0.64/0.66	WORST_CASE(?,O(n^1))  
0.64/0.66	
0.64/0.66	Preprocessing Cost Relations
0.64/0.66	=====================================
0.64/0.66	
0.64/0.66	#### Computed strongly connected components 
0.64/0.66	0. recursive  : [eval_sipma91_bb1_in/9,eval_sipma91_bb2_in/9]
0.64/0.66	1. recursive  : [eval_sipma91_bb3_in/13,eval_sipma91_bb4_in/13,eval_sipma91_bb5_in/13,eval_sipma91_bb6_in/13,eval_sipma91_bb7_in/13]
0.64/0.66	2. non_recursive  : [eval_sipma91_stop/10]
0.64/0.66	3. non_recursive  : [eval_sipma91_bb8_in/10]
0.64/0.66	4. non_recursive  : [exit_location/1]
0.64/0.66	5. non_recursive  : [eval_sipma91_bb3_in_loop_cont/11]
0.64/0.66	6. non_recursive  : [eval_sipma91_bb1_in_loop_cont/11]
0.64/0.66	7. non_recursive  : [eval_sipma91_3/10]
0.64/0.66	8. non_recursive  : [eval_sipma91_2/10]
0.64/0.66	9. non_recursive  : [eval_sipma91_1/10]
0.64/0.66	10. non_recursive  : [eval_sipma91_0/10]
0.64/0.66	11. non_recursive  : [eval_sipma91_bb0_in/10]
0.64/0.66	12. non_recursive  : [eval_sipma91_start/10]
0.64/0.66	
0.64/0.66	#### Obtained direct recursion through partial evaluation 
0.64/0.66	0. SCC is partially evaluated into eval_sipma91_bb1_in/9
0.64/0.66	1. SCC is partially evaluated into eval_sipma91_bb3_in/13
0.64/0.66	2. SCC is completely evaluated into other SCCs
0.64/0.66	3. SCC is completely evaluated into other SCCs
0.64/0.66	4. SCC is completely evaluated into other SCCs
0.64/0.66	5. SCC is partially evaluated into eval_sipma91_bb3_in_loop_cont/11
0.64/0.66	6. SCC is partially evaluated into eval_sipma91_bb1_in_loop_cont/11
0.64/0.66	7. SCC is partially evaluated into eval_sipma91_3/10
0.64/0.66	8. SCC is completely evaluated into other SCCs
0.64/0.66	9. SCC is completely evaluated into other SCCs
0.64/0.66	10. SCC is completely evaluated into other SCCs
0.64/0.66	11. SCC is completely evaluated into other SCCs
0.64/0.66	12. SCC is partially evaluated into eval_sipma91_start/10
0.64/0.66	
0.64/0.66	Control-Flow Refinement of Cost Relations
0.64/0.66	=====================================
0.64/0.66	
0.64/0.66	### Specialization of cost equations eval_sipma91_bb1_in/9 
0.64/0.66	* CE 5 is refined into CE [16] 
0.64/0.66	* CE 6 is refined into CE [17] 
0.64/0.66	* CE 4 is refined into CE [18] 
0.64/0.66	
0.64/0.66	
0.64/0.66	### Cost equations --> "Loop" of eval_sipma91_bb1_in/9 
0.64/0.66	* CEs [18] --> Loop 16 
0.64/0.66	* CEs [16] --> Loop 17 
0.64/0.66	* CEs [17] --> Loop 18 
0.64/0.66	
0.64/0.66	### Ranking functions of CR eval_sipma91_bb1_in(V_y1_0,V_y1_1,V_y2_0,V_y2_1,B,C,D,E,F) 
0.64/0.66	* RF of phase [16]: [-V_y1_0/11+101/11]
0.64/0.66	
0.64/0.66	#### Partial ranking functions of CR eval_sipma91_bb1_in(V_y1_0,V_y1_1,V_y2_0,V_y2_1,B,C,D,E,F) 
0.64/0.66	* Partial RF of phase [16]:
0.64/0.66	  - RF of loop [16:1]:
0.64/0.66	    -V_y1_0/11+101/11
0.64/0.66	
0.64/0.66	
0.64/0.66	### Specialization of cost equations eval_sipma91_bb3_in/13 
0.64/0.66	* CE 13 is refined into CE [19] 
