s(19) =< aux(16)*(1/3) with precondition: [V_limit=1,B=4,V_i_0>=0,V_size>=V_i_0+3] * Chain [[23,24,25,26,27,28,34],33,36]: 2*it(23)+2*it(24)+1*it(25)+5*it(26)+4*it(28)+2*s(19)+1*s(23)+1*s(24)+1*s(25)+1 Such that:aux(8) =< V_size/2-V_limit/2-V_i_0/2 aux(12) =< V_size/3-V_limit/3-V_i_0/3 aux(19) =< V_size-V_i_0 aux(20) =< V_size/2-V_i_0/2 aux(21) =< V_size/3-V_i_0/3 aux(4) =< aux(19) it(23) =< aux(19) it(24) =< aux(19) it(25) =< aux(19) it(26) =< aux(19) it(28) =< aux(19) it(25) =< aux(8) s(25) =< aux(8) it(25) =< aux(20) it(28) =< aux(20) aux(4) =< aux(20) s(24) =< aux(20) s(25) =< aux(20) it(24) =< aux(12) s(25) =< aux(12) it(24) =< aux(21) s(23) =< aux(21) s(24) =< aux(21) s(25) =< aux(21) it(23) =< aux(21) s(25) =< aux(4)*(1/3) s(24) =< aux(4)*(1/3) s(23) =< aux(19)*(1/3) s(19) =< aux(19)*(1/3) with precondition: [B=4,V_i_0>=0,V_size>=V_i_0+2] * Chain [[23,24,25,26,27,28,34],32,36]: 2*it(23)+2*it(24)+1*it(25)+5*it(26)+4*it(28)+2*s(19)+1*s(23)+1*s(24)+1*s(25)+1 Such that:aux(8) =< V_size/2-V_limit/2-V_i_0/2 aux(12) =< V_size/3-V_limit/3-V_i_0/3 aux(22) =< V_size-V_i_0 aux(23) =< V_size/2-V_i_0/2 aux(24) =< V_size/3-V_i_0/3 aux(4) =< aux(22) it(23) =< aux(22) it(24) =< aux(22) it(25) =< aux(22) it(26) =< aux(22) it(28) =< aux(22) it(25) =< aux(8) s(25) =< aux(8) it(25) =< aux(23) it(28) =< aux(23) aux(4) =< aux(23) s(24) =< aux(23) s(25) =< aux(23) it(24) =< aux(12) s(25) =< aux(12) it(24) =< aux(24) s(23) =< aux(24) s(24) =< aux(24) s(25) =< aux(24) it(23) =< aux(24) s(25) =< aux(4)*(1/3) s(24) =< aux(4)*(1/3) s(23) =< aux(22)*(1/3) s(19) =< aux(22)*(1/3) with precondition: [B=4,0>=V_limit,V_i_0>=0,V_size>=V_i_0+2] * Chain [[23,24,25,26,27,28,34],31,36]: 2*it(23)+2*it(24)+1*it(25)+5*it(26)+4*it(28)+2*s(19)+1*s(23)+1*s(24)+1*s(25)+1*s(26)+2 Such that:s(26) =< 1/3 aux(8) =< V_size/2-V_limit/2-V_i_0/2 aux(12) =< V_size/3-V_limit/3-V_i_0/3 aux(25) =< V_size-V_i_0 aux(26) =< V_size/2-V_i_0/2 aux(27) =< V_size/3-V_i_0/3 aux(4) =< aux(25) it(23) =< aux(25) it(24) =< aux(25) it(25) =< aux(25) it(26) =< aux(25) it(28) =< aux(25) it(25) =< aux(8) s(25) =< aux(8) it(25) =< aux(26) it(28) =< aux(26) aux(4) =< aux(26) s(24) =< aux(26) s(25) =< aux(26) it(24) =< aux(12) s(25) =< aux(12) it(24) =< aux(27) s(23) =< aux(27) s(24) =< aux(27) s(25) =< aux(27) it(23) =< aux(27) s(25) =< aux(4)*(1/3) s(24) =< aux(4)*(1/3) s(23) =< aux(25)*(1/3) s(19) =< aux(25)*(1/3) with precondition: [B=4,V_limit>=1,V_i_0>=0,V_size>=V_i_0+3] * Chain [[23,24,25,26,27,28,34],30,36]: 4*it(23)+5*it(25)+5*it(26)+2*s(19)+1*s(23)+1*s(24)+1*s(25)+1*s(27)+1*s(28)+2 Such that:aux(7) =< V_size-V_limit-V_i_0 aux(6) =< V_size-V_i_0 aux(10) =< V_size/2-V_i_0/2 aux(14) =< V_size/3-V_i_0/3 s(27) =< V_limit