/export/starexec/sandbox2/solver/bin/starexec_run_C /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^1)) Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [eval_foo_0/4,eval_foo_1/5,eval_foo_4/5,eval_foo_5/6,eval_foo_bb1_in/4,eval_foo_bb2_in/4,eval_foo_bb3_in/4,eval_foo_bb4_in/4] 1. non_recursive : [eval_foo_stop/1] 2. non_recursive : [eval_foo__critedge_in/1] 3. non_recursive : [eval_foo_bb1_in_loop_cont/2] 4. non_recursive : [eval_foo_bb0_in/4] 5. non_recursive : [eval_foo_start/4] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into eval_foo_bb1_in/4 1. SCC is completely evaluated into other SCCs 2. SCC is completely evaluated into other SCCs 3. SCC is completely evaluated into other SCCs 4. SCC is partially evaluated into eval_foo_bb0_in/4 5. SCC is partially evaluated into eval_foo_start/4 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations eval_foo_bb1_in/4 * CE 5 is refined into CE [8] * CE 6 is refined into CE [9] * CE 7 is refined into CE [10] * CE 3 is refined into CE [11] * CE 4 is refined into CE [12] ### Cost equations --> "Loop" of eval_foo_bb1_in/4 * CEs [11] --> Loop 8 * CEs [12] --> Loop 9 * CEs [8] --> Loop 10 * CEs [9] --> Loop 11 * CEs [10] --> Loop 12 ### Ranking functions of CR eval_foo_bb1_in(V__03,V__01,V__0,B) * RF of phase [8]: [V__03/2+V__01/2-V__0/2-1/2] * RF of phase [9]: [V__03] #### Partial ranking functions of CR eval_foo_bb1_in(V__03,V__01,V__0,B) * Partial RF of phase [8]: - RF of loop [8:1]: V__03/2+V__01/2-V__0/2-1/2 * Partial RF of phase [9]: - RF of loop [9:1]: V__03 ### Specialization of cost equations eval_foo_bb0_in/4 * CE 2 is refined into CE [13,14,15,16,17] ### Cost equations --> "Loop" of eval_foo_bb0_in/4 * CEs [16] --> Loop 13 * CEs [17] --> Loop 14 * CEs [13] --> Loop 15 * CEs [14] --> Loop 16 * CEs [15] --> Loop 17 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) ### Specialization of cost equations eval_foo_start/4 * CE 1 is refined into CE [18,19,20,21,22] ### Cost equations --> "Loop" of eval_foo_start/4 * CEs [22] --> Loop 18 * CEs [21] --> Loop 19 * CEs [20] --> Loop 20 * CEs [19] --> Loop 21 * CEs [18] --> Loop 22 ### Ranking functions of CR eval_foo_start(V_x,V_y,V_z,B) #### Partial ranking functions of CR eval_foo_start(V_x,V_y,V_z,B) Computing Bounds ===================================== #### Cost of chains of eval_foo_bb1_in(V__03,V__01,V__0,B): * Chain [[9],12]: 1*it(9)+0 Such that:it(9) =< V__03 with precondition: [B=2,V__03>=1,V__01>=1,V__0>=V__01] * Chain [[9],11]: 1*it(9)+0 Such that:it(9) =< V__03 with precondition: [B=2,V__03>=1,V__01>=1,V__0>=V__01] * Chain [[9],10]: 1*it(9)+0 Such that:it(9) =< V__03 with precondition: [B=2,V__03>=1,V__01>=1,V__0>=V__01] * Chain [[8],[9],12]: 1*it(8)+1*s(1)+0 Such that:it([[9],12]) =< 1 aux(7) =< V__03+V__01-V__0 aux(13) =< V__03/2+V__01/2-V__0/2 