0.06/0.31	WORST_CASE(?,O(n^2))  
0.06/0.31	
0.06/0.31	Preprocessing Cost Relations
0.06/0.31	=====================================
0.06/0.31	
0.06/0.31	#### Computed strongly connected components 
0.06/0.31	0. recursive  : [eval_foo_3/4,eval_foo_4/5,eval_foo_bb2_in/4,eval_foo_bb3_in/4]
0.06/0.31	1. non_recursive  : [eval_foo_stop/1]
0.06/0.31	2. non_recursive  : [eval_foo_bb4_in/1]
0.06/0.31	3. non_recursive  : [eval_foo_bb2_in_loop_cont/2]
0.06/0.31	4. non_recursive  : [eval_foo_bb1_in/2]
0.06/0.31	5. non_recursive  : [eval_foo_bb0_in/2]
0.06/0.31	6. non_recursive  : [eval_foo_start/5]
0.06/0.31	
0.06/0.31	#### Obtained direct recursion through partial evaluation 
0.06/0.31	0. SCC is partially evaluated into eval_foo_bb2_in/4
0.06/0.31	1. SCC is completely evaluated into other SCCs
0.06/0.31	2. SCC is completely evaluated into other SCCs
0.06/0.31	3. SCC is completely evaluated into other SCCs
0.06/0.31	4. SCC is partially evaluated into eval_foo_bb1_in/2
0.06/0.31	5. SCC is partially evaluated into eval_foo_bb0_in/2
0.06/0.31	6. SCC is partially evaluated into eval_foo_start/5
0.06/0.31	
0.06/0.31	Control-Flow Refinement of Cost Relations
0.06/0.31	=====================================
0.06/0.31	
0.06/0.31	### Specialization of cost equations eval_foo_bb2_in/4 
0.06/0.31	* CE 7 is refined into CE [8] 
0.06/0.31	* CE 5 is refined into CE [9] 
0.06/0.31	* CE 6 is refined into CE [10] 
0.06/0.31	
0.06/0.31	
0.06/0.31	### Cost equations --> "Loop" of eval_foo_bb2_in/4 
0.06/0.31	* CEs [9] --> Loop 8 
0.06/0.31	* CEs [10] --> Loop 9 
0.06/0.31	* CEs [8] --> Loop 10 
0.06/0.31	
0.06/0.31	### Ranking functions of CR eval_foo_bb2_in(V_r,V__01,V__0,B) 
0.06/0.31	
0.06/0.31	#### Partial ranking functions of CR eval_foo_bb2_in(V_r,V__01,V__0,B) 
0.06/0.31	* Partial RF of phase [8,9]:
0.06/0.31	  - RF of loop [8:1]:
0.06/0.31	    V__01+1
0.06/0.31	    -V_r+V__01+1
0.06/0.31	  - RF of loop [9:1]:
0.06/0.31	    V__0+1 depends on loops [8:1] 
0.06/0.31	    -V__01/2+V__0+1/2 depends on loops [8:1] 
0.06/0.31	    -V_r+V__0+1 depends on loops [8:1] 
0.06/0.31	
0.06/0.31	
0.06/0.31	### Specialization of cost equations eval_foo_bb1_in/2 
0.06/0.31	* CE 4 is refined into CE [11] 
0.06/0.31	
0.06/0.31	
0.06/0.31	### Cost equations --> "Loop" of eval_foo_bb1_in/2 
0.06/0.31	* CEs [11] --> Loop 11 
0.06/0.31	
0.06/0.31	### Ranking functions of CR eval_foo_bb1_in(V_r,B) 
0.06/0.31	
0.06/0.31	#### Partial ranking functions of CR eval_foo_bb1_in(V_r,B) 
0.06/0.31	
0.06/0.31	
0.06/0.31	### Specialization of cost equations eval_foo_bb0_in/2 
0.06/0.31	* CE 2 is refined into CE [12] 
0.06/0.31	* CE 3 is refined into CE [13] 
0.06/0.31	
0.06/0.31	
0.06/0.31	### Cost equations --> "Loop" of eval_foo_bb0_in/2 
0.06/0.31	* CEs [12] --> Loop 12 
0.06/0.31	* CEs [13] --> Loop 13 
0.06/0.31	
0.06/0.31	### Ranking functions of CR eval_foo_bb0_in(V_r,B) 
0.06/0.31	
0.06/0.31	#### Partial ranking functions of CR eval_foo_bb0_in(V_r,B) 
0.06/0.31	
0.06/0.31	
0.06/0.31	### Specialization of cost equations eval_foo_start/5 
0.06/0.31	* CE 1 is refined into CE [14,15] 
0.06/0.31	
0.06/0.31	
0.06/0.31	### Cost equations --> "Loop" of eval_foo_start/5 
0.06/0.31	* CEs [15] --> Loop 14 
0.06/0.31	* CEs [14] --> Loop 15 
0.06/0.31	
0.06/0.31	### Ranking functions of CR eval_foo_start(V_r,V_da,V_db,V_temp,B) 