s(28) =< V_limit/3 aux(28) =< V_size/2-V_limit/2-V_i_0/2 aux(29) =< V_size/3-V_limit/3-V_i_0/3 aux(1) =< aux(6) aux(4) =< aux(6) it(23) =< aux(6) it(25) =< aux(6) it(26) =< aux(6) aux(1) =< aux(7) aux(4) =< aux(7) it(23) =< aux(7) it(25) =< aux(7) it(26) =< aux(7) it(25) =< aux(28) s(25) =< aux(28) aux(4) =< aux(10) it(25) =< aux(10) s(24) =< aux(10) s(25) =< aux(10) aux(4) =< aux(28) it(23) =< aux(29) s(25) =< aux(29) s(23) =< aux(29) s(24) =< aux(29) it(23) =< aux(14) s(25) =< aux(4)*(1/3) s(24) =< aux(4)*(1/3) s(23) =< aux(1)*(1/3) s(19) =< aux(1)*(1/3) with precondition: [B=4,V_limit>=2,V_i_0>=0,V_size>=V_i_0+V_limit+2] * Chain [[23,24,25,26,27,28,34],29,36]: 2*it(23)+2*it(24)+1*it(25)+6*it(26)+4*it(28)+2*s(19)+1*s(23)+1*s(24)+1*s(25)+1*s(30)+2 Such that:aux(8) =< V_size/2-V_limit/2-V_i_0/2 aux(10) =< V_size/2-V_i_0/2 aux(12) =< V_size/3-V_limit/3-V_i_0/3 aux(30) =< V_size-V_i_0 aux(31) =< V_size/3-V_i_0/3 aux(13) =< aux(30) it(26) =< aux(30) s(30) =< aux(30) aux(13) =< aux(31) s(30) =< aux(31) aux(4) =< aux(30) it(23) =< aux(30) it(24) =< aux(30) it(25) =< aux(30) it(28) =< aux(30) it(25) =< aux(8) s(25) =< aux(8) aux(4) =< aux(10) it(25) =< aux(10) it(28) =< aux(10) s(24) =< aux(10) s(25) =< aux(10) it(24) =< aux(12) s(25) =< aux(12) it(24) =< aux(13) s(23) =< aux(13) s(24) =< aux(13) s(25) =< aux(13) it(23) =< aux(31) it(24) =< aux(31) it(23) =< aux(13) s(25) =< aux(4)*(1/3) s(24) =< aux(4)*(1/3) s(23) =< aux(30)*(1/3) s(19) =< aux(30)*(1/3) with precondition: [B=4,V_limit>=2,V_i_0>=0,V_size>=V_i_0+4] * Chain [36]: 0 with precondition: [B=4,V_i_0>=0,V_i_0>=V_size] * Chain [35,36]: 1*s(1)+2 Such that:s(1) =< 1/3 with precondition: [V_limit=1,B=4,V_i_0+2=V_size,V_i_0>=0] * Chain [33,36]: 1 with precondition: [B=4,V_i_0+1=V_size,V_i_0>=0] * Chain [32,36]: 1 with precondition: [B=4,V_i_0+1=V_size,0>=V_limit,V_i_0>=0] * Chain [31,36]: 1*s(26)+2 Such that:s(26) =< 1/3 with precondition: [B=4,V_i_0+2=V_size,V_limit>=1,V_i_0>=0] * Chain [30,36]: 1*s(27)+1*s(28)+2 Such that:s(27) =< V_limit s(28) =< V_limit/3 with precondition: [B=4,V_i_0+V_limit+1=V_size,V_limit>=2,V_i_0>=0] * Chain [29,36]: 1*s(29)+1*s(30)+2 Such that:s(29) =< V_size-V_i_0 s(30) =< V_size/3-V_i_0/3 with precondition: [B=4,V_i_0>=0,V_size>=V_i_0+3,V_i_0+V_limit+1>=V_size] #### Cost of chains of eval_xdr3dfcoord_bb0_in(V_size,V_limit,B): * Chain [49]: 1 with precondition: [V_size=1] * Chain [48]: 1 with precondition: [V_size=1,0>=V_limit] * Chain [47]: 1*s(31)+2 Such that:s(31) =< 1/3 with precondition: [V_size=2,V_limit=1] * Chain [46]: 1*s(32)+2 Such that:s(32) =< 1/3 with precondition: [V_size=2,V_limit>=1] * Chain [45]: 1*s(33)+4*s(38)+5*s(39)+5*s(40)+2*s(41)+1*s(42)+2*s(43)+2 