0.02/0.22	WORST_CASE(?,O(n^1))  
0.02/0.22	
0.02/0.22	Preprocessing Cost Relations
0.02/0.22	=====================================
0.02/0.22	
0.02/0.22	#### Computed strongly connected components 
0.02/0.22	0. recursive  : [f2/4,f3/4]
0.02/0.22	1. non_recursive  : [exit_location/1]
0.02/0.22	2. non_recursive  : [f2_loop_cont/2]
0.02/0.22	3. non_recursive  : [f1/4]
0.02/0.22	
0.02/0.22	#### Obtained direct recursion through partial evaluation 
0.02/0.22	0. SCC is partially evaluated into f2/4
0.02/0.22	1. SCC is completely evaluated into other SCCs
0.02/0.22	2. SCC is completely evaluated into other SCCs
0.02/0.22	3. SCC is partially evaluated into f1/4
0.02/0.22	
0.02/0.22	Control-Flow Refinement of Cost Relations
0.02/0.22	=====================================
0.02/0.22	
0.02/0.22	### Specialization of cost equations f2/4 
0.02/0.22	* CE 6 is refined into CE [7] 
0.02/0.22	* CE 3 is refined into CE [8] 
0.02/0.22	* CE 2 is refined into CE [9] 
0.02/0.22	* CE 5 is discarded (unfeasible) 
0.02/0.22	* CE 4 is refined into CE [10] 
0.02/0.22	
0.02/0.22	
0.02/0.22	### Cost equations --> "Loop" of f2/4 
0.02/0.22	* CEs [8] --> Loop 7 
0.02/0.22	* CEs [9] --> Loop 8 
0.02/0.22	* CEs [10] --> Loop 9 
0.02/0.22	* CEs [7] --> Loop 10 
0.02/0.22	
0.02/0.22	### Ranking functions of CR f2(A,B,C,D) 
0.02/0.22	* RF of phase [7]: [A-C,B-C]
0.02/0.22	* RF of phase [8]: [A-C+1]
0.02/0.22	
0.02/0.22	#### Partial ranking functions of CR f2(A,B,C,D) 
0.02/0.22	* Partial RF of phase [7]:
0.02/0.22	  - RF of loop [7:1]:
0.02/0.22	    A-C
0.02/0.22	    B-C
0.02/0.22	* Partial RF of phase [8]:
0.02/0.22	  - RF of loop [8:1]:
0.02/0.22	    A-C+1
0.02/0.22	
0.02/0.22	
0.02/0.22	### Specialization of cost equations f1/4 
0.02/0.22	* CE 1 is refined into CE [11,12,13] 
0.02/0.22	
0.02/0.22	
0.02/0.22	### Cost equations --> "Loop" of f1/4 
0.02/0.22	* CEs [13] --> Loop 11 
0.02/0.22	* CEs [12] --> Loop 12 
0.02/0.22	* CEs [11] --> Loop 13 
0.02/0.22	
0.02/0.22	### Ranking functions of CR f1(A,B,C,D) 
0.02/0.22	
0.02/0.22	#### Partial ranking functions of CR f1(A,B,C,D) 
0.02/0.22	
0.02/0.22	
0.02/0.22	Computing Bounds
0.02/0.22	=====================================
0.02/0.22	
0.02/0.22	#### Cost of chains of f2(A,B,C,D):
0.02/0.22	* Chain [[8],10]: 1*it(8)+0
0.02/0.22	  Such that:it(8) =< A-C+1
0.02/0.22	
0.02/0.22	  with precondition: [D=2,B>=1,C>=B+1,A>=C] 
0.02/0.22	
0.02/0.22	* Chain [[8],9,[7],10]: 1*it(7)+1*it(8)+1
0.02/0.22	  Such that:it(8) =< A-C+1
0.02/0.22	it(7) =< B
0.02/0.22	
0.02/0.22	  with precondition: [D=2,B>=1,C>=B+1,A>=C] 
0.02/0.22	
0.02/0.22	* Chain [[8],9,10]: 1*it(8)+1
0.02/0.22	  Such that:it(8) =< A-C+1
0.02/0.22	
0.02/0.22	  with precondition: [D=2,B>=1,C>=B+1,A>=C] 
0.02/0.22	
0.02/0.22	* Chain [10]: 0
0.02/0.22	  with precondition: [D=2,B>=1,C>=0,A>=B,A+1>=C] 
0.02/0.22	
0.02/0.22	* Chain [9,[7],10]: 1*it(7)+1
0.02/0.22	  Such that:it(7) =< B
0.02/0.22	
0.02/0.22	  with precondition: [D=2,A+1=C,B>=1,A>=B] 
0.02/0.22	
0.02/0.22	* Chain [9,10]: 1
0.02/0.22	  with precondition: [D=2,A+1=C,B>=1,A>=B] 
0.02/0.22	
0.02/0.22	
0.02/0.22	#### Cost of chains of f1(A,B,C,D):
0.02/0.22	* Chain [13]: 1*s(6)+1
0.02/0.22	  Such that:s(6) =< B
0.02/0.22	
0.02/0.22	  with precondition: [A=B,A>=1] 
0.02/0.22	
0.02/0.22	* Chain [12]: 0
0.02/0.22	  with precondition: [B>=1,A>=B] 
0.02/0.22	
0.02/0.22	* Chain [11]: 1*s(7)+3*s(9)+1
0.02/0.22	  Such that:s(8) =< A-B
0.02/0.22	s(7) =< B
0.02/0.22	s(9) =< s(8)
0.02/0.22	
0.02/0.22	  with precondition: [B>=1,A>=B+1] 
0.02/0.22	
0.02/0.22	
0.02/0.22	Closed-form bounds of f1(A,B,C,D): 
0.02/0.22	-------------------------------------
0.02/0.22	* Chain [13] with precondition: [A=B,A>=1] 
0.02/0.22	    - Upper bound: B+1 
0.02/0.22	    - Complexity: n 
0.02/0.22	* Chain [12] with precondition: [B>=1,A>=B] 
0.02/0.22	    - Upper bound: 0 
0.02/0.22	    - Complexity: constant 
0.02/0.22	* Chain [11] with precondition: [B>=1,A>=B+1] 
0.02/0.22	    - Upper bound: 3*A-2*B+1 
0.02/0.22	    - Complexity: n 
0.02/0.22	
0.02/0.22	### Maximum cost of f1(A,B,C,D): 3*A-2*B+1 
0.02/0.22	Asymptotic class: n 
0.02/0.22	* Total analysis performed in 161 ms.
0.02/0.22	
0.02/0.32	EOF