0.39/0.41 WORST_CASE(?,O(n^2)) 0.39/0.41 0.39/0.41 Preprocessing Cost Relations 0.39/0.41 ===================================== 0.39/0.41 0.39/0.41 #### Computed strongly connected components 0.39/0.41 0. recursive : [evalNestedMultipleDepbb1in/5,evalNestedMultipleDepbb2in/5] 0.39/0.41 1. recursive : [evalNestedMultipleDepbb2in_loop_cont/10,evalNestedMultipleDepbb3in/9,evalNestedMultipleDepbbin/9] 0.39/0.41 2. non_recursive : [evalNestedMultipleDepstop/6] 0.39/0.41 3. non_recursive : [evalNestedMultipleDepreturnin/6] 0.39/0.41 4. non_recursive : [exit_location/1] 0.39/0.41 5. non_recursive : [evalNestedMultipleDepbb3in_loop_cont/7] 0.39/0.41 6. non_recursive : [evalNestedMultipleDepentryin/6] 0.39/0.41 7. non_recursive : [evalNestedMultipleDepstart/6] 0.39/0.41 0.39/0.41 #### Obtained direct recursion through partial evaluation 0.39/0.41 0. SCC is partially evaluated into evalNestedMultipleDepbb2in/5 0.39/0.41 1. SCC is partially evaluated into evalNestedMultipleDepbb3in/9 0.39/0.41 2. SCC is completely evaluated into other SCCs 0.39/0.41 3. SCC is completely evaluated into other SCCs 0.39/0.41 4. SCC is completely evaluated into other SCCs 0.39/0.41 5. SCC is partially evaluated into evalNestedMultipleDepbb3in_loop_cont/7 0.39/0.41 6. SCC is partially evaluated into evalNestedMultipleDepentryin/6 0.39/0.41 7. SCC is partially evaluated into evalNestedMultipleDepstart/6 0.39/0.41 0.39/0.41 Control-Flow Refinement of Cost Relations 0.39/0.41 ===================================== 0.39/0.41 0.39/0.41 ### Specialization of cost equations evalNestedMultipleDepbb2in/5 0.39/0.41 * CE 11 is refined into CE [12] 0.39/0.41 * CE 10 is refined into CE [13] 0.39/0.41 * CE 9 is refined into CE [14] 0.39/0.41 0.39/0.41 0.39/0.41 ### Cost equations --> "Loop" of evalNestedMultipleDepbb2in/5 0.39/0.41 * CEs [14] --> Loop 12 0.39/0.41 * CEs [12] --> Loop 13 0.39/0.41 * CEs [13] --> Loop 14 0.39/0.41 0.39/0.41 ### Ranking functions of CR evalNestedMultipleDepbb2in(A,D,E,F,G) 0.39/0.41 * RF of phase [12]: [-D+E] 0.39/0.41 0.39/0.41 #### Partial ranking functions of CR evalNestedMultipleDepbb2in(A,D,E,F,G) 0.39/0.41 * Partial RF of phase [12]: 0.39/0.41 - RF of loop [12:1]: 0.39/0.41 -D+E 0.39/0.41 0.39/0.41 0.39/0.41 ### Specialization of cost equations evalNestedMultipleDepbb3in/9 0.39/0.41 * CE 5 is refined into CE [15] 0.39/0.41 * CE 3 is refined into CE [16,17] 0.39/0.41 * CE 6 is refined into CE [18] 0.39/0.41 * CE 4 is refined into CE [19,20] 0.39/0.41 0.39/0.41 0.39/0.41 ### Cost equations --> "Loop" of evalNestedMultipleDepbb3in/9 0.39/0.41 * CEs [20] --> Loop 15 0.39/0.41 * CEs [19] --> Loop 16 0.39/0.41 * CEs [15] --> Loop 17 0.39/0.41 * CEs [16] --> Loop 18 0.39/0.41 * CEs [17] --> Loop 19 0.39/0.41 * CEs [18] --> Loop 20 