0.04/0.34	WORST_CASE(?,O(n^2))  
0.04/0.34	
0.04/0.34	Preprocessing Cost Relations
0.04/0.34	=====================================
0.04/0.34	
0.04/0.34	#### Computed strongly connected components 
0.04/0.34	0. recursive  : [eval_ax_bb2_in/4,eval_ax_bb3_in/4]
0.04/0.34	1. recursive  : [eval_ax_12/8,eval_ax_13/8,eval_ax_bb1_in/8,eval_ax_bb2_in_loop_cont/9,eval_ax_bb4_in/8]
0.04/0.34	2. non_recursive  : [eval_ax_stop/7]
0.04/0.34	3. non_recursive  : [eval_ax_bb5_in/7]
0.04/0.34	4. non_recursive  : [exit_location/1]
0.04/0.34	5. non_recursive  : [eval_ax_bb1_in_loop_cont/8]
0.04/0.34	6. non_recursive  : [eval_ax_6/7]
0.04/0.34	7. non_recursive  : [eval_ax_5/7]
0.04/0.34	8. non_recursive  : [eval_ax_4/7]
0.04/0.34	9. non_recursive  : [eval_ax_3/7]
0.04/0.34	10. non_recursive  : [eval_ax_2/7]
0.04/0.34	11. non_recursive  : [eval_ax_1/7]
0.04/0.34	12. non_recursive  : [eval_ax_0/7]
0.04/0.34	13. non_recursive  : [eval_ax_bb0_in/7]
0.04/0.34	14. non_recursive  : [eval_ax_start/7]
0.04/0.34	
0.04/0.34	#### Obtained direct recursion through partial evaluation 
0.04/0.34	0. SCC is partially evaluated into eval_ax_bb2_in/4
0.04/0.34	1. SCC is partially evaluated into eval_ax_bb1_in/8
0.04/0.34	2. SCC is completely evaluated into other SCCs
0.04/0.34	3. SCC is completely evaluated into other SCCs
0.04/0.34	4. SCC is completely evaluated into other SCCs
0.04/0.34	5. SCC is partially evaluated into eval_ax_bb1_in_loop_cont/8
0.04/0.34	6. SCC is partially evaluated into eval_ax_6/7
0.04/0.34	7. SCC is completely evaluated into other SCCs
0.04/0.34	8. SCC is completely evaluated into other SCCs
0.04/0.34	9. SCC is completely evaluated into other SCCs
0.04/0.34	10. SCC is completely evaluated into other SCCs
0.04/0.34	11. SCC is completely evaluated into other SCCs
0.04/0.34	12. SCC is completely evaluated into other SCCs
0.04/0.34	13. SCC is completely evaluated into other SCCs
0.04/0.34	14. SCC is partially evaluated into eval_ax_start/7
0.04/0.34	
0.04/0.34	Control-Flow Refinement of Cost Relations
0.04/0.34	=====================================
0.04/0.34	
0.04/0.34	### Specialization of cost equations eval_ax_bb2_in/4 
0.04/0.34	* CE 12 is refined into CE [13] 
0.04/0.34	* CE 11 is refined into CE [14] 
0.04/0.34	* CE 10 is refined into CE [15] 
0.04/0.34	
0.04/0.34	
0.04/0.34	### Cost equations --> "Loop" of eval_ax_bb2_in/4 
0.04/0.34	* CEs [15] --> Loop 12 
0.04/0.34	* CEs [13] --> Loop 13 
0.04/0.34	* CEs [14] --> Loop 14 
0.04/0.34	
0.04/0.34	### Ranking functions of CR eval_ax_bb2_in(V__01,V_n,B,C) 
