0.03/0.13	WORST_CASE(?,O(n^1))  
0.03/0.13	
0.03/0.13	Preprocessing Cost Relations
0.03/0.13	=====================================
0.03/0.13	
0.03/0.13	#### Computed strongly connected components 
0.03/0.13	0. recursive  : [(div)/4]
0.03/0.13	1. non_recursive  : [end/3]
0.03/0.13	2. non_recursive  : [exit_location/1]
0.03/0.13	3. non_recursive  : [div_loop_cont/4]
0.03/0.13	4. non_recursive  : [start/3]
0.03/0.13	
0.03/0.13	#### Obtained direct recursion through partial evaluation 
0.03/0.13	0. SCC is partially evaluated into (div)/4
0.03/0.13	1. SCC is completely evaluated into other SCCs
0.03/0.13	2. SCC is completely evaluated into other SCCs
0.03/0.13	3. SCC is partially evaluated into div_loop_cont/4
0.03/0.13	4. SCC is partially evaluated into start/3
0.03/0.13	
0.03/0.13	Control-Flow Refinement of Cost Relations
0.03/0.13	=====================================
0.03/0.13	
0.03/0.13	### Specialization of cost equations (div)/4 
0.03/0.13	* CE 5 is refined into CE [8] 
0.03/0.13	* CE 3 is refined into CE [9] 
0.03/0.13	* CE 2 is refined into CE [10] 
0.03/0.13	* CE 4 is refined into CE [11] 
0.03/0.13	
0.03/0.13	
0.03/0.13	### Cost equations --> "Loop" of (div)/4 
0.03/0.13	* CEs [11] --> Loop 8 
0.03/0.13	* CEs [8] --> Loop 9 
0.03/0.13	* CEs [9] --> Loop 10 
0.03/0.13	* CEs [10] --> Loop 11 
0.03/0.13	
0.03/0.13	### Ranking functions of CR div(A,B,C,D) 
0.03/0.13	* RF of phase [8]: [-A+B,B-1]
0.03/0.13	
0.03/0.13	#### Partial ranking functions of CR div(A,B,C,D) 
0.03/0.13	* Partial RF of phase [8]:
0.03/0.13	  - RF of loop [8:1]:
0.03/0.13	    -A+B
0.03/0.13	    B-1
0.03/0.13	
0.03/0.13	
0.03/0.13	### Specialization of cost equations div_loop_cont/4 
0.03/0.13	* CE 7 is refined into CE [12] 
0.03/0.13	* CE 6 is refined into CE [13] 
0.03/0.13	
0.03/0.13	
0.03/0.13	### Cost equations --> "Loop" of div_loop_cont/4 
0.03/0.13	* CEs [12] --> Loop 12 
0.03/0.13	* CEs [13] --> Loop 13 
0.03/0.13	
0.03/0.13	### Ranking functions of CR div_loop_cont(A,B,C,D) 
0.03/0.13	
0.03/0.13	#### Partial ranking functions of CR div_loop_cont(A,B,C,D) 
0.03/0.13	
0.03/0.13	
0.03/0.13	### Specialization of cost equations start/3 
0.03/0.13	* CE 1 is refined into CE [14,15,16,17,18] 
0.03/0.13	
0.03/0.13	
0.03/0.13	### Cost equations --> "Loop" of start/3 
0.03/0.13	* CEs [15] --> Loop 14 
0.03/0.13	* CEs [16,18] --> Loop 15 
0.03/0.13	* CEs [14] --> Loop 16 
0.03/0.13	* CEs [17] --> Loop 17 
0.03/0.13	
0.03/0.13	### Ranking functions of CR start(A,B,C) 
0.03/0.13	
0.03/0.13	#### Partial ranking functions of CR start(A,B,C) 
0.03/0.13	
0.03/0.13	
0.03/0.13	Computing Bounds
0.03/0.13	=====================================
0.03/0.13	
0.03/0.13	#### Cost of chains of div(A,B,C,D):
0.03/0.13	* Chain [[8],10]: 1*it(8)+0
0.03/0.13	  Such that:it(8) =< -A+B
0.03/0.13	
0.03/0.13	  with precondition: [C=2,D>=1,A>=D,B>=A+D] 
0.03/0.13	
0.03/0.13	* Chain [[8],9]: 1*it(8)+0
0.03/0.13	  Such that:it(8) =< -A+B
0.03/0.13	
0.03/0.13	  with precondition: [C=3,A>=1,B>=A+1] 
0.03/0.13	
0.03/0.13	* Chain [11]: 0
0.03/0.13	  with precondition: [C=2,D=B,0>=A] 
0.03/0.13	
0.03/0.13	* Chain [10]: 0
0.03/0.13	  with precondition: [C=2,B=D,A>=B] 
0.03/0.13	
0.03/0.13	* Chain [9]: 0
0.03/0.13	  with precondition: [C=3] 
0.03/0.13	
0.03/0.13	
0.03/0.13	#### Cost of chains of div_loop_cont(A,B,C,D):
0.03/0.13	* Chain [13]: 0
0.03/0.13	  with precondition: [A=2] 
0.03/0.13	
0.03/0.13	* Chain [12]: 0
0.03/0.13	  with precondition: [A=3] 
0.03/0.13	
0.03/0.13	
0.03/0.13	#### Cost of chains of start(A,B,C):
0.03/0.13	* Chain [17]: 0
0.03/0.13	  with precondition: [] 
0.03/0.13	
0.03/0.13	* Chain [16]: 0
0.03/0.13	  with precondition: [0>=A] 
0.03/0.13	
0.03/0.13	* Chain [15]: 2*s(1)+0
0.03/0.13	  Such that:aux(1) =< -A+B
0.03/0.13	s(1) =< aux(1)
0.03/0.13	
0.03/0.13	  with precondition: [A>=1,B>=A+1] 
0.03/0.13	
0.03/0.13	* Chain [14]: 0
0.03/0.13	  with precondition: [A>=B] 
0.03/0.13	
0.03/0.13	
0.03/0.13	Closed-form bounds of start(A,B,C): 
0.03/0.13	-------------------------------------
0.03/0.13	* Chain [17] with precondition: [] 
0.03/0.13	    - Upper bound: 0 
0.03/0.13	    - Complexity: constant 
0.03/0.13	* Chain [16] with precondition: [0>=A] 
0.03/0.13	    - Upper bound: 0 
0.03/0.13	    - Complexity: constant 
0.03/0.13	* Chain [15] with precondition: [A>=1,B>=A+1] 
0.03/0.13	    - Upper bound: -2*A+2*B 
0.03/0.13	    - Complexity: n 
0.03/0.13	* Chain [14] with precondition: [A>=B] 
0.03/0.13	    - Upper bound: 0 
0.03/0.13	    - Complexity: constant 
0.03/0.13	
0.03/0.13	### Maximum cost of start(A,B,C): nat(-A+B)*2 
0.03/0.13	Asymptotic class: n 
0.03/0.13	* Total analysis performed in 71 ms.
0.03/0.13	
0.03/0.23	EOF