0.39/0.41 0.39/0.41 ### Ranking functions of CR evalNestedMultipleDepbb3in(A,B,C,D,E,F,G,H,I) 0.39/0.41 * RF of phase [15]: [-A+B] 0.39/0.41 * RF of phase [16]: [-A+B] 0.39/0.41 0.39/0.41 #### Partial ranking functions of CR evalNestedMultipleDepbb3in(A,B,C,D,E,F,G,H,I) 0.39/0.41 * Partial RF of phase [15]: 0.39/0.41 - RF of loop [15:1]: 0.39/0.41 -A+B 0.39/0.41 * Partial RF of phase [16]: 0.39/0.41 - RF of loop [16:1]: 0.39/0.41 -A+B 0.39/0.41 0.39/0.41 0.39/0.41 ### Specialization of cost equations evalNestedMultipleDepbb3in_loop_cont/7 0.39/0.41 * CE 7 is refined into CE [21] 0.39/0.41 * CE 8 is refined into CE [22] 0.39/0.41 0.39/0.41 0.39/0.41 ### Cost equations --> "Loop" of evalNestedMultipleDepbb3in_loop_cont/7 0.39/0.41 * CEs [21] --> Loop 21 0.39/0.41 * CEs [22] --> Loop 22 0.39/0.41 0.39/0.41 ### Ranking functions of CR evalNestedMultipleDepbb3in_loop_cont(A,B,C,D,E,F,G) 0.39/0.41 0.39/0.41 #### Partial ranking functions of CR evalNestedMultipleDepbb3in_loop_cont(A,B,C,D,E,F,G) 0.39/0.41 0.39/0.41 0.39/0.41 ### Specialization of cost equations evalNestedMultipleDepentryin/6 0.39/0.41 * CE 2 is refined into CE [23,24,25,26,27,28,29,30,31] 0.39/0.41 0.39/0.41 0.39/0.41 ### Cost equations --> "Loop" of evalNestedMultipleDepentryin/6 0.39/0.41 * CEs [27] --> Loop 23 0.39/0.41 * CEs [26,31] --> Loop 24 0.39/0.41 * CEs [28] --> Loop 25 0.39/0.41 * CEs [24] --> Loop 26 0.39/0.41 * CEs [23,29] --> Loop 27 0.39/0.41 * CEs [30] --> Loop 28 0.39/0.41 * CEs [25] --> Loop 29 0.39/0.41 0.39/0.41 ### Ranking functions of CR evalNestedMultipleDepentryin(A,B,C,D,E,F) 0.39/0.41 0.39/0.41 #### Partial ranking functions of CR evalNestedMultipleDepentryin(A,B,C,D,E,F) 0.39/0.41 0.39/0.41 0.39/0.41 ### Specialization of cost equations evalNestedMultipleDepstart/6 0.39/0.41 * CE 1 is refined into CE [32,33,34,35,36,37,38] 0.39/0.41 0.39/0.41 0.39/0.41 ### Cost equations --> "Loop" of evalNestedMultipleDepstart/6 0.39/0.41 * CEs [38] --> Loop 30 0.39/0.41 * CEs [37] --> Loop 31 0.39/0.41 * CEs [36] --> Loop 32 0.39/0.41 * CEs [35] --> Loop 33 0.39/0.41 * CEs [34] --> Loop 34 0.39/0.41 * CEs [33] --> Loop 35 0.39/0.41 * CEs [32] --> Loop 36 0.39/0.41 0.39/0.41 ### Ranking functions of CR evalNestedMultipleDepstart(A,B,C,D,E,F) 0.39/0.41 0.39/0.41 #### Partial ranking functions of CR evalNestedMultipleDepstart(A,B,C,D,E,F) 0.39/0.41 0.39/0.41 0.39/0.41 Computing Bounds 0.39/0.41 ===================================== 0.39/0.41 0.39/0.41 #### Cost of chains of evalNestedMultipleDepbb2in(A,D,E,F,G): 0.39/0.41 * Chain [[12],14]: 1*it(12)+0 0.39/0.41 Such that:it(12) =< -D+G 0.39/0.41 0.39/0.41 with precondition: [F=2,E=G,A>=0,D>=0,E>=D+1] 0.39/0.41 0.39/0.41 * Chain [[12],13]: 1*it(12)+0 0.39/0.41 Such that:it(12) =< -D+E 0.39/0.41 0.39/0.41 