0.04/0.33	WORST_CASE(?,O(n^2))  
0.04/0.33	
0.04/0.33	Preprocessing Cost Relations
0.04/0.33	=====================================
0.04/0.33	
0.04/0.33	#### Computed strongly connected components 
0.04/0.33	0. recursive  : [eval_sipmabubble_bb2_in/4,eval_sipmabubble_bb3_in/4,eval_sipmabubble_bb4_in/4,eval_sipmabubble_bb5_in/4]
0.04/0.33	1. recursive  : [eval_sipmabubble_29/7,eval_sipmabubble_30/7,eval_sipmabubble_bb1_in/7,eval_sipmabubble_bb2_in_loop_cont/8,eval_sipmabubble_bb6_in/7]
0.04/0.33	2. non_recursive  : [eval_sipmabubble_stop/5]
0.04/0.33	3. non_recursive  : [eval_sipmabubble_bb7_in/5]
0.04/0.33	4. non_recursive  : [exit_location/1]
0.04/0.33	5. non_recursive  : [eval_sipmabubble_bb1_in_loop_cont/6]
0.04/0.33	6. non_recursive  : [eval_sipmabubble_6/5]
0.04/0.33	7. non_recursive  : [eval_sipmabubble_5/5]
0.04/0.33	8. non_recursive  : [eval_sipmabubble_4/5]
0.04/0.33	9. non_recursive  : [eval_sipmabubble_3/5]
0.04/0.33	10. non_recursive  : [eval_sipmabubble_2/5]
0.04/0.33	11. non_recursive  : [eval_sipmabubble_1/5]
0.04/0.33	12. non_recursive  : [eval_sipmabubble_0/5]
0.04/0.33	13. non_recursive  : [eval_sipmabubble_bb0_in/5]
0.04/0.33	14. non_recursive  : [eval_sipmabubble_start/5]
0.04/0.33	
0.04/0.33	#### Obtained direct recursion through partial evaluation 
0.04/0.33	0. SCC is partially evaluated into eval_sipmabubble_bb2_in/4
0.04/0.33	1. SCC is partially evaluated into eval_sipmabubble_bb1_in/7
0.04/0.33	2. SCC is completely evaluated into other SCCs
0.04/0.33	3. SCC is completely evaluated into other SCCs
0.04/0.33	4. SCC is completely evaluated into other SCCs
0.04/0.33	5. SCC is partially evaluated into eval_sipmabubble_bb1_in_loop_cont/6
0.04/0.33	6. SCC is partially evaluated into eval_sipmabubble_6/5
0.04/0.33	7. SCC is completely evaluated into other SCCs
0.04/0.33	8. SCC is completely evaluated into other SCCs
0.04/0.33	9. SCC is completely evaluated into other SCCs
0.04/0.33	10. SCC is completely evaluated into other SCCs
0.04/0.33	11. SCC is completely evaluated into other SCCs
0.04/0.33	12. SCC is completely evaluated into other SCCs
0.04/0.33	13. SCC is completely evaluated into other SCCs
0.04/0.33	14. SCC is partially evaluated into eval_sipmabubble_start/5
0.04/0.33	
0.04/0.33	Control-Flow Refinement of Cost Relations
0.04/0.33	=====================================
0.04/0.33	
0.04/0.33	### Specialization of cost equations eval_sipmabubble_bb2_in/4 
0.04/0.33	* CE 11 is refined into CE [12] 
0.04/0.33	* CE 10 is refined into CE [13] 
0.04/0.33	* CE 9 is refined into CE [14] 
0.04/0.33	
0.04/0.33	
0.04/0.33	### Cost equations --> "Loop" of eval_sipmabubble_bb2_in/4 
0.04/0.33	* CEs [14] --> Loop 12 
0.04/0.33	* CEs [12] --> Loop 13 
0.04/0.33	* CEs [13] --> Loop 14 
0.04/0.33	
0.04/0.33	### Ranking functions of CR eval_sipmabubble_bb2_in(V_i_0,V_j_0,B,C) 
