0.05/0.29	WORST_CASE(?,O(n^1))  
0.05/0.29	
0.05/0.29	Preprocessing Cost Relations
0.05/0.29	=====================================
0.05/0.29	
0.05/0.29	#### Computed strongly connected components 
0.05/0.29	0. recursive  : [eval_foo_3/4,eval_foo_4/5,eval_foo_bb3_in/4,eval_foo_bb4_in/4,eval_foo_bb5_in/5]
0.05/0.29	1. recursive  : [eval_foo__critedge_in/5,eval_foo_bb1_in/3,eval_foo_bb2_in/3,eval_foo_bb3_in_loop_cont/6]
0.05/0.29	2. non_recursive  : [eval_foo_stop/1]
0.05/0.29	3. non_recursive  : [eval_foo_bb6_in/1]
0.05/0.29	4. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.05/0.29	5. non_recursive  : [eval_foo_bb0_in/3]
0.05/0.29	6. non_recursive  : [eval_foo_start/3]
0.05/0.29	
0.05/0.29	#### Obtained direct recursion through partial evaluation 
0.05/0.29	0. SCC is partially evaluated into eval_foo_bb3_in/4
0.05/0.29	1. SCC is partially evaluated into eval_foo_bb1_in/3
0.05/0.29	2. SCC is completely evaluated into other SCCs
0.05/0.29	3. SCC is completely evaluated into other SCCs
0.05/0.29	4. SCC is completely evaluated into other SCCs
0.05/0.29	5. SCC is partially evaluated into eval_foo_bb0_in/3
0.05/0.29	6. SCC is partially evaluated into eval_foo_start/3
0.05/0.29	
0.05/0.29	Control-Flow Refinement of Cost Relations
0.05/0.29	=====================================
0.05/0.29	
0.05/0.29	### Specialization of cost equations eval_foo_bb3_in/4 
0.05/0.29	* CE 7 is refined into CE [8] 
0.05/0.29	* CE 5 is refined into CE [9] 
0.05/0.29	* CE 6 is refined into CE [10] 
0.05/0.29	
0.05/0.29	
0.05/0.29	### Cost equations --> "Loop" of eval_foo_bb3_in/4 
0.05/0.29	* CEs [10] --> Loop 8 
0.05/0.29	* CEs [8] --> Loop 9 
0.05/0.29	* CEs [9] --> Loop 10 
0.05/0.29	
0.05/0.29	### Ranking functions of CR eval_foo_bb3_in(V_1,V__1,B,C) 
0.05/0.29	* RF of phase [8]: [-V_1+V__1+1,V__1]
0.05/0.29	
0.05/0.29	#### Partial ranking functions of CR eval_foo_bb3_in(V_1,V__1,B,C) 
0.05/0.29	* Partial RF of phase [8]:
0.05/0.29	  - RF of loop [8:1]:
0.05/0.29	    -V_1+V__1+1
0.05/0.29	    V__1
0.05/0.29	
0.05/0.29	
0.05/0.29	### Specialization of cost equations eval_foo_bb1_in/3 
0.05/0.29	* CE 4 is refined into CE [11] 
0.05/0.29	* CE 3 is refined into CE [12,13,14,15] 
0.05/0.29	
0.05/0.29	
0.05/0.29	### Cost equations --> "Loop" of eval_foo_bb1_in/3 
0.05/0.29	* CEs [15] --> Loop 11 
0.05/0.29	* CEs [14] --> Loop 12 
0.05/0.29	* CEs [13] --> Loop 13 
0.05/0.29	* CEs [12] --> Loop 14 
0.05/0.29	* CEs [11] --> Loop 15 
0.05/0.29	
0.05/0.29	### Ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 
0.05/0.29	* RF of phase [11,13,14]: [V__0/2-1/2]
0.05/0.29	* RF of phase [12]: [V__0/2-1/2,-V__01]
0.05/0.29	
0.05/0.29	#### Partial ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 
0.05/0.29	* Partial RF of phase [11,13,14]:
0.05/0.29	  - RF of loop [11:1,13:1]:
0.05/0.29	    V__0/2-1/2