0.64/0.66	* CE 12 is refined into CE [20] 
0.64/0.66	* CE 10 is refined into CE [21] 
0.64/0.66	* CE 11 is refined into CE [22] 
0.64/0.66	* CE 9 is refined into CE [23] 
0.64/0.66	
0.64/0.66	
0.64/0.66	### Cost equations --> "Loop" of eval_sipma91_bb3_in/13 
0.64/0.66	* CEs [21] --> Loop 19 
0.64/0.66	* CEs [22] --> Loop 20 
0.64/0.66	* CEs [23] --> Loop 21 
0.64/0.66	* CEs [19] --> Loop 22 
0.64/0.66	* CEs [20] --> Loop 23 
0.64/0.66	
0.64/0.66	### Ranking functions of CR eval_sipma91_bb3_in(V_5,V_6,V_y1_1,V_y1_2,V_y2_1,V_y2_2,B,C,D,E,F,G,H) 
0.64/0.66	
0.64/0.66	#### Partial ranking functions of CR eval_sipma91_bb3_in(V_5,V_6,V_y1_1,V_y1_2,V_y2_1,V_y2_2,B,C,D,E,F,G,H) 
0.64/0.66	* Partial RF of phase [19,20]:
0.64/0.66	  - RF of loop [19:1]:
0.64/0.66	    V_y1_1/9-110/9 depends on loops [20:1] 
0.64/0.66	    V_y2_1-2
0.64/0.66	  - RF of loop [20:1]:
0.64/0.66	    -V_y1_1+111 depends on loops [19:1] 
0.64/0.66	
0.64/0.66	
0.64/0.66	### Specialization of cost equations eval_sipma91_bb3_in_loop_cont/11 
0.64/0.66	* CE 15 is refined into CE [24] 
0.64/0.66	* CE 14 is refined into CE [25] 
0.64/0.66	
0.64/0.66	
0.64/0.66	### Cost equations --> "Loop" of eval_sipma91_bb3_in_loop_cont/11 
0.64/0.66	* CEs [24] --> Loop 24 
0.64/0.66	* CEs [25] --> Loop 25 
0.64/0.66	
0.64/0.66	### Ranking functions of CR eval_sipma91_bb3_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 
0.64/0.66	
0.64/0.66	#### Partial ranking functions of CR eval_sipma91_bb3_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 
0.64/0.66	
0.64/0.66	
0.64/0.66	### Specialization of cost equations eval_sipma91_bb1_in_loop_cont/11 
0.64/0.66	* CE 8 is refined into CE [26,27,28,29,30,31] 
0.64/0.66	* CE 7 is refined into CE [32] 
0.64/0.66	
0.64/0.66	
0.64/0.66	### Cost equations --> "Loop" of eval_sipma91_bb1_in_loop_cont/11 
0.64/0.66	* CEs [28,31] --> Loop 26 
0.64/0.66	* CEs [29] --> Loop 27 
0.64/0.66	* CEs [30] --> Loop 28 
0.64/0.66	* CEs [26,27] --> Loop 29 
0.64/0.66	* CEs [32] --> Loop 30 
0.64/0.66	
0.64/0.66	### Ranking functions of CR eval_sipma91_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 
0.64/0.66	
0.64/0.66	#### Partial ranking functions of CR eval_sipma91_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 
0.64/0.66	
0.64/0.66	
0.64/0.66	### Specialization of cost equations eval_sipma91_3/10 
0.64/0.66	* CE 2 is refined into CE [33] 
0.64/0.66	* CE 3 is refined into CE [34,35,36,37,38] 
0.64/0.66	
0.64/0.66	
0.64/0.66	### Cost equations --> "Loop" of eval_sipma91_3/10 
0.64/0.66	* CEs [33] --> Loop 31 
0.64/0.66	* CEs [34,35,37,38] --> Loop 32 
0.64/0.66	* CEs [36] --> Loop 33 
0.64/0.66	
0.64/0.66	### Ranking functions of CR eval_sipma91_3(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B) 
0.64/0.66	
0.64/0.66	#### Partial ranking functions of CR eval_sipma91_3(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B) 
0.64/0.66	
0.64/0.66	
0.64/0.66	### Specialization of cost equations eval_sipma91_start/10 
