0.03/0.23 WORST_CASE(?,O(n^1)) 0.03/0.23 0.03/0.23 Preprocessing Cost Relations 0.03/0.23 ===================================== 0.03/0.23 0.03/0.23 #### Computed strongly connected components 0.03/0.23 0. recursive : [eval2/6] 0.03/0.23 1. recursive : [eval1/4,eval2_loop_cont/5] 0.03/0.23 2. non_recursive : [exit_location/1] 0.03/0.23 3. non_recursive : [eval1_loop_cont/2] 0.03/0.23 4. non_recursive : [start/4] 0.03/0.23 0.03/0.23 #### Obtained direct recursion through partial evaluation 0.03/0.23 0. SCC is partially evaluated into eval2/6 0.03/0.23 1. SCC is partially evaluated into eval1/4 0.03/0.23 2. SCC is completely evaluated into other SCCs 0.03/0.23 3. SCC is completely evaluated into other SCCs 0.03/0.23 4. SCC is partially evaluated into start/4 0.03/0.23 0.03/0.23 Control-Flow Refinement of Cost Relations 0.03/0.23 ===================================== 0.03/0.23 0.03/0.23 ### Specialization of cost equations eval2/6 0.03/0.23 * CE 7 is refined into CE [8] 0.03/0.23 * CE 6 is refined into CE [9] 0.03/0.23 * CE 5 is refined into CE [10] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of eval2/6 0.03/0.23 * CEs [10] --> Loop 8 0.03/0.23 * CEs [8] --> Loop 9 0.03/0.23 * CEs [9] --> Loop 10 0.03/0.23 0.03/0.23 ### Ranking functions of CR eval2(A,B,C,D,E,F) 0.03/0.23 * RF of phase [8]: [-B+C] 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR eval2(A,B,C,D,E,F) 0.03/0.23 * Partial RF of phase [8]: 0.03/0.23 - RF of loop [8:1]: 0.03/0.23 -B+C 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations eval1/4 0.03/0.23 * CE 2 is refined into CE [11,12] 0.03/0.23 * CE 4 is refined into CE [13] 0.03/0.23 * CE 3 is refined into CE [14,15] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of eval1/4 0.03/0.23 * CEs [15] --> Loop 11 0.03/0.23 * CEs [14] --> Loop 12 0.03/0.23 * CEs [12] --> Loop 13 0.03/0.23 * CEs [11] --> Loop 14 0.03/0.23 * CEs [13] --> Loop 15 0.03/0.23 0.03/0.23 ### Ranking functions of CR eval1(A,B,C,D) 0.03/0.23 * RF of phase [11]: [A-B,A-C] 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR eval1(A,B,C,D) 0.03/0.23 * Partial RF of phase [11]: 0.03/0.23 - RF of loop [11:1]: 0.03/0.23 A-B 0.03/0.23 A-C 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations start/4 0.03/0.23 * CE 1 is refined into CE [16,17,18,19,20,21,22] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of start/4 0.03/0.23 * CEs [22] --> Loop 16 0.03/0.23 * CEs [21] --> Loop 17 0.03/0.23 * CEs [20] --> Loop 18 0.03/0.23 * CEs [19] --> Loop 19 0.03/0.23 * CEs [18] --> Loop 20 0.03/0.23 * CEs [17] --> Loop 21 0.03/0.23 * CEs [16] --> Loop 22 0.03/0.23 0.03/0.23 ### Ranking functions of CR start(A,B,C,D) 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR start(A,B,C,D) 0.03/0.23 0.03/0.23 0.03/0.23 Computing Bounds 0.03/0.23 ===================================== 0.03/0.23 0.03/0.23 #### Cost of chains of eval2(A,B,C,D,E,F): 0.03/0.23 * Chain [[8],10]: 1*it(8)+0 0.03/0.23 Such that:it(8) =< C-F 0.03/0.23 0.03/0.23 with precondition: [D=2,A=E+1,B=F,A>=B+1,C>=B+1] 0.03/0.23 0.03/0.23 * Chain [[8],9]: 1*it(8)+0 0.03/0.23 Such that:it(8) =< -B+C 0.03/0.23 0.03/0.23 with precondition: [D=3,A>=B+1,C>=B+1] 0.03/0.23 0.03/0.23 * Chain [10]: 0 0.03/0.23 with precondition: [D=2,A=E+1,C=F,A>=B+1,B>=C] 0.03/0.23 0.03/0.23 * Chain [9]: 0 0.03/0.23 with precondition: [D=3,A>=B+1] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of eval1(A,B,C,D): 0.03/0.23 * Chain [[11],15]: 1*it(11)+0 0.03/0.23 Such that:it(11) =< A-B 0.03/0.23 0.03/0.23 with precondition: [D=3,A>=B+1,B>=C] 0.03/0.23 0.03/0.23 * Chain [[11],14]: 1*it(11)+0 0.03/0.23 Such that:it(11) =< A-B 0.03/0.23 0.03/0.23 with precondition: [D=3,A>=B+2,B>=C] 0.03/0.23 0.03/0.23 * Chain [15]: 0 0.03/0.23 with precondition: [D=3] 0.03/0.23 0.03/0.23 * Chain [14]: 0 0.03/0.23 with precondition: [D=3,A>=B+1] 0.03/0.23 0.03/0.23 * Chain [13]: 1*s(1)+0 0.03/0.23 Such that:s(1) =< -B+C 0.03/0.23 0.03/0.23 with precondition: [D=3,A>=B+1,C>=B+1] 0.03/0.23 0.03/0.23 * Chain [12,[11],15]: 1*it(11)+1*s(2)+1 0.03/0.23 Such that:it(11) =< A-B 0.03/0.23 s(2) =< -B+C 0.03/0.23 0.03/0.23 with precondition: [D=3,A>=B+2,C>=B+1] 0.03/0.23 0.03/0.23 * Chain [12,[11],14]: 1*it(11)+1*s(2)+1 0.03/0.23 Such that:it(11) =< A-B 0.03/0.23 s(2) =< -B+C 0.03/0.23 0.03/0.23 with precondition: [D=3,A>=B+3,C>=B+1] 0.03/0.23 0.03/0.23 * Chain [12,15]: 1*s(2)+1 0.03/0.23 Such that:s(2) =< -B+C 0.03/0.23 0.03/0.23 with precondition: [D=3,A>=B+1,C>=B+1] 0.03/0.23 0.03/0.23 * Chain [12,14]: 1*s(2)+1 0.03/0.23 Such that:s(2) =< -B+C 0.03/0.23 0.03/0.23 with precondition: [D=3,A>=B+2,C>=B+1] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of start(A,B,C,D): 0.03/0.23 * Chain [22]: 0 0.03/0.23 with precondition: [] 0.03/0.23 0.03/0.23 * Chain [21]: 0 0.03/0.23 with precondition: [A>=B+1] 0.03/0.23 0.03/0.23 * Chain [20]: 2*s(9)+1 0.03/0.23 Such that:s(8) =< -B+C 0.03/0.23 s(9) =< s(8) 0.03/0.23 0.03/0.23 with precondition: [A>=B+1,C>=B+1] 0.03/0.23 0.03/0.23 * Chain [19]: 1*s(10)+0 0.03/0.23 Such that:s(10) =< A-B 0.03/0.23 0.03/0.23 with precondition: [A>=B+1,B>=C] 0.03/0.23 0.03/0.23 * Chain [18]: 1*s(11)+2*s(13)+1 0.03/0.23 Such that:s(11) =< A-B 0.03/0.23 s(12) =< -B+C 0.03/0.23 s(13) =< s(12) 0.03/0.23 0.03/0.23 with precondition: [A>=B+2,C>=B+1] 0.03/0.23 0.03/0.23 * Chain [17]: 1*s(14)+0 0.03/0.23 Such that:s(14) =< A-B 0.03/0.23 0.03/0.23 with precondition: [A>=B+2,B>=C] 0.03/0.23 0.03/0.23 * Chain [16]: 1*s(15)+1*s(16)+1 0.03/0.23 Such that:s(15) =< A-B 0.03/0.23 s(16) =< -B+C 0.03/0.23 0.03/0.23 with precondition: [A>=B+3,C>=B+1] 0.03/0.23 0.03/0.23 0.03/0.23 Closed-form bounds of start(A,B,C,D): 0.03/0.23 ------------------------------------- 0.03/0.23 * Chain [22] with precondition: [] 0.03/0.23 - Upper bound: 0 0.03/0.23 - Complexity: constant 0.03/0.23 * Chain [21] with precondition: [A>=B+1] 0.03/0.23 - Upper bound: 0 0.03/0.23 - Complexity: constant 0.03/0.23 * Chain [20] with precondition: [A>=B+1,C>=B+1] 0.03/0.23 - Upper bound: -2*B+2*C+1 0.03/0.23 - Complexity: n 0.03/0.23 * Chain [19] with precondition: [A>=B+1,B>=C] 0.03/0.23 - Upper bound: A-B 0.03/0.23 - Complexity: n 0.03/0.23 * Chain [18] with precondition: [A>=B+2,C>=B+1] 0.03/0.23 - Upper bound: A-3*B+2*C+1 0.03/0.23 - Complexity: n 0.03/0.23 * Chain [17] with precondition: [A>=B+2,B>=C] 0.03/0.23 - Upper bound: A-B 0.03/0.23 - Complexity: n 0.03/0.23 * Chain [16] with precondition: [A>=B+3,C>=B+1] 0.03/0.23 - Upper bound: A-2*B+C+1 0.03/0.23 - Complexity: n 0.03/0.23 0.03/0.23 ### Maximum cost of start(A,B,C,D): nat(-B+C)*2+1+nat(A-B) 0.03/0.23 Asymptotic class: n 0.03/0.23 * Total analysis performed in 175 ms. 0.03/0.23 0.03/0.34 EOF