0.03/0.19	WORST_CASE(?,O(n^1))  
0.03/0.19	
0.03/0.19	Preprocessing Cost Relations
0.03/0.19	=====================================
0.03/0.19	
0.03/0.19	#### Computed strongly connected components 
0.03/0.19	0. recursive  : [f1/9]
0.03/0.19	1. non_recursive  : [exit_location/1]
0.03/0.19	2. non_recursive  : [f2/5]
0.03/0.19	3. non_recursive  : [f1_loop_cont/6]
0.03/0.19	4. non_recursive  : [f3/5]
0.03/0.19	
0.03/0.19	#### Obtained direct recursion through partial evaluation 
0.03/0.19	0. SCC is partially evaluated into f1/9
0.03/0.19	1. SCC is completely evaluated into other SCCs
0.03/0.19	2. SCC is completely evaluated into other SCCs
0.03/0.19	3. SCC is partially evaluated into f1_loop_cont/6
0.03/0.19	4. SCC is partially evaluated into f3/5
0.03/0.19	
0.03/0.19	Control-Flow Refinement of Cost Relations
0.03/0.19	=====================================
0.03/0.19	
0.03/0.19	### Specialization of cost equations f1/9 
0.03/0.19	* CE 5 is refined into CE [8] 
0.03/0.19	* CE 2 is refined into CE [9] 
0.03/0.19	* CE 3 is refined into CE [10] 
0.03/0.19	* CE 4 is refined into CE [11] 
0.03/0.19	
0.03/0.19	
0.03/0.19	### Cost equations --> "Loop" of f1/9 
0.03/0.19	* CEs [11] --> Loop 8 
0.03/0.19	* CEs [8] --> Loop 9 
0.03/0.19	* CEs [10] --> Loop 10 
0.03/0.19	* CEs [9] --> Loop 11 
0.03/0.19	
0.03/0.19	### Ranking functions of CR f1(A,B,C,D,F,G,H,I,J) 
0.03/0.19	* RF of phase [8]: [-B/2+C/2-1/2]
0.03/0.19	
0.03/0.19	#### Partial ranking functions of CR f1(A,B,C,D,F,G,H,I,J) 
0.03/0.19	* Partial RF of phase [8]:
0.03/0.19	  - RF of loop [8:1]:
0.03/0.19	    -B/2+C/2-1/2
0.03/0.19	
0.03/0.19	
0.03/0.19	### Specialization of cost equations f1_loop_cont/6 
0.03/0.19	* CE 7 is refined into CE [12] 
0.03/0.19	* CE 6 is refined into CE [13] 
0.03/0.19	
0.03/0.19	
0.03/0.19	### Cost equations --> "Loop" of f1_loop_cont/6 
0.03/0.19	* CEs [12] --> Loop 12 
0.03/0.19	* CEs [13] --> Loop 13 
0.03/0.19	
0.03/0.19	### Ranking functions of CR f1_loop_cont(A,B,C,D,E,F) 
0.03/0.19	
0.03/0.19	#### Partial ranking functions of CR f1_loop_cont(A,B,C,D,E,F) 
0.03/0.19	
0.03/0.19	
0.03/0.19	### Specialization of cost equations f3/5 
0.03/0.19	* CE 1 is refined into CE [14,15,16,17,18,19] 
0.03/0.19	
0.03/0.19	
0.03/0.19	### Cost equations --> "Loop" of f3/5 
0.03/0.19	* CEs [14] --> Loop 14 
0.03/0.19	* CEs [17] --> Loop 15 
0.03/0.19	* CEs [15,19] --> Loop 16 
0.03/0.19	* CEs [16] --> Loop 17 
0.03/0.19	* CEs [18] --> Loop 18 
0.03/0.19	
0.03/0.19	### Ranking functions of CR f3(A,B,C,D,F) 
0.03/0.19	
0.03/0.19	#### Partial ranking functions of CR f3(A,B,C,D,F) 
0.03/0.19	
0.03/0.19	