Such that:s(33) =< 1/3 s(34) =< V_size s(35) =< V_size/2 s(36) =< V_size/3 s(37) =< s(34) s(38) =< s(34) s(39) =< s(34) s(40) =< s(34) s(39) =< s(35) s(41) =< s(35) s(37) =< s(35) s(38) =< s(36) s(41) =< s(36) s(42) =< s(36) s(41) =< s(37)*(1/3) s(42) =< s(34)*(1/3) s(43) =< s(34)*(1/3) with precondition: [V_limit=1,V_size>=3] * Chain [44]: 1*s(44)+1*s(45)+2 Such that:s(44) =< V_limit s(45) =< V_limit/3 with precondition: [V_size=V_limit+1,V_size>=3] * Chain [43]: 0 with precondition: [0>=V_size] * Chain [42]: 2*s(52)+2*s(53)+1*s(54)+5*s(55)+4*s(56)+1*s(57)+1*s(58)+1*s(59)+2*s(60)+1 Such that:s(48) =< V_size s(49) =< V_size/2 s(46) =< V_size/2-V_limit/2 s(50) =< V_size/3 s(47) =< V_size/3-V_limit/3 s(51) =< s(48) s(52) =< s(48) s(53) =< s(48) s(54) =< s(48) s(55) =< s(48) s(56) =< s(48) s(54) =< s(46) s(57) =< s(46) s(54) =< s(49) s(56) =< s(49) s(51) =< s(49) s(58) =< s(49) s(57) =< s(49) s(53) =< s(47) s(57) =< s(47) s(53) =< s(50) s(59) =< s(50) s(58) =< s(50) s(57) =< s(50) s(52) =< s(50) s(57) =< s(51)*(1/3) s(58) =< s(51)*(1/3) s(59) =< s(48)*(1/3) s(60) =< s(48)*(1/3) with precondition: [0>=V_limit,V_size>=2] * Chain [41]: 2*s(67)+2*s(68)+1*s(69)+5*s(70)+4*s(71)+1*s(72)+1*s(73)+1*s(74)+2*s(75)+1 Such that:s(63) =< V_size s(64) =< V_size/2 s(61) =< V_size/2-V_limit/2 s(65) =< V_size/3 s(62) =< V_size/3-V_limit/3 s(66) =< s(63) s(67) =< s(63) s(68) =< s(63) s(69) =< s(63) s(70) =< s(63) s(71) =< s(63) s(69) =< s(61) s(72) =< s(61) s(69) =< s(64) s(71) =< s(64) s(66) =< s(64) s(73) =< s(64) s(72) =< s(64) s(68) =< s(62) s(72) =< s(62) s(68) =< s(65) s(74) =< s(65) s(73) =< s(65) s(72) =< s(65) s(67) =< s(65) s(72) =< s(66)*(1/3) s(73) =< s(66)*(1/3) s(74) =< s(63)*(1/3) s(75) =< s(63)*(1/3) with precondition: [V_size>=2] * Chain [40]: 1*s(76)+2*s(83)+2*s(84)+1*s(85)+5*s(86)+4*s(87)+1*s(88)+1*s(89)+1*s(90)+2*s(91)+2 Such that:s(76) =< 1/3 s(79) =< V_size s(80) =< V_size/2 s(77) =< V_size/2-V_limit/2 s(81) =< V_size/3 s(78) =< V_size/3-V_limit/3 s(82) =< s(79) s(83) =< s(79) s(84) =< s(79) s(85) =< s(79) s(86) =< s(79) s(87) =< s(79) s(85) =< s(77) s(88) =< s(77) s(85) =< s(80) s(87) =< s(80) s(82) =< s(80) s(89) =< s(80) s(88) =< s(80) s(84) =< s(78) s(88) =< s(78) s(84) =< s(81) s(90) =< s(81) s(89) =< s(81) s(88) =< s(81) s(83) =< s(81) s(88) =< s(82)*(1/3) s(89) =< s(82)*(1/3) s(90) =< s(79)*(1/3) s(91) =< s(79)*(1/3) with precondition: [V_size>=3,V_limit>=1] * Chain [39]: 1*s(92)+1*s(93)+2 Such that:s(92) =< V_size s(93) =< V_size/3 with precondition: [V_size>=3,V_limit+1>=V_size] * Chain [38]: 6*s(100)+1*s(101)+2*s(103)+2*s(104)+1*s(105)+4*s(106)+1*s(107)+1*s(108)+1*s(109)+2*s(110)+2 Such that:s(97) =< V_size s(95) =< V_size/2 s(94) =< V_size/2-V_limit/2 