0.03/0.14	WORST_CASE(?,O(n^1))  
0.03/0.14	
0.03/0.14	Preprocessing Cost Relations
0.03/0.14	=====================================
0.03/0.14	
0.03/0.14	#### Computed strongly connected components 
0.03/0.14	0. recursive  : [f1/4]
0.03/0.14	1. non_recursive  : [exit_location/1]
0.03/0.14	2. non_recursive  : [f1_loop_cont/2]
0.03/0.14	3. non_recursive  : [f3/4]
0.03/0.14	
0.03/0.14	#### Obtained direct recursion through partial evaluation 
0.03/0.14	0. SCC is partially evaluated into f1/4
0.03/0.14	1. SCC is completely evaluated into other SCCs
0.03/0.14	2. SCC is completely evaluated into other SCCs
0.03/0.14	3. SCC is partially evaluated into f3/4
0.03/0.14	
0.03/0.14	Control-Flow Refinement of Cost Relations
0.03/0.14	=====================================
0.03/0.14	
0.03/0.14	### Specialization of cost equations f1/4 
0.03/0.14	* CE 4 is refined into CE [5] 
0.03/0.14	* CE 3 is refined into CE [6] 
0.03/0.14	* CE 2 is refined into CE [7] 
0.03/0.14	
0.03/0.14	
0.03/0.14	### Cost equations --> "Loop" of f1/4 
0.03/0.14	* CEs [6] --> Loop 5 
0.03/0.14	* CEs [7] --> Loop 6 
0.03/0.14	* CEs [5] --> Loop 7 
0.03/0.14	
0.03/0.14	### Ranking functions of CR f1(A,B,C,D) 
0.03/0.14	* RF of phase [5]: [B-C-1]
0.03/0.14	* RF of phase [6]: [A-B]
0.03/0.14	
0.03/0.14	#### Partial ranking functions of CR f1(A,B,C,D) 
0.03/0.14	* Partial RF of phase [5]:
0.03/0.14	  - RF of loop [5:1]:
0.03/0.14	    B-C-1
0.03/0.14	* Partial RF of phase [6]:
0.03/0.14	  - RF of loop [6:1]:
0.03/0.14	    A-B
0.03/0.14	
0.03/0.14	
0.03/0.14	### Specialization of cost equations f3/4 
0.03/0.14	* CE 1 is refined into CE [8,9,10] 
0.03/0.14	
0.03/0.14	
0.03/0.14	### Cost equations --> "Loop" of f3/4 
0.03/0.14	* CEs [10] --> Loop 8 
0.03/0.14	* CEs [9] --> Loop 9 
0.03/0.14	* CEs [8] --> Loop 10 
0.03/0.14	
0.03/0.14	### Ranking functions of CR f3(A,B,C,D) 
0.03/0.14	
0.03/0.14	#### Partial ranking functions of CR f3(A,B,C,D) 
0.03/0.14	
0.03/0.14	
0.03/0.14	Computing Bounds
0.03/0.14	=====================================
0.03/0.14	
0.03/0.14	#### Cost of chains of f1(A,B,C,D):
0.03/0.14	* Chain [[6],[5],7]: 1*it(5)+1*it(6)+0
0.03/0.14	  Such that:it(6) =< A-B
0.03/0.14	it(5) =< A-C
0.03/0.14	
0.03/0.14	  with precondition: [D=2,A>=B+1,B>=C+1] 
0.03/0.14	
0.03/0.14	* Chain [[6],7]: 1*it(6)+0
0.03/0.14	  Such that:it(6) =< A-B
0.03/0.14	
0.03/0.14	  with precondition: [D=2,A>=B+1,B>=C+1] 
0.03/0.14	
0.03/0.14	* Chain [[5],7]: 1*it(5)+0
0.03/0.14	  Such that:it(5) =< B-C
0.03/0.14	
0.03/0.14	  with precondition: [D=2,B>=A,B>=C+2] 
0.03/0.14	
0.03/0.14	* Chain [7]: 0
0.03/0.14	  with precondition: [D=2,B>=C+1] 
0.03/0.14	
0.03/0.14	
0.03/0.14	#### Cost of chains of f3(A,B,C,D):
0.03/0.14	* Chain [10]: 1*s(4)+0
0.03/0.14	  Such that:s(4) =< B-C
0.03/0.14	
0.03/0.14	  with precondition: [B>=A,B>=C+2] 
0.03/0.14	
0.03/0.14	* Chain [9]: 1*s(5)+2*s(7)+0
0.03/0.14	  Such that:s(6) =< A-B
0.03/0.14	s(5) =< A-C
0.03/0.14	s(7) =< s(6)
0.03/0.14	
0.03/0.14	  with precondition: [A>=B+1,B>=C+1] 
0.03/0.14	
0.03/0.14	* Chain [8]: 0
0.03/0.14	  with precondition: [B>=C+1] 
0.03/0.14	
0.03/0.14	
0.03/0.14	Closed-form bounds of f3(A,B,C,D): 
0.03/0.14	-------------------------------------
0.03/0.14	* Chain [10] with precondition: [B>=A,B>=C+2] 
0.03/0.14	    - Upper bound: B-C 
0.03/0.14	    - Complexity: n 
0.03/0.14	* Chain [9] with precondition: [A>=B+1,B>=C+1] 
0.03/0.14	    - Upper bound: 3*A-2*B-C 
0.03/0.14	    - Complexity: n 
0.03/0.14	* Chain [8] with precondition: [B>=C+1] 
0.03/0.14	    - Upper bound: 0 
0.03/0.14	    - Complexity: constant 
0.03/0.14	
0.03/0.14	### Maximum cost of f3(A,B,C,D): max([B-C,nat(A-B)*2+nat(A-C)]) 
0.03/0.14	Asymptotic class: n 
0.03/0.14	* Total analysis performed in 84 ms.
0.03/0.14	
0.03/0.24	EOF