0.06/0.37	WORST_CASE(?,O(n^2))  
0.06/0.37	
0.06/0.37	Preprocessing Cost Relations
0.06/0.37	=====================================
0.06/0.37	
0.06/0.37	#### Computed strongly connected components 
0.06/0.37	0. recursive  : [evalrealheapsortstep1bb2in/3,evalrealheapsortstep1bb3in/3,evalrealheapsortstep1bb4in/3]
0.06/0.37	1. recursive  : [evalrealheapsortstep1bb3in_loop_cont/7,evalrealheapsortstep1bb5in/6,evalrealheapsortstep1bb6in/6]
0.06/0.37	2. non_recursive  : [evalrealheapsortstep1stop/4]
0.06/0.37	3. non_recursive  : [evalrealheapsortstep1returnin/4]
0.06/0.37	4. non_recursive  : [exit_location/1]
0.06/0.37	5. non_recursive  : [evalrealheapsortstep1bb6in_loop_cont/5]
0.06/0.37	6. non_recursive  : [evalrealheapsortstep1entryin/4]
0.06/0.37	7. non_recursive  : [evalrealheapsortstep1start/4]
0.06/0.37	
0.06/0.37	#### Obtained direct recursion through partial evaluation 
0.06/0.37	0. SCC is partially evaluated into evalrealheapsortstep1bb3in/3
0.06/0.37	1. SCC is partially evaluated into evalrealheapsortstep1bb6in/6
0.06/0.37	2. SCC is completely evaluated into other SCCs
0.06/0.37	3. SCC is completely evaluated into other SCCs
0.06/0.37	4. SCC is completely evaluated into other SCCs
0.06/0.37	5. SCC is partially evaluated into evalrealheapsortstep1bb6in_loop_cont/5
0.06/0.37	6. SCC is partially evaluated into evalrealheapsortstep1entryin/4
0.06/0.37	7. SCC is partially evaluated into evalrealheapsortstep1start/4
0.06/0.37	
0.06/0.37	Control-Flow Refinement of Cost Relations
0.06/0.37	=====================================
0.06/0.37	
0.06/0.37	### Specialization of cost equations evalrealheapsortstep1bb3in/3 
0.06/0.37	* CE 13 is refined into CE [14] 
0.06/0.37	* CE 10 is refined into CE [15] 
0.06/0.37	* CE 12 is refined into CE [16] 
0.06/0.37	* CE 11 is refined into CE [17] 
0.06/0.37	
0.06/0.37	
0.06/0.37	### Cost equations --> "Loop" of evalrealheapsortstep1bb3in/3 
0.06/0.37	* CEs [17] --> Loop 14 
0.06/0.37	* CEs [14] --> Loop 15 
0.06/0.37	* CEs [15] --> Loop 16 
0.06/0.37	* CEs [16] --> Loop 17 
0.06/0.37	
0.06/0.37	### Ranking functions of CR evalrealheapsortstep1bb3in(C,G,H) 
0.06/0.37	* RF of phase [14]: [C]
0.06/0.37	
0.06/0.37	#### Partial ranking functions of CR evalrealheapsortstep1bb3in(C,G,H) 
0.06/0.37	* Partial RF of phase [14]:
0.06/0.37	  - RF of loop [14:1]:
0.06/0.37	    C
0.06/0.37	
0.06/0.37	
0.06/0.37	### Specialization of cost equations evalrealheapsortstep1bb6in/6 
0.06/0.37	* CE 6 is refined into CE [18] 
0.06/0.37	* CE 4 is refined into CE [19,20] 
0.06/0.37	* CE 7 is refined into CE [21] 
0.06/0.37	* CE 5 is refined into CE [22,23,24] 
0.06/0.37	
0.06/0.37	
0.06/0.37	### Cost equations --> "Loop" of evalrealheapsortstep1bb6in/6 
0.06/0.37	* CEs [24] --> Loop 18 
0.06/0.37	* CEs [23] --> Loop 19 
0.06/0.37	* CEs [22] --> Loop 20 
0.06/0.37	* CEs [18] --> Loop 21 
0.06/0.37	* CEs [19,20] --> Loop 22 