with precondition: [F=3,A>=0,D>=0,E>=D+1] 0.39/0.41 0.39/0.41 * Chain [14]: 0 0.39/0.41 with precondition: [F=2,D=G,A>=0,D>=0,D>=E] 0.39/0.41 0.39/0.41 * Chain [13]: 0 0.39/0.41 with precondition: [F=3,A>=0,D>=0] 0.39/0.41 0.39/0.41 0.39/0.41 #### Cost of chains of evalNestedMultipleDepbb3in(A,B,C,D,E,F,G,H,I): 0.39/0.41 * Chain [[16],20]: 1*it(16)+0 0.39/0.41 Such that:it(16) =< -A+B 0.39/0.41 0.39/0.41 with precondition: [F=3,0>=E,A>=0,B>=A+1] 0.39/0.41 0.39/0.41 * Chain [[16],18]: 1*it(16)+0 0.39/0.41 Such that:it(16) =< -A+B 0.39/0.41 0.39/0.41 with precondition: [F=3,0>=E,A>=0,B>=A+2] 0.39/0.41 0.39/0.41 * Chain [[16],17]: 1*it(16)+0 0.39/0.41 Such that:it(16) =< -A+G 0.39/0.41 0.39/0.41 with precondition: [F=4,I=0,B=G,B=H,0>=E,A>=0,B>=A+1] 0.39/0.41 0.39/0.41 * Chain [[15],20]: 1*it(15)+1*s(3)+0 0.39/0.41 Such that:it(15) =< -A+B 0.39/0.41 aux(1) =< E 0.39/0.41 s(3) =< it(15)*aux(1) 0.39/0.41 0.39/0.41 with precondition: [F=3,A>=0,E>=1,B>=A+1] 0.39/0.41 0.39/0.41 * Chain [[15],19]: 1*it(15)+1*s(3)+1*s(4)+0 0.39/0.41 Such that:it(15) =< -A+B 0.39/0.41 aux(2) =< E 0.39/0.41 s(4) =< aux(2) 0.39/0.41 s(3) =< it(15)*aux(2) 0.39/0.41 0.39/0.41 with precondition: [F=3,A>=0,E>=1,B>=A+2] 0.39/0.41 0.39/0.41 * Chain [[15],18]: 1*it(15)+1*s(3)+0 0.39/0.41 Such that:it(15) =< -A+B 0.39/0.41 aux(1) =< E 0.39/0.41 s(3) =< it(15)*aux(1) 0.39/0.41 0.39/0.41 with precondition: [F=3,A>=0,E>=1,B>=A+2] 0.39/0.41 0.39/0.41 * Chain [[15],17]: 1*it(15)+1*s(3)+0 0.39/0.41 Such that:it(15) =< -A+G 0.39/0.41 aux(1) =< E 0.39/0.41 s(3) =< it(15)*aux(1) 0.39/0.41 0.39/0.41 with precondition: [F=4,B=G,B=H,E=I,A>=0,E>=1,B>=A+1] 0.39/0.41 0.39/0.41 * Chain [20]: 0 0.39/0.41 with precondition: [F=3,A>=0] 0.39/0.41 0.39/0.41 * Chain [19]: 1*s(4)+0 0.39/0.41 Such that:s(4) =< E 0.39/0.41 0.39/0.41 with precondition: [F=3,A>=0,E>=1,B>=A+1] 0.39/0.41 0.39/0.41 * Chain [18]: 0 0.39/0.41 with precondition: [F=3,A>=0,B>=A+1] 0.39/0.41 0.39/0.41 * Chain [17]: 0 0.39/0.41 with precondition: [F=4,H=C,I=D,A=G,A>=0,A>=B] 0.39/0.41 0.39/0.41 0.39/0.41 #### Cost of chains of evalNestedMultipleDepbb3in_loop_cont(A,B,C,D,E,F,G): 0.39/0.41 * Chain [22]: 0 0.39/0.41 with precondition: [A=3] 0.39/0.41 0.39/0.41 * Chain [21]: 0 0.39/0.41 with precondition: [A=4] 0.39/0.41 0.39/0.41 0.39/0.41 #### Cost of chains of evalNestedMultipleDepentryin(A,B,C,D,E,F): 0.39/0.41 * Chain [29]: 0 0.39/0.41 with precondition: [] 0.39/0.41 0.39/0.41 * Chain [28]: 0 0.39/0.41 with precondition: [0>=B] 0.39/0.41 0.39/0.41 * Chain [27]: 2*s(16)+0 0.39/0.41 Such that:aux(6) =< B 0.39/0.41 s(16) =< aux(6) 0.39/0.41 0.39/0.41 with precondition: [0>=E,B>=1] 0.39/0.41 0.39/0.41 * Chain [26]: 1*s(18)+0 0.39/0.41 Such that:s(18) =< B 0.39/0.41 0.39/0.41 with precondition: [0>=E,B>=2] 