/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_foo_0/5,eval_foo_1/6,eval_foo__critedge_in/5,eval_foo_bb1_in/5,eval_foo_bb2_in/5,eval_foo_bb3_in/5,eval_foo_bb4_in/5,eval_foo_bb5_in/5,eval_foo_bb6_in/5,eval_foo_bb7_in/5] 1. non_recursive : [eval_foo_stop/1] 2. non_recursive : [eval_foo_bb8_in/1] 3. non_recursive : [eval_foo_bb1_in_loop_cont/2] 4. non_recursive : [eval_foo_bb0_in/5] 5. non_recursive : [eval_foo_start/5] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into eval_foo_bb1_in/5 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/5 5. SCC is partially evaluated into eval_foo_start/5 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations eval_foo_bb1_in/5 * CE 5 is refined into CE [8] * CE 7 is refined into CE [9] * CE 6 is refined into CE [10] * CE 4 is refined into CE [11] * CE 3 is refined into CE [12] ### Cost equations --> "Loop" of eval_foo_bb1_in/5 * CEs [12] --> Loop 8 * CEs [8] --> Loop 9 * CEs [9] --> Loop 10 * CEs [10] --> Loop 11 * CEs [11] --> Loop 12 ### Ranking functions of CR eval_foo_bb1_in(V_an,V_bn,V__01,V__0,B) * RF of phase [9,11]: [V_an+V_bn-V__01-V__0+1] * RF of phase [10]: [V_an-V__0+1] * RF of phase [12]: [V_bn-V__01+1] #### Partial ranking functions of CR eval_foo_bb1_in(V_an,V_bn,V__01,V__0,B) * Partial RF of phase [9,11]: - RF of loop [9:1]: V_an-V__0+1 - RF of loop [11:1]: V_bn-V__01+1 * Partial RF of phase [10]: - RF of loop [10:1]: V_an-V__0+1 * Partial RF of phase [12]: - RF of loop [12:1]: V_bn-V__01+1 ### Specialization of cost equations eval_foo_bb0_in/5 * CE 2 is refined into CE [13,14,15,16] ### Cost equations --> "Loop" of eval_foo_bb0_in/5 * CEs [13] --> Loop 13 * CEs [14] --> Loop 14 * CEs [15] --> Loop 15 * CEs [16] --> Loop 16 ### Ranking functions of CR eval_foo_bb0_in(V_i,V_j,V_an,V_bn,B) #### Partial ranking functions of CR eval_foo_bb0_in(V_i,V_j,V_an,V_bn,B) ### Specialization of cost equations eval_foo_start/5 * CE 1 is refined into CE [17,18,19,20] ### Cost equations --> "Loop" of eval_foo_start/5 * CEs [20] --> Loop 17 * CEs [19] --> Loop 18 * CEs [18] --> Loop 19 * CEs [17] --> Loop 20 ### Ranking functions of CR eval_foo_start(V_i,V_j,V_an,V_bn,B) #### Partial ranking functions of CR eval_foo_start(V_i,V_j,V_an,V_bn,B) Computing Bounds ===================================== #### Cost of chains of eval_foo_bb1_in(V_an,V_bn,V__01,V__0,B): * Chain [[12],8]: 1*it(12)+0 Such that:it(12) =< V_bn-V__01+1 with precondition: [B=2,V__0>=V_an+1,V_bn>=V__01] * Chain [[10],8]: 1*it(10)+0 Such that:it(10) =< V_an-V__0+1 with precondition: [B=2,V__01>=V_bn+1,V_an>=V__0] * Chain [[9,11],[12],8]: 1*it(9)+1*it(11)+1*it(12)+0 Such that:it(9) =< V_an-V__0+1 it(11) =< V_bn-V__01 aux(3) =< V_an+V_bn-V__01-V__0+1 aux(4) =< V_an+V_bn-V__01-V__0+2 aux(5) =< V_bn-V__01+1 aux(2) =< aux(3) aux(2) =< aux(4) it(12) =< aux(4) it(11) =< aux(5) it(12) =< aux(5) it(9) =< aux(3) it(11) =< aux(3) it(9) =< aux(2) it(11) =< aux(2) with