s(98) =< V_size/3 s(96) =< V_size/3-V_limit/3 s(99) =< s(97) s(100) =< s(97) s(101) =< s(97) s(99) =< s(98) s(101) =< s(98) s(102) =< s(97) s(103) =< s(97) s(104) =< s(97) s(105) =< s(97) s(106) =< s(97) s(105) =< s(94) s(107) =< s(94) s(102) =< s(95) s(105) =< s(95) s(106) =< s(95) s(108) =< s(95) s(107) =< s(95) s(104) =< s(96) s(107) =< s(96) s(104) =< s(99) s(109) =< s(99) s(108) =< s(99) s(107) =< s(99) s(103) =< s(98) s(104) =< s(98) s(103) =< s(99) s(107) =< s(102)*(1/3) s(108) =< s(102)*(1/3) s(109) =< s(97)*(1/3) s(110) =< s(97)*(1/3) with precondition: [V_size>=4,V_limit>=2] * Chain [37]: 1*s(115)+1*s(116)+4*s(121)+5*s(122)+5*s(123)+1*s(124)+1*s(125)+1*s(126)+2*s(127)+2 Such that:s(112) =< V_size s(111) =< V_size-V_limit s(113) =< V_size/2 s(117) =< V_size/2-V_limit/2 s(114) =< V_size/3 s(118) =< V_size/3-V_limit/3 s(115) =< V_limit s(116) =< V_limit/3 s(119) =< s(112) s(120) =< s(112) s(121) =< s(112) s(122) =< s(112) s(123) =< s(112) s(119) =< s(111) s(120) =< s(111) s(121) =< s(111) s(122) =< s(111) s(123) =< s(111) s(122) =< s(117) s(124) =< s(117) s(120) =< s(113) s(122) =< s(113) s(125) =< s(113) s(124) =< s(113) s(120) =< s(117) s(121) =< s(118) s(124) =< s(118) s(126) =< s(118) s(125) =< s(118) s(121) =< s(114) s(124) =< s(120)*(1/3) s(125) =< s(120)*(1/3) s(126) =< s(119)*(1/3) s(127) =< s(119)*(1/3) with precondition: [V_limit>=2,V_size>=V_limit+2] #### Cost of chains of eval_xdr3dfcoord_start(V_size,V_limit,B): * Chain [62]: 1 with precondition: [V_size=1] * Chain [61]: 1 with precondition: [V_size=1,0>=V_limit] * Chain [60]: 1*s(128)+2 Such that:s(128) =< 1/3 with precondition: [V_size=2,V_limit=1] * Chain [59]: 1*s(129)+2 Such that:s(129) =< 1/3 with precondition: [V_size=2,V_limit>=1] * Chain [58]: 1*s(130)+4*s(135)+5*s(136)+5*s(137)+2*s(138)+1*s(139)+2*s(140)+2 Such that:s(130) =< 1/3 s(131) =< V_size s(132) =< V_size/2 s(133) =< V_size/3 s(134) =< s(131) s(135) =< s(131) s(136) =< s(131) s(137) =< s(131) s(136) =< s(132) s(138) =< s(132) s(134) =< s(132) s(135) =< s(133) s(138) =< s(133) s(139) =< s(133) s(138) =< s(134)*(1/3) s(139) =< s(131)*(1/3) s(140) =< s(131)*(1/3) with precondition: [V_limit=1,V_size>=3] * Chain [57]: 1*s(141)+1*s(142)+2 Such that:s(141) =< V_limit s(142) =< V_limit/3 with precondition: [V_size=V_limit+1,V_size>=3] * Chain [56]: 0 with precondition: [0>=V_size] * Chain [55]: 2*s(149)+2*s(150)+1*s(151)+5*s(152)+4*s(153)+1*s(154)+1*s(155)+1*s(156)+2*s(157)+1 Such that:s(143) =< V_size s(144) =< V_size/2 s(145) =< V_size/2-V_limit/2 s(146) =< V_size/3 s(147) =< V_size/3-V_limit/3 