0.03/0.12	WORST_CASE(?,O(n^1))  
0.03/0.12	
0.03/0.12	Preprocessing Cost Relations
0.03/0.12	=====================================
0.03/0.12	
0.03/0.12	#### Computed strongly connected components 
0.03/0.12	0. recursive  : [f/4]
0.03/0.12	1. non_recursive  : [exit_location/1]
0.03/0.12	2. non_recursive  : [f_loop_cont/2]
0.03/0.12	3. non_recursive  : [start/4]
0.03/0.12	
0.03/0.12	#### Obtained direct recursion through partial evaluation 
0.03/0.12	0. SCC is partially evaluated into f/4
0.03/0.12	1. SCC is completely evaluated into other SCCs
0.03/0.12	2. SCC is completely evaluated into other SCCs
0.03/0.12	3. SCC is partially evaluated into start/4
0.03/0.12	
0.03/0.12	Control-Flow Refinement of Cost Relations
0.03/0.12	=====================================
0.03/0.12	
0.03/0.12	### Specialization of cost equations f/4 
0.03/0.12	* CE 4 is refined into CE [5] 
0.03/0.12	* CE 3 is refined into CE [6] 
0.03/0.12	* CE 2 is refined into CE [7] 
0.03/0.12	
0.03/0.12	
0.03/0.12	### Cost equations --> "Loop" of f/4 
0.03/0.12	* CEs [6] --> Loop 5 
0.03/0.12	* CEs [7] --> Loop 6 
0.03/0.12	* CEs [5] --> Loop 7 
0.03/0.12	
0.03/0.12	### Ranking functions of CR f(A,B,C,D) 
0.03/0.12	* RF of phase [5,6]: [2*A-B-C-1]
0.03/0.12	
0.03/0.12	#### Partial ranking functions of CR f(A,B,C,D) 
0.03/0.12	* Partial RF of phase [5,6]:
0.03/0.12	  - RF of loop [5:1]:
0.03/0.12	    A-C
0.03/0.12	  - RF of loop [6:1]:
0.03/0.12	    A-B
0.03/0.12	
0.03/0.12	
0.03/0.12	### Specialization of cost equations start/4 
0.03/0.12	* CE 1 is refined into CE [8,9] 
0.03/0.12	
0.03/0.12	
0.03/0.12	### Cost equations --> "Loop" of start/4 
0.03/0.12	* CEs [9] --> Loop 8 
0.03/0.12	* CEs [8] --> Loop 9 
0.03/0.12	
0.03/0.12	### Ranking functions of CR start(A,B,C,D) 
0.03/0.12	
0.03/0.12	#### Partial ranking functions of CR start(A,B,C,D) 
0.03/0.12	
0.03/0.12	
0.03/0.12	Computing Bounds
0.03/0.12	=====================================
0.03/0.12	
0.03/0.12	#### Cost of chains of f(A,B,C,D):
0.03/0.12	* Chain [[5,6],7]: 1*it(5)+1*it(6)+0
0.03/0.12	  Such that:it(6) =< A-B
0.03/0.12	it(5) =< A-C
0.03/0.12	aux(3) =< 2*A-B-C
0.03/0.12	it(5) =< aux(3)
0.03/0.12	it(6) =< aux(3)
0.03/0.12	
0.03/0.12	  with precondition: [D=2,A>=B+1,A>=C+1] 
0.03/0.12	
0.03/0.12	* Chain [7]: 0
0.03/0.12	  with precondition: [D=2] 
0.03/0.12	
0.03/0.12	
0.03/0.12	#### Cost of chains of start(A,B,C,D):
0.03/0.12	* Chain [9]: 0
0.03/0.12	  with precondition: [] 
0.03/0.12	
0.03/0.12	* Chain [8]: 1*s(1)+1*s(2)+0
0.03/0.12	  Such that:s(1) =< A-B
0.03/0.12	s(2) =< A-C
0.03/0.12	s(3) =< 2*A-B-C
0.03/0.12	s(2) =< s(3)
0.03/0.12	s(1) =< s(3)
0.03/0.12	
0.03/0.12	  with precondition: [A>=B+1,A>=C+1] 
0.03/0.12	
0.03/0.12	
0.03/0.12	Closed-form bounds of start(A,B,C,D): 
0.03/0.12	-------------------------------------
0.03/0.12	* Chain [9] with precondition: [] 
0.03/0.12	    - Upper bound: 0 
0.03/0.12	    - Complexity: constant 
0.03/0.12	* Chain [8] with precondition: [A>=B+1,A>=C+1] 
0.03/0.12	    - Upper bound: 2*A-B-C 
0.03/0.12	    - Complexity: n 
0.03/0.12	
0.03/0.12	### Maximum cost of start(A,B,C,D): nat(A-C)+nat(A-B) 
0.03/0.12	Asymptotic class: n 
0.03/0.12	* Total analysis performed in 64 ms.
0.03/0.12	
0.03/0.22	EOF