1.17/1.21	WORST_CASE(?,O(n^1))  
1.17/1.21	
1.17/1.21	Preprocessing Cost Relations
1.17/1.21	=====================================
1.17/1.21	
1.17/1.21	#### Computed strongly connected components 
1.17/1.21	0. recursive  : [eval_heapsort_14/16,eval_heapsort_15/16,eval_heapsort_17/16,eval_heapsort_18/16,eval_heapsort_bb10_in/16,eval_heapsort_bb1_in/16,eval_heapsort_bb2_in/16,eval_heapsort_bb3_in/16,eval_heapsort_bb4_in/16,eval_heapsort_bb5_in/16,eval_heapsort_bb6_in/16,eval_heapsort_bb7_in/16,eval_heapsort_bb8_in/16,eval_heapsort_bb9_in/16]
1.17/1.21	1. non_recursive  : [eval_heapsort_stop/9]
1.17/1.21	2. non_recursive  : [eval_heapsort_bb11_in/9]
1.17/1.21	3. non_recursive  : [exit_location/1]
1.17/1.21	4. non_recursive  : [eval_heapsort_bb1_in_loop_cont/10]
1.17/1.21	5. non_recursive  : [eval_heapsort_9/9]
1.17/1.21	6. non_recursive  : [eval_heapsort_8/9]
1.17/1.21	7. non_recursive  : [eval_heapsort_7/9]
1.17/1.21	8. non_recursive  : [eval_heapsort_6/9]
1.17/1.21	9. non_recursive  : [eval_heapsort_5/9]
1.17/1.21	10. non_recursive  : [eval_heapsort_4/9]
1.17/1.21	11. non_recursive  : [eval_heapsort_3/9]
1.17/1.21	12. non_recursive  : [eval_heapsort_2/9]
1.17/1.21	13. non_recursive  : [eval_heapsort_1/9]
1.17/1.21	14. non_recursive  : [eval_heapsort_0/9]
1.17/1.21	15. non_recursive  : [eval_heapsort_bb0_in/9]
1.17/1.21	16. non_recursive  : [eval_heapsort_start/9]
1.17/1.21	
1.17/1.21	#### Obtained direct recursion through partial evaluation 
1.17/1.21	0. SCC is partially evaluated into eval_heapsort_bb1_in/16
1.17/1.21	1. SCC is completely evaluated into other SCCs
1.17/1.21	2. SCC is completely evaluated into other SCCs
1.17/1.21	3. SCC is completely evaluated into other SCCs
1.17/1.21	4. SCC is partially evaluated into eval_heapsort_bb1_in_loop_cont/10
1.17/1.21	5. SCC is partially evaluated into eval_heapsort_9/9
1.17/1.21	6. SCC is completely evaluated into other SCCs
1.17/1.21	7. SCC is completely evaluated into other SCCs
1.17/1.21	8. SCC is completely evaluated into other SCCs
1.17/1.21	9. SCC is completely evaluated into other SCCs
1.17/1.21	10. SCC is completely evaluated into other SCCs
1.17/1.21	11. SCC is completely evaluated into other SCCs
1.17/1.21	12. SCC is completely evaluated into other SCCs
1.17/1.21	13. SCC is completely evaluated into other SCCs
1.17/1.21	14. SCC is completely evaluated into other SCCs
1.17/1.21	15. SCC is completely evaluated into other SCCs
1.17/1.21	16. SCC is partially evaluated into eval_heapsort_start/9
1.17/1.21	
1.17/1.21	Control-Flow Refinement of Cost Relations
1.17/1.21	=====================================
1.17/1.21	
1.17/1.21	### Specialization of cost equations eval_heapsort_bb1_in/16 
1.17/1.21	* CE 12 is refined into CE [15] 
1.17/1.21	* CE 7 is refined into CE [16] 