precondition: [B=2,V_bn>=V__01,V_an>=V__0] * Chain [[9,11],[10],8]: 1*it(9)+1*it(10)+1*it(11)+0 Such that:it(9) =< V_an-V__0 it(11) =< V_bn-V__01+1 aux(6) =< V_an+V_bn-V__01-V__0+1 aux(7) =< V_an+V_bn-V__01-V__0+2 aux(8) =< V_an-V__0+1 aux(2) =< aux(6) aux(2) =< aux(7) it(10) =< aux(7) it(9) =< aux(8) it(10) =< aux(8) it(9) =< aux(6) it(11) =< aux(6) it(9) =< aux(2) it(11) =< aux(2) with precondition: [B=2,V_bn>=V__01,V_an>=V__0] * Chain [8]: 0 with precondition: [B=2,V__0>=V_an+1,V__01>=V_bn+1] #### Cost of chains of eval_foo_bb0_in(V_i,V_j,V_an,V_bn,B): * Chain [16]: 1*s(15)+1*s(16)+1*s(21)+1*s(22)+1*s(24)+1*s(25)+0 Such that:s(17) =< -V_i-V_j+V_an+V_bn+1 s(18) =< -V_i-V_j+V_an+V_bn+2 s(15) =< -V_i+V_an s(19) =< -V_i+V_an+1 s(16) =< -V_j+V_bn s(20) =< -V_j+V_bn+1 s(21) =< s(19) s(22) =< s(20) s(23) =< s(17) s(23) =< s(18) s(24) =< s(18) s(15) =< s(19) s(24) =< s(19) s(15) =< s(17) s(22) =< s(17) s(15) =< s(23) s(22) =< s(23) s(25) =< s(18) s(16) =< s(20) s(25) =< s(20) s(21) =< s(17) s(16) =< s(17) s(21) =< s(23) s(16) =< s(23) with precondition: [V_an>=V_i,V_bn>=V_j] * Chain [15]: 1*s(26)+0 Such that:s(26) =< -V_i+V_an+1 with precondition: [V_an>=V_i,V_j>=V_bn+1] * Chain [14]: 1*s(27)+0 Such that:s(27) =< -V_j+V_bn+1 with precondition: [V_bn>=V_j,V_i>=V_an+1] * Chain [13]: 0 with precondition: [V_i>=V_an+1,V_j>=V_bn+1] #### Cost of chains of eval_foo_start(V_i,V_j,V_an,V_bn,B): * Chain [20]: 1*s(30)+1*s(32)+1*s(34)+1*s(35)+1*s(37)+1*s(38)+0 Such that:s(28) =< -V_i-V_j+V_an+V_bn+1 s(29) =< -V_i-V_j+V_an+V_bn+2 s(30) =< -V_i+V_an s(31) =< -V_i+V_an+1 s(32) =< -V_j+V_bn s(33) =< -V_j+V_bn+1 s(34) =< s(31) s(35) =< s(33) s(36) =< s(28) s(36) =< s(29) s(37) =< s(29) s(30) =< s(31) s(37) =< s(31) s(30) =< s(28) s(35) =< s(28) s(30) =< s(36) s(35) =< s(36) s(38) =< s(29) s(32) =< s(33) s(38) =< s(33) s(34) =< s(28) s(32) =< s(28) s(34) =< s(36) s(32) =< s(36) with precondition: [V_an>=V_i,V_bn>=V_j] * Chain [19]: 1*s(39)+0 Such that:s(39) =< -V_i+V_an+1 with precondition: [V_an>=V_i,V_j>=V_bn+1] * Chain [18]: 1*s(40)+0 Such that:s(40) =< -V_j+V_bn+1 with precondition: [V_bn>=V_j,V_i>=V_an+1] * Chain [17]: 0 with precondition: [V_i>=V_an+1,V_j>=V_bn+1] Closed-form bounds of eval_foo_start(V_i,V_j,V_an,V_bn,B): ------------------------------------- * Chain [20] with precondition: [V_an>=V_i,V_bn>=V_j] - Upper bound: -4*V_i-4*V_j+4*V_an+4*V_bn+6 - Complexity: n * Chain [19] with precondition: [V_an>=V_i,V_j>=V_bn+1] - Upper bound: -V_i+V_an+1 - Complexity: n * Chain [18] with precondition: [V_bn>=V_j,V_i>=V_an+1] - Upper bound: -V_j+V_bn+1 - Complexity: n * Chain [17] with precondition: [V_i>=V_an+1,V_j>=V_bn+1] - Upper bound: 0 - Complexity: constant ### Maximum cost of eval_foo_start(V_i,V_j,V_an,V_bn,B): max([nat(-V_j+V_bn+1),nat(-V_j+V_bn)+nat(-V_i+V_an)+nat(-V_j+V_bn+1)+nat(-V_i-V_j+V_an+V_bn+2)*2+nat(-V_i+V_an+1)]) Asymptotic class: n * Total analysis performed in 275 ms.