1.58/1.60	WORST_CASE(?,O(n^2))  
1.58/1.60	
1.58/1.60	Preprocessing Cost Relations
1.58/1.60	=====================================
1.58/1.60	
1.58/1.60	#### Computed strongly connected components 
1.58/1.60	0. recursive  : [eval_xnu_15/9,eval_xnu_16/9,eval_xnu_bb3_in/9,eval_xnu_bb4_in/9]
1.58/1.60	1. recursive  : [eval_xnu_10/20,eval_xnu_11/20,eval_xnu_12/20,eval_xnu_13/20,eval_xnu_bb1_in/20,eval_xnu_bb2_in/20,eval_xnu_bb3_in_loop_cont/21]
1.58/1.60	2. non_recursive  : [eval_xnu_stop/11]
1.58/1.60	3. non_recursive  : [eval_xnu_bb5_in/11]
1.58/1.60	4. non_recursive  : [exit_location/1]
1.58/1.60	5. non_recursive  : [eval_xnu_bb1_in_loop_cont/12]
1.58/1.60	6. non_recursive  : [eval_xnu_8/11]
1.58/1.60	7. non_recursive  : [eval_xnu_7/11]
1.58/1.60	8. non_recursive  : [eval_xnu_6/11]
1.58/1.60	9. non_recursive  : [eval_xnu_5/11]
1.58/1.60	10. non_recursive  : [eval_xnu_4/11]
1.58/1.60	11. non_recursive  : [eval_xnu_3/11]
1.58/1.60	12. non_recursive  : [eval_xnu_2/11]
1.58/1.60	13. non_recursive  : [eval_xnu_1/11]
1.58/1.60	14. non_recursive  : [eval_xnu_0/11]
1.58/1.60	15. non_recursive  : [eval_xnu_bb0_in/11]
1.58/1.60	16. non_recursive  : [eval_xnu_start/11]
1.58/1.60	
1.58/1.60	#### Obtained direct recursion through partial evaluation 
1.58/1.60	0. SCC is partially evaluated into eval_xnu_bb3_in/9
1.58/1.60	1. SCC is partially evaluated into eval_xnu_bb1_in/20
1.58/1.60	2. SCC is completely evaluated into other SCCs
1.58/1.60	3. SCC is completely evaluated into other SCCs
1.58/1.60	4. SCC is completely evaluated into other SCCs
1.58/1.60	5. SCC is partially evaluated into eval_xnu_bb1_in_loop_cont/12
1.58/1.60	6. SCC is partially evaluated into eval_xnu_8/11
1.58/1.60	7. SCC is completely evaluated into other SCCs
1.58/1.60	8. SCC is completely evaluated into other SCCs
1.58/1.60	9. SCC is completely evaluated into other SCCs
1.58/1.60	10. SCC is completely evaluated into other SCCs
1.58/1.60	11. SCC is completely evaluated into other SCCs
1.58/1.60	12. SCC is completely evaluated into other SCCs
1.58/1.60	13. SCC is completely evaluated into other SCCs
1.58/1.60	14. SCC is completely evaluated into other SCCs
1.58/1.60	15. SCC is completely evaluated into other SCCs
1.58/1.60	16. SCC is partially evaluated into eval_xnu_start/11
1.58/1.60	
1.58/1.60	Control-Flow Refinement of Cost Relations
1.58/1.60	=====================================