0.04/0.34	* RF of phase [12]: [-V__01+V_n-1]
0.04/0.34	
0.04/0.34	#### Partial ranking functions of CR eval_ax_bb2_in(V__01,V_n,B,C) 
0.04/0.34	* Partial RF of phase [12]:
0.04/0.34	  - RF of loop [12:1]:
0.04/0.34	    -V__01+V_n-1
0.04/0.34	
0.04/0.34	
0.04/0.34	### Specialization of cost equations eval_ax_bb1_in/8 
0.04/0.34	* CE 4 is discarded (unfeasible) 
0.04/0.34	* CE 3 is refined into CE [16,17] 
0.04/0.34	* CE 6 is refined into CE [18,19] 
0.04/0.34	* CE 7 is refined into CE [20] 
0.04/0.34	* CE 5 is refined into CE [21] 
0.04/0.34	
0.04/0.34	
0.04/0.34	### Cost equations --> "Loop" of eval_ax_bb1_in/8 
0.04/0.34	* CEs [21] --> Loop 15 
0.04/0.34	* CEs [17] --> Loop 16 
0.04/0.34	* CEs [16] --> Loop 17 
0.04/0.34	* CEs [19] --> Loop 18 
0.04/0.34	* CEs [18,20] --> Loop 19 
0.04/0.34	
0.04/0.34	### Ranking functions of CR eval_ax_bb1_in(V__0,V__01,V_3,V_n,B,C,D,E) 
0.04/0.34	* RF of phase [15]: [-V__0+V_n-2]
0.04/0.34	
0.04/0.34	#### Partial ranking functions of CR eval_ax_bb1_in(V__0,V__01,V_3,V_n,B,C,D,E) 
0.04/0.34	* Partial RF of phase [15]:
0.04/0.34	  - RF of loop [15:1]:
0.04/0.34	    -V__0+V_n-2
0.04/0.34	
0.04/0.34	
0.04/0.34	### Specialization of cost equations eval_ax_bb1_in_loop_cont/8 
0.04/0.34	* CE 8 is refined into CE [22] 
0.04/0.34	* CE 9 is refined into CE [23] 
0.04/0.34	
0.04/0.34	
0.04/0.34	### Cost equations --> "Loop" of eval_ax_bb1_in_loop_cont/8 
0.04/0.34	* CEs [22] --> Loop 20 
0.04/0.34	* CEs [23] --> Loop 21 
0.04/0.34	
0.04/0.34	### Ranking functions of CR eval_ax_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 
0.04/0.34	
0.04/0.34	#### Partial ranking functions of CR eval_ax_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 
0.04/0.34	
0.04/0.34	
0.04/0.34	### Specialization of cost equations eval_ax_6/7 
0.04/0.34	* CE 2 is refined into CE [24,25,26,27,28,29] 
0.04/0.34	
0.04/0.34	
0.04/0.34	### Cost equations --> "Loop" of eval_ax_6/7 
0.04/0.34	* CEs [27,29] --> Loop 22 
0.04/0.34	* CEs [26] --> Loop 23 
0.04/0.34	* CEs [24] --> Loop 24 
0.04/0.34	* CEs [28] --> Loop 25 
0.04/0.34	* CEs [25] --> Loop 26 
0.04/0.34	
0.04/0.34	### Ranking functions of CR eval_ax_6(V__0,V__01,V_3,V_i,V_j,V_n,B) 
0.04/0.34	
0.04/0.34	#### Partial ranking functions of CR eval_ax_6(V__0,V__01,V_3,V_i,V_j,V_n,B) 
0.04/0.34	
0.04/0.34	
0.04/0.34	### Specialization of cost equations eval_ax_start/7 
0.04/0.34	* CE 1 is refined into CE [30,31,32,33,34] 
0.04/0.34	
0.04/0.34	
0.04/0.34	### Cost equations --> "Loop" of eval_ax_start/7 