0.06/0.37	* CEs [21] --> Loop 23 
0.06/0.37	
0.06/0.37	### Ranking functions of CR evalrealheapsortstep1bb6in(A,B,C,G,H,I) 
0.06/0.37	* RF of phase [18,19,20]: [A-B]
0.06/0.37	
0.06/0.37	#### Partial ranking functions of CR evalrealheapsortstep1bb6in(A,B,C,G,H,I) 
0.06/0.37	* Partial RF of phase [18,19,20]:
0.06/0.37	  - RF of loop [18:1,19:1,20:1]:
0.06/0.37	    A-B
0.06/0.37	
0.06/0.37	
0.06/0.37	### Specialization of cost equations evalrealheapsortstep1bb6in_loop_cont/5 
0.06/0.37	* CE 8 is refined into CE [25] 
0.06/0.37	* CE 9 is refined into CE [26] 
0.06/0.37	
0.06/0.37	
0.06/0.37	### Cost equations --> "Loop" of evalrealheapsortstep1bb6in_loop_cont/5 
0.06/0.37	* CEs [25] --> Loop 24 
0.06/0.37	* CEs [26] --> Loop 25 
0.06/0.37	
0.06/0.37	### Ranking functions of CR evalrealheapsortstep1bb6in_loop_cont(A,B,C,D,E) 
0.06/0.37	
0.06/0.37	#### Partial ranking functions of CR evalrealheapsortstep1bb6in_loop_cont(A,B,C,D,E) 
0.06/0.37	
0.06/0.37	
0.06/0.37	### Specialization of cost equations evalrealheapsortstep1entryin/4 
0.06/0.37	* CE 3 is refined into CE [27,28,29,30] 
0.06/0.37	* CE 2 is refined into CE [31] 
0.06/0.37	
0.06/0.37	
0.06/0.37	### Cost equations --> "Loop" of evalrealheapsortstep1entryin/4 
0.06/0.37	* CEs [27,28,29,30] --> Loop 26 
0.06/0.37	* CEs [31] --> Loop 27 
0.06/0.37	
0.06/0.37	### Ranking functions of CR evalrealheapsortstep1entryin(A,B,C,G) 
0.06/0.37	
0.06/0.37	#### Partial ranking functions of CR evalrealheapsortstep1entryin(A,B,C,G) 
0.06/0.37	
0.06/0.37	
0.06/0.37	### Specialization of cost equations evalrealheapsortstep1start/4 
0.06/0.37	* CE 1 is refined into CE [32,33] 
0.06/0.37	
0.06/0.37	
0.06/0.37	### Cost equations --> "Loop" of evalrealheapsortstep1start/4 
0.06/0.37	* CEs [33] --> Loop 28 
0.06/0.37	* CEs [32] --> Loop 29 
0.06/0.37	
0.06/0.37	### Ranking functions of CR evalrealheapsortstep1start(A,B,C,G) 
0.06/0.37	
0.06/0.37	#### Partial ranking functions of CR evalrealheapsortstep1start(A,B,C,G) 
0.06/0.37	
0.06/0.37	
0.06/0.37	Computing Bounds
0.06/0.37	=====================================
0.06/0.37	
0.06/0.37	#### Cost of chains of evalrealheapsortstep1bb3in(C,G,H):
0.06/0.37	* Chain [[14],17]: 1*it(14)+0
0.06/0.37	  Such that:it(14) =< C
0.06/0.37	
0.06/0.37	  with precondition: [G=2,0>=H,C>=1,2*H+1>=0] 
0.06/0.37	
0.06/0.37	* Chain [[14],16]: 1*it(14)+0
0.06/0.37	  Such that:it(14) =< C-H
0.06/0.37	
0.06/0.37	  with precondition: [G=2,H>=1,C>=2*H+1] 
0.06/0.37	
0.06/0.37	* Chain [[14],15]: 1*it(14)+0
0.06/0.37	  Such that:it(14) =< C
0.06/0.37	
0.06/0.37	  with precondition: [G=3,C>=1] 
0.06/0.37	
0.06/0.37	* Chain [16]: 0
0.06/0.37	  with precondition: [G=2,C=H,C>=1] 
0.06/0.37	
0.06/0.37	* Chain [15]: 0
0.06/0.37	  with precondition: [G=3,2*C+1>=0] 
0.06/0.37	
0.06/0.37	
0.06/0.37	#### Cost of chains of evalrealheapsortstep1bb6in(A,B,C,G,H,I):
0.06/0.37	* Chain [[18,19,20],23]: 3*it(18)+1*s(5)+1*s(6)+0
