0.63/0.63 MAYBE 0.63/0.63 0.63/0.63 Preprocessing Cost Relations 0.63/0.63 ===================================== 0.63/0.63 0.63/0.63 #### Computed strongly connected components 0.63/0.63 0. recursive : [eval_foo_14/8,eval_foo_15/9,eval_foo_4/7,eval_foo_5/8,eval_foo_7/9,eval_foo_8/10,eval_foo_bb10_in/7,eval_foo_bb11_in/7,eval_foo_bb12_in/7,eval_foo_bb1_in/7,eval_foo_bb2_in/7,eval_foo_bb3_in/7,eval_foo_bb4_in/7,eval_foo_bb5_in/7,eval_foo_bb6_in/7,eval_foo_bb7_in/8,eval_foo_bb8_in/8,eval_foo_bb9_in/7] 0.63/0.63 1. non_recursive : [eval_foo_stop/1] 0.63/0.63 2. non_recursive : [eval_foo__critedge_in/1] 0.63/0.63 3. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.63/0.63 4. non_recursive : [eval_foo_bb0_in/7] 0.63/0.63 5. non_recursive : [eval_foo_start/7] 0.63/0.63 0.63/0.63 #### Obtained direct recursion through partial evaluation 0.63/0.63 0. SCC is partially evaluated into eval_foo_bb1_in/7 0.63/0.63 1. SCC is completely evaluated into other SCCs 0.63/0.63 2. SCC is completely evaluated into other SCCs 0.63/0.63 3. SCC is completely evaluated into other SCCs 0.63/0.63 4. SCC is partially evaluated into eval_foo_bb0_in/7 0.63/0.63 5. SCC is partially evaluated into eval_foo_start/7 0.63/0.63 0.63/0.63 Control-Flow Refinement of Cost Relations 0.63/0.63 ===================================== 0.63/0.63 0.63/0.63 ### Specialization of cost equations eval_foo_bb1_in/7 0.63/0.63 * CE 10 is refined into CE [11] 0.63/0.63 * CE 6 is refined into CE [12] 0.63/0.63 * CE 3 is refined into CE [13] 0.63/0.63 * CE 4 is refined into CE [14] 0.63/0.63 * CE 9 is refined into CE [15] 0.63/0.63 * CE 5 is refined into CE [16] 0.63/0.63 * CE 8 is refined into CE [17] 0.63/0.63 * CE 7 is refined into CE [18] 0.63/0.63 0.63/0.63 0.63/0.63 ### Cost equations --> "Loop" of eval_foo_bb1_in/7 0.63/0.63 * CEs [15] --> Loop 11 0.63/0.63 * CEs [16] --> Loop 12 0.63/0.63 * CEs [17] --> Loop 13 0.63/0.63 * CEs [18] --> Loop 14 0.63/0.63 * CEs [11] --> Loop 15 0.63/0.63 * CEs [12] --> Loop 16 0.63/0.63 * CEs [13] --> Loop 17 0.63/0.63 * CEs [14] --> Loop 18 0.63/0.63 0.63/0.63 ### Ranking functions of CR eval_foo_bb1_in(V_an,V_bn,V__010,V__05,V__01,V__0,B) 0.63/0.63 * RF of phase [14]: [V_an-V__0+1] 0.63/0.63 0.63/0.63 #### Partial ranking functions of CR eval_foo_bb1_in(V_an,V_bn,V__010,V__05,V__01,V__0,B) 0.63/0.63 * Partial RF of phase [11,13]: 0.63/0.63 - RF of loop [13:1]: 0.63/0.63 V_an-V__0+1 0.63/0.63 * Partial RF of phase [14]: 0.63/0.63 - RF of loop [14:1]: 0.63/0.63 V_an-V__0+1 0.63/0.63 0.63/0.63 0.63/0.63 ### Specialization of cost equations eval_foo_bb0_in/7 0.63/0.63 * CE 2 is refined into CE [19,20,21,22,23,24,25,26,27,28,29] 0.63/0.63 0.63/0.63 0.63/0.63 ### Cost equations --> "Loop" of eval_foo_bb0_in/7 0.63/0.63 * CEs [28] --> Loop 19 0.63/0.63 * CEs [27,29] --> Loop 20 0.63/0.63 * CEs [19] --> Loop 21 0.63/0.63 * CEs [21] --> Loop 22 0.63/0.63 * CEs [20] --> Loop 23 0.63/0.63 * CEs [22] --> Loop 24 0.63/0.63 * CEs [23] --> Loop 25 0.63/0.63 * CEs [25] --> Loop 26 0.63/0.63 * CEs [24] --> Loop 27 0.63/0.63 * CEs [26] --> Loop 28 0.63/0.63 0.63/0.63 ### Ranking functions of CR eval_foo_bb0_in(V_i,V_j,V_k,V_an,V_bn,V_tk,B) 0.63/0.63 0.63/0.63 #### Partial ranking functions of CR eval_foo_bb0_in(V_i,V_j,V_k,V_an,V_bn,V_tk,B) 0.63/0.63 0.63/0.63 0.63/0.63 ### Specialization of cost equations eval_foo_start/7 0.63/0.63 * CE 1 is refined into CE [30,31,32,33,34,35,36,37,38,39] 0.63/0.63 0.63/0.63 0.63/0.63 ### Cost equations --> "Loop" of eval_foo_start/7 0.63/0.63 * CEs [39] --> Loop 29 0.63/0.63 * CEs [38] --> Loop 30 0.63/0.63 * CEs [37] --> Loop 31 0.63/0.63 * CEs [36] --> Loop 32 0.63/0.63 * CEs [35] --> Loop 33 0.63/0.63 * CEs [34] --> Loop 34 0.63/0.63 * CEs [33] --> Loop 35 0.63/0.63 * CEs [32] --> Loop 36 0.63/0.63 * CEs [31] --> Loop 37 0.63/0.63 * CEs [30] --> Loop 38 0.63/0.63 0.63/0.63 ### Ranking functions of CR eval_foo_start(V_i,V_j,V_k,V_an,V_bn,V_tk,B) 0.63/0.63 0.63/0.63 #### Partial ranking functions of CR eval_foo_start(V_i,V_j,V_k,V_an,V_bn,V_tk,B) 0.63/0.63 0.63/0.63 0.63/0.63 Computing Bounds 0.63/0.63 ===================================== 0.63/0.63 0.63/0.63 #### Cost of chains of eval_foo_bb1_in(V_an,V_bn,V__010,V__05,V__01,V__0,B): 0.63/0.63 * Chain [[14],18]: 1*it(14)+0 0.63/0.63 Such that:it(14) =< V_an-V__0+1 0.63/0.63 0.63/0.63 with precondition: [B=2,V__01>=V_bn+1,V__05>=V__010+1,V_an>=V__0] 0.63/0.63 0.63/0.63 * Chain [[12]]...: 1*it(12)+0 0.63/0.63 with precondition: [V__0>=V_an+1,V_bn>=V__01,V__05>=V__010+1,B=2] 0.63/0.63 0.63/0.63 * Chain [[12],18]: 1*it(12)+0 0.63/0.63 with precondition: [B=2,V__0>=V_an+1,V__05>=V__010+1,V_bn>=V__01] 0.63/0.63 0.63/0.63 * Chain [[12],17]: 1*it(12)+0 0.63/0.63 with precondition: [B=2,V__0>=V_an+1,V__05>=V__010+1,V_bn>=V__01] 0.63/0.63 0.63/0.63 * Chain [[11,13]]...: 1*it(11)+1*it(13)+0 0.63/0.63 Such that:it(13) =< V_an-V__0+1 0.63/0.63 0.63/0.63 with precondition: [V__05>=V__010+1,V_an>=V__0,V_bn>=V__01,B=2] 0.63/0.63 0.63/0.63 * Chain [[11,13],[14],18]: 1*it(11)+1*it(13)+1*it(14)+0 0.63/0.63 Such that:it(13) =< V_an-V__0 0.63/0.63 aux(1) =< V_an-V__0+1 0.63/0.63 it(13) =< aux(1) 0.63/0.63 it(14) =< aux(1) 0.63/0.63 0.63/0.63 with precondition: [B=2,V__05>=V__010+1,V_bn>=V__01,V_an>=V__0] 0.63/0.63 0.63/0.63 * Chain [[11,13],[12]]...: 2*it(11)+1*it(13)+0 0.63/0.63 Such that:it(13) =< V_an-V__0+1 0.63/0.63 0.63/0.63 with precondition: [B=2,V__05>=V__010+1,V_bn>=V__01,V_an>=V__0] 0.63/0.63 0.63/0.63 * Chain [[11,13],[12],18]: 2*it(11)+1*it(13)+0 0.63/0.63 Such that:it(13) =< V_an-V__0+1 0.63/0.63 0.63/0.63 with precondition: [B=2,V__05>=V__010+1,V_bn>=V__01,V_an>=V__0] 0.63/0.63 0.63/0.63 * Chain [[11,13],[12],17]: 2*it(11)+1*it(13)+0 0.63/0.63 