0.64/0.66	* CE 1 is refined into CE [39,40,41] 
0.64/0.66	
0.64/0.66	
0.64/0.66	### Cost equations --> "Loop" of eval_sipma91_start/10 
0.64/0.66	* CEs [41] --> Loop 34 
0.64/0.66	* CEs [40] --> Loop 35 
0.64/0.66	* CEs [39] --> Loop 36 
0.64/0.66	
0.64/0.66	### Ranking functions of CR eval_sipma91_start(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B) 
0.64/0.66	
0.64/0.66	#### Partial ranking functions of CR eval_sipma91_start(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B) 
0.64/0.66	
0.64/0.66	
0.64/0.66	Computing Bounds
0.64/0.66	=====================================
0.64/0.66	
0.64/0.66	#### Cost of chains of eval_sipma91_bb1_in(V_y1_0,V_y1_1,V_y2_0,V_y2_1,B,C,D,E,F):
0.64/0.66	* Chain [[16],18]: 1*it(16)+0
0.64/0.66	  Such that:it(16) =< -V_y1_0/11+101/11
0.64/0.66	
0.64/0.66	  with precondition: [B=3,100>=V_y1_0,V_y2_0>=1] 
0.64/0.66	
0.64/0.66	* Chain [[16],17]: 1*it(16)+0
0.64/0.66	  Such that:it(16) =< -V_y1_0/11+101/11
0.64/0.66	
0.64/0.66	  with precondition: [B=4,C=D,V_y1_0+11*E=11*V_y2_0+C,V_y1_0+11*F=11*V_y2_0+C,111>=C,V_y2_0>=1,C>=101,C>=V_y1_0+11] 
0.64/0.66	
0.64/0.66	* Chain [18]: 0
0.64/0.66	  with precondition: [B=3,V_y2_0>=1,11*V_y2_0+89>=V_y1_0] 
0.64/0.66	
0.64/0.66	
0.64/0.66	#### Cost of chains of eval_sipma91_bb3_in(V_5,V_6,V_y1_1,V_y1_2,V_y2_1,V_y2_2,B,C,D,E,F,G,H):
0.64/0.66	* Chain [[19,20],22]: 1*it(19)+1*it(20)+0
0.64/0.66	  Such that:aux(3) =< -V_y1_1+111
0.64/0.66	it(19) =< V_y2_1
0.64/0.66	it(20) =< it(19)*9+aux(3)
0.64/0.66	
0.64/0.66	  with precondition: [B=3,V_y2_1>=2] 
0.64/0.66	
0.64/0.66	* Chain [[19,20],21,23]: 1*it(19)+1*it(20)+1
0.64/0.66	  Such that:aux(3) =< -V_y1_1+111
0.64/0.66	aux(4) =< -V_y1_1+F+11
0.64/0.66	it(19) =< V_y2_1
0.64/0.66	it(20) =< it(19)*9+aux(4)
0.64/0.66	it(20) =< it(19)*9+aux(3)
0.64/0.66	
0.64/0.66	  with precondition: [B=2,G=1,H=1,E+10*D=C+11,F+10*D=C+10,D>=1,C>=10*D+90,V_y2_1>=D+1,C+9*V_y2_1+1>=9*D+V_y1_1] 
0.64/0.66	
0.64/0.66	* Chain [[19,20],21,22]: 1*it(19)+1*it(20)+1
0.64/0.66	  Such that:aux(3) =< -V_y1_1+111
0.64/0.66	it(19) =< V_y2_1
0.64/0.66	it(20) =< it(19)*9+aux(3)
0.64/0.66	
0.64/0.66	  with precondition: [B=3,V_y2_1>=2] 
0.64/0.66	
0.64/0.66	* Chain [23]: 0
0.64/0.66	  with precondition: [B=2,C=V_5,D=V_6,E=V_y1_1,F=V_y1_2,H=V_y2_2,V_y2_1=G,1>=V_y2_1] 
0.64/0.66	
0.64/0.66	* Chain [22]: 0
0.64/0.66	  with precondition: [B=3] 
0.64/0.66	
0.64/0.66	* Chain [21,23]: 1
0.64/0.66	  with precondition: [V_y2_1=2,B=2,G=1,V_5=C,V_6=D,V_y1_1=E+10,V_y1_2=F,V_y2_2=H,V_y1_1>=111] 
0.64/0.66	
0.64/0.66	* Chain [21,22]: 1
0.64/0.66	  with precondition: [V_y2_1=2,B=3,V_y1_1>=111] 
0.64/0.66	
0.64/0.66	
0.64/0.66	#### Cost of chains of eval_sipma91_bb3_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K):
0.64/0.66	* Chain [25]: 0
0.64/0.66	  with precondition: [A=2,100>=D] 
0.64/0.66	
0.64/0.66	* Chain [24]: 0
0.64/0.66	  with precondition: [A=3,100>=D] 
0.64/0.66	
0.64/0.66	