1.58/1.60	
1.58/1.60	### Specialization of cost equations eval_xnu_bb3_in/9 
1.58/1.60	* CE 15 is refined into CE [16] 
1.58/1.60	* CE 14 is refined into CE [17] 
1.58/1.60	* CE 13 is refined into CE [18] 
1.58/1.60	
1.58/1.60	
1.58/1.60	### Cost equations --> "Loop" of eval_xnu_bb3_in/9 
1.58/1.60	* CEs [18] --> Loop 15 
1.58/1.60	* CEs [16] --> Loop 16 
1.58/1.60	* CEs [17] --> Loop 17 
1.58/1.60	
1.58/1.60	### Ranking functions of CR eval_xnu_bb3_in(V__end_0,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,B,C,D) 
1.58/1.60	* RF of phase [15]: [V__end_0-V_k_0,V_i_0-V_k_0+1]
1.58/1.60	
1.58/1.60	#### Partial ranking functions of CR eval_xnu_bb3_in(V__end_0,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,B,C,D) 
1.58/1.60	* Partial RF of phase [15]:
1.58/1.60	  - RF of loop [15:1]:
1.58/1.60	    V__end_0-V_k_0
1.58/1.60	    V_i_0-V_k_0+1
1.58/1.60	
1.58/1.60	
1.58/1.60	### Specialization of cost equations eval_xnu_bb1_in/20 
1.58/1.60	* CE 9 is refined into CE [19] 
1.58/1.60	* CE 7 is refined into CE [20,21] 
1.58/1.60	* CE 8 is refined into CE [22,23] 
1.58/1.60	* CE 10 is refined into CE [24] 
1.58/1.60	* CE 6 is refined into CE [25,26] 
1.58/1.60	* CE 4 is refined into CE [27] 
1.58/1.60	* CE 5 is refined into CE [28] 
1.58/1.60	* CE 3 is refined into CE [29] 
1.58/1.60	
1.58/1.60	
1.58/1.60	### Cost equations --> "Loop" of eval_xnu_bb1_in/20 
1.58/1.60	* CEs [26] --> Loop 18 
1.58/1.60	* CEs [27] --> Loop 19 
1.58/1.60	* CEs [28] --> Loop 20 
1.58/1.60	* CEs [29] --> Loop 21 
1.58/1.60	* CEs [25] --> Loop 22 
1.58/1.60	* CEs [19] --> Loop 23 
1.58/1.60	* CEs [23] --> Loop 24 
1.58/1.60	* CEs [20,21,22] --> Loop 25 
1.58/1.60	* CEs [24] --> Loop 26 
1.58/1.60	
1.58/1.60	### Ranking functions of CR eval_xnu_bb1_in(V__end_0,V_1,V_2,V_4,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,V_len,B,C,D,E,F,G,H,I,J,K) 
1.58/1.60	* RF of phase [18,19,20,21,22]: [-V_i_0+V_len]
1.58/1.60	
1.58/1.60	#### Partial ranking functions of CR eval_xnu_bb1_in(V__end_0,V_1,V_2,V_4,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,V_len,B,C,D,E,F,G,H,I,J,K) 
1.58/1.60	* Partial RF of phase [18,19,20,21,22]:
1.58/1.60	  - RF of loop [18:1]:
1.58/1.60	    -V_beg_0+V_end_0 depends on loops [21:1] 
1.58/1.60	    -V_beg_0+V_i_0 depends on loops [19:1,21:1] 
1.58/1.60	    -V_beg_0/2+V_len/2-1/2
1.58/1.60	  - RF of loop [18:1,19:1,20:1,21:1,22:1]:
1.58/1.60	    -V_i_0+V_len
1.58/1.60	  - RF of loop [18:1,20:1,21:1,22:1]:
1.58/1.60	    -V_end_0+V_len
1.58/1.60	  - RF of loop [20:1,22:1]:
1.58/1.60	    -V_beg_0+V_len
1.58/1.60	
1.58/1.60	
1.58/1.60	### Specialization of cost equations eval_xnu_bb1_in_loop_cont/12 
1.58/1.60	* CE 11 is refined into CE [30] 
1.58/1.60	* CE 12 is refined into CE [31] 
1.58/1.60	
1.58/1.60	
1.58/1.60	### Cost equations --> "Loop" of eval_xnu_bb1_in_loop_cont/12 
1.58/1.60	* CEs [30] --> Loop 27 
1.58/1.60	* CEs [31] --> Loop 28 
1.58/1.60	
1.58/1.60	### Ranking functions of CR eval_xnu_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 
1.58/1.60	
1.58/1.60	#### Partial ranking functions of CR eval_xnu_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 
1.58/1.60	
1.58/1.60	
1.58/1.60	### Specialization of cost equations eval_xnu_8/11 
1.58/1.60	* CE 2 is refined into CE [32,33,34,35,36] 
1.58/1.60	
1.58/1.60	
1.58/1.60	### Cost equations --> "Loop" of eval_xnu_8/11 
1.58/1.60	* CEs [34] --> Loop 29 
1.58/1.60	* CEs [33,36] --> Loop 30 
1.58/1.60	* CEs [35] --> Loop 31 
1.58/1.60	* CEs [32] --> Loop 32 
1.58/1.60	
1.58/1.60	### Ranking functions of CR eval_xnu_8(V__end_0,V_1,V_2,V_4,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,V_len,B) 
1.58/1.60	
1.58/1.60	#### Partial ranking functions of CR eval_xnu_8(V__end_0,V_1,V_2,V_4,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,V_len,B) 
1.58/1.60	
1.58/1.60	
1.58/1.60	### Specialization of cost equations eval_xnu_start/11 
1.58/1.60	* CE 1 is refined into CE [37,38,39,40] 
1.58/1.60	
1.58/1.60	
1.58/1.60	### Cost equations --> "Loop" of eval_xnu_start/11 
1.58/1.60	* CEs [40] --> Loop 33 
1.58/1.60	* CEs [39] --> Loop 34 
1.58/1.60	* CEs [38] --> Loop 35 
1.58/1.60	* CEs [37] --> Loop 36 
1.58/1.60	
1.58/1.60	### Ranking functions of CR eval_xnu_start(V__end_0,V_1,V_2,V_4,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,V_len,B) 
1.58/1.60	
1.58/1.60	#### Partial ranking functions of CR eval_xnu_start(V__end_0,V_1,V_2,V_4,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,V_len,B) 
1.58/1.60	
1.58/1.60	
1.58/1.60	Computing Bounds
1.58/1.60	=====================================
1.58/1.60	
1.58/1.60	#### Cost of chains of eval_xnu_bb3_in(V__end_0,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,B,C,D):
1.58/1.60	* Chain [[15],17]: 1*it(15)+0
