0.03/0.11	WORST_CASE(?,O(n^1))  
0.03/0.11	
0.03/0.11	Preprocessing Cost Relations
0.03/0.11	=====================================
0.03/0.11	
0.03/0.11	#### Computed strongly connected components 
0.03/0.11	0. recursive  : [f/4]
0.03/0.11	1. non_recursive  : [exit_location/1]
0.03/0.11	2. non_recursive  : [f_loop_cont/2]
0.03/0.11	3. non_recursive  : [start/4]
0.03/0.11	
0.03/0.11	#### Obtained direct recursion through partial evaluation 
0.03/0.11	0. SCC is partially evaluated into f/4
0.03/0.11	1. SCC is completely evaluated into other SCCs
0.03/0.11	2. SCC is completely evaluated into other SCCs
0.03/0.11	3. SCC is partially evaluated into start/4
0.03/0.11	
0.03/0.11	Control-Flow Refinement of Cost Relations
0.03/0.11	=====================================
0.03/0.11	
0.03/0.11	### Specialization of cost equations f/4 
0.03/0.11	* CE 4 is refined into CE [5] 
0.03/0.11	* CE 3 is refined into CE [6] 
0.03/0.11	* CE 2 is refined into CE [7] 
0.03/0.11	
0.03/0.11	
0.03/0.11	### Cost equations --> "Loop" of f/4 
0.03/0.11	* CEs [6] --> Loop 5 
0.03/0.11	* CEs [7] --> Loop 6 
0.03/0.11	* CEs [5] --> Loop 7 
0.03/0.11	
0.03/0.11	### Ranking functions of CR f(A,B,C,D) 
0.03/0.11	* RF of phase [5,6]: [A-B-C]
0.03/0.11	
0.03/0.11	#### Partial ranking functions of CR f(A,B,C,D) 
0.03/0.11	* Partial RF of phase [5,6]:
0.03/0.11	  - RF of loop [5:1,6:1]:
0.03/0.11	    A-B-C
0.03/0.11	
0.03/0.11	
0.03/0.11	### Specialization of cost equations start/4 
0.03/0.11	* CE 1 is refined into CE [8,9] 
0.03/0.11	
0.03/0.11	
0.03/0.11	### Cost equations --> "Loop" of start/4 
0.03/0.11	* CEs [9] --> Loop 8 
0.03/0.11	* CEs [8] --> Loop 9 
0.03/0.11	
0.03/0.11	### Ranking functions of CR start(A,B,C,D) 
0.03/0.11	
0.03/0.11	#### Partial ranking functions of CR start(A,B,C,D) 
0.03/0.11	
0.03/0.11	
0.03/0.11	Computing Bounds
0.03/0.11	=====================================
0.03/0.11	
0.03/0.11	#### Cost of chains of f(A,B,C,D):
0.03/0.11	* Chain [[5,6],7]: 2*it(5)+0
0.03/0.11	  Such that:aux(3) =< A-B-C
0.03/0.11	it(5) =< aux(3)
0.03/0.11	
0.03/0.11	  with precondition: [D=2,A>=B+C+1] 
0.03/0.11	
0.03/0.11	* Chain [7]: 0
0.03/0.11	  with precondition: [D=2] 
0.03/0.11	
0.03/0.11	
0.03/0.11	#### Cost of chains of start(A,B,C,D):
0.03/0.11	* Chain [9]: 0
0.03/0.11	  with precondition: [] 
0.03/0.11	
0.03/0.11	* Chain [8]: 2*s(2)+0
0.03/0.11	  Such that:s(1) =< A-B-C
0.03/0.11	s(2) =< s(1)
0.03/0.11	
0.03/0.11	  with precondition: [A>=B+C+1] 
0.03/0.11	
0.03/0.11	
0.03/0.11	Closed-form bounds of start(A,B,C,D): 
0.03/0.11	-------------------------------------
0.03/0.11	* Chain [9] with precondition: [] 
0.03/0.11	    - Upper bound: 0 
0.03/0.11	    - Complexity: constant 
0.03/0.11	* Chain [8] with precondition: [A>=B+C+1] 
0.03/0.11	    - Upper bound: 2*A-2*B-2*C 
0.03/0.11	    - Complexity: n 
0.03/0.11	
0.03/0.11	### Maximum cost of start(A,B,C,D): nat(A-B-C)*2 
0.03/0.11	Asymptotic class: n 
0.03/0.11	* Total analysis performed in 53 ms.
0.03/0.11	
0.03/0.21	EOF