0.03/0.19	WORST_CASE(?,O(n^1))  
0.03/0.19	
0.03/0.19	Preprocessing Cost Relations
0.03/0.19	=====================================
0.03/0.19	
0.03/0.19	#### Computed strongly connected components 
0.03/0.19	0. recursive  : [eval/3]
0.03/0.19	1. non_recursive  : [exit_location/1]
0.03/0.19	2. non_recursive  : [eval_loop_cont/2]
0.03/0.19	3. non_recursive  : [start/3]
0.03/0.19	
0.03/0.19	#### Obtained direct recursion through partial evaluation 
0.03/0.19	0. SCC is partially evaluated into eval/3
0.03/0.19	1. SCC is completely evaluated into other SCCs
0.03/0.19	2. SCC is completely evaluated into other SCCs
0.03/0.19	3. SCC is partially evaluated into start/3
0.03/0.19	
0.03/0.19	Control-Flow Refinement of Cost Relations
0.03/0.19	=====================================
0.03/0.19	
0.03/0.19	### Specialization of cost equations eval/3 
0.03/0.19	* CE 4 is refined into CE [5] 
0.03/0.19	* CE 2 is refined into CE [6] 
0.03/0.19	* CE 3 is refined into CE [7] 
0.03/0.19	
0.03/0.19	
0.03/0.19	### Cost equations --> "Loop" of eval/3 
0.03/0.19	* CEs [6] --> Loop 5 
0.03/0.19	* CEs [7] --> Loop 6 
0.03/0.19	* CEs [5] --> Loop 7 
0.03/0.19	
0.03/0.19	### Ranking functions of CR eval(A,B,C) 
0.03/0.19	* RF of phase [5,6]: [A+B-2]
0.03/0.19	
0.03/0.19	#### Partial ranking functions of CR eval(A,B,C) 
0.03/0.19	* Partial RF of phase [5,6]:
0.03/0.19	  - RF of loop [5:1]:
0.03/0.19	    A-1
0.03/0.19	    A-B depends on loops [6:1] 
0.03/0.19	  - RF of loop [6:1]:
0.03/0.19	    -A+B depends on loops [5:1] 
0.03/0.19	    B-1
0.03/0.19	
0.03/0.19	
0.03/0.19	### Specialization of cost equations start/3 
0.03/0.19	* CE 1 is refined into CE [8,9] 
0.03/0.19	
0.03/0.19	
0.03/0.19	### Cost equations --> "Loop" of start/3 
0.03/0.19	* CEs [9] --> Loop 8 
0.03/0.19	* CEs [8] --> Loop 9 
0.03/0.19	
0.03/0.19	### Ranking functions of CR start(A,B,C) 
0.03/0.19	
0.03/0.19	#### Partial ranking functions of CR start(A,B,C) 
0.03/0.19	
0.03/0.19	
0.03/0.19	Computing Bounds
0.03/0.19	=====================================
0.03/0.19	
0.03/0.19	#### Cost of chains of eval(A,B,C):
0.03/0.19	* Chain [[5,6],7]: 1*it(5)+1*it(6)+0
0.03/0.19	  Such that:aux(4) =< -A+B
0.03/0.19	aux(2) =< A-B
0.03/0.19	aux(1) =< 2*A+B
0.03/0.19	aux(14) =< A
0.03/0.19	aux(15) =< A+B
0.03/0.19	aux(16) =< A+2*B
0.03/0.19	aux(17) =< B
0.03/0.19	aux(3) =< aux(14)
0.03/0.19	it(5) =< aux(14)
0.03/0.19	aux(1) =< aux(15)
0.03/0.19	aux(3) =< aux(15)
0.03/0.19	it(5) =< aux(15)
0.03/0.19	it(6) =< aux(15)
0.03/0.19	aux(1) =< aux(16)
0.03/0.19	aux(3) =< aux(16)
0.03/0.19	aux(1) =< aux(17)
0.03/0.19	it(6) =< aux(17)
0.03/0.19	it(6) =< aux(3)+aux(4)
0.03/0.19	aux(1) =< it(6)*aux(17)
0.03/0.19	it(5) =< aux(1)+aux(2)
0.03/0.19	
0.03/0.19	  with precondition: [C=2,A>=1,B>=1,A+B>=3] 
0.03/0.19	
0.03/0.19	* Chain [7]: 0
0.03/0.19	  with precondition: [C=2] 
0.03/0.19	
0.03/0.19	
0.03/0.19	#### Cost of chains of start(A,B,C):
0.03/0.19	* Chain [9]: 0
0.03/0.19	  with precondition: [] 
0.03/0.19	
0.03/0.19	* Chain [8]: 1*s(9)+1*s(10)+0
0.03/0.19	  Such that:s(1) =< -A+B
0.03/0.19	s(4) =< A
0.03/0.19	s(2) =< A-B
0.03/0.19	s(5) =< A+B
0.03/0.19	s(6) =< A+2*B
0.03/0.19	s(3) =< 2*A+B
0.03/0.19	aux(18) =< B
0.03/0.19	s(1) =< aux(18)
0.03/0.19	s(8) =< s(4)
0.03/0.19	s(9) =< s(4)
0.03/0.19	s(3) =< s(5)
0.03/0.19	s(8) =< s(5)
0.03/0.19	s(9) =< s(5)
0.03/0.19	s(10) =< s(5)
0.03/0.19	s(3) =< s(6)
0.03/0.19	s(8) =< s(6)
0.03/0.19	s(3) =< aux(18)
0.03/0.19	s(10) =< aux(18)
0.03/0.19	s(10) =< s(8)+s(1)
0.03/0.19	s(3) =< s(10)*aux(18)
0.03/0.19	s(9) =< s(3)+s(2)
0.03/0.19	
0.03/0.19	  with precondition: [A>=1,B>=1,A+B>=3] 
0.03/0.19	
0.03/0.19	
0.03/0.19	Closed-form bounds of start(A,B,C): 
0.03/0.19	-------------------------------------
0.03/0.19	* Chain [9] with precondition: [] 
0.03/0.19	    - Upper bound: 0 
0.03/0.19	    - Complexity: constant 
0.03/0.19	* Chain [8] with precondition: [A>=1,B>=1,A+B>=3] 
0.03/0.19	    - Upper bound: 2*A+B 
0.03/0.19	    - Complexity: n 
0.03/0.19	
0.03/0.19	### Maximum cost of start(A,B,C): nat(A+B)+nat(A) 
0.03/0.19	Asymptotic class: n 
0.03/0.19	* Total analysis performed in 117 ms.
0.03/0.19	
0.03/0.29	EOF