0.06/0.15	WORST_CASE(?,O(n^1))  
0.06/0.15	
0.06/0.15	Preprocessing Cost Relations
0.06/0.15	=====================================
0.06/0.15	
0.06/0.15	#### Computed strongly connected components 
0.06/0.15	0. recursive  : [eval_foo_2/3,eval_foo_3/4,eval_foo_6/5,eval_foo_7/6,eval_foo_bb1_in/3,eval_foo_bb2_in/3]
0.06/0.15	1. non_recursive  : [eval_foo_stop/1]
0.06/0.15	2. non_recursive  : [eval_foo_bb3_in/1]
0.06/0.15	3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.06/0.15	4. non_recursive  : [eval_foo_bb0_in/3]
0.06/0.15	5. non_recursive  : [eval_foo_start/5]
0.06/0.15	
0.06/0.15	#### Obtained direct recursion through partial evaluation 
0.06/0.15	0. SCC is partially evaluated into eval_foo_bb1_in/3
0.06/0.15	1. SCC is completely evaluated into other SCCs
0.06/0.15	2. SCC is completely evaluated into other SCCs
0.06/0.15	3. SCC is completely evaluated into other SCCs
0.06/0.15	4. SCC is partially evaluated into eval_foo_bb0_in/3
0.06/0.15	5. SCC is partially evaluated into eval_foo_start/5
0.06/0.15	
0.06/0.15	Control-Flow Refinement of Cost Relations
0.06/0.15	=====================================
0.06/0.15	
0.06/0.15	### Specialization of cost equations eval_foo_bb1_in/3 
0.06/0.15	* CE 5 is refined into CE [6] 
0.06/0.15	* CE 4 is refined into CE [7] 
0.06/0.15	* CE 3 is refined into CE [8] 
0.06/0.15	
0.06/0.15	
0.06/0.15	### Cost equations --> "Loop" of eval_foo_bb1_in/3 
0.06/0.15	* CEs [7] --> Loop 6 
0.06/0.15	* CEs [8] --> Loop 7 
0.06/0.15	* CEs [6] --> Loop 8 
0.06/0.15	
0.06/0.15	### Ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 
0.06/0.15	* RF of phase [6,7]: [-V__01+V__0]
0.06/0.15	
0.06/0.15	#### Partial ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 
0.06/0.15	* Partial RF of phase [6,7]:
0.06/0.15	  - RF of loop [6:1]:
0.06/0.15	    -V__01/2+V__0/2
0.06/0.15	  - RF of loop [7:1]:
0.06/0.15	    -V__01+V__0
0.06/0.15	
0.06/0.15	
0.06/0.15	### Specialization of cost equations eval_foo_bb0_in/3 
0.06/0.15	* CE 2 is refined into CE [9,10] 
0.06/0.15	
0.06/0.15	
0.06/0.15	### Cost equations --> "Loop" of eval_foo_bb0_in/3 
0.06/0.15	* CEs [9] --> Loop 9 
0.06/0.15	* CEs [10] --> Loop 10 
0.06/0.15	
0.06/0.15	### Ranking functions of CR eval_foo_bb0_in(V_i,V_j,B) 
0.06/0.15	
0.06/0.15	#### Partial ranking functions of CR eval_foo_bb0_in(V_i,V_j,B) 
0.06/0.15	
0.06/0.15	
0.06/0.15	### Specialization of cost equations eval_foo_start/5 
0.06/0.15	* CE 1 is refined into CE [11,12] 
0.06/0.15	
0.06/0.15	
0.06/0.15	### Cost equations --> "Loop" of eval_foo_start/5 
0.06/0.15	* CEs [12] --> Loop 11 
0.06/0.15	* CEs [11] --> Loop 12 
0.06/0.15	
0.06/0.15	### Ranking functions of CR eval_foo_start(V_i,V_j,V_nondetNat,V_nondetPos,B) 
0.06/0.15	
0.06/0.15	#### Partial ranking functions of CR eval_foo_start(V_i,V_j,V_nondetNat,V_nondetPos,B) 
0.06/0.15	
0.06/0.15	
0.06/0.15	Computing Bounds
0.06/0.15	=====================================
0.06/0.15	
0.06/0.15	#### Cost of chains of eval_foo_bb1_in(V__01,V__0,B):
0.06/0.15	* Chain [[6,7],8]: 1*it(6)+1*it(7)+0
0.06/0.15	  Such that:aux(1) =< -V__01+V__0
0.06/0.15	it(6) =< -V__01/2+V__0/2
0.06/0.15	it(6) =< aux(1)
0.06/0.15	it(7) =< aux(1)
0.06/0.15	
0.06/0.15	  with precondition: [B=2,V__0>=V__01+1] 
0.06/0.15	
0.06/0.15	* Chain [8]: 0
0.06/0.15	  with precondition: [B=2,V__01>=V__0] 
0.06/0.15	
0.06/0.15	
0.06/0.15	#### Cost of chains of eval_foo_bb0_in(V_i,V_j,B):
0.06/0.15	* Chain [10]: 0
0.06/0.15	  with precondition: [V_j>=V_i] 
0.06/0.15	
0.06/0.15	* Chain [9]: 1*s(2)+1*s(3)+0
0.06/0.15	  Such that:s(1) =< V_i-V_j
0.06/0.15	s(2) =< V_i/2-V_j/2
0.06/0.15	s(2) =< s(1)
0.06/0.15	s(3) =< s(1)
0.06/0.15	
0.06/0.15	  with precondition: [V_i>=V_j+1] 
0.06/0.15	
0.06/0.15	
0.06/0.15	#### Cost of chains of eval_foo_start(V_i,V_j,V_nondetNat,V_nondetPos,B):
0.06/0.15	* Chain [12]: 0
0.06/0.15	  with precondition: [V_j>=V_i] 
0.06/0.15	
0.06/0.15	* Chain [11]: 1*s(5)+1*s(6)+0
0.06/0.15	  Such that:s(4) =< V_i-V_j
0.06/0.15	s(5) =< V_i/2-V_j/2
0.06/0.15	s(5) =< s(4)
0.06/0.15	s(6) =< s(4)
0.06/0.15	
0.06/0.15	  with precondition: [V_i>=V_j+1] 
0.06/0.15	
0.06/0.15	
0.06/0.15	Closed-form bounds of eval_foo_start(V_i,V_j,V_nondetNat,V_nondetPos,B): 
0.06/0.15	-------------------------------------
0.06/0.15	* Chain [12] with precondition: [V_j>=V_i] 
0.06/0.15	    - Upper bound: 0 
0.06/0.15	    - Complexity: constant 
0.06/0.15	* Chain [11] with precondition: [V_i>=V_j+1] 
0.06/0.15	    - Upper bound: 3/2*V_i-3/2*V_j 
0.06/0.15	    - Complexity: n 
0.06/0.15	
0.06/0.15	### Maximum cost of eval_foo_start(V_i,V_j,V_nondetNat,V_nondetPos,B): nat(V_i/2-V_j/2)+nat(V_i-V_j) 
0.06/0.15	Asymptotic class: n 
0.06/0.15	* Total analysis performed in 74 ms.
0.06/0.15	
0.06/0.25	EOF