1.58/1.60	  Such that:it(15) =< -V_k_0+C
1.58/1.60	
1.58/1.60	  with precondition: [B=2,V__end_0=C,V__end_0=D,V_beg_0>=0,V_i_0+1>=V__end_0,V_end_0>=V_beg_0,V_k_0>=V_beg_0,V__end_0>=V_end_0,V_i_0>=V_end_0,V__end_0>=V_k_0+1] 
1.58/1.60	
1.58/1.60	* Chain [[15],16]: 1*it(15)+0
1.58/1.60	  Such that:it(15) =< V__end_0-V_k_0
1.58/1.60	
1.58/1.60	  with precondition: [B=3,V_beg_0>=0,V_i_0+1>=V__end_0,V_end_0>=V_beg_0,V_k_0>=V_beg_0,V__end_0>=V_end_0,V_i_0>=V_end_0,V__end_0>=V_k_0+1] 
1.58/1.60	
1.58/1.60	* Chain [17]: 0
1.58/1.60	  with precondition: [B=2,V_k_0=V__end_0,C=V_7,V_k_0=D,V_beg_0>=0,V_end_0>=V_beg_0,V_i_0>=V_end_0,V_k_0>=V_end_0,V_i_0+1>=V_k_0] 
1.58/1.60	
1.58/1.60	* Chain [16]: 0
1.58/1.60	  with precondition: [B=3,V_beg_0>=0,V_i_0+1>=V__end_0,V_end_0>=V_beg_0,V_k_0>=V_beg_0,V__end_0>=V_end_0,V_i_0>=V_end_0,V__end_0>=V_k_0] 
1.58/1.60	
1.58/1.60	
1.58/1.60	#### Cost of chains of eval_xnu_bb1_in(V__end_0,V_1,V_2,V_4,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,V_len,B,C,D,E,F,G,H,I,J,K):
1.58/1.60	* Chain [[18,19,20,21,22],26]: 1*it(18)+1*it(19)+2*it(20)+1*it(21)+1*s(5)+1*s(6)+0
1.58/1.60	  Such that:it(18) =< -V_beg_0/2+V_len/2
1.58/1.60	aux(15) =< V_end_0
1.58/1.60	aux(6) =< V_i_0
1.58/1.60	aux(22) =< V_len
1.58/1.60	aux(23) =< -V_beg_0+V_end_0
1.58/1.60	aux(24) =< -V_beg_0+V_i_0
1.58/1.60	aux(25) =< -V_beg_0+V_len
1.58/1.60	aux(26) =< -V_end_0+V_len
1.58/1.60	aux(27) =< -V_i_0+V_len
1.58/1.60	aux(15) =< aux(23)
1.58/1.60	aux(6) =< aux(24)
1.58/1.60	aux(9) =< aux(25)
1.58/1.60	it(20) =< aux(25)
1.58/1.60	s(6) =< aux(25)
1.58/1.60	it(18) =< aux(26)
1.58/1.60	it(20) =< aux(26)
1.58/1.60	it(21) =< aux(26)
1.58/1.60	it(18) =< aux(27)
1.58/1.60	it(19) =< aux(27)
1.58/1.60	it(20) =< aux(27)
1.58/1.60	it(21) =< aux(27)
1.58/1.60	aux(9) =< aux(22)
1.58/1.60	aux(12) =< aux(22)
1.58/1.60	aux(11) =< it(21)*aux(22)
1.58/1.60	aux(1) =< it(21)*aux(22)
1.58/1.60	it(18) =< it(21)+it(19)+aux(6)
1.58/1.60	it(18) =< it(21)+it(19)+aux(24)
1.58/1.60	aux(13) =< it(21)*aux(12)
1.58/1.60	aux(1) =< it(21)*aux(12)
1.58/1.60	aux(4) =< aux(11)
1.58/1.60	aux(4) =< aux(13)
1.58/1.60	s(5) =< aux(1)+aux(23)
1.58/1.60	it(18) =< aux(1)+aux(23)
1.58/1.60	s(5) =< aux(4)+aux(15)
1.58/1.60	it(18) =< aux(4)+aux(15)
1.58/1.60	s(5) =< it(18)*aux(9)
1.58/1.60	
1.58/1.60	  with precondition: [B=3,V_beg_0>=0,V_end_0>=V_beg_0,V_i_0>=V_end_0,V_len>=V_i_0+1] 
1.58/1.60	