0.04/0.33	* RF of phase [12]: [V_i_0-V_j_0]
0.04/0.33	
0.04/0.33	#### Partial ranking functions of CR eval_sipmabubble_bb2_in(V_i_0,V_j_0,B,C) 
0.04/0.33	* Partial RF of phase [12]:
0.04/0.33	  - RF of loop [12:1]:
0.04/0.33	    V_i_0-V_j_0
0.04/0.33	
0.04/0.33	
0.04/0.33	### Specialization of cost equations eval_sipmabubble_bb1_in/7 
0.04/0.33	* CE 5 is refined into CE [15] 
0.04/0.33	* CE 3 is refined into CE [16,17] 
0.04/0.33	* CE 6 is refined into CE [18] 
0.04/0.33	* CE 4 is refined into CE [19,20] 
0.04/0.33	
0.04/0.33	
0.04/0.33	### Cost equations --> "Loop" of eval_sipmabubble_bb1_in/7 
0.04/0.33	* CEs [20] --> Loop 15 
0.04/0.33	* CEs [19] --> Loop 16 
0.04/0.33	* CEs [15] --> Loop 17 
0.04/0.33	* CEs [17] --> Loop 18 
0.04/0.33	* CEs [16] --> Loop 19 
0.04/0.33	* CEs [18] --> Loop 20 
0.04/0.33	
0.04/0.33	### Ranking functions of CR eval_sipmabubble_bb1_in(V_24,V_i_0,V_j_0,B,C,D,E) 
0.04/0.33	* RF of phase [15]: [V_i_0]
0.04/0.33	
0.04/0.33	#### Partial ranking functions of CR eval_sipmabubble_bb1_in(V_24,V_i_0,V_j_0,B,C,D,E) 
0.04/0.33	* Partial RF of phase [15]:
0.04/0.33	  - RF of loop [15:1]:
0.04/0.33	    V_i_0
0.04/0.33	
0.04/0.33	
0.04/0.33	### Specialization of cost equations eval_sipmabubble_bb1_in_loop_cont/6 
0.04/0.33	* CE 7 is refined into CE [21] 
0.04/0.33	* CE 8 is refined into CE [22] 
0.04/0.33	
0.04/0.33	
0.04/0.33	### Cost equations --> "Loop" of eval_sipmabubble_bb1_in_loop_cont/6 
0.04/0.33	* CEs [21] --> Loop 21 
0.04/0.33	* CEs [22] --> Loop 22 
0.04/0.33	
0.04/0.33	### Ranking functions of CR eval_sipmabubble_bb1_in_loop_cont(A,B,C,D,E,F) 
0.04/0.33	
0.04/0.33	#### Partial ranking functions of CR eval_sipmabubble_bb1_in_loop_cont(A,B,C,D,E,F) 
0.04/0.33	
0.04/0.33	
0.04/0.33	### Specialization of cost equations eval_sipmabubble_6/5 
0.04/0.33	* CE 2 is refined into CE [23,24,25,26,27,28,29,30] 
0.04/0.33	
0.04/0.33	
0.04/0.33	### Cost equations --> "Loop" of eval_sipmabubble_6/5 
0.04/0.33	* CEs [28] --> Loop 23 
0.04/0.33	* CEs [27,29] --> Loop 24 
0.04/0.33	* CEs [26] --> Loop 25 
0.04/0.33	* CEs [30] --> Loop 26 
0.04/0.33	* CEs [23,24] --> Loop 27 
0.04/0.33	* CEs [25] --> Loop 28 
0.04/0.33	
0.04/0.33	### Ranking functions of CR eval_sipmabubble_6(V_24,V_i_0,V_j_0,V_n,B) 
0.04/0.33	
0.04/0.33	#### Partial ranking functions of CR eval_sipmabubble_6(V_24,V_i_0,V_j_0,V_n,B) 
0.04/0.33	
0.04/0.33	
0.04/0.33	### Specialization of cost equations eval_sipmabubble_start/5 
0.04/0.33	* CE 1 is refined into CE [31,32,33,34,35,36] 
0.04/0.33	
0.04/0.33	
0.04/0.33	### Cost equations --> "Loop" of eval_sipmabubble_start/5 
0.04/0.33	* CEs [36] --> Loop 29 
0.04/0.33	* CEs [35] --> Loop 30 
0.04/0.33	* CEs [34] --> Loop 31 
0.04/0.33	* CEs [33] --> Loop 32 
0.04/0.33	* CEs [32] --> Loop 33 
0.04/0.33	* CEs [31] --> Loop 34 
0.04/0.33	