1.17/1.21	* CE 3 is refined into CE [17] 
1.17/1.21	* CE 10 is refined into CE [18] 
1.17/1.21	* CE 11 is discarded (unfeasible) 
1.17/1.21	* CE 5 is refined into CE [19] 
1.17/1.21	* CE 9 is refined into CE [20] 
1.17/1.21	* CE 6 is refined into CE [21] 
1.17/1.21	* CE 8 is refined into CE [22] 
1.17/1.21	* CE 4 is refined into CE [23] 
1.17/1.21	
1.17/1.21	
1.17/1.21	### Cost equations --> "Loop" of eval_heapsort_bb1_in/16 
1.17/1.21	* CEs [20] --> Loop 15 
1.17/1.21	* CEs [21] --> Loop 16 
1.17/1.21	* CEs [22] --> Loop 17 
1.17/1.21	* CEs [23] --> Loop 18 
1.17/1.21	* CEs [15] --> Loop 19 
1.17/1.21	* CEs [16] --> Loop 20 
1.17/1.21	* CEs [17] --> Loop 21 
1.17/1.21	* CEs [19] --> Loop 22 
1.17/1.21	* CEs [18] --> Loop 23 
1.17/1.21	
1.17/1.21	### Ranking functions of CR eval_heapsort_bb1_in(V_13,V_2,V_4,V_8,V_i_0,V_max_1,V_max_3,V_size,B,C,D,E,F,G,H,I) 
1.17/1.21	* RF of phase [15,16,17]: [-V_i_0+V_size/2]
1.17/1.21	
1.17/1.21	#### Partial ranking functions of CR eval_heapsort_bb1_in(V_13,V_2,V_4,V_8,V_i_0,V_max_1,V_max_3,V_size,B,C,D,E,F,G,H,I) 
1.17/1.21	* Partial RF of phase [15,16,17]:
1.17/1.21	  - RF of loop [15:1,16:1]:
1.17/1.21	    -V_i_0/2+V_size/4
1.17/1.21	  - RF of loop [17:1]:
1.17/1.21	    -V_i_0+V_size/2
1.17/1.21	
1.17/1.21	
1.17/1.21	### Specialization of cost equations eval_heapsort_bb1_in_loop_cont/10 
1.17/1.21	* CE 14 is refined into CE [24] 
1.17/1.21	* CE 13 is refined into CE [25] 
1.17/1.21	
1.17/1.21	
1.17/1.21	### Cost equations --> "Loop" of eval_heapsort_bb1_in_loop_cont/10 
1.17/1.21	* CEs [24] --> Loop 24 
1.17/1.21	* CEs [25] --> Loop 25 
1.17/1.21	
1.17/1.21	### Ranking functions of CR eval_heapsort_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 
1.17/1.21	
1.17/1.21	#### Partial ranking functions of CR eval_heapsort_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 
1.17/1.21	
1.17/1.21	
1.17/1.21	### Specialization of cost equations eval_heapsort_9/9 
1.17/1.21	* CE 2 is refined into CE [26,27,28,29,30,31,32,33,34,35,36,37,38] 
1.17/1.21	
1.17/1.21	
1.17/1.21	### Cost equations --> "Loop" of eval_heapsort_9/9 
1.17/1.21	* CEs [29] --> Loop 26 
1.17/1.21	* CEs [28,34,37] --> Loop 27 
1.17/1.21	* CEs [30,33,38] --> Loop 28 
1.17/1.21	* CEs [26] --> Loop 29 
1.17/1.21	* CEs [27,32,35] --> Loop 30 
1.17/1.21	* CEs [31] --> Loop 31 
1.17/1.21	* CEs [36] --> Loop 32 
1.17/1.21	
1.17/1.21	### Ranking functions of CR eval_heapsort_9(V_13,V_2,V_4,V_8,V_i_0,V_max_1,V_max_3,V_size,B) 
1.17/1.21	
1.17/1.21	#### Partial ranking functions of CR eval_heapsort_9(V_13,V_2,V_4,V_8,V_i_0,V_max_1,V_max_3,V_size,B) 
1.17/1.21	
1.17/1.21	
1.17/1.21	### Specialization of cost equations eval_heapsort_start/9 
1.17/1.21	* CE 1 is refined into CE [39,40,41,42,43,44,45] 
1.17/1.21	
1.17/1.21	