1.58/1.60	* Chain [[18,19,20,21,22],25]: 1*it(18)+1*it(19)+2*it(20)+1*it(21)+1*s(5)+2*s(6)+0
1.58/1.60	  Such that:it(18) =< -V_beg_0/2+V_len/2
1.58/1.60	aux(15) =< V_end_0
1.58/1.60	aux(6) =< V_i_0
1.58/1.60	aux(22) =< V_len
1.58/1.60	aux(28) =< -V_beg_0+V_end_0
1.58/1.60	aux(29) =< -V_beg_0+V_i_0
1.58/1.60	aux(30) =< -V_beg_0+V_len
1.58/1.60	aux(31) =< -V_end_0+V_len
1.58/1.60	aux(32) =< -V_i_0+V_len
1.58/1.60	aux(15) =< aux(28)
1.58/1.60	aux(6) =< aux(29)
1.58/1.60	it(18) =< aux(30)
1.58/1.60	s(6) =< aux(30)
1.58/1.60	aux(9) =< aux(30)
1.58/1.60	it(20) =< aux(30)
1.58/1.60	it(18) =< aux(31)
1.58/1.60	it(20) =< aux(31)
1.58/1.60	it(21) =< aux(31)
1.58/1.60	it(18) =< aux(32)
1.58/1.60	it(19) =< aux(32)
1.58/1.60	it(20) =< aux(32)
1.58/1.60	it(21) =< aux(32)
1.58/1.60	aux(9) =< aux(22)
1.58/1.60	aux(12) =< aux(22)
1.58/1.60	aux(11) =< it(21)*aux(22)
1.58/1.60	aux(1) =< it(21)*aux(22)
1.58/1.60	it(18) =< it(21)+it(19)+aux(6)
1.58/1.60	it(18) =< it(21)+it(19)+aux(29)
1.58/1.60	aux(13) =< it(21)*aux(12)
1.58/1.60	aux(1) =< it(21)*aux(12)
1.58/1.60	aux(4) =< aux(11)
1.58/1.60	aux(4) =< aux(13)
1.58/1.60	s(5) =< aux(1)+aux(28)
1.58/1.60	it(18) =< aux(1)+aux(28)
1.58/1.60	s(5) =< aux(4)+aux(15)
1.58/1.60	it(18) =< aux(4)+aux(15)
1.58/1.60	s(5) =< it(18)*aux(9)
1.58/1.60	
1.58/1.60	  with precondition: [B=3,V_beg_0>=0,V_end_0>=V_beg_0,V_i_0>=V_end_0,V_len>=V_i_0+2] 
1.58/1.60	
1.58/1.60	* Chain [[18,19,20,21,22],24]: 1*it(18)+1*it(19)+2*it(20)+1*it(21)+1*s(5)+2*s(6)+0
1.58/1.60	  Such that:it(18) =< -V_beg_0/2+V_len/2
1.58/1.60	aux(15) =< V_end_0
1.58/1.60	aux(6) =< V_i_0
1.58/1.60	aux(22) =< V_len
1.58/1.60	aux(33) =< -V_beg_0+V_end_0
1.58/1.60	aux(34) =< -V_beg_0+V_i_0
1.58/1.60	aux(35) =< -V_beg_0+V_len
1.58/1.60	aux(36) =< -V_end_0+V_len
1.58/1.60	aux(37) =< -V_i_0+V_len
1.58/1.60	aux(15) =< aux(33)
1.58/1.60	aux(6) =< aux(34)
1.58/1.60	it(18) =< aux(35)
1.58/1.60	s(6) =< aux(35)
1.58/1.60	aux(9) =< aux(35)
1.58/1.60	it(20) =< aux(35)
1.58/1.60	it(18) =< aux(36)
1.58/1.60	it(20) =< aux(36)
1.58/1.60	it(21) =< aux(36)
1.58/1.60	it(18) =< aux(37)
1.58/1.60	it(19) =< aux(37)
1.58/1.60	it(20) =< aux(37)
1.58/1.60	it(21) =< aux(37)
1.58/1.60	aux(9) =< aux(22)
1.58/1.60	aux(12) =< aux(22)
1.58/1.60	aux(11) =< it(21)*aux(22)
1.58/1.60	aux(1) =< it(21)*aux(22)
1.58/1.60	it(18) =< it(21)+it(19)+aux(6)
1.58/1.60	it(18) =< it(21)+it(19)+aux(34)