s(148) =< s(143) s(149) =< s(143) s(150) =< s(143) s(151) =< s(143) s(152) =< s(143) s(153) =< s(143) s(151) =< s(145) s(154) =< s(145) s(151) =< s(144) s(153) =< s(144) s(148) =< s(144) s(155) =< s(144) s(154) =< s(144) s(150) =< s(147) s(154) =< s(147) s(150) =< s(146) s(156) =< s(146) s(155) =< s(146) s(154) =< s(146) s(149) =< s(146) s(154) =< s(148)*(1/3) s(155) =< s(148)*(1/3) s(156) =< s(143)*(1/3) s(157) =< s(143)*(1/3) with precondition: [0>=V_limit,V_size>=2] * Chain [54]: 2*s(164)+2*s(165)+1*s(166)+5*s(167)+4*s(168)+1*s(169)+1*s(170)+1*s(171)+2*s(172)+1 Such that:s(158) =< V_size s(159) =< V_size/2 s(160) =< V_size/2-V_limit/2 s(161) =< V_size/3 s(162) =< V_size/3-V_limit/3 s(163) =< s(158) s(164) =< s(158) s(165) =< s(158) s(166) =< s(158) s(167) =< s(158) s(168) =< s(158) s(166) =< s(160) s(169) =< s(160) s(166) =< s(159) s(168) =< s(159) s(163) =< s(159) s(170) =< s(159) s(169) =< s(159) s(165) =< s(162) s(169) =< s(162) s(165) =< s(161) s(171) =< s(161) s(170) =< s(161) s(169) =< s(161) s(164) =< s(161) s(169) =< s(163)*(1/3) s(170) =< s(163)*(1/3) s(171) =< s(158)*(1/3) s(172) =< s(158)*(1/3) with precondition: [V_size>=2] * Chain [53]: 1*s(173)+2*s(180)+2*s(181)+1*s(182)+5*s(183)+4*s(184)+1*s(185)+1*s(186)+1*s(187)+2*s(188)+2 Such that:s(173) =< 1/3 s(174) =< V_size s(175) =< V_size/2 s(176) =< V_size/2-V_limit/2 s(177) =< V_size/3 s(178) =< V_size/3-V_limit/3 s(179) =< s(174) s(180) =< s(174) s(181) =< s(174) s(182) =< s(174) s(183) =< s(174) s(184) =< s(174) s(182) =< s(176) s(185) =< s(176) s(182) =< s(175) s(184) =< s(175) s(179) =< s(175) s(186) =< s(175) s(185) =< s(175) s(181) =< s(178) s(185) =< s(178) s(181) =< s(177) s(187) =< s(177) s(186) =< s(177) s(185) =< s(177) s(180) =< s(177) s(185) =< s(179)*(1/3) s(186) =< s(179)*(1/3) s(187) =< s(174)*(1/3) s(188) =< s(174)*(1/3) with precondition: [V_size>=3,V_limit>=1] * Chain [52]: 1*s(189)+1*s(190)+2 Such that:s(189) =< V_size s(190) =< V_size/3 with precondition: [V_size>=3,V_limit+1>=V_size] * Chain [51]: 6*s(197)+1*s(198)+2*s(200)+2*s(201)+1*s(202)+4*s(203)+1*s(204)+1*s(205)+1*s(206)+2*s(207)+2 Such that:s(191) =< V_size s(192) =< V_size/2 s(193) =< V_size/2-V_limit/2 s(194) =< V_size/3 s(195) =< V_size/3-V_limit/3 s(196) =< s(191) s(197) =< s(191) s(198) =< s(191) s(196) =< s(194) s(198) =< s(194) s(199) =< s(191) s(200) =< s(191) s(201) =< s(191) s(202) =< s(191) s(203) =< s(191) s(202) =< s(193) s(204) =< s(193) s(199) =< s(192) s(202) =< s(192) s(203) =< s(192) s(205) =< s(192) s(204) =< s(192) s(201) =< s(195) s(204) =< s(195) s(201) =< s(196) s(206) =< s(196) s(205) =< s(196) s(204) =< s(196) s(200) =< s(194) s(201) =< s(194) s(200) =< s(196) s(204) =< s(199)*(1/3) s(205) =< s(199)*(1/3) s(206) =< s(191)*(1/3) s(207) =< s(191)*(1/3) with precondition: [V_size>=4,V_limit>=2] * Chain [50]: 1*s(214)+1*s(215)+4*s(218)+5*s(219)+5*s(220)+1*s(221)+1*s(222)+1*s(223)+2*s(224)+2 Such that:s(208) =< V_size s(209) =< V_size-V_limit s(210) =< V_size/2 s(211) =< V_size/2-V_limit/2 s(212) =< V_size/3 s(213) =< V_size/3-V_limit/3 s(214) =< V_limit s(215) =< V_limit/3 s(216) =< s(208) s(217) =< s(208) s(218) =< s(208) s(219) =< s(208) s(220) =< s(208) s(216) =< s(209) s(217) =< s(209) s(218) =< s(209) s(219) =< s(209) s(220) =< s(209) s(219) =< s(211) s(221) =< s(211) s(217) =< s(210) s(219) =< s(210) s(222) =< s(210) s(221) =< s(210) s(217) =< s(211) s(218) =< s(213) s(221) =< s(213) s(223) =< s(213) s(222) =< s(213) s(218) =< s(212) s(221) =< s(217)*(1/3) s(222) =< s(217)*(1/3) s(223) =< s(216)*(1/3) s(224) =< s(216)*(1/3) with precondition: [V_limit>=2,V_size>=V_limit+2] Closed-form bounds of eval_xdr3dfcoord_start(V_size,V_limit,B): ------------------------------------- * Chain [62] with precondition: [V_size=1] - Upper bound: 1 - Complexity: constant * Chain [61] with precondition: [V_size=1,0>=V_limit] - Upper bound: 1 - Complexity: constant * Chain [60] with precondition: [V_size=2,V_limit=1] - Upper bound: 7/3 - Complexity: constant * Chain [59] with precondition: [V_size=2,V_limit>=1] - Upper bound: 7/3 - Complexity: constant * Chain [58] with precondition: [V_limit=1,V_size>=3] - Upper bound: 16*V_size+7/3 - Complexity: n * Chain [57] with precondition: [V_size=V_limit+1,V_size>=3] - Upper bound: 4/3*V_limit+2 - Complexity: n * Chain [56] with precondition: [0>=V_size] - Upper bound: 0 - Complexity: constant * Chain [55] with precondition: [0>=V_limit,V_size>=2] - Upper bound: 16*V_size-V_limit/2+1 - Complexity: n * Chain [54] with precondition: [V_size>=2] - Upper bound: V_size/3+(V_size/2+(44/3*V_size+1+nat(V_size/2-V_limit/2))) - Complexity: n * Chain [53] with precondition: [V_size>=3,V_limit>=1] - Upper bound: V_size/3+(V_size/2+(44/3*V_size+7/3+nat(V_size/2-V_limit/2))) - Complexity: n * Chain [52] with precondition: [V_size>=3,V_limit+1>=V_size] - Upper bound: 4/3*V_size+2 - Complexity: n * Chain [51] with precondition: [V_size>=4,V_limit>=2] - Upper bound: V_size/2+(53/3*V_size+2+nat(V_size/2-V_limit/2)) - Complexity: n * Chain [50] with precondition: [V_limit>=2,V_size>=V_limit+2] - Upper bound: 16*V_size+V_limit/2+2 - Complexity: n ### Maximum cost of eval_xdr3dfcoord_start(V_size,V_limit,B): max([max([7/3,nat(V_limit)+2+nat(V_limit/3)]),nat(V_size)+1+max([nat(V_size/3)+1,41/3*nat(V_size)+nat(V_size/2)+max([nat(V_size/2-V_limit/2)+1+max([max([nat(V_size)*3,nat(V_size/3-V_limit/3)+nat(V_limit)+nat(V_limit/3)]),1/3+nat(V_size/3)]),4/3+nat(V_size/2)+nat(V_size/3)])])]) Asymptotic class: n * Total analysis performed in 1217 ms.