0.64/0.66	#### Cost of chains of eval_sipma91_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K):
0.64/0.66	* Chain [30]: 0
0.64/0.66	  with precondition: [A=3,100>=D] 
0.64/0.66	
0.64/0.66	* Chain [29]: 1
0.64/0.66	  with precondition: [A=4,I=2,100>=D,F>=111] 
0.64/0.66	
0.64/0.66	* Chain [28]: 0
0.64/0.66	  with precondition: [A=4,100>=D] 
0.64/0.66	
0.64/0.66	* Chain [27]: 0
0.64/0.66	  with precondition: [A=4,100>=D,1>=I] 
0.64/0.66	
0.64/0.66	* Chain [26]: 3*s(9)+3*s(10)+1
0.64/0.66	  Such that:aux(7) =< -F+111
0.64/0.66	aux(8) =< I
0.64/0.66	s(9) =< aux(8)
0.64/0.66	s(10) =< s(9)*9+aux(7)
0.64/0.66	
0.64/0.66	  with precondition: [A=4,100>=D,I>=2] 
0.64/0.66	
0.64/0.66	
0.64/0.66	#### Cost of chains of eval_sipma91_3(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B):
0.64/0.66	* Chain [33]: 1*s(15)+1
0.64/0.66	  Such that:s(15) =< 1/11
0.64/0.66	
0.64/0.66	  with precondition: [V_x=100] 
0.64/0.66	
0.64/0.66	* Chain [32]: 3*s(16)+3*s(21)+3*s(22)+1
0.64/0.66	  Such that:s(19) =< 10
0.64/0.66	aux(9) =< -V_x+122
0.64/0.66	s(20) =< -V_x/11+122/11
0.64/0.66	aux(10) =< -V_x/11+101/11
0.64/0.66	s(16) =< aux(10)
0.64/0.66	s(19) =< aux(9)
0.64/0.66	s(20) =< aux(9)
0.64/0.66	s(21) =< s(20)
0.64/0.66	s(22) =< s(21)*9+s(19)
0.64/0.66	
0.64/0.66	  with precondition: [100>=V_x] 
0.64/0.66	
0.64/0.66	* Chain [31]: 0
0.64/0.66	  with precondition: [V_x>=101] 
0.64/0.66	
0.64/0.66	
0.64/0.66	#### Cost of chains of eval_sipma91_start(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B):
0.64/0.66	* Chain [36]: 1*s(23)+1
0.64/0.66	  Such that:s(23) =< 1/11
0.64/0.66	
0.64/0.66	  with precondition: [V_x=100] 
0.64/0.66	
0.64/0.66	* Chain [35]: 3*s(28)+3*s(29)+3*s(30)+1
0.64/0.66	  Such that:s(24) =< 10
0.64/0.66	s(25) =< -V_x+122
0.64/0.66	s(27) =< -V_x/11+101/11
0.64/0.66	s(26) =< -V_x/11+122/11
0.64/0.66	s(28) =< s(27)
0.64/0.66	s(24) =< s(25)
0.64/0.66	s(26) =< s(25)
0.64/0.66	s(29) =< s(26)
0.64/0.66	s(30) =< s(29)*9+s(24)
0.64/0.66	
0.64/0.66	  with precondition: [100>=V_x] 
0.64/0.66	
0.64/0.66	* Chain [34]: 0
0.64/0.66	  with precondition: [V_x>=101] 
0.64/0.66	
0.64/0.66	
0.64/0.66	Closed-form bounds of eval_sipma91_start(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B): 
0.64/0.66	-------------------------------------
0.64/0.66	* Chain [36] with precondition: [V_x=100] 
0.64/0.66	    - Upper bound: 12/11 
0.64/0.66	    - Complexity: constant 
0.64/0.66	* Chain [35] with precondition: [100>=V_x] 
0.64/0.66	    - Upper bound: -3*V_x+4304/11 
0.64/0.66	    - Complexity: n 
0.64/0.66	* Chain [34] with precondition: [V_x>=101] 
0.64/0.66	    - Upper bound: 0 
0.64/0.66	    - Complexity: constant 
0.64/0.66	
0.64/0.66	### Maximum cost of eval_sipma91_start(V_5,V_6,V_x,V_y1_0,V_y1_1,V_y1_2,V_y2_0,V_y2_1,V_y2_2,B): max([12/11,nat(-V_x/11+101/11)*3+31+nat(-V_x/11+122/11)*30]) 
0.64/0.66	Asymptotic class: n 
0.64/0.66	* Total analysis performed in 544 ms.
0.64/0.66	
0.65/0.76	EOF