1.58/1.60	aux(13) =< it(21)*aux(12)
1.58/1.60	aux(1) =< it(21)*aux(12)
1.58/1.60	aux(4) =< aux(11)
1.58/1.60	aux(4) =< aux(13)
1.58/1.60	s(5) =< aux(1)+aux(33)
1.58/1.60	it(18) =< aux(1)+aux(33)
1.58/1.60	s(5) =< aux(4)+aux(15)
1.58/1.60	it(18) =< aux(4)+aux(15)
1.58/1.60	s(5) =< it(18)*aux(9)
1.58/1.60	
1.58/1.60	  with precondition: [B=3,V_beg_0>=0,V_end_0>=V_beg_0,V_i_0>=V_end_0,V_len>=V_i_0+2] 
1.58/1.60	
1.58/1.60	* Chain [[18,19,20,21,22],23]: 1*it(18)+1*it(19)+2*it(20)+1*it(21)+1*s(5)+1*s(6)+0
1.58/1.60	  Such that:aux(14) =< -V_beg_0+V_end_0
1.58/1.60	aux(15) =< -V_beg_0+V_end_0+H-I
1.58/1.60	aux(3) =< -V_beg_0+V_i_0
1.58/1.60	aux(6) =< -V_beg_0+V_i_0+H-J
1.58/1.60	aux(17) =< -V_beg_0+H
1.58/1.60	aux(16) =< -V_beg_0+J
1.58/1.60	it(18) =< -V_beg_0/2+H/2
1.58/1.60	aux(19) =< -V_end_0+I
1.58/1.60	aux(18) =< -V_end_0+J
1.58/1.60	aux(15) =< V_end_0+H-I
1.58/1.60	aux(6) =< V_i_0-V_len+H
1.58/1.60	aux(22) =< J
1.58/1.60	aux(38) =< -V_i_0+J
1.58/1.60	aux(9) =< aux(16)
1.58/1.60	it(20) =< aux(16)
1.58/1.60	s(6) =< aux(16)
1.58/1.60	it(20) =< aux(17)
1.58/1.60	s(6) =< aux(17)
1.58/1.60	it(18) =< aux(18)
1.58/1.60	it(20) =< aux(18)
1.58/1.60	it(21) =< aux(18)
1.58/1.60	it(18) =< aux(19)
1.58/1.60	it(20) =< aux(19)
1.58/1.60	it(21) =< aux(19)
1.58/1.60	it(18) =< aux(38)
1.58/1.60	it(19) =< aux(38)
1.58/1.61	it(20) =< aux(38)
1.58/1.61	it(21) =< aux(38)
1.58/1.61	aux(9) =< aux(22)
1.58/1.61	aux(12) =< aux(22)
1.58/1.61	aux(11) =< it(21)*aux(22)
1.58/1.61	aux(1) =< it(21)*aux(22)
1.58/1.61	it(18) =< it(21)+it(19)+aux(6)
1.58/1.61	it(18) =< it(21)+it(19)+aux(3)
1.58/1.61	aux(13) =< it(21)*aux(12)
1.58/1.61	aux(1) =< it(21)*aux(12)
1.58/1.61	aux(4) =< aux(11)
1.58/1.61	aux(4) =< aux(13)
1.58/1.61	s(5) =< aux(1)+aux(14)
1.58/1.61	it(18) =< aux(1)+aux(14)
1.58/1.61	s(5) =< aux(4)+aux(15)
1.58/1.61	it(18) =< aux(4)+aux(15)
1.58/1.61	s(5) =< it(18)*aux(9)
1.58/1.61	
1.58/1.61	  with precondition: [B=4,V_len=D,V_len=J,V_beg_0>=0,V_end_0>=V_beg_0,V_i_0>=V_end_0,C>=V_end_0,V_len>=V_i_0+1,I>=C,I>=H,V_len>=I,C+H>=V_beg_0+I] 
1.58/1.61	
1.58/1.61	* Chain [26]: 0
1.58/1.61	  with precondition: [B=3,V_beg_0>=0,V_end_0>=V_beg_0,V_i_0>=V_end_0] 
1.58/1.61	
1.58/1.61	* Chain [25]: 1*s(7)+0
1.58/1.61	  Such that:s(7) =< -V_beg_0+V_i_0+1
1.58/1.61	
1.58/1.61	  with precondition: [B=3,V_beg_0>=0,V_end_0>=V_beg_0,V_i_0>=V_end_0,V_len>=V_i_0+1] 
1.58/1.61	
