0.03/0.20	WORST_CASE(?,O(n^1))  
0.03/0.20	
0.03/0.20	Preprocessing Cost Relations
0.03/0.20	=====================================
0.03/0.20	
0.03/0.20	#### Computed strongly connected components 
0.03/0.20	0. recursive  : [f4/14]
0.03/0.20	1. non_recursive  : [exit_location/1]
0.03/0.20	2. non_recursive  : [f6/8]
0.03/0.20	3. non_recursive  : [f4_loop_cont/9]
0.03/0.20	4. non_recursive  : [f5/8]
0.03/0.20	
0.03/0.20	#### Obtained direct recursion through partial evaluation 
0.03/0.20	0. SCC is partially evaluated into f4/14
0.03/0.20	1. SCC is completely evaluated into other SCCs
0.03/0.20	2. SCC is completely evaluated into other SCCs
0.03/0.20	3. SCC is partially evaluated into f4_loop_cont/9
0.03/0.20	4. SCC is partially evaluated into f5/8
0.03/0.20	
0.03/0.20	Control-Flow Refinement of Cost Relations
0.03/0.20	=====================================
0.03/0.20	
0.03/0.20	### Specialization of cost equations f4/14 
0.03/0.20	* CE 5 is refined into CE [8] 
0.03/0.20	* CE 4 is refined into CE [9] 
0.03/0.20	* CE 3 is refined into CE [10] 
0.03/0.20	
0.03/0.20	
0.03/0.20	### Cost equations --> "Loop" of f4/14 
0.03/0.20	* CEs [10] --> Loop 8 
0.03/0.20	* CEs [8] --> Loop 9 
0.03/0.20	* CEs [9] --> Loop 10 
0.03/0.20	
0.03/0.20	### Ranking functions of CR f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 
0.03/0.20	* RF of phase [8]: [A+1]
0.03/0.20	
0.03/0.20	#### Partial ranking functions of CR f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 
0.03/0.20	* Partial RF of phase [8]:
0.03/0.20	  - RF of loop [8:1]:
0.03/0.20	    A+1
0.03/0.20	
0.03/0.20	
0.03/0.20	### Specialization of cost equations f4_loop_cont/9 
0.03/0.20	* CE 7 is refined into CE [11] 
0.03/0.20	* CE 6 is refined into CE [12] 
0.03/0.20	
0.03/0.20	
0.03/0.20	### Cost equations --> "Loop" of f4_loop_cont/9 
0.03/0.20	* CEs [11] --> Loop 11 
0.03/0.20	* CEs [12] --> Loop 12 
0.03/0.20	
0.03/0.20	### Ranking functions of CR f4_loop_cont(A,B,C,D,E,F,G,H,I) 
0.03/0.20	
0.03/0.20	#### Partial ranking functions of CR f4_loop_cont(A,B,C,D,E,F,G,H,I) 
0.03/0.20	
0.03/0.20	
0.03/0.20	### Specialization of cost equations f5/8 
0.03/0.20	* CE 1 is refined into CE [13] 
0.03/0.20	* CE 2 is refined into CE [14,15,16,17] 
0.03/0.20	
0.03/0.20	
0.03/0.20	### Cost equations --> "Loop" of f5/8 
0.03/0.20	* CEs [13] --> Loop 13 
0.03/0.20	* CEs [15,17] --> Loop 14 
0.03/0.20	* CEs [16] --> Loop 15 
0.03/0.20	* CEs [14] --> Loop 16 
0.03/0.20	
0.03/0.20	### Ranking functions of CR f5(A,B,C,D,E,F,G,H) 
0.03/0.20	
0.03/0.20	#### Partial ranking functions of CR f5(A,B,C,D,E,F,G,H) 
0.03/0.20	
0.03/0.20	
0.03/0.20	Computing Bounds
0.03/0.20	=====================================
0.03/0.20	
0.03/0.20	#### Cost of chains of f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N):
0.03/0.20	* Chain [[8],10]: 1*it(8)+0
0.03/0.20	  Such that:it(8) =< A+1
0.03/0.20	
0.03/0.20	  with precondition: [H=2,J=0,K=0,L=0,M=0,N=0,0>=I+1,I>=B,A+B>=I] 
0.03/0.20	
0.03/0.20	* Chain [[8],9]: 1*it(8)+0
0.03/0.20	  Such that:it(8) =< A+1
0.03/0.20	
0.03/0.20	  with precondition: [H=3,0>=B+1,A>=0] 
0.03/0.20	
0.03/0.20	* Chain [10]: 0
0.03/0.20	  with precondition: [H=2,J=0,K=0,L=0,M=0,N=0,A=I,0>=A+1,0>=B+1] 
0.03/0.20	
0.03/0.20	* Chain [9]: 0
0.03/0.20	  with precondition: [H=3,0>=B+1] 
0.03/0.20	
0.03/0.20	
0.03/0.20	#### Cost of chains of f4_loop_cont(A,B,C,D,E,F,G,H,I):
0.03/0.20	* Chain [12]: 0
0.03/0.20	  with precondition: [A=2,0>=C+1] 
0.03/0.20	
0.03/0.20	* Chain [11]: 0
0.03/0.20	  with precondition: [A=3,0>=C+1] 
0.03/0.20	
0.03/0.20	
0.03/0.20	#### Cost of chains of f5(A,B,C,D,E,F,G,H):
0.03/0.20	* Chain [16]: 0
0.03/0.20	  with precondition: [0>=A+1,0>=B+1] 
0.03/0.20	
0.03/0.20	* Chain [15]: 0
0.03/0.20	  with precondition: [0>=B+1] 
0.03/0.20	
0.03/0.20	* Chain [14]: 2*s(1)+0
0.03/0.20	  Such that:aux(1) =< A+1
0.03/0.20	s(1) =< aux(1)
0.03/0.20	
0.03/0.20	  with precondition: [0>=B+1,A>=0] 
0.03/0.20	
0.03/0.20	* Chain [13]: 0
0.03/0.20	  with precondition: [B>=0] 
0.03/0.20	
0.03/0.20	
0.03/0.20	Closed-form bounds of f5(A,B,C,D,E,F,G,H): 
0.03/0.20	-------------------------------------
0.03/0.20	* Chain [16] with precondition: [0>=A+1,0>=B+1] 
0.03/0.20	    - Upper bound: 0 
0.03/0.20	    - Complexity: constant 
0.03/0.20	* Chain [15] with precondition: [0>=B+1] 
0.03/0.20	    - Upper bound: 0 
0.03/0.20	    - Complexity: constant 
0.03/0.20	* Chain [14] with precondition: [0>=B+1,A>=0] 
0.03/0.20	    - Upper bound: 2*A+2 
0.03/0.20	    - Complexity: n 
0.03/0.20	* Chain [13] with precondition: [B>=0] 
0.03/0.20	    - Upper bound: 0 
0.03/0.20	    - Complexity: constant 
0.03/0.20	
0.03/0.20	### Maximum cost of f5(A,B,C,D,E,F,G,H): nat(A+1)*2 
0.03/0.20	Asymptotic class: n 
0.03/0.20	* Total analysis performed in 136 ms.
0.03/0.20	
0.03/0.30	EOF