0.04/0.34	* CEs [34] --> Loop 27 
0.04/0.34	* CEs [33] --> Loop 28 
0.04/0.34	* CEs [32] --> Loop 29 
0.04/0.34	* CEs [31] --> Loop 30 
0.04/0.34	* CEs [30] --> Loop 31 
0.04/0.34	
0.04/0.34	### Ranking functions of CR eval_ax_start(V__0,V__01,V_3,V_i,V_j,V_n,B) 
0.04/0.34	
0.04/0.34	#### Partial ranking functions of CR eval_ax_start(V__0,V__01,V_3,V_i,V_j,V_n,B) 
0.04/0.34	
0.04/0.34	
0.04/0.34	Computing Bounds
0.04/0.34	=====================================
0.04/0.34	
0.04/0.34	#### Cost of chains of eval_ax_bb2_in(V__01,V_n,B,C):
0.04/0.34	* Chain [[12],14]: 1*it(12)+0
0.04/0.34	  Such that:it(12) =< -V__01+C
0.04/0.34	
0.04/0.34	  with precondition: [B=2,V_n=C+1,V__01>=0,V_n>=V__01+2] 
0.04/0.34	
0.04/0.34	* Chain [[12],13]: 1*it(12)+0
0.04/0.34	  Such that:it(12) =< -V__01+V_n
0.04/0.34	
0.04/0.34	  with precondition: [B=3,V__01>=0,V_n>=V__01+2] 
0.04/0.34	
0.04/0.34	* Chain [14]: 0
0.04/0.34	  with precondition: [B=2,V__01=C,V__01>=0,V__01+1>=V_n] 
0.04/0.34	
0.04/0.34	* Chain [13]: 0
0.04/0.34	  with precondition: [B=3,V__01>=0] 
0.04/0.34	
0.04/0.34	
0.04/0.34	#### Cost of chains of eval_ax_bb1_in(V__0,V__01,V_3,V_n,B,C,D,E):
0.04/0.34	* Chain [[15],19]: 1*it(15)+1*s(3)+0
0.04/0.34	  Such that:it(15) =< -V__0+V_n
0.04/0.34	aux(1) =< V_n
0.04/0.34	s(3) =< it(15)*aux(1)
0.04/0.34	
0.04/0.34	  with precondition: [B=3,V__0>=0,V_n>=V__0+3] 
0.04/0.34	
0.04/0.34	* Chain [[15],18]: 1*it(15)+1*s(3)+1*s(4)+0
0.04/0.34	  Such that:it(15) =< -V__0+V_n
0.04/0.34	aux(2) =< V_n
0.04/0.34	s(4) =< aux(2)
0.04/0.34	s(3) =< it(15)*aux(2)
0.04/0.34	
0.04/0.34	  with precondition: [B=3,V__0>=0,V_n>=V__0+3] 
0.04/0.34	
0.04/0.34	* Chain [[15],16]: 1*it(15)+1*s(3)+1*s(5)+0
0.04/0.34	  Such that:it(15) =< -V__0+C
0.04/0.34	aux(3) =< C+2
0.04/0.34	s(5) =< aux(3)
0.04/0.34	s(3) =< it(15)*aux(3)
0.04/0.34	
0.04/0.34	  with precondition: [B=4,V_n=C+2,V_n=D+1,V_n=E+1,V__0>=0,V_n>=V__0+3] 
0.04/0.34	
0.04/0.34	* Chain [19]: 0
0.04/0.34	  with precondition: [B=3,V__0>=0] 
0.04/0.34	
0.04/0.34	* Chain [18]: 1*s(4)+0
0.04/0.34	  Such that:s(4) =< V_n
0.04/0.34	
0.04/0.34	  with precondition: [B=3,V__0>=0,V_n>=2] 
0.04/0.34	
0.04/0.34	* Chain [17]: 0
0.04/0.34	  with precondition: [V__0=0,B=4,C=0,D=0,E=1,1>=V_n] 
0.04/0.34	
0.04/0.34	* Chain [16]: 1*s(5)+0
0.04/0.34	  Such that:s(5) =< V_n
0.04/0.34	
0.04/0.34	  with precondition: [B=4,D+1=V_n,V__0=C,V__0+1=E,D>=1,V__0+1>=D] 
0.04/0.34	
0.04/0.34	
0.04/0.34	#### Cost of chains of eval_ax_bb1_in_loop_cont(A,B,C,D,E,F,G,H):