1.17/1.21	### Cost equations --> "Loop" of eval_heapsort_start/9 
1.17/1.21	* CEs [45] --> Loop 33 
1.17/1.21	* CEs [44] --> Loop 34 
1.17/1.21	* CEs [43] --> Loop 35 
1.17/1.21	* CEs [42] --> Loop 36 
1.17/1.21	* CEs [41] --> Loop 37 
1.17/1.21	* CEs [40] --> Loop 38 
1.17/1.21	* CEs [39] --> Loop 39 
1.17/1.21	
1.17/1.21	### Ranking functions of CR eval_heapsort_start(V_13,V_2,V_4,V_8,V_i_0,V_max_1,V_max_3,V_size,B) 
1.17/1.21	
1.17/1.21	#### Partial ranking functions of CR eval_heapsort_start(V_13,V_2,V_4,V_8,V_i_0,V_max_1,V_max_3,V_size,B) 
1.17/1.21	
1.17/1.21	
1.17/1.21	Computing Bounds
1.17/1.21	=====================================
1.17/1.21	
1.17/1.21	#### Cost of chains of eval_heapsort_bb1_in(V_13,V_2,V_4,V_8,V_i_0,V_max_1,V_max_3,V_size,B,C,D,E,F,G,H,I):
1.17/1.21	* Chain [[15,16,17],22]: 2*it(15)+1*it(17)+0
1.17/1.21	  Such that:aux(5) =< -V_i_0+V_size/2
1.17/1.21	aux(6) =< -V_i_0/2+V_size/4
1.17/1.21	it(15) =< aux(5)
1.17/1.21	it(17) =< aux(5)
1.17/1.21	it(15) =< aux(6)
1.17/1.21	
1.17/1.21	  with precondition: [B=2,V_size=2*G,V_size=2*H,V_size=2*I,V_size=D,V_size+1=E,0>=F,V_i_0>=1,V_size>=4*V_i_0] 
1.17/1.21	
1.17/1.21	* Chain [[15,16,17],21]: 2*it(15)+1*it(17)+0
1.17/1.21	  Such that:aux(1) =< -V_i_0+V_size/2
1.17/1.21	aux(2) =< -V_i_0+E/2
1.17/1.21	aux(3) =< -V_i_0/2+V_size/4
1.17/1.21	aux(4) =< -V_i_0/2+E/4
1.17/1.21	it(15) =< aux(1)
1.17/1.21	it(17) =< aux(1)
1.17/1.21	it(15) =< aux(2)
1.17/1.21	it(17) =< aux(2)
1.17/1.21	it(15) =< aux(3)
1.17/1.21	it(15) =< aux(4)
1.17/1.21	
1.17/1.21	  with precondition: [B=2,D=2*G,D=2*H,D=2*I,D+1=E,V_i_0>=1,D>=4*V_i_0,V_size>=2*V_i_0+1,D>=V_size+1,2*V_size>=D] 
1.17/1.21	
1.17/1.21	* Chain [[15,16,17],20]: 2*it(15)+1*it(17)+0
1.17/1.21	  Such that:aux(1) =< -V_i_0+V_size/2
1.17/1.21	aux(2) =< -V_i_0+H
1.17/1.21	aux(3) =< -V_i_0/2+V_size/4
1.17/1.21	aux(4) =< -V_i_0/2+H/2
1.17/1.21	it(15) =< aux(1)
1.17/1.21	it(17) =< aux(1)
1.17/1.21	it(15) =< aux(2)
1.17/1.21	it(17) =< aux(2)
1.17/1.21	it(15) =< aux(3)
1.17/1.21	it(15) =< aux(4)
1.17/1.21	
1.17/1.21	  with precondition: [B=2,D=2*G,D=2*H,D=2*I,D+1=E,0>=C,0>=F,V_i_0>=1,D>=4*V_i_0,V_size>=D+1] 
1.17/1.21	
1.17/1.21	* Chain [[15,16,17],19]: 2*it(15)+1*it(17)+0
1.17/1.21	  Such that:aux(2) =< -V_i_0+V_size
1.17/1.21	aux(1) =< -V_i_0+V_size/2
1.17/1.21	aux(4) =< -V_i_0/2+V_size/2
1.17/1.21	aux(3) =< -V_i_0/2+V_size/4
1.17/1.21	it(15) =< aux(1)
1.17/1.21	it(17) =< aux(1)
1.17/1.21	it(15) =< aux(2)
1.17/1.21	it(17) =< aux(2)
1.17/1.21	it(15) =< aux(3)
1.17/1.21	it(15) =< aux(4)
1.17/1.21	
1.17/1.21	  with precondition: [B=3,V_i_0>=1,V_size>=2*V_i_0+1] 
1.17/1.21	
1.17/1.21	* Chain [[15,16,17],18,21]: 2*it(15)+1*it(17)+1
1.17/1.21	  Such that:aux(7) =< -V_i_0+V_size/2
1.17/1.21	aux(8) =< -V_i_0/2+V_size/4
1.17/1.21	it(15) =< aux(7)
1.17/1.21	it(17) =< aux(7)