0.04/0.33	### Ranking functions of CR eval_sipmabubble_start(V_24,V_i_0,V_j_0,V_n,B) 
0.04/0.33	
0.04/0.33	#### Partial ranking functions of CR eval_sipmabubble_start(V_24,V_i_0,V_j_0,V_n,B) 
0.04/0.33	
0.04/0.33	
0.04/0.33	Computing Bounds
0.04/0.33	=====================================
0.04/0.33	
0.04/0.33	#### Cost of chains of eval_sipmabubble_bb2_in(V_i_0,V_j_0,B,C):
0.04/0.33	* Chain [[12],14]: 1*it(12)+0
0.04/0.33	  Such that:it(12) =< -V_j_0+C
0.04/0.33	
0.04/0.33	  with precondition: [B=2,V_i_0=C,V_j_0>=0,V_i_0>=V_j_0+1] 
0.04/0.33	
0.04/0.33	* Chain [[12],13]: 1*it(12)+0
0.04/0.33	  Such that:it(12) =< V_i_0-V_j_0
0.04/0.33	
0.04/0.33	  with precondition: [B=3,V_j_0>=0,V_i_0>=V_j_0+1] 
0.04/0.33	
0.04/0.33	* Chain [14]: 0
0.04/0.33	  with precondition: [B=2,V_j_0=V_i_0,V_j_0=C,V_j_0>=0] 
0.04/0.33	
0.04/0.33	* Chain [13]: 0
0.04/0.33	  with precondition: [B=3,V_j_0>=0,V_i_0>=V_j_0] 
0.04/0.33	
0.04/0.33	
0.04/0.33	#### Cost of chains of eval_sipmabubble_bb1_in(V_24,V_i_0,V_j_0,B,C,D,E):
0.04/0.33	* Chain [[15],20]: 1*it(15)+1*s(3)+0
0.04/0.33	  Such that:aux(3) =< V_i_0
0.04/0.33	it(15) =< aux(3)
0.04/0.33	s(3) =< it(15)*aux(3)
0.04/0.33	
0.04/0.33	  with precondition: [B=3,V_i_0>=1] 
0.04/0.33	
0.04/0.33	* Chain [[15],19]: 1*it(15)+1*s(3)+0
0.04/0.33	  Such that:aux(4) =< V_i_0
0.04/0.33	it(15) =< aux(4)
0.04/0.33	s(3) =< it(15)*aux(4)
0.04/0.33	
0.04/0.33	  with precondition: [B=3,V_i_0>=1] 
0.04/0.33	
0.04/0.33	* Chain [[15],18]: 2*it(15)+1*s(3)+0
0.04/0.33	  Such that:aux(5) =< V_i_0
0.04/0.33	it(15) =< aux(5)
0.04/0.33	s(3) =< it(15)*aux(5)
0.04/0.33	
0.04/0.33	  with precondition: [B=3,V_i_0>=2] 
0.04/0.33	
0.04/0.33	* Chain [[15],16,20]: 1*it(15)+1*s(3)+1
0.04/0.33	  Such that:aux(6) =< V_i_0
0.04/0.33	it(15) =< aux(6)
0.04/0.33	s(3) =< it(15)*aux(6)
0.04/0.33	
0.04/0.33	  with precondition: [B=3,V_i_0>=1] 
0.04/0.33	
0.04/0.33	* Chain [[15],16,17]: 1*it(15)+1*s(3)+1
0.04/0.33	  Such that:aux(7) =< V_i_0
0.04/0.33	it(15) =< aux(7)
0.04/0.33	s(3) =< it(15)*aux(7)
0.04/0.33	
0.04/0.33	  with precondition: [B=4,C+1=0,D+1=0,E=0,V_i_0>=1] 
0.04/0.33	
0.04/0.33	* Chain [20]: 0
0.04/0.33	  with precondition: [B=3] 
0.04/0.33	
0.04/0.33	* Chain [19]: 0
0.04/0.33	  with precondition: [B=3,V_i_0>=0] 
0.04/0.33	
0.04/0.33	* Chain [18]: 1*s(4)+0
0.04/0.33	  Such that:s(4) =< V_i_0
0.04/0.33	
0.04/0.33	  with precondition: [B=3,V_i_0>=1] 
0.04/0.33	
0.04/0.33	* Chain [17]: 0
0.04/0.33	  with precondition: [B=4,C=V_24,E=V_j_0,V_i_0=D,0>=V_i_0+1] 
0.04/0.33	
0.04/0.33	* Chain [16,20]: 1
0.04/0.33	  with precondition: [V_i_0=0,B=3] 
0.04/0.33	
0.04/0.33	* Chain [16,17]: 1
0.04/0.33	  with precondition: [V_i_0=0,B=4,C+1=0,D+1=0,E=0] 
0.04/0.33	
0.04/0.33	
0.04/0.33	#### Cost of chains of eval_sipmabubble_bb1_in_loop_cont(A,B,C,D,E,F):
0.04/0.33	* Chain [22]: 0
0.04/0.33	  with precondition: [A=3] 
