0.04/0.33	WORST_CASE(?,O(n^2))  
0.04/0.33	
0.04/0.33	Preprocessing Cost Relations
0.04/0.33	=====================================
0.04/0.33	
0.04/0.33	#### Computed strongly connected components 
0.04/0.33	0. recursive  : [eval_foo_bb1_in/3,eval_foo_bb2_in/3]
0.04/0.33	1. non_recursive  : [eval_foo_stop/1]
0.04/0.33	2. non_recursive  : [eval_foo_bb3_in/1]
0.04/0.33	3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.04/0.33	4. non_recursive  : [eval_foo_bb0_in/3]
0.04/0.33	5. non_recursive  : [eval_foo_start/3]
0.04/0.33	
0.04/0.33	#### Obtained direct recursion through partial evaluation 
0.04/0.33	0. SCC is partially evaluated into eval_foo_bb1_in/3
0.04/0.33	1. SCC is completely evaluated into other SCCs
0.04/0.33	2. SCC is completely evaluated into other SCCs
0.04/0.33	3. SCC is completely evaluated into other SCCs
0.04/0.33	4. SCC is partially evaluated into eval_foo_bb0_in/3
0.04/0.33	5. SCC is partially evaluated into eval_foo_start/3
0.04/0.33	
0.04/0.33	Control-Flow Refinement of Cost Relations
0.04/0.33	=====================================
0.04/0.33	
0.04/0.33	### Specialization of cost equations eval_foo_bb1_in/3 
0.04/0.33	* CE 5 is refined into CE [6] 
0.04/0.33	* CE 3 is refined into CE [7] 
0.04/0.33	* CE 4 is refined into CE [8] 
0.04/0.33	
0.04/0.33	
0.04/0.33	### Cost equations --> "Loop" of eval_foo_bb1_in/3 
0.04/0.33	* CEs [7] --> Loop 6 
0.04/0.33	* CEs [8] --> Loop 7 
0.04/0.33	* CEs [6] --> Loop 8 
0.04/0.33	
0.04/0.33	### Ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 
0.04/0.33	
0.04/0.33	#### Partial ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 
0.04/0.33	* Partial RF of phase [6,7]:
0.04/0.33	  - RF of loop [6:1]:
0.04/0.33	    V__0+1 depends on loops [7:1] 
0.04/0.33	    -V__01/2 depends on loops [7:1] 
0.04/0.33	  - RF of loop [7:1]:
0.04/0.33	    V__01+1 depends on loops [6:1] 
0.04/0.33	    V__01+2*V__0+1
0.04/0.33	
0.04/0.33	
0.04/0.33	### Specialization of cost equations eval_foo_bb0_in/3 
0.04/0.33	* CE 2 is refined into CE [9,10] 
0.04/0.33	
0.04/0.33	
0.04/0.33	### Cost equations --> "Loop" of eval_foo_bb0_in/3 
0.04/0.33	* CEs [10] --> Loop 9 
0.04/0.33	* CEs [9] --> Loop 10 
0.04/0.33	
0.04/0.33	### Ranking functions of CR eval_foo_bb0_in(V_a,V_b,B) 
0.04/0.33	
0.04/0.33	#### Partial ranking functions of CR eval_foo_bb0_in(V_a,V_b,B) 
0.04/0.33	
0.04/0.33	
0.04/0.33	### Specialization of cost equations eval_foo_start/3 
0.04/0.33	* CE 1 is refined into CE [11,12] 
0.04/0.33	
0.04/0.33	
0.04/0.33	### Cost equations --> "Loop" of eval_foo_start/3 
0.04/0.33	* CEs [12] --> Loop 11 
0.04/0.33	* CEs [11] --> Loop 12 
0.04/0.33	
0.04/0.33	### Ranking functions of CR eval_foo_start(V_a,V_b,B) 
0.04/0.33	
0.04/0.33	#### Partial ranking functions of CR eval_foo_start(V_a,V_b,B) 