1.58/1.61	* Chain [23]: 0
1.58/1.61	  with precondition: [B=4,C=V__end_0,D=V_1,E=V_2,F=V_4,G=V_7,K=V_k_0,V_beg_0=H,V_end_0=I,V_i_0=J,V_beg_0>=0,V_end_0>=V_beg_0,V_i_0>=V_end_0,V_i_0>=V_len] 
1.58/1.61	
1.58/1.61	
1.58/1.61	#### Cost of chains of eval_xnu_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L):
1.58/1.61	* Chain [28]: 0
1.58/1.61	  with precondition: [A=3] 
1.58/1.61	
1.58/1.61	* Chain [27]: 0
1.58/1.61	  with precondition: [A=4] 
1.58/1.61	
1.58/1.61	
1.58/1.61	#### Cost of chains of eval_xnu_8(V__end_0,V_1,V_2,V_4,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,V_len,B):
1.58/1.61	* Chain [32]: 0
1.58/1.61	  with precondition: [] 
1.58/1.61	
1.58/1.61	* Chain [31]: 0
1.58/1.61	  with precondition: [0>=V_len] 
1.58/1.61	
1.58/1.61	* Chain [30]: 1*s(72)+2*s(74)+10*s(81)+2*s(90)+0
1.58/1.61	  Such that:s(72) =< 1
1.58/1.61	aux(52) =< V_len
1.58/1.61	aux(53) =< V_len/2
1.58/1.61	s(74) =< aux(53)
1.58/1.61	s(81) =< aux(52)
1.58/1.61	s(74) =< aux(52)
1.58/1.61	s(85) =< aux(52)
1.58/1.61	s(86) =< s(81)*aux(52)
1.58/1.61	s(87) =< s(81)*aux(52)
1.58/1.61	s(74) =< s(81)+s(81)
1.58/1.61	s(88) =< s(81)*s(85)
1.58/1.61	s(87) =< s(81)*s(85)
1.58/1.61	s(89) =< s(86)
1.58/1.61	s(89) =< s(88)
1.58/1.61	s(90) =< s(87)
1.58/1.61	s(74) =< s(87)
1.58/1.61	s(90) =< s(89)
1.58/1.61	s(74) =< s(89)
1.58/1.61	s(90) =< s(74)*aux(52)
1.58/1.61	
1.58/1.61	  with precondition: [V_len>=1] 
1.58/1.61	
1.58/1.61	* Chain [29]: 2*s(122)+12*s(125)+2*s(135)+0
1.58/1.61	  Such that:s(116) =< V_len/2
1.58/1.61	aux(55) =< V_len
1.58/1.61	s(122) =< s(116)
1.58/1.61	s(122) =< aux(55)
1.58/1.61	s(125) =< aux(55)
1.58/1.61	s(130) =< aux(55)
1.58/1.61	s(131) =< s(125)*aux(55)
1.58/1.61	s(132) =< s(125)*aux(55)
1.58/1.61	s(122) =< s(125)+s(125)
1.58/1.61	s(133) =< s(125)*s(130)
1.58/1.61	s(132) =< s(125)*s(130)
1.58/1.61	s(134) =< s(131)
1.58/1.61	s(134) =< s(133)
1.58/1.61	s(135) =< s(132)
1.58/1.61	s(122) =< s(132)
1.58/1.61	s(135) =< s(134)
1.58/1.61	s(122) =< s(134)
1.58/1.61	s(135) =< s(122)*aux(55)
1.58/1.61	
1.58/1.61	  with precondition: [V_len>=2] 
1.58/1.61	
1.58/1.61	
1.58/1.61	#### Cost of chains of eval_xnu_start(V__end_0,V_1,V_2,V_4,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,V_len,B):
1.58/1.61	* Chain [36]: 0
1.58/1.61	  with precondition: [] 
1.58/1.61	
1.58/1.61	* Chain [35]: 0
1.58/1.61	  with precondition: [0>=V_len] 
1.58/1.61	