0.04/0.33	
0.04/0.33	* Chain [21]: 0
0.04/0.33	  with precondition: [A=4] 
0.04/0.33	
0.04/0.33	
0.04/0.33	#### Cost of chains of eval_sipmabubble_6(V_24,V_i_0,V_j_0,V_n,B):
0.04/0.33	* Chain [28]: 0
0.04/0.33	  with precondition: [] 
0.04/0.33	
0.04/0.33	* Chain [27]: 1
0.04/0.33	  with precondition: [V_n=0] 
0.04/0.33	
0.04/0.33	* Chain [26]: 0
0.04/0.33	  with precondition: [0>=V_n+1] 
0.04/0.33	
0.04/0.33	* Chain [25]: 0
0.04/0.33	  with precondition: [V_n>=0] 
0.04/0.33	
0.04/0.33	* Chain [24]: 5*s(16)+4*s(17)+1
0.04/0.33	  Such that:aux(9) =< V_n
0.04/0.33	s(16) =< aux(9)
0.04/0.33	s(17) =< s(16)*aux(9)
0.04/0.33	
0.04/0.33	  with precondition: [V_n>=1] 
0.04/0.33	
0.04/0.33	* Chain [23]: 2*s(22)+1*s(23)+0
0.04/0.33	  Such that:s(21) =< V_n
0.04/0.33	s(22) =< s(21)
0.04/0.33	s(23) =< s(22)*s(21)
0.04/0.33	
0.04/0.33	  with precondition: [V_n>=2] 
0.04/0.33	
0.04/0.33	
0.04/0.33	#### Cost of chains of eval_sipmabubble_start(V_24,V_i_0,V_j_0,V_n,B):
0.04/0.33	* Chain [34]: 0
0.04/0.33	  with precondition: [] 
0.04/0.33	
0.04/0.33	* Chain [33]: 1
0.04/0.33	  with precondition: [V_n=0] 
0.04/0.33	
0.04/0.33	* Chain [32]: 0
0.04/0.33	  with precondition: [0>=V_n+1] 
0.04/0.33	
0.04/0.33	* Chain [31]: 0
0.04/0.33	  with precondition: [V_n>=0] 
0.04/0.33	
0.04/0.33	* Chain [30]: 5*s(25)+4*s(26)+1
0.04/0.33	  Such that:s(24) =< V_n
0.04/0.33	s(25) =< s(24)
0.04/0.33	s(26) =< s(25)*s(24)
0.04/0.33	
0.04/0.33	  with precondition: [V_n>=1] 
0.04/0.33	
0.04/0.33	* Chain [29]: 2*s(28)+1*s(29)+0
0.04/0.33	  Such that:s(27) =< V_n
0.04/0.33	s(28) =< s(27)
0.04/0.33	s(29) =< s(28)*s(27)
0.04/0.33	
0.04/0.33	  with precondition: [V_n>=2] 
0.04/0.33	
0.04/0.33	
0.04/0.33	Closed-form bounds of eval_sipmabubble_start(V_24,V_i_0,V_j_0,V_n,B): 
0.04/0.33	-------------------------------------
0.04/0.33	* Chain [34] with precondition: [] 
0.04/0.33	    - Upper bound: 0 
0.04/0.33	    - Complexity: constant 
0.04/0.33	* Chain [33] with precondition: [V_n=0] 
0.04/0.33	    - Upper bound: 1 
0.04/0.33	    - Complexity: constant 
0.04/0.33	* Chain [32] with precondition: [0>=V_n+1] 
0.04/0.33	    - Upper bound: 0 
0.04/0.33	    - Complexity: constant 
0.04/0.33	* Chain [31] with precondition: [V_n>=0] 
0.04/0.33	    - Upper bound: 0 
0.04/0.33	    - Complexity: constant 
0.04/0.33	* Chain [30] with precondition: [V_n>=1] 
0.04/0.33	    - Upper bound: 5*V_n+1+4*V_n*V_n 
0.04/0.33	    - Complexity: n^2 
0.04/0.33	* Chain [29] with precondition: [V_n>=2] 
0.04/0.33	    - Upper bound: 2*V_n+V_n*V_n 
0.04/0.33	    - Complexity: n^2 
0.04/0.33	
0.04/0.33	### Maximum cost of eval_sipmabubble_start(V_24,V_i_0,V_j_0,V_n,B): max([1,nat(V_n)*3+1+nat(V_n)*3*nat(V_n)+(nat(V_n)*nat(V_n)+nat(V_n)*2)]) 
0.04/0.33	Asymptotic class: n^2 
0.04/0.33	* Total analysis performed in 251 ms.
0.04/0.33	
0.04/0.43	EOF