1.17/1.21	it(15) =< aux(8)
1.17/1.21	
1.17/1.21	  with precondition: [B=2,2*V_size=D,2*V_size+1=E,V_size=G,V_size=H,V_size=I,V_i_0>=1,F>=1,V_size>=4*V_i_0] 
1.17/1.21	
1.17/1.21	* Chain [[15,16,17],18,19]: 2*it(15)+1*it(17)+1
1.17/1.21	  Such that:aux(9) =< -V_i_0+V_size/2
1.17/1.21	aux(10) =< -V_i_0/2+V_size/4
1.17/1.21	it(15) =< aux(9)
1.17/1.21	it(17) =< aux(9)
1.17/1.21	it(15) =< aux(10)
1.17/1.21	
1.17/1.21	  with precondition: [B=3,V_i_0>=1,V_size>=4*V_i_0] 
1.17/1.21	
1.17/1.21	* Chain [23]: 0
1.17/1.21	  with precondition: [V_i_0=1,B=2,G=1,C=V_13,D=V_2,E=V_4,F=V_8,H=V_max_1,I=V_max_3,0>=V_size] 
1.17/1.21	
1.17/1.21	* Chain [22]: 0
1.17/1.21	  with precondition: [B=2,C=V_13,2*V_i_0=V_size,2*V_i_0=D,2*V_i_0+1=E,V_i_0=G,V_i_0=H,V_i_0=I,0>=F,V_i_0>=1] 
1.17/1.21	
1.17/1.21	* Chain [21]: 0
1.17/1.21	  with precondition: [B=2,C=V_13,F=V_8,2*V_i_0=D,2*V_i_0+1=E,V_i_0=G,V_i_0=H,V_i_0=I,V_size>=1,2*V_i_0>=V_size+1] 
1.17/1.21	
1.17/1.21	* Chain [20]: 0
1.17/1.21	  with precondition: [B=2,2*V_i_0=D,2*V_i_0+1=E,V_i_0=G,V_i_0=H,V_i_0=I,0>=C,0>=F,V_i_0>=1,V_size>=2*V_i_0+1] 
1.17/1.21	
1.17/1.21	* Chain [19]: 0
1.17/1.21	  with precondition: [B=3,V_i_0>=1] 
1.17/1.21	
1.17/1.21	* Chain [18,21]: 1
1.17/1.21	  with precondition: [B=2,V_size=2*V_i_0,V_13=C,2*V_size=D,2*V_size+1=E,V_size=G,V_size=H,V_size=I,V_size>=2,F>=1] 
1.17/1.21	
1.17/1.21	* Chain [18,19]: 1
1.17/1.21	  with precondition: [B=3,2*V_i_0=V_size,V_i_0>=1] 
1.17/1.21	
1.17/1.21	
1.17/1.21	#### Cost of chains of eval_heapsort_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J):
1.17/1.21	* Chain [25]: 0
1.17/1.21	  with precondition: [A=2] 
1.17/1.21	
1.17/1.21	* Chain [24]: 0
1.17/1.21	  with precondition: [A=3] 
1.17/1.21	
1.17/1.21	
1.17/1.21	#### Cost of chains of eval_heapsort_9(V_13,V_2,V_4,V_8,V_i_0,V_max_1,V_max_3,V_size,B):
1.17/1.21	* Chain [32]: 0
1.17/1.21	  with precondition: [] 
1.17/1.21	
1.17/1.21	* Chain [31]: 0
1.17/1.21	  with precondition: [V_size=1] 
1.17/1.21	
1.17/1.21	* Chain [30]: 1
1.17/1.21	  with precondition: [V_size=2] 
1.17/1.21	
1.17/1.21	* Chain [29]: 0
1.17/1.21	  with precondition: [0>=V_size] 
1.17/1.21	
1.17/1.21	* Chain [28]: 4*s(5)+2*s(6)+0
1.17/1.21	  Such that:aux(13) =< V_size
1.17/1.21	aux(14) =< V_size/2
1.17/1.21	aux(15) =< V_size/4
1.17/1.21	s(5) =< aux(14)
1.17/1.21	s(6) =< aux(14)
1.17/1.21	s(5) =< aux(13)
1.17/1.21	s(6) =< aux(13)
1.17/1.21	s(5) =< aux(15)
1.17/1.21	
1.17/1.21	  with precondition: [V_size>=3] 
1.17/1.21	
1.17/1.21	* Chain [27]: 6*s(15)+3*s(16)+1
1.17/1.21	  Such that:aux(16) =< V_size/2
1.17/1.21	aux(17) =< V_size/4
1.17/1.21	s(15) =< aux(16)
1.17/1.21	s(16) =< aux(16)
1.17/1.21	s(15) =< aux(17)
1.17/1.21	
1.17/1.21	  with precondition: [V_size>=4] 
1.17/1.21	
1.17/1.21	* Chain [26]: 2*s(29)+1*s(30)+0