0.04/0.33	
0.04/0.33	
0.04/0.33	Computing Bounds
0.04/0.33	=====================================
0.04/0.33	
0.04/0.33	#### Cost of chains of eval_foo_bb1_in(V__01,V__0,B):
0.04/0.33	* Chain [[6,7],8]: 1*it(6)+1*it(7)+0
0.04/0.33	  Such that:aux(29) =< V__01+2*V__0
0.04/0.33	it(7) =< V__01+2*V__0+1
0.04/0.33	aux(52) =< V__01+2*V__0+1/2
0.04/0.33	aux(2) =< -V__01/2
0.04/0.33	aux(4) =< V__0+1
0.04/0.33	aux(50) =< aux(29)
0.04/0.33	aux(42) =< aux(29)+1/2
0.04/0.33	aux(1) =< it(7)*aux(52)
0.04/0.33	aux(3) =< it(7)*aux(50)
0.04/0.33	aux(1) =< it(7)*aux(42)
0.04/0.33	aux(3) =< it(7)*aux(29)
0.04/0.33	it(6) =< aux(3)+aux(4)
0.04/0.33	it(6) =< aux(1)+aux(2)
0.04/0.33	
0.04/0.33	  with precondition: [B=2,V__0>=0] 
0.04/0.33	
0.04/0.33	* Chain [8]: 0
0.04/0.33	  with precondition: [B=2,0>=V__0+1] 
0.04/0.33	
0.04/0.33	
0.04/0.33	#### Cost of chains of eval_foo_bb0_in(V_a,V_b,B):
0.04/0.33	* Chain [10]: 0
0.04/0.33	  with precondition: [0>=V_a+1] 
0.04/0.33	
0.04/0.33	* Chain [9]: 1*s(2)+1*s(10)+0
0.04/0.33	  Such that:s(5) =< V_a+1
0.04/0.33	s(1) =< 2*V_a+V_b
0.04/0.33	s(2) =< 2*V_a+V_b+1
0.04/0.33	s(3) =< 2*V_a+V_b+1/2
0.04/0.33	s(4) =< -V_b/2
0.04/0.33	s(6) =< s(1)
0.04/0.33	s(7) =< s(1)+1/2
0.04/0.33	s(8) =< s(2)*s(3)
0.04/0.33	s(9) =< s(2)*s(6)
0.04/0.33	s(8) =< s(2)*s(7)
0.04/0.33	s(9) =< s(2)*s(1)
0.04/0.33	s(10) =< s(9)+s(5)
0.04/0.33	s(10) =< s(8)+s(4)
0.04/0.33	
0.04/0.33	  with precondition: [V_a>=0] 
0.04/0.33	
0.04/0.33	
0.04/0.33	#### Cost of chains of eval_foo_start(V_a,V_b,B):
0.04/0.33	* Chain [12]: 0
0.04/0.33	  with precondition: [0>=V_a+1] 
0.04/0.33	
0.04/0.33	* Chain [11]: 1*s(13)+1*s(20)+0
0.04/0.33	  Such that:s(11) =< V_a+1
0.04/0.33	s(12) =< 2*V_a+V_b
0.04/0.33	s(13) =< 2*V_a+V_b+1
0.04/0.33	s(14) =< 2*V_a+V_b+1/2
0.04/0.33	s(15) =< -V_b/2
0.04/0.33	s(16) =< s(12)
0.04/0.33	s(17) =< s(12)+1/2
0.04/0.33	s(18) =< s(13)*s(14)
0.04/0.33	s(19) =< s(13)*s(16)
0.04/0.33	s(18) =< s(13)*s(17)
0.04/0.33	s(19) =< s(13)*s(12)
0.04/0.33	s(20) =< s(19)+s(11)
0.04/0.33	s(20) =< s(18)+s(15)
0.04/0.33	
0.04/0.33	  with precondition: [V_a>=0] 
0.04/0.33	
0.04/0.33	
0.04/0.33	Closed-form bounds of eval_foo_start(V_a,V_b,B): 
0.04/0.33	-------------------------------------
0.04/0.33	* Chain [12] with precondition: [0>=V_a+1] 
0.04/0.33	    - Upper bound: 0 
0.04/0.33	    - Complexity: constant 
0.04/0.33	* Chain [11] with precondition: [V_a>=0] 
0.04/0.33	    - Upper bound: V_a+1+nat(2*V_a+V_b+1)*nat(2*V_a+V_b)+nat(2*V_a+V_b+1) 
0.04/0.33	    - Complexity: n^2 
0.04/0.33	
0.04/0.33	### Maximum cost of eval_foo_start(V_a,V_b,B): nat(2*V_a+V_b+1)*nat(2*V_a+V_b)+nat(V_a+1)+nat(2*V_a+V_b+1) 
0.04/0.33	Asymptotic class: n^2 
0.04/0.33	* Total analysis performed in 226 ms.
0.04/0.33	
0.04/0.43	EOF