0.03/0.19	Computing Bounds
0.03/0.19	=====================================
0.03/0.19	
0.03/0.19	#### Cost of chains of f1(A,B,C,D,F,G,H,I,J):
0.03/0.19	* Chain [[8],11]: 1*it(8)+0
0.03/0.19	  Such that:it(8) =< -B+H
0.03/0.19	
0.03/0.19	  with precondition: [A=0,F=2,G=0,B+C=2*H,B+C=2*I,C>=B+2] 
0.03/0.19	
0.03/0.19	* Chain [[8],10]: 1*it(8)+0
0.03/0.19	  Such that:it(8) =< -B+H
0.03/0.19	
0.03/0.19	  with precondition: [A=0,F=2,G=1,B+C+1=2*H,B+C+1=2*I,C>=B+3] 
0.03/0.19	
0.03/0.19	* Chain [[8],9]: 1*it(8)+0
0.03/0.19	  Such that:it(8) =< -B/2+C/2
0.03/0.19	
0.03/0.19	  with precondition: [A=0,F=3,C>=B+2] 
0.03/0.19	
0.03/0.19	* Chain [11]: 0
0.03/0.19	  with precondition: [A=0,F=2,G=0,B=H,C=I,B>=C] 
0.03/0.19	
0.03/0.19	* Chain [10]: 0
0.03/0.19	  with precondition: [A=0,F=2,G=1,C=B+1,C=H,C=I] 
0.03/0.19	
0.03/0.19	* Chain [9]: 0
0.03/0.19	  with precondition: [A=0,F=3] 
0.03/0.19	
0.03/0.19	
0.03/0.19	#### Cost of chains of f1_loop_cont(A,B,C,D,E,F):
0.03/0.19	* Chain [13]: 0
0.03/0.19	  with precondition: [A=2] 
0.03/0.19	
0.03/0.19	* Chain [12]: 0
0.03/0.19	  with precondition: [A=3] 
0.03/0.19	
0.03/0.19	
0.03/0.19	#### Cost of chains of f3(A,B,C,D,F):
0.03/0.19	* Chain [18]: 0
0.03/0.19	  with precondition: [] 
0.03/0.19	
0.03/0.19	* Chain [17]: 0
0.03/0.19	  with precondition: [C=B+1] 
0.03/0.19	
0.03/0.19	* Chain [16]: 2*s(1)+0
0.03/0.19	  Such that:aux(1) =< -B/2+C/2
0.03/0.19	s(1) =< aux(1)
0.03/0.19	
0.03/0.19	  with precondition: [C>=B+2] 
0.03/0.19	
0.03/0.19	* Chain [15]: 1*s(3)+0
0.03/0.19	  Such that:s(3) =< -B/2+C/2+1/2
0.03/0.19	
0.03/0.19	  with precondition: [C>=B+3] 
0.03/0.19	
0.03/0.19	* Chain [14]: 0
0.03/0.19	  with precondition: [B>=C] 
0.03/0.19	
0.03/0.19	
0.03/0.19	Closed-form bounds of f3(A,B,C,D,F): 
0.03/0.19	-------------------------------------
0.03/0.19	* Chain [18] with precondition: [] 
0.03/0.19	    - Upper bound: 0 
0.03/0.19	    - Complexity: constant 
0.03/0.19	* Chain [17] with precondition: [C=B+1] 
0.03/0.19	    - Upper bound: 0 
0.03/0.19	    - Complexity: constant 
0.03/0.19	* Chain [16] with precondition: [C>=B+2] 
0.03/0.19	    - Upper bound: -B+C 
0.03/0.19	    - Complexity: n 
0.03/0.19	* Chain [15] with precondition: [C>=B+3] 
0.03/0.19	    - Upper bound: -B/2+C/2+1/2 
0.03/0.19	    - Complexity: n 
0.03/0.19	* Chain [14] with precondition: [B>=C] 
0.03/0.19	    - Upper bound: 0 
0.03/0.19	    - Complexity: constant 
0.03/0.19	
0.03/0.19	### Maximum cost of f3(A,B,C,D,F): max([nat(-B/2+C/2+1/2),nat(-B/2+C/2)*2]) 
0.03/0.19	Asymptotic class: n 
0.03/0.19	* Total analysis performed in 127 ms.
0.03/0.19	
0.03/0.29	EOF