1.17/1.21	  Such that:aux(18) =< V_size/2
1.17/1.21	aux(19) =< V_size/4
1.17/1.21	s(29) =< aux(18)
1.17/1.21	s(30) =< aux(18)
1.17/1.21	s(29) =< aux(19)
1.17/1.21	
1.17/1.21	  with precondition: [V_size>=5] 
1.17/1.21	
1.17/1.21	
1.17/1.21	#### Cost of chains of eval_heapsort_start(V_13,V_2,V_4,V_8,V_i_0,V_max_1,V_max_3,V_size,B):
1.17/1.21	* Chain [39]: 0
1.17/1.21	  with precondition: [] 
1.17/1.21	
1.17/1.21	* Chain [38]: 0
1.17/1.21	  with precondition: [V_size=1] 
1.17/1.21	
1.17/1.21	* Chain [37]: 1
1.17/1.21	  with precondition: [V_size=2] 
1.17/1.21	
1.17/1.21	* Chain [36]: 0
1.17/1.21	  with precondition: [0>=V_size] 
1.17/1.21	
1.17/1.21	* Chain [35]: 4*s(34)+2*s(35)+0
1.17/1.21	  Such that:s(31) =< V_size
1.17/1.21	s(32) =< V_size/2
1.17/1.21	s(33) =< V_size/4
1.17/1.21	s(34) =< s(32)
1.17/1.21	s(35) =< s(32)
1.17/1.21	s(34) =< s(31)
1.17/1.21	s(35) =< s(31)
1.17/1.21	s(34) =< s(33)
1.17/1.21	
1.17/1.21	  with precondition: [V_size>=3] 
1.17/1.21	
1.17/1.21	* Chain [34]: 6*s(38)+3*s(39)+1
1.17/1.21	  Such that:s(36) =< V_size/2
1.17/1.21	s(37) =< V_size/4
1.17/1.21	s(38) =< s(36)
1.17/1.21	s(39) =< s(36)
1.17/1.21	s(38) =< s(37)
1.17/1.21	
1.17/1.21	  with precondition: [V_size>=4] 
1.17/1.21	
1.17/1.21	* Chain [33]: 2*s(42)+1*s(43)+0
1.17/1.21	  Such that:s(40) =< V_size/2
1.17/1.21	s(41) =< V_size/4
1.17/1.21	s(42) =< s(40)
1.17/1.21	s(43) =< s(40)
1.17/1.21	s(42) =< s(41)
1.17/1.21	
1.17/1.21	  with precondition: [V_size>=5] 
1.17/1.21	
1.17/1.21	
1.17/1.21	Closed-form bounds of eval_heapsort_start(V_13,V_2,V_4,V_8,V_i_0,V_max_1,V_max_3,V_size,B): 
1.17/1.21	-------------------------------------
1.17/1.21	* Chain [39] with precondition: [] 
1.17/1.21	    - Upper bound: 0 
1.17/1.21	    - Complexity: constant 
1.17/1.21	* Chain [38] with precondition: [V_size=1] 
1.17/1.21	    - Upper bound: 0 
1.17/1.21	    - Complexity: constant 
1.17/1.21	* Chain [37] with precondition: [V_size=2] 
1.17/1.21	    - Upper bound: 1 
1.17/1.21	    - Complexity: constant 
1.17/1.21	* Chain [36] with precondition: [0>=V_size] 
1.17/1.21	    - Upper bound: 0 
1.17/1.21	    - Complexity: constant 
1.17/1.21	* Chain [35] with precondition: [V_size>=3] 
1.17/1.21	    - Upper bound: 3*V_size 
1.17/1.21	    - Complexity: n 
1.17/1.21	* Chain [34] with precondition: [V_size>=4] 
1.17/1.21	    - Upper bound: 9/2*V_size+1 
1.17/1.21	    - Complexity: n 
1.17/1.21	* Chain [33] with precondition: [V_size>=5] 
1.17/1.21	    - Upper bound: 3/2*V_size 
1.17/1.21	    - Complexity: n 
1.17/1.21	
1.17/1.21	### Maximum cost of eval_heapsort_start(V_13,V_2,V_4,V_8,V_i_0,V_max_1,V_max_3,V_size,B): max([1,nat(V_size/2)*3+1+nat(V_size/2)*3+nat(V_size/2)*3]) 
1.17/1.21	Asymptotic class: n 
1.17/1.21	* Total analysis performed in 1054 ms.
1.17/1.21	
1.21/1.31	EOF