0.03/0.20	WORST_CASE(?,O(n^2))  
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  : [f4/4]
0.03/0.20	1. non_recursive  : [exit_location/1]
0.03/0.20	2. non_recursive  : [f4_loop_cont/2]
0.03/0.20	3. non_recursive  : [f0/4]
0.03/0.20	
0.03/0.20	#### Obtained direct recursion through partial evaluation 
0.03/0.20	0. SCC is partially evaluated into f4/4
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 f0/4
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 f4/4 
0.03/0.20	* CE 4 is refined into CE [5] 
0.03/0.20	* CE 2 is refined into CE [6] 
0.03/0.20	* CE 3 is refined into CE [7] 
0.03/0.20	
0.03/0.20	
0.03/0.20	### Cost equations --> "Loop" of f4/4 
0.03/0.20	* CEs [6] --> Loop 5 
0.03/0.20	* CEs [7] --> Loop 6 
0.03/0.20	* CEs [5] --> Loop 7 
0.03/0.20	
0.03/0.20	### Ranking functions of CR f4(A,B,C,D) 
0.03/0.20	
0.03/0.20	#### Partial ranking functions of CR f4(A,B,C,D) 
0.03/0.20	* Partial RF of phase [5,6]:
0.03/0.20	  - RF of loop [5:1]:
0.03/0.20	    A-B depends on loops [6:1] 
0.03/0.20	    -B+C-1 depends on loops [6:1] 
0.03/0.20	  - RF of loop [6:1]:
0.03/0.20	    -A+B+1 depends on loops [5:1] 
0.03/0.20	    -A+C-1
0.03/0.20	
0.03/0.20	
0.03/0.20	### Specialization of cost equations f0/4 
0.03/0.20	* CE 1 is refined into CE [8,9] 
0.03/0.20	
0.03/0.20	
0.03/0.20	### Cost equations --> "Loop" of f0/4 
0.03/0.20	* CEs [9] --> Loop 8 
0.03/0.20	* CEs [8] --> Loop 9 
0.03/0.20	
0.03/0.20	### Ranking functions of CR f0(A,B,C,D) 
0.03/0.20	
0.03/0.20	#### Partial ranking functions of CR f0(A,B,C,D) 
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):
0.03/0.20	* Chain [[5,6],7]: 1*it(5)+1*it(6)+0
0.03/0.20	  Such that:it(6) =< -A+C
0.03/0.20	aux(8) =< -B+C
0.03/0.20	aux(25) =< C
0.03/0.20	aux(26) =< A-B
0.03/0.20	aux(8) =< aux(26)
0.03/0.20	aux(21) =< aux(25)
0.03/0.20	aux(22) =< it(6)*aux(21)
0.03/0.20	aux(3) =< it(6)*aux(21)
0.03/0.20	aux(14) =< it(6)*aux(25)
0.03/0.20	aux(3) =< it(6)*aux(25)
0.03/0.20	aux(7) =< aux(22)
0.03/0.20	aux(7) =< aux(14)
0.03/0.20	it(5) =< aux(3)+aux(26)
0.03/0.20	it(5) =< aux(7)+aux(8)
0.03/0.20	
0.03/0.20	  with precondition: [D=2,B>=0,C>=A+1,A>=B,C>=B+2] 
0.03/0.20	
0.03/0.20	* Chain [7]: 0
0.03/0.20	  with precondition: [D=2,B>=0,C>=A+1,A>=B] 
0.03/0.20	
0.03/0.20	
0.03/0.20	#### Cost of chains of f0(A,B,C,D):
0.03/0.20	* Chain [9]: 0
0.03/0.20	  with precondition: [C>=1] 
0.03/0.20	
0.03/0.20	* Chain [8]: 1*s(1)+1*s(10)+0
0.03/0.20	  Such that:aux(27) =< C
0.03/0.20	s(1) =< aux(27)
0.03/0.20	s(5) =< aux(27)
0.03/0.20	s(6) =< s(1)*s(5)
0.03/0.20	s(7) =< s(1)*s(5)
0.03/0.20	s(8) =< s(1)*aux(27)
0.03/0.20	s(7) =< s(1)*aux(27)
0.03/0.20	s(9) =< s(6)
0.03/0.20	s(9) =< s(8)
0.03/0.20	s(10) =< s(7)
0.03/0.20	s(10) =< s(9)
0.03/0.20	
0.03/0.20	  with precondition: [C>=2] 
0.03/0.20	
0.03/0.20	
0.03/0.20	Closed-form bounds of f0(A,B,C,D): 
0.03/0.20	-------------------------------------
0.03/0.20	* Chain [9] with precondition: [C>=1] 
0.03/0.20	    - Upper bound: 0 
0.03/0.20	    - Complexity: constant 
0.03/0.20	* Chain [8] with precondition: [C>=2] 
0.03/0.20	    - Upper bound: C*C+C 
0.03/0.20	    - Complexity: n^2 
0.03/0.20	
0.03/0.20	### Maximum cost of f0(A,B,C,D): C*C+C 
0.03/0.20	Asymptotic class: n^2 
0.03/0.20	* Total analysis performed in 129 ms.
0.03/0.20	
0.03/0.30	EOF