0.39/0.41 0.39/0.41 * Chain [25]: 0 0.39/0.41 with precondition: [B>=1] 0.39/0.41 0.39/0.41 * Chain [24]: 2*s(19)+1*s(21)+2*s(22)+0 0.39/0.41 Such that:aux(7) =< B 0.39/0.41 aux(8) =< E 0.39/0.41 s(19) =< aux(7) 0.39/0.41 s(21) =< aux(8) 0.39/0.41 s(22) =< s(19)*aux(8) 0.39/0.41 0.39/0.41 with precondition: [B>=1,E>=1] 0.39/0.41 0.39/0.41 * Chain [23]: 2*s(28)+2*s(29)+1*s(30)+0 0.39/0.41 Such that:s(26) =< B 0.39/0.41 s(27) =< E 0.39/0.41 s(28) =< s(26) 0.39/0.41 s(29) =< s(28)*s(27) 0.39/0.41 s(30) =< s(27) 0.39/0.41 0.39/0.41 with precondition: [B>=2,E>=1] 0.39/0.41 0.39/0.41 0.39/0.41 #### Cost of chains of evalNestedMultipleDepstart(A,B,C,D,E,F): 0.39/0.41 * Chain [36]: 0 0.39/0.41 with precondition: [] 0.39/0.41 0.39/0.41 * Chain [35]: 0 0.39/0.41 with precondition: [0>=B] 0.39/0.41 0.39/0.41 * Chain [34]: 2*s(32)+0 0.39/0.41 Such that:s(31) =< B 0.39/0.41 s(32) =< s(31) 0.39/0.41 0.39/0.41 with precondition: [0>=E,B>=1] 0.39/0.41 0.39/0.41 * Chain [33]: 1*s(33)+0 0.39/0.41 Such that:s(33) =< B 0.39/0.41 0.39/0.41 with precondition: [0>=E,B>=2] 0.39/0.41 0.39/0.41 * Chain [32]: 0 0.39/0.41 with precondition: [B>=1] 0.39/0.41 0.39/0.41 * Chain [31]: 2*s(36)+1*s(37)+2*s(38)+0 0.39/0.41 Such that:s(34) =< B 0.39/0.41 s(35) =< E 0.39/0.41 s(36) =< s(34) 0.39/0.41 s(37) =< s(35) 0.39/0.41 s(38) =< s(36)*s(35) 0.39/0.41 0.39/0.41 with precondition: [B>=1,E>=1] 0.39/0.41 0.39/0.41 * Chain [30]: 2*s(41)+2*s(42)+1*s(43)+0 0.39/0.41 Such that:s(39) =< B 0.39/0.41 s(40) =< E 0.39/0.41 s(41) =< s(39) 0.39/0.41 s(42) =< s(41)*s(40) 0.39/0.41 s(43) =< s(40) 0.39/0.41 0.39/0.41 with precondition: [B>=2,E>=1] 0.39/0.41 0.39/0.41 0.39/0.41 Closed-form bounds of evalNestedMultipleDepstart(A,B,C,D,E,F): 0.39/0.41 ------------------------------------- 0.39/0.41 * Chain [36] with precondition: [] 0.39/0.41 - Upper bound: 0 0.39/0.41 - Complexity: constant 0.39/0.41 * Chain [35] with precondition: [0>=B] 0.39/0.41 - Upper bound: 0 0.39/0.41 - Complexity: constant 0.39/0.41 * Chain [34] with precondition: [0>=E,B>=1] 0.39/0.41 - Upper bound: 2*B 0.39/0.41 - Complexity: n 0.39/0.41 * Chain [33] with precondition: [0>=E,B>=2] 0.39/0.41 - Upper bound: B 0.39/0.41 - Complexity: n 0.39/0.41 * Chain [32] with precondition: [B>=1] 0.39/0.41 - Upper bound: 0 0.39/0.41 - Complexity: constant 0.39/0.41 * Chain [31] with precondition: [B>=1,E>=1] 0.39/0.41 - Upper bound: 2*B*E+2*B+E 0.39/0.41 - Complexity: n^2 0.39/0.41 * Chain [30] with precondition: [B>=2,E>=1] 0.39/0.41 - Upper bound: 2*B*E+2*B+E 0.39/0.41 - Complexity: n^2 0.39/0.41 0.39/0.41 ### Maximum cost of evalNestedMultipleDepstart(A,B,C,D,E,F): nat(B)*2*nat(E)+nat(E)+nat(B)+nat(B) 0.39/0.41 Asymptotic class: n^2 0.39/0.41 * Total analysis performed in 332 ms. 0.39/0.41 0.41/0.51 EOF