0.05/0.29	  - RF of loop [14:1]:
0.05/0.29	    V__0-1
0.05/0.29	* Partial RF of phase [12]:
0.05/0.29	  - RF of loop [12:1]:
0.05/0.29	    V__0/2-1/2
0.05/0.29	    -V__01
0.05/0.29	
0.05/0.29	
0.05/0.29	### Specialization of cost equations eval_foo_bb0_in/3 
0.05/0.29	* CE 2 is refined into CE [16,17,18,19] 
0.05/0.29	
0.05/0.29	
0.05/0.29	### Cost equations --> "Loop" of eval_foo_bb0_in/3 
0.05/0.29	* CEs [19] --> Loop 16 
0.05/0.29	* CEs [17] --> Loop 17 
0.05/0.29	* CEs [16] --> Loop 18 
0.05/0.29	* CEs [18] --> Loop 19 
0.05/0.29	
0.05/0.29	### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 
0.05/0.29	
0.05/0.29	#### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 
0.05/0.29	
0.05/0.29	
0.05/0.29	### Specialization of cost equations eval_foo_start/3 
0.05/0.29	* CE 1 is refined into CE [20,21,22,23] 
0.05/0.29	
0.05/0.29	
0.05/0.29	### Cost equations --> "Loop" of eval_foo_start/3 
0.05/0.29	* CEs [23] --> Loop 20 
0.05/0.29	* CEs [22] --> Loop 21 
0.05/0.29	* CEs [21] --> Loop 22 
0.05/0.29	* CEs [20] --> Loop 23 
0.05/0.29	
0.05/0.29	### Ranking functions of CR eval_foo_start(V_x,V_y,B) 
0.05/0.29	
0.05/0.29	#### Partial ranking functions of CR eval_foo_start(V_x,V_y,B) 
0.05/0.29	
0.05/0.29	
0.05/0.29	Computing Bounds
0.05/0.29	=====================================
0.05/0.29	
0.05/0.29	#### Cost of chains of eval_foo_bb3_in(V_1,V__1,B,C):
0.05/0.29	* Chain [[8],10]: 1*it(8)+0
0.05/0.29	  Such that:it(8) =< V__1-C
0.05/0.29	
0.05/0.29	  with precondition: [B=2,V_1>=1,C>=V_1,V__1>=C+1] 
0.05/0.29	
0.05/0.29	* Chain [[8],9]: 1*it(8)+0
0.05/0.29	  Such that:it(8) =< V__1-C
0.05/0.29	
0.05/0.29	  with precondition: [B=2,V_1=C+1,V_1>=1,V__1>=V_1] 
0.05/0.29	
0.05/0.29	* Chain [10]: 0
0.05/0.29	  with precondition: [B=2,V__1=C,V_1>=1,V__1>=V_1] 
0.05/0.29	
0.05/0.29	* Chain [9]: 0
0.05/0.29	  with precondition: [B=2,V__1=C,V_1>=1,V_1>=V__1+1] 
0.05/0.29	
0.05/0.29	
0.05/0.29	#### Cost of chains of eval_foo_bb1_in(V__01,V__0,B):
0.05/0.29	* Chain [[12],[11,13,14],15]: 4*it(11)+1*it(12)+1*it(14)+0
0.05/0.29	  Such that:it(12) =< -V__01
0.05/0.29	it(14) =< 2*V__01+V__0
0.05/0.29	aux(7) =< V__01+V__0/2
0.05/0.29	it(11) =< aux(7)
0.05/0.29	it(14) =< aux(7)
0.05/0.29	
0.05/0.29	  with precondition: [B=3,0>=V__01+1,V__0+2*V__01>=2] 
0.05/0.29	
0.05/0.29	* Chain [[12],15]: 1*it(12)+0
0.05/0.29	  Such that:it(12) =< -V__01
0.05/0.29	it(12) =< V__0/2
0.05/0.29	
0.05/0.29	  with precondition: [B=3,0>=V__01+1,V__0>=2,1>=2*V__01+V__0] 
0.05/0.29	
0.05/0.29	* Chain [[11,13,14],15]: 2*it(11)+1*it(14)+2*s(5)+0
0.05/0.29	  Such that:it(14) =< V__0
0.05/0.29	aux(5) =< V__01+V__0/2
0.05/0.29	aux(6) =< V__0/2
0.05/0.29	s(5) =< aux(5)
0.05/0.29	it(14) =< aux(5)
0.05/0.29	it(11) =< aux(6)
0.05/0.29	it(14) =< aux(6)
0.05/0.29	
0.05/0.29	  with precondition: [B=3,V__01>=0,V__0>=2] 
0.05/0.29	
