0.03/0.15	WORST_CASE(?,O(n^1))  
0.03/0.15	
0.03/0.15	Preprocessing Cost Relations
0.03/0.15	=====================================
0.03/0.15	
0.03/0.15	#### Computed strongly connected components 
0.03/0.15	0. recursive  : [eval/4]
0.03/0.15	1. non_recursive  : [exit_location/1]
0.03/0.15	2. non_recursive  : [eval_loop_cont/2]
0.03/0.15	3. non_recursive  : [start/4]
0.03/0.15	
0.03/0.15	#### Obtained direct recursion through partial evaluation 
0.03/0.15	0. SCC is partially evaluated into eval/4
0.03/0.15	1. SCC is completely evaluated into other SCCs
0.03/0.15	2. SCC is completely evaluated into other SCCs
0.03/0.15	3. SCC is partially evaluated into start/4
0.03/0.15	
0.03/0.15	Control-Flow Refinement of Cost Relations
0.03/0.15	=====================================
0.03/0.15	
0.03/0.15	### Specialization of cost equations eval/4 
0.03/0.15	* CE 4 is refined into CE [5] 
0.03/0.15	* CE 2 is refined into CE [6] 
0.03/0.15	* CE 3 is refined into CE [7] 
0.03/0.15	
0.03/0.15	
0.03/0.15	### Cost equations --> "Loop" of eval/4 
0.03/0.15	* CEs [6] --> Loop 5 
0.03/0.15	* CEs [7] --> Loop 6 
0.03/0.15	* CEs [5] --> Loop 7 
0.03/0.15	
0.03/0.15	### Ranking functions of CR eval(A,B,C,D) 
0.03/0.15	* RF of phase [5]: [A,A+B,A+B-C]
0.03/0.15	* RF of phase [6]: [A+B,A+B-C,B,B-C]
0.03/0.15	
0.03/0.15	#### Partial ranking functions of CR eval(A,B,C,D) 
0.03/0.15	* Partial RF of phase [5]:
0.03/0.15	  - RF of loop [5:1]:
0.03/0.15	    A
0.03/0.15	    A+B
0.03/0.15	    A+B-C
0.03/0.15	* Partial RF of phase [6]:
0.03/0.15	  - RF of loop [6:1]:
0.03/0.15	    A+B
0.03/0.15	    A+B-C
0.03/0.15	    B
0.03/0.15	    B-C
0.03/0.15	
0.03/0.15	
0.03/0.15	### Specialization of cost equations start/4 
0.03/0.15	* CE 1 is refined into CE [8,9,10,11] 
0.03/0.15	
0.03/0.15	
0.03/0.15	### Cost equations --> "Loop" of start/4 
0.03/0.15	* CEs [11] --> Loop 8 
0.03/0.15	* CEs [10] --> Loop 9 
0.03/0.15	* CEs [9] --> Loop 10 
0.03/0.15	* CEs [8] --> Loop 11 
0.03/0.15	
0.03/0.15	### Ranking functions of CR start(A,B,C,D) 
0.03/0.15	
0.03/0.15	#### Partial ranking functions of CR start(A,B,C,D) 
0.03/0.15	
0.03/0.15	
0.03/0.15	Computing Bounds
0.03/0.15	=====================================
0.03/0.15	
0.03/0.15	#### Cost of chains of eval(A,B,C,D):
0.03/0.15	* Chain [[6],7]: 1*it(6)+0
0.03/0.15	  Such that:it(6) =< A+B-C
0.03/0.15	
0.03/0.15	  with precondition: [D=2,0>=A,C>=0,A+B>=C+1] 
0.03/0.15	
0.03/0.15	* Chain [[5],[6],7]: 1*it(5)+1*it(6)+0
0.03/0.15	  Such that:it(5) =< A
0.03/0.15	it(6) =< B-C
0.03/0.15	
0.03/0.15	  with precondition: [D=2,A>=1,C>=0,B>=C+1] 
0.03/0.15	
0.03/0.15	* Chain [[5],7]: 1*it(5)+0
0.03/0.15	  Such that:it(5) =< A
0.03/0.15	it(5) =< A+B-C
0.03/0.15	
0.03/0.15	  with precondition: [D=2,A>=1,C>=0,A+B>=C+1] 
0.03/0.15	
0.03/0.15	* Chain [7]: 0
0.03/0.15	  with precondition: [D=2] 
0.03/0.15	
0.03/0.15	
0.03/0.15	#### Cost of chains of start(A,B,C,D):
0.03/0.15	* Chain [11]: 0
0.03/0.15	  with precondition: [] 
0.03/0.15	
0.03/0.15	* Chain [10]: 1*s(1)+0
0.03/0.15	  Such that:s(1) =< A+B-C
0.03/0.15	
0.03/0.15	  with precondition: [0>=A,C>=0,A+B>=C+1] 
0.03/0.15	
0.03/0.15	* Chain [9]: 1*s(2)+1*s(3)+0
0.03/0.15	  Such that:s(2) =< A
0.03/0.15	s(3) =< B-C
0.03/0.15	
0.03/0.15	  with precondition: [A>=1,C>=0,B>=C+1] 
0.03/0.15	
0.03/0.15	* Chain [8]: 1*s(4)+0
0.03/0.15	  Such that:s(4) =< A
0.03/0.15	s(4) =< A+B-C
0.03/0.15	
0.03/0.15	  with precondition: [A>=1,C>=0,A+B>=C+1] 
0.03/0.15	
0.03/0.15	
0.03/0.15	Closed-form bounds of start(A,B,C,D): 
0.03/0.15	-------------------------------------
0.03/0.15	* Chain [11] with precondition: [] 
0.03/0.15	    - Upper bound: 0 
0.03/0.15	    - Complexity: constant 
0.03/0.15	* Chain [10] with precondition: [0>=A,C>=0,A+B>=C+1] 
0.03/0.15	    - Upper bound: A+B-C 
0.03/0.15	    - Complexity: n 
0.03/0.15	* Chain [9] with precondition: [A>=1,C>=0,B>=C+1] 
0.03/0.15	    - Upper bound: A+B-C 
0.03/0.15	    - Complexity: n 
0.03/0.15	* Chain [8] with precondition: [A>=1,C>=0,A+B>=C+1] 
0.03/0.15	    - Upper bound: A 
0.03/0.15	    - Complexity: n 
0.03/0.15	
0.03/0.15	### Maximum cost of start(A,B,C,D): max([nat(A+B-C),nat(B-C)+nat(A)]) 
0.03/0.15	Asymptotic class: n 
0.03/0.15	* Total analysis performed in 95 ms.
0.03/0.15	
0.03/0.25	EOF