1.58/1.61	* Chain [34]: 1*s(136)+2*s(139)+10*s(140)+2*s(146)+0
1.58/1.61	  Such that:s(136) =< 1
1.58/1.61	s(137) =< V_len
1.58/1.61	s(138) =< V_len/2
1.58/1.61	s(139) =< s(138)
1.58/1.61	s(140) =< s(137)
1.58/1.61	s(139) =< s(137)
1.58/1.61	s(141) =< s(137)
1.58/1.61	s(142) =< s(140)*s(137)
1.58/1.61	s(143) =< s(140)*s(137)
1.58/1.61	s(139) =< s(140)+s(140)
1.58/1.61	s(144) =< s(140)*s(141)
1.58/1.61	s(143) =< s(140)*s(141)
1.58/1.61	s(145) =< s(142)
1.58/1.61	s(145) =< s(144)
1.58/1.61	s(146) =< s(143)
1.58/1.61	s(139) =< s(143)
1.58/1.61	s(146) =< s(145)
1.58/1.61	s(139) =< s(145)
1.58/1.61	s(146) =< s(139)*s(137)
1.58/1.61	
1.58/1.61	  with precondition: [V_len>=1] 
1.58/1.61	
1.58/1.61	* Chain [33]: 2*s(149)+12*s(150)+2*s(156)+0
1.58/1.61	  Such that:s(148) =< V_len
1.58/1.61	s(147) =< V_len/2
1.58/1.61	s(149) =< s(147)
1.58/1.61	s(149) =< s(148)
1.58/1.61	s(150) =< s(148)
1.58/1.61	s(151) =< s(148)
1.58/1.61	s(152) =< s(150)*s(148)
1.58/1.61	s(153) =< s(150)*s(148)
1.58/1.61	s(149) =< s(150)+s(150)
1.58/1.61	s(154) =< s(150)*s(151)
1.58/1.61	s(153) =< s(150)*s(151)
1.58/1.61	s(155) =< s(152)
1.58/1.61	s(155) =< s(154)
1.58/1.61	s(156) =< s(153)
1.58/1.61	s(149) =< s(153)
1.58/1.61	s(156) =< s(155)
1.58/1.61	s(149) =< s(155)
1.58/1.61	s(156) =< s(149)*s(148)
1.58/1.61	
1.58/1.61	  with precondition: [V_len>=2] 
1.58/1.61	
1.58/1.61	
1.58/1.61	Closed-form bounds of eval_xnu_start(V__end_0,V_1,V_2,V_4,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,V_len,B): 
1.58/1.61	-------------------------------------
1.58/1.61	* Chain [36] with precondition: [] 
1.58/1.61	    - Upper bound: 0 
1.58/1.61	    - Complexity: constant 
1.58/1.61	* Chain [35] with precondition: [0>=V_len] 
1.58/1.61	    - Upper bound: 0 
1.58/1.61	    - Complexity: constant 
1.58/1.61	* Chain [34] with precondition: [V_len>=1] 
1.58/1.61	    - Upper bound: 10*V_len+1+2*V_len*V_len+V_len 
1.58/1.61	    - Complexity: n^2 
1.58/1.61	* Chain [33] with precondition: [V_len>=2] 
1.58/1.61	    - Upper bound: 2*V_len*V_len+12*V_len+V_len 
1.58/1.61	    - Complexity: n^2 
1.58/1.61	
1.58/1.61	### Maximum cost of eval_xnu_start(V__end_0,V_1,V_2,V_4,V_7,V_beg_0,V_end_0,V_i_0,V_k_0,V_len,B): nat(V_len)*2*nat(V_len)+nat(V_len)*10+nat(V_len/2)*2+max([1,nat(V_len)*2]) 
1.58/1.61	Asymptotic class: n^2 
1.58/1.61	* Total analysis performed in 1438 ms.
1.58/1.61	
1.61/1.71	EOF