0.05/0.29	* Chain [15]: 0
0.05/0.29	  with precondition: [B=3,1>=V__0] 
0.05/0.29	
0.05/0.29	
0.05/0.29	#### Cost of chains of eval_foo_bb0_in(V_x,V_y,B):
0.05/0.29	* Chain [19]: 0
0.05/0.29	  with precondition: [1>=V_x] 
0.05/0.29	
0.05/0.29	* Chain [18]: 1*s(7)+0
0.05/0.29	  Such that:s(7) =< V_x/2
0.05/0.29	s(7) =< -V_y
0.05/0.29	
0.05/0.29	  with precondition: [0>=V_y+1,V_x>=2,1>=2*V_y+V_x] 
0.05/0.29	
0.05/0.29	* Chain [17]: 1*s(8)+1*s(9)+4*s(11)+0
0.05/0.29	  Such that:s(9) =< V_x+2*V_y
0.05/0.29	s(10) =< V_x/2+V_y
0.05/0.29	s(8) =< -V_y
0.05/0.29	s(11) =< s(10)
0.05/0.29	s(9) =< s(10)
0.05/0.29	
0.05/0.29	  with precondition: [0>=V_y+1,V_x+2*V_y>=2] 
0.05/0.29	
0.05/0.29	* Chain [16]: 1*s(12)+2*s(15)+2*s(16)+0
0.05/0.29	  Such that:s(12) =< V_x
0.05/0.29	s(14) =< V_x/2
0.05/0.29	s(13) =< V_x/2+V_y
0.05/0.29	s(15) =< s(13)
0.05/0.29	s(12) =< s(13)
0.05/0.29	s(16) =< s(14)
0.05/0.29	s(12) =< s(14)
0.05/0.29	
0.05/0.29	  with precondition: [V_x>=2,V_y>=0] 
0.05/0.29	
0.05/0.29	
0.05/0.29	#### Cost of chains of eval_foo_start(V_x,V_y,B):
0.05/0.29	* Chain [23]: 0
0.05/0.29	  with precondition: [1>=V_x] 
0.05/0.29	
0.05/0.29	* Chain [22]: 1*s(17)+0
0.05/0.29	  Such that:s(17) =< V_x/2
0.05/0.29	s(17) =< -V_y
0.05/0.29	
0.05/0.29	  with precondition: [0>=V_y+1,V_x>=2,1>=2*V_y+V_x] 
0.05/0.29	
0.05/0.29	* Chain [21]: 1*s(18)+1*s(20)+4*s(21)+0
0.05/0.29	  Such that:s(18) =< V_x+2*V_y
0.05/0.29	s(19) =< V_x/2+V_y
0.05/0.29	s(20) =< -V_y
0.05/0.29	s(21) =< s(19)
0.05/0.29	s(18) =< s(19)
0.05/0.29	
0.05/0.29	  with precondition: [0>=V_y+1,V_x+2*V_y>=2] 
0.05/0.29	
0.05/0.29	* Chain [20]: 1*s(22)+2*s(25)+2*s(26)+0
0.05/0.29	  Such that:s(22) =< V_x
0.05/0.29	s(23) =< V_x/2
0.05/0.29	s(24) =< V_x/2+V_y
0.05/0.29	s(25) =< s(24)
0.05/0.29	s(22) =< s(24)
0.05/0.29	s(26) =< s(23)
0.05/0.29	s(22) =< s(23)
0.05/0.29	
0.05/0.29	  with precondition: [V_x>=2,V_y>=0] 
0.05/0.29	
0.05/0.29	
0.05/0.29	Closed-form bounds of eval_foo_start(V_x,V_y,B): 
0.05/0.29	-------------------------------------
0.05/0.29	* Chain [23] with precondition: [1>=V_x] 
0.05/0.29	    - Upper bound: 0 
0.05/0.29	    - Complexity: constant 
0.05/0.29	* Chain [22] with precondition: [0>=V_y+1,V_x>=2,1>=2*V_y+V_x] 
0.05/0.29	    - Upper bound: V_x/2 
0.05/0.29	    - Complexity: n 
0.05/0.29	* Chain [21] with precondition: [0>=V_y+1,V_x+2*V_y>=2] 
0.05/0.29	    - Upper bound: 3*V_x+5*V_y 
0.05/0.29	    - Complexity: n 
0.05/0.29	* Chain [20] with precondition: [V_x>=2,V_y>=0] 
0.05/0.29	    - Upper bound: 3*V_x+2*V_y 
0.05/0.29	    - Complexity: n 
0.05/0.29	
0.05/0.29	### Maximum cost of eval_foo_start(V_x,V_y,B): max([nat(V_x/2),nat(V_x/2+V_y)*2+max([nat(V_x/2)*2+nat(V_x),nat(V_x+2*V_y)+nat(-V_y)+nat(V_x/2+V_y)*2])]) 
0.05/0.29	Asymptotic class: n 
0.05/0.29	* Total analysis performed in 204 ms.
0.05/0.29	
0.05/0.39	EOF