Such that:it(13) =< V_an-V__0+1 0.63/0.63 0.63/0.63 with precondition: [B=2,V__05>=V__010+1,V_bn>=V__01,V_an>=V__0] 0.63/0.63 0.63/0.63 * Chain [[11,13],16]: 1*it(11)+1*it(13)+0 0.63/0.63 Such that:it(13) =< V_an-V__0 0.63/0.63 0.63/0.63 with precondition: [B=2,V__05>=V__010+1,V_bn>=V__01,V_an>=V__0] 0.63/0.63 0.63/0.63 * Chain [[11,13],15]: 1*it(11)+1*it(13)+0 0.63/0.63 Such that:it(13) =< V_an-V__0 0.63/0.63 0.63/0.63 with precondition: [B=2,V__05>=V__010+1,V_bn>=V__01,V_an>=V__0,V_bn>=V__01+V__05] 0.63/0.63 0.63/0.63 * Chain [18]: 0 0.63/0.63 with precondition: [B=2,V__0>=V_an+1,V__01>=V_bn+1] 0.63/0.63 0.63/0.63 * Chain [17]: 0 0.63/0.63 with precondition: [B=2,V__0>=V_an+1,V__010>=V__05] 0.63/0.63 0.63/0.63 * Chain [16]: 0 0.63/0.63 with precondition: [B=2,V__01>=V_bn+1,V__010>=V__05,V_an>=V__0] 0.63/0.63 0.63/0.63 * Chain [15]: 0 0.63/0.63 with precondition: [B=2,V__010>=V__05,V_bn>=V__01,V_an>=V__0] 0.63/0.63 0.63/0.63 0.63/0.63 #### Cost of chains of eval_foo_bb0_in(V_i,V_j,V_k,V_an,V_bn,V_tk,B): 0.63/0.63 * Chain [28]: 0 0.63/0.63 with precondition: [V_an>=V_i,V_bn>=V_j,V_tk>=V_k] 0.63/0.63 0.63/0.63 * Chain [27]: 1*s(15)+1*s(16)+3*s(17)+6*s(18)+0 0.63/0.63 Such that:s(13) =< -V_i+V_an 0.63/0.63 s(14) =< -V_i+V_an+1 0.63/0.63 s(15) =< s(13) 0.63/0.63 s(16) =< s(13) 0.63/0.63 s(17) =< s(14) 0.63/0.63 s(16) =< s(14) 0.63/0.63 0.63/0.63 with precondition: [V_an>=V_i,V_bn>=V_j,V_k>=V_tk+1] 0.63/0.63 0.63/0.63 * Chain [26]: 1*s(19)+1*s(20)+0 0.63/0.63 Such that:s(19) =< -V_i+V_an 0.63/0.63 0.63/0.63 with precondition: [V_an>=V_i,V_bn>=V_j,V_k>=V_tk+1,V_bn>=V_j+V_k] 0.63/0.63 0.63/0.63 * Chain [25]: 0 0.63/0.63 with precondition: [V_an>=V_i,V_tk>=V_k,V_j>=V_bn+1] 0.63/0.63 0.63/0.63 * Chain [24]: 1*s(21)+0 0.63/0.63 Such that:s(21) =< -V_i+V_an+1 0.63/0.63 0.63/0.63 with precondition: [V_an>=V_i,V_j>=V_bn+1,V_k>=V_tk+1] 0.63/0.63 0.63/0.63 * Chain [23]: 1*s(22)+0 0.63/0.63 with precondition: [V_bn>=V_j,V_i>=V_an+1,V_k>=V_tk+1] 0.63/0.63 0.63/0.63 * Chain [22]: 0 0.63/0.63 with precondition: [V_tk>=V_k,V_i>=V_an+1] 0.63/0.63 0.63/0.63 * Chain [21]: 0 0.63/0.63 with precondition: [V_i>=V_an+1,V_j>=V_bn+1] 0.63/0.63 0.63/0.63 * Chain [20]...: 2*s(23)+3*s(24)+0 0.63/0.63 Such that:aux(5) =< -V_i+V_an+1 0.63/0.63 s(23) =< aux(5) 0.63/0.63 0.63/0.63 with precondition: [V_an>=V_i,V_bn>=V_j,V_k>=V_tk+1] 0.63/0.63 0.63/0.63 * Chain [19]...: 1*s(27)+0 0.63/0.63 with precondition: [V_bn>=V_j,V_i>=V_an+1,V_k>=V_tk+1] 0.63/0.63 0.63/0.63 0.63/0.63 #### Cost of chains of eval_foo_start(V_i,V_j,V_k,V_an,V_bn,V_tk,B): 0.63/0.63 * Chain [38]: 0 0.63/0.63 with precondition: [V_an>=V_i,V_bn>=V_j,V_tk>=V_k] 0.63/0.63 0.63/0.63 * Chain [37]: 1*s(30)+1*s(31)+3*s(32)+6*s(33)+0 0.63/0.63 Such that:s(28) =< -V_i+V_an 0.63/0.63 s(29) =< -V_i+V_an+1 0.63/0.63 s(30) =< s(28) 0.63/0.63 s(31) =< s(28) 0.63/0.63 s(32) =< s(29) 