it(8) =< aux(13) s(1) =< it([[9],12])*aux(7) it(8) =< it([[9],12])*(1/2)+aux(13) with precondition: [B=2,V__03>=1,V__0>=1,V__01>=V__0+1] * Chain [[8],[9],11]: 1*it(8)+1*s(2)+0 Such that:it([[9],11]) =< 1 aux(20) =< V__03+V__01-V__0 aux(26) =< V__03/2+V__01/2-V__0/2 it(8) =< aux(26) s(2) =< it([[9],11])*aux(20) it(8) =< it([[9],11])*(1/2)+aux(26) with precondition: [B=2,V__03>=1,V__0>=1,V__01>=V__0+1] * Chain [[8],[9],10]: 1*it(8)+1*s(3)+0 Such that:it([[9],10]) =< 1 aux(33) =< V__03+V__01-V__0 aux(39) =< V__03/2+V__01/2-V__0/2 it(8) =< aux(39) s(3) =< it([[9],10])*aux(33) it(8) =< it([[9],10])*(1/2)+aux(39) with precondition: [B=2,V__03>=1,V__0>=1,V__01>=V__0+1] * Chain [[8],12]: 1*it(8)+0 Such that:it(8) =< V__03/2+V__01/2-V__0/2 with precondition: [B=2,V__03>=1,V__0>=1,V__01>=V__0+1] * Chain [[8],10]: 1*it(8)+0 Such that:it(8) =< V__03/2+V__01/2-V__0/2 with precondition: [B=2,V__03>=1,V__0>=1,V__01>=V__0+1] * Chain [12]: 0 with precondition: [B=2,0>=V__03] * Chain [11]: 0 with precondition: [B=2,0>=V__01] * Chain [10]: 0 with precondition: [B=2,0>=V__0] #### Cost of chains of eval_foo_bb0_in(V_x,V_y,V_z,B): * Chain [17]: 0 with precondition: [0>=V_x] * Chain [16]: 0 with precondition: [0>=V_y] * Chain [15]: 0 with precondition: [0>=V_z] * Chain [14]: 2*s(27)+3*s(28)+3*s(29)+0 Such that:s(24) =< 1 s(25) =< -V_x+V_y+V_z s(26) =< -V_x/2+V_y/2+V_z/2 s(27) =< s(26) s(28) =< s(26) s(29) =< s(24)*s(25) s(28) =< s(24)*(1/2)+s(26) with precondition: [V_x>=1,V_z>=1,V_y>=V_x+1] * Chain [13]: 3*s(31)+0 Such that:s(30) =< V_z s(31) =< s(30) with precondition: [V_y>=1,V_z>=1,V_x>=V_y] #### Cost of chains of eval_foo_start(V_x,V_y,V_z,B): * Chain [22]: 0 with precondition: [0>=V_x] * Chain [21]: 0 with precondition: [0>=V_y] * Chain [20]: 0 with precondition: [0>=V_z] * Chain [19]: 2*s(35)+3*s(36)+3*s(37)+0 Such that:s(32) =< 1 s(33) =< -V_x+V_y+V_z s(34) =< -V_x/2+V_y/2+V_z/2 s(35) =< s(34) s(36) =< s(34) s(37) =< s(32)*s(33) s(36) =< s(32)*(1/2)+s(34) with precondition: [V_x>=1,V_z>=1,V_y>=V_x+1] * Chain [18]: 3*s(39)+0 Such that:s(38) =< V_z s(39) =< s(38) with precondition: [V_y>=1,V_z>=1,V_x>=V_y] Closed-form bounds of eval_foo_start(V_x,V_y,V_z,B): ------------------------------------- * Chain [22] with precondition: [0>=V_x] - Upper bound: 0 - Complexity: constant * Chain [21] with precondition: [0>=V_y] - Upper bound: 0 - Complexity: constant * Chain [20] with precondition: [0>=V_z] - Upper bound: 0 - Complexity: constant * Chain [19] with precondition: [V_x>=1,V_z>=1,V_y>=V_x+1] - Upper bound: -11/2*V_x+11/2*V_y+11/2*V_z - Complexity: n * Chain [18] with precondition: [V_y>=1,V_z>=1,V_x>=V_y] - Upper bound: 3*V_z - Complexity: n ### Maximum cost of eval_foo_start(V_x,V_y,V_z,B): max([nat(V_z)*3,nat(-V_x/2+V_y/2+V_z/2)*5+nat(-V_x+V_y+V_z)*3]) Asymptotic class: n * Total analysis performed in 251 ms.