0.02/0.16	WORST_CASE(?,O(n^1))  
0.02/0.16	
0.02/0.16	Preprocessing Cost Relations
0.02/0.16	=====================================
0.02/0.16	
0.02/0.16	#### Computed strongly connected components 
0.02/0.16	0. recursive  : [f/8]
0.02/0.16	1. non_recursive  : [end/5]
0.02/0.16	2. non_recursive  : [exit_location/1]
0.02/0.16	3. non_recursive  : [f_loop_cont/6]
0.02/0.16	4. non_recursive  : [sqrt/5]
0.02/0.16	
0.02/0.16	#### Obtained direct recursion through partial evaluation 
0.02/0.16	0. SCC is partially evaluated into f/8
0.02/0.16	1. SCC is completely evaluated into other SCCs
0.02/0.16	2. SCC is completely evaluated into other SCCs
0.02/0.16	3. SCC is partially evaluated into f_loop_cont/6
0.02/0.16	4. SCC is partially evaluated into sqrt/5
0.02/0.16	
0.02/0.16	Control-Flow Refinement of Cost Relations
0.02/0.16	=====================================
0.02/0.16	
0.02/0.16	### Specialization of cost equations f/8 
0.02/0.16	* CE 4 is refined into CE [7] 
0.02/0.16	* CE 3 is refined into CE [8] 
0.02/0.16	* CE 2 is refined into CE [9] 
0.02/0.16	
0.02/0.16	
0.02/0.16	### Cost equations --> "Loop" of f/8 
0.02/0.16	* CEs [9] --> Loop 7 
0.02/0.16	* CEs [7] --> Loop 8 
0.02/0.16	* CEs [8] --> Loop 9 
0.02/0.16	
0.02/0.16	### Ranking functions of CR f(A,B,C,D,E,F,G,H) 
0.02/0.16	* RF of phase [7]: [-C/2+D/2+1/2]
0.02/0.16	
0.02/0.16	#### Partial ranking functions of CR f(A,B,C,D,E,F,G,H) 
0.02/0.16	* Partial RF of phase [7]:
0.02/0.16	  - RF of loop [7:1]:
0.02/0.16	    -C/2+D/2+1/2
0.02/0.16	
0.02/0.16	
0.02/0.16	### Specialization of cost equations f_loop_cont/6 
0.02/0.16	* CE 6 is refined into CE [10] 
0.02/0.16	* CE 5 is refined into CE [11] 
0.02/0.16	
0.02/0.16	
0.02/0.17	### Cost equations --> "Loop" of f_loop_cont/6 
0.02/0.17	* CEs [10] --> Loop 10 
0.02/0.17	* CEs [11] --> Loop 11 
0.02/0.17	
0.02/0.17	### Ranking functions of CR f_loop_cont(A,B,C,D,E,F) 
0.02/0.17	
0.02/0.17	#### Partial ranking functions of CR f_loop_cont(A,B,C,D,E,F) 
0.02/0.17	
0.02/0.17	
0.02/0.17	### Specialization of cost equations sqrt/5 
0.02/0.17	* CE 1 is refined into CE [12,13,14,15] 
0.02/0.17	
0.02/0.17	
0.02/0.17	### Cost equations --> "Loop" of sqrt/5 
0.02/0.17	* CEs [12,15] --> Loop 12 
0.02/0.17	* CEs [13] --> Loop 13 
0.02/0.17	* CEs [14] --> Loop 14 
0.02/0.17	
0.02/0.17	### Ranking functions of CR sqrt(A,B,C,D,E) 
0.02/0.17	
0.02/0.17	#### Partial ranking functions of CR sqrt(A,B,C,D,E) 
0.02/0.17	
0.02/0.17	
0.02/0.17	Computing Bounds
0.02/0.17	=====================================
0.02/0.17	
0.02/0.17	#### Cost of chains of f(A,B,C,D,E,F,G,H):
0.02/0.17	* Chain [[7],9]: 1*it(7)+0
0.02/0.17	  Such that:it(7) =< -C/2+D/2+1/2
0.02/0.17	
0.02/0.17	  with precondition: [E=2,B=2*A+1,2*F+1=G,B>=0,2*F>=B+1,H>=D+1,D+2*F+1>=H,B+H>=4*F+C] 
0.02/0.17	
0.02/0.17	* Chain [[7],8]: 1*it(7)+0
0.02/0.17	  Such that:it(7) =< -C/2+D/2+1/2
0.02/0.17	
0.02/0.17	  with precondition: [E=3,B=2*A+1,B>=0,D>=C] 
0.02/0.17	
0.02/0.17	* Chain [9]: 0
0.02/0.17	  with precondition: [E=2,2*A+1=B,A=F,2*A+1=G,C=H,C>=D+1] 
0.02/0.17	
0.02/0.17	* Chain [8]: 0
0.02/0.17	  with precondition: [E=3,B=2*A+1] 
0.02/0.17	
0.02/0.17	
0.02/0.17	#### Cost of chains of f_loop_cont(A,B,C,D,E,F):
0.02/0.17	* Chain [11]: 0
0.02/0.17	  with precondition: [A=2] 
0.02/0.17	
0.02/0.17	* Chain [10]: 0
0.02/0.17	  with precondition: [A=3] 
0.02/0.17	
0.02/0.17	
0.02/0.17	#### Cost of chains of sqrt(A,B,C,D,E):
0.02/0.17	* Chain [14]: 0
0.02/0.17	  with precondition: [] 
0.02/0.17	
0.02/0.17	* Chain [13]: 0
0.02/0.17	  with precondition: [0>=D] 
0.02/0.17	
0.02/0.17	* Chain [12]: 2*s(1)+0
0.02/0.17	  Such that:aux(1) =< D/2
0.02/0.17	s(1) =< aux(1)
0.02/0.17	
0.02/0.17	  with precondition: [D>=1] 
0.02/0.17	
0.02/0.17	
0.02/0.17	Closed-form bounds of sqrt(A,B,C,D,E): 
0.02/0.17	-------------------------------------
0.02/0.17	* Chain [14] with precondition: [] 
0.02/0.17	    - Upper bound: 0 
0.02/0.17	    - Complexity: constant 
0.02/0.17	* Chain [13] with precondition: [0>=D] 
0.02/0.17	    - Upper bound: 0 
0.02/0.17	    - Complexity: constant 
0.02/0.17	* Chain [12] with precondition: [D>=1] 
0.02/0.17	    - Upper bound: D 
0.02/0.17	    - Complexity: n 
0.02/0.17	
0.02/0.17	### Maximum cost of sqrt(A,B,C,D,E): nat(D/2)*2 
0.02/0.17	Asymptotic class: n 
0.02/0.17	* Total analysis performed in 106 ms.
0.02/0.17	
0.02/0.27	EOF