0.03/0.17	WORST_CASE(?,O(n^1))  
0.03/0.17	
0.03/0.17	Preprocessing Cost Relations
0.03/0.17	=====================================
0.03/0.17	
0.03/0.17	#### Computed strongly connected components 
0.03/0.17	0. recursive  : [eval/3]
0.03/0.17	1. non_recursive  : [exit_location/1]
0.03/0.17	2. non_recursive  : [eval_loop_cont/2]
0.03/0.17	3. non_recursive  : [start/3]
0.03/0.17	
0.03/0.17	#### Obtained direct recursion through partial evaluation 
0.03/0.17	0. SCC is partially evaluated into eval/3
0.03/0.17	1. SCC is completely evaluated into other SCCs
0.03/0.17	2. SCC is completely evaluated into other SCCs
0.03/0.17	3. SCC is partially evaluated into start/3
0.03/0.17	
0.03/0.17	Control-Flow Refinement of Cost Relations
0.03/0.17	=====================================
0.03/0.17	
0.03/0.17	### Specialization of cost equations eval/3 
0.03/0.17	* CE 5 is refined into CE [6] 
0.03/0.17	* CE 2 is refined into CE [7] 
0.03/0.17	* CE 4 is refined into CE [8] 
0.03/0.17	* CE 3 is refined into CE [9] 
0.03/0.17	
0.03/0.17	
0.03/0.17	### Cost equations --> "Loop" of eval/3 
0.03/0.17	* CEs [7] --> Loop 6 
0.03/0.17	* CEs [8] --> Loop 7 
0.03/0.17	* CEs [9] --> Loop 8 
0.03/0.17	* CEs [6] --> Loop 9 
0.03/0.17	
0.03/0.17	### Ranking functions of CR eval(A,B,C) 
0.03/0.17	* RF of phase [6]: [A,A-B,A+B]
0.03/0.17	* RF of phase [7,8]: [A+B]
0.03/0.17	
0.03/0.17	#### Partial ranking functions of CR eval(A,B,C) 
0.03/0.17	* Partial RF of phase [6]:
0.03/0.17	  - RF of loop [6:1]:
0.03/0.17	    A
0.03/0.17	    A-B
0.03/0.17	    A+B
0.03/0.17	* Partial RF of phase [7,8]:
0.03/0.17	  - RF of loop [7:1]:
0.03/0.17	    -A+B depends on loops [8:1] 
0.03/0.17	    A+B
0.03/0.17	    B
0.03/0.17	  - RF of loop [8:1]:
0.03/0.17	    A+1
0.03/0.17	    A-B+1 depends on loops [7:1] 
0.03/0.17	
0.03/0.17	
0.03/0.17	### Specialization of cost equations start/3 
0.03/0.17	* CE 1 is refined into CE [10,11,12,13] 
0.03/0.17	
0.03/0.17	
0.03/0.17	### Cost equations --> "Loop" of start/3 
0.03/0.17	* CEs [13] --> Loop 10 
0.03/0.17	* CEs [12] --> Loop 11 
0.03/0.17	* CEs [11] --> Loop 12 
0.03/0.17	* CEs [10] --> Loop 13 
0.03/0.17	
0.03/0.17	### Ranking functions of CR start(A,B,C) 
0.03/0.17	
0.03/0.17	#### Partial ranking functions of CR start(A,B,C) 
0.03/0.17	
0.03/0.17	
0.03/0.17	Computing Bounds
0.03/0.17	=====================================
0.03/0.17	
0.03/0.17	#### Cost of chains of eval(A,B,C):
0.03/0.17	* Chain [[7,8],9]: 1*it(7)+1*it(8)+0
0.03/0.17	  Such that:it(8) =< A+1
0.03/0.17	it(7) =< B
0.03/0.17	aux(7) =< A+B
0.03/0.17	it(7) =< aux(7)
0.03/0.17	it(8) =< aux(7)
0.03/0.17	
0.03/0.17	  with precondition: [C=2,B>=A,A+B>=1] 
0.03/0.17	
0.03/0.17	* Chain [[6],[7,8],9]: 1*it(6)+1*it(7)+1*it(8)+0
0.03/0.17	  Such that:it(6) =< A-B
0.03/0.17	it(7) =< B
0.03/0.17	it(8) =< B+1
0.03/0.17	aux(7) =< 2*B
0.03/0.17	it(7) =< aux(7)
0.03/0.17	it(8) =< aux(7)
0.03/0.17	
0.03/0.17	  with precondition: [C=2,2*B>=1,A>=B+1] 
0.03/0.17	
0.03/0.17	* Chain [[6],9]: 1*it(6)+0
0.03/0.17	  Such that:it(6) =< A-B
0.03/0.17	it(6) =< A+B
0.03/0.17	
0.03/0.17	  with precondition: [C=2,A>=B+1,A+B>=1] 
0.03/0.17	
0.03/0.17	* Chain [9]: 0
0.03/0.17	  with precondition: [C=2] 
0.03/0.17	
0.03/0.17	
0.03/0.17	#### Cost of chains of start(A,B,C):
0.03/0.17	* Chain [13]: 0
0.03/0.17	  with precondition: [] 
0.03/0.17	
0.03/0.17	* Chain [12]: 1*s(1)+1*s(2)+1*s(3)+0
0.03/0.17	  Such that:s(1) =< A-B
0.03/0.17	s(2) =< B
0.03/0.17	s(3) =< B+1
0.03/0.17	s(4) =< 2*B
0.03/0.17	s(2) =< s(4)
0.03/0.17	s(3) =< s(4)
0.03/0.17	
0.03/0.17	  with precondition: [2*B>=1,A>=B+1] 
0.03/0.17	
0.03/0.17	* Chain [11]: 1*s(5)+1*s(6)+0
0.03/0.17	  Such that:s(5) =< A+1
0.03/0.17	s(7) =< A+B
0.03/0.17	s(6) =< B
0.03/0.17	s(5) =< B+1
0.03/0.17	s(6) =< s(7)
0.03/0.17	s(5) =< s(7)
0.03/0.17	
0.03/0.17	  with precondition: [B>=A,A+B>=1] 
0.03/0.17	
0.03/0.17	* Chain [10]: 1*s(8)+0
0.03/0.17	  Such that:s(8) =< A-B
0.03/0.17	s(8) =< A+B
0.03/0.17	
0.03/0.17	  with precondition: [A>=B+1,A+B>=1] 
0.03/0.17	
0.03/0.17	
0.03/0.17	Closed-form bounds of start(A,B,C): 
0.03/0.17	-------------------------------------
0.03/0.17	* Chain [13] with precondition: [] 
0.03/0.17	    - Upper bound: 0 
0.03/0.17	    - Complexity: constant 
0.03/0.17	* Chain [12] with precondition: [2*B>=1,A>=B+1] 
0.03/0.17	    - Upper bound: A+B+1 
0.03/0.17	    - Complexity: n 
0.03/0.17	* Chain [11] with precondition: [B>=A,A+B>=1] 
0.03/0.17	    - Upper bound: nat(A+1)+B 
0.03/0.17	    - Complexity: n 
0.03/0.17	* Chain [10] with precondition: [A>=B+1,A+B>=1] 
0.03/0.17	    - Upper bound: A-B 
0.03/0.17	    - Complexity: n 
0.03/0.17	
0.03/0.17	### Maximum cost of start(A,B,C): max([nat(A-B),nat(B)+max([nat(A+1),nat(A-B)+nat(B+1)])]) 
0.03/0.17	Asymptotic class: n 
0.03/0.17	* Total analysis performed in 110 ms.
0.03/0.17	
0.03/0.27	EOF