0.63/0.63 s(31) =< s(29) 0.63/0.63 0.63/0.63 with precondition: [V_an>=V_i,V_bn>=V_j,V_k>=V_tk+1] 0.63/0.63 0.63/0.63 * Chain [36]: 1*s(34)+1*s(35)+0 0.63/0.63 Such that:s(34) =< -V_i+V_an 0.63/0.63 0.63/0.63 with precondition: [V_an>=V_i,V_bn>=V_j,V_k>=V_tk+1,V_bn>=V_j+V_k] 0.63/0.63 0.63/0.63 * Chain [35]: 0 0.63/0.63 with precondition: [V_an>=V_i,V_tk>=V_k,V_j>=V_bn+1] 0.63/0.63 0.63/0.63 * Chain [34]: 1*s(36)+0 0.63/0.63 Such that:s(36) =< -V_i+V_an+1 0.63/0.63 0.63/0.63 with precondition: [V_an>=V_i,V_j>=V_bn+1,V_k>=V_tk+1] 0.63/0.63 0.63/0.63 * Chain [33]: 1*s(37)+0 0.63/0.63 with precondition: [V_bn>=V_j,V_i>=V_an+1,V_k>=V_tk+1] 0.63/0.63 0.63/0.63 * Chain [32]: 0 0.63/0.63 with precondition: [V_tk>=V_k,V_i>=V_an+1] 0.63/0.63 0.63/0.63 * Chain [31]: 0 0.63/0.63 with precondition: [V_i>=V_an+1,V_j>=V_bn+1] 0.63/0.63 0.63/0.63 * Chain [30]...: 2*s(39)+3*s(40)+0 0.63/0.63 Such that:s(38) =< -V_i+V_an+1 0.63/0.63 s(39) =< s(38) 0.63/0.63 0.63/0.63 with precondition: [V_an>=V_i,V_bn>=V_j,V_k>=V_tk+1] 0.63/0.63 0.63/0.63 * Chain [29]...: 1*s(41)+0 0.63/0.63 with precondition: [V_bn>=V_j,V_i>=V_an+1,V_k>=V_tk+1] 0.63/0.63 0.63/0.63 0.63/0.63 Closed-form bounds of eval_foo_start(V_i,V_j,V_k,V_an,V_bn,V_tk,B): 0.63/0.63 ------------------------------------- 0.63/0.63 * Chain [38] with precondition: [V_an>=V_i,V_bn>=V_j,V_tk>=V_k] 0.63/0.63 - Upper bound: 0 0.63/0.63 - Complexity: constant 0.63/0.63 * Chain [37] with precondition: [V_an>=V_i,V_bn>=V_j,V_k>=V_tk+1] 0.63/0.63 - Upper bound: inf 0.63/0.63 - Complexity: infinity 0.63/0.63 * Chain [36] with precondition: [V_an>=V_i,V_bn>=V_j,V_k>=V_tk+1,V_bn>=V_j+V_k] 0.63/0.63 - Upper bound: inf 0.63/0.63 - Complexity: infinity 0.63/0.63 * Chain [35] with precondition: [V_an>=V_i,V_tk>=V_k,V_j>=V_bn+1] 0.63/0.63 - Upper bound: 0 0.63/0.63 - Complexity: constant 0.63/0.63 * Chain [34] with precondition: [V_an>=V_i,V_j>=V_bn+1,V_k>=V_tk+1] 0.63/0.63 - Upper bound: -V_i+V_an+1 0.63/0.63 - Complexity: n 0.63/0.63 * Chain [33] with precondition: [V_bn>=V_j,V_i>=V_an+1,V_k>=V_tk+1] 0.63/0.63 - Upper bound: inf 0.63/0.63 - Complexity: infinity 0.63/0.63 * Chain [32] with precondition: [V_tk>=V_k,V_i>=V_an+1] 0.63/0.63 - Upper bound: 0 0.63/0.63 - Complexity: constant 0.63/0.63 * Chain [31] with precondition: [V_i>=V_an+1,V_j>=V_bn+1] 0.63/0.63 - Upper bound: 0 0.63/0.63 - Complexity: constant 0.63/0.63 * Chain [30]... with precondition: [V_an>=V_i,V_bn>=V_j,V_k>=V_tk+1] 0.63/0.63 - Upper bound: inf 0.63/0.63 - Complexity: infinity 0.63/0.63 * Chain [29]... with precondition: [V_bn>=V_j,V_i>=V_an+1,V_k>=V_tk+1] 0.63/0.63 - Upper bound: inf 0.63/0.63 - Complexity: infinity 0.63/0.63 0.63/0.63 ### Maximum cost of eval_foo_start(V_i,V_j,V_k,V_an,V_bn,V_tk,B): inf 0.63/0.63 Asymptotic class: infinity 0.63/0.63 * Total analysis performed in 510 ms. 0.63/0.63 0.65/0.73 EOF