0.06/0.37	  Such that:aux(1) =< A
0.06/0.37	aux(5) =< A-B
0.06/0.37	it(18) =< aux(5)
0.06/0.37	aux(2) =< aux(1)+1
0.06/0.37	s(5) =< it(18)*aux(1)
0.06/0.37	s(6) =< it(18)*aux(2)
0.06/0.37	
0.06/0.37	  with precondition: [G=3,A>=3,B>=1,A>=B+1] 
0.06/0.37	
0.06/0.37	* Chain [[18,19,20],22]: 3*it(18)+1*s(5)+1*s(6)+1*s(7)+0
0.06/0.37	  Such that:aux(6) =< A
0.06/0.37	aux(7) =< A-B
0.06/0.37	s(7) =< aux(6)
0.06/0.37	it(18) =< aux(7)
0.06/0.37	aux(2) =< aux(6)+1
0.06/0.37	s(5) =< it(18)*aux(6)
0.06/0.37	s(6) =< it(18)*aux(2)
0.06/0.37	
0.06/0.37	  with precondition: [G=3,B>=1,A>=B+2] 
0.06/0.37	
0.06/0.37	* Chain [[18,19,20],21]: 3*it(18)+1*s(5)+1*s(6)+0
0.06/0.37	  Such that:aux(1) =< H
0.06/0.37	aux(8) =< -B+H
0.06/0.37	it(18) =< aux(8)
0.06/0.37	aux(2) =< aux(1)+1
0.06/0.37	s(5) =< it(18)*aux(1)
0.06/0.37	s(6) =< it(18)*aux(2)
0.06/0.37	
0.06/0.37	  with precondition: [G=4,A=H,A>=3,B>=1,2*I+1>=0,A>=B+1,A>=I+1] 
0.06/0.37	
0.06/0.37	* Chain [23]: 0
0.06/0.37	  with precondition: [G=3,A>=3,B>=1] 
0.06/0.37	
0.06/0.37	* Chain [22]: 1*s(7)+0
0.06/0.37	  Such that:s(7) =< B
0.06/0.37	
0.06/0.37	  with precondition: [G=3,A>=3,B>=1,A>=B+1] 
0.06/0.37	
0.06/0.37	
0.06/0.37	#### Cost of chains of evalrealheapsortstep1bb6in_loop_cont(A,B,C,D,E):
0.06/0.37	* Chain [25]: 0
0.06/0.37	  with precondition: [A=3,B>=3] 
0.06/0.37	
0.06/0.37	* Chain [24]: 0
0.06/0.37	  with precondition: [A=4,B>=3] 
0.06/0.37	
0.06/0.37	
0.06/0.37	#### Cost of chains of evalrealheapsortstep1entryin(A,B,C,G):
0.06/0.37	* Chain [27]: 0
0.06/0.37	  with precondition: [2>=A] 
0.06/0.37	
0.06/0.37	* Chain [26]: 1*s(17)+10*s(18)+3*s(20)+3*s(21)+0
0.06/0.37	  Such that:s(17) =< 1
0.06/0.37	aux(12) =< A
0.06/0.37	s(18) =< aux(12)
0.06/0.37	s(19) =< aux(12)+1
0.06/0.37	s(20) =< s(18)*aux(12)
0.06/0.37	s(21) =< s(18)*s(19)
0.06/0.37	
0.06/0.37	  with precondition: [A>=3] 
0.06/0.37	
0.06/0.37	
0.06/0.37	#### Cost of chains of evalrealheapsortstep1start(A,B,C,G):
0.06/0.37	* Chain [29]: 0
0.06/0.37	  with precondition: [2>=A] 
0.06/0.37	
0.06/0.37	* Chain [28]: 1*s(35)+10*s(37)+3*s(39)+3*s(40)+0
0.06/0.37	  Such that:s(35) =< 1
0.06/0.37	s(36) =< A
0.06/0.37	s(37) =< s(36)
0.06/0.37	s(38) =< s(36)+1
0.06/0.37	s(39) =< s(37)*s(36)
0.06/0.37	s(40) =< s(37)*s(38)
0.06/0.37	
0.06/0.37	  with precondition: [A>=3] 
0.06/0.37	
0.06/0.37	
0.06/0.37	Closed-form bounds of evalrealheapsortstep1start(A,B,C,G): 
0.06/0.37	-------------------------------------
0.06/0.37	* Chain [29] with precondition: [2>=A] 
0.06/0.37	    - Upper bound: 0 
0.06/0.37	    - Complexity: constant 
0.06/0.37	* Chain [28] with precondition: [A>=3] 
0.06/0.37	    - Upper bound: 13*A+1+6*A*A 
0.06/0.37	    - Complexity: n^2 
0.06/0.37	
0.06/0.37	### Maximum cost of evalrealheapsortstep1start(A,B,C,G): nat(A)*13+1+nat(A)*6*nat(A) 
0.06/0.37	Asymptotic class: n^2 
0.06/0.37	* Total analysis performed in 285 ms.
0.06/0.37	
0.06/0.47	EOF