0.04/0.34	* Chain [21]: 0
0.04/0.34	  with precondition: [A=3] 
0.04/0.34	
0.04/0.34	* Chain [20]: 0
0.04/0.34	  with precondition: [A=4] 
0.04/0.34	
0.04/0.34	
0.04/0.34	#### Cost of chains of eval_ax_6(V__0,V__01,V_3,V_i,V_j,V_n,B):
0.04/0.34	* Chain [26]: 0
0.04/0.34	  with precondition: [] 
0.04/0.34	
0.04/0.34	* Chain [25]: 1*s(13)+0
0.04/0.34	  Such that:s(13) =< 2
0.04/0.34	
0.04/0.34	  with precondition: [V_n=2] 
0.04/0.34	
0.04/0.34	* Chain [24]: 0
0.04/0.34	  with precondition: [1>=V_n] 
0.04/0.34	
0.04/0.34	* Chain [23]: 1*s(14)+0
0.04/0.34	  Such that:s(14) =< V_n
0.04/0.34	
0.04/0.34	  with precondition: [V_n>=2] 
0.04/0.34	
0.04/0.35	* Chain [22]: 5*s(17)+3*s(19)+0
0.04/0.35	  Such that:aux(8) =< V_n
0.04/0.35	s(17) =< aux(8)
0.04/0.35	s(19) =< s(17)*aux(8)
0.04/0.35	
0.04/0.35	  with precondition: [V_n>=3] 
0.04/0.35	
0.04/0.35	
0.04/0.35	#### Cost of chains of eval_ax_start(V__0,V__01,V_3,V_i,V_j,V_n,B):
0.04/0.35	* Chain [31]: 0
0.04/0.35	  with precondition: [] 
0.04/0.35	
0.04/0.35	* Chain [30]: 1*s(24)+0
0.04/0.35	  Such that:s(24) =< 2
0.04/0.35	
0.04/0.35	  with precondition: [V_n=2] 
0.04/0.35	
0.04/0.35	* Chain [29]: 0
0.04/0.35	  with precondition: [1>=V_n] 
0.04/0.35	
0.04/0.35	* Chain [28]: 1*s(25)+0
0.04/0.35	  Such that:s(25) =< V_n
0.04/0.35	
0.04/0.35	  with precondition: [V_n>=2] 
0.04/0.35	
0.04/0.35	* Chain [27]: 5*s(27)+3*s(28)+0
0.04/0.35	  Such that:s(26) =< V_n
0.04/0.35	s(27) =< s(26)
0.04/0.35	s(28) =< s(27)*s(26)
0.04/0.35	
0.04/0.35	  with precondition: [V_n>=3] 
0.04/0.35	
0.04/0.35	
0.04/0.35	Closed-form bounds of eval_ax_start(V__0,V__01,V_3,V_i,V_j,V_n,B): 
0.04/0.35	-------------------------------------
0.04/0.35	* Chain [31] with precondition: [] 
0.04/0.35	    - Upper bound: 0 
0.04/0.35	    - Complexity: constant 
0.04/0.35	* Chain [30] with precondition: [V_n=2] 
0.04/0.35	    - Upper bound: 2 
0.04/0.35	    - Complexity: constant 
0.04/0.35	* Chain [29] with precondition: [1>=V_n] 
0.04/0.35	    - Upper bound: 0 
0.04/0.35	    - Complexity: constant 
0.04/0.35	* Chain [28] with precondition: [V_n>=2] 
0.04/0.35	    - Upper bound: V_n 
0.04/0.35	    - Complexity: n 
0.04/0.35	* Chain [27] with precondition: [V_n>=3] 
0.04/0.35	    - Upper bound: 3*V_n*V_n+5*V_n 
0.04/0.35	    - Complexity: n^2 
0.04/0.35	
0.04/0.35	### Maximum cost of eval_ax_start(V__0,V__01,V_3,V_i,V_j,V_n,B): max([2,nat(V_n)*3*nat(V_n)+nat(V_n)*4+nat(V_n)]) 
0.04/0.35	Asymptotic class: n^2 
0.04/0.35	* Total analysis performed in 265 ms.
0.04/0.35	
0.04/0.45	EOF