0.06/0.31	
0.06/0.31	#### Partial ranking functions of CR eval_foo_start(V_r,V_da,V_db,V_temp,B) 
0.06/0.31	
0.06/0.31	
0.06/0.31	Computing Bounds
0.06/0.31	=====================================
0.06/0.31	
0.06/0.31	#### Cost of chains of eval_foo_bb2_in(V_r,V__01,V__0,B):
0.06/0.31	* Chain [[8,9],10]: 1*it(8)+1*it(9)+0
0.06/0.31	  Such that:aux(13) =< -V_r+V__01
0.06/0.31	it(8) =< -V_r+V__01+1
0.06/0.31	aux(25) =< V_r
0.06/0.31	aux(21) =< V__01
0.06/0.31	aux(12) =< -V__01/2+V__0+1
0.06/0.31	aux(6) =< -V__01/2+V__0+1/2
0.06/0.31	aux(15) =< V__0
0.06/0.31	aux(2) =< V__0+1
0.06/0.31	aux(26) =< -V_r+V__0+1
0.06/0.31	aux(12) =< aux(26)
0.06/0.31	aux(13) =< aux(25)
0.06/0.31	aux(15) =< aux(25)
0.06/0.31	aux(23) =< aux(13)
0.06/0.31	aux(23) =< aux(15)-1/2
0.06/0.31	aux(21) =< aux(15)
0.06/0.31	aux(17) =< aux(13)
0.06/0.31	aux(16) =< it(8)*aux(15)
0.06/0.31	aux(5) =< it(8)*aux(15)
0.06/0.31	aux(14) =< it(8)*aux(13)
0.06/0.31	aux(1) =< it(8)*aux(13)
0.06/0.31	aux(24) =< it(8)*aux(23)
0.06/0.31	aux(3) =< it(8)*aux(23)
0.06/0.31	aux(22) =< it(8)*aux(21)
0.06/0.31	aux(5) =< it(8)*aux(21)
0.06/0.31	aux(18) =< it(8)*aux(17)
0.06/0.31	aux(3) =< it(8)*aux(17)
0.06/0.31	aux(1) =< it(8)*aux(17)
0.06/0.31	aux(11) =< aux(16)
0.06/0.31	aux(7) =< aux(14)
0.06/0.31	aux(9) =< aux(24)
0.06/0.31	aux(11) =< aux(22)
0.06/0.31	aux(9) =< aux(18)
0.06/0.31	aux(7) =< aux(18)
0.06/0.31	it(9) =< aux(5)+aux(6)
0.06/0.31	it(9) =< aux(3)+aux(26)
0.06/0.31	it(9) =< aux(1)+aux(2)
0.06/0.31	it(9) =< aux(11)+aux(12)
0.06/0.31	it(9) =< aux(9)+aux(26)
0.06/0.31	it(9) =< aux(7)+aux(26)
0.06/0.31	
0.06/0.31	  with precondition: [B=2,V__0>=V_r,2*V_r>=V__01,V__01>=V__0] 
0.06/0.31	
0.06/0.31	
0.06/0.31	#### Cost of chains of eval_foo_bb1_in(V_r,B):
0.06/0.31	* Chain [11]: 1*s(2)+1*s(23)+0
0.06/0.31	  Such that:s(6) =< V_r+1/2
0.06/0.31	s(8) =< 2*V_r+1
0.06/0.31	aux(27) =< V_r
0.06/0.31	aux(28) =< V_r+1
0.06/0.31	aux(29) =< 2*V_r
0.06/0.31	s(2) =< aux(28)
0.06/0.31	s(4) =< aux(29)
0.06/0.31	s(7) =< aux(29)
0.06/0.31	s(7) =< aux(27)
0.06/0.31	s(10) =< aux(27)
0.06/0.31	s(10) =< s(7)-1/2
0.06/0.31	s(4) =< s(7)
0.06/0.31	s(11) =< aux(27)
0.06/0.31	s(12) =< s(2)*s(7)
0.06/0.31	s(13) =< s(2)*s(7)
0.06/0.31	s(14) =< s(2)*aux(27)
0.06/0.31	s(15) =< s(2)*aux(27)
0.06/0.31	s(16) =< s(2)*s(10)
0.06/0.31	s(17) =< s(2)*s(10)
0.06/0.31	s(18) =< s(2)*s(4)
0.06/0.31	s(13) =< s(2)*s(4)
0.06/0.31	s(19) =< s(2)*s(11)
0.06/0.31	s(17) =< s(2)*s(11)
0.06/0.31	s(15) =< s(2)*s(11)
0.06/0.31	s(20) =< s(12)
0.06/0.31	s(21) =< s(14)
0.06/0.31	s(22) =< s(16)
0.06/0.31	s(20) =< s(18)
0.06/0.31	s(22) =< s(19)
0.06/0.31	s(21) =< s(19)
0.06/0.31	s(23) =< s(13)+s(6)
0.06/0.31	s(23) =< s(17)+aux(28)
0.06/0.31	s(23) =< s(15)+s(8)
0.06/0.31	s(23) =< s(20)+aux(28)
0.06/0.31	s(23) =< s(22)+aux(28)
0.06/0.31	s(23) =< s(21)+aux(28)
0.06/0.31	
0.06/0.31	  with precondition: [V_r>=0] 
0.06/0.31	
0.06/0.31	
0.06/0.31	#### Cost of chains of eval_foo_bb0_in(V_r,B):
0.06/0.31	* Chain [13]: 0
0.06/0.31	  with precondition: [0>=V_r+1] 
0.06/0.31	
0.06/0.31	* Chain [12]: 1*s(29)+1*s(45)+0
0.06/0.31	  Such that:s(26) =< V_r
0.06/0.31	s(27) =< V_r+1
0.06/0.31	s(24) =< V_r+1/2
0.06/0.31	s(28) =< 2*V_r
0.06/0.31	s(25) =< 2*V_r+1
0.06/0.31	s(29) =< s(27)
0.06/0.31	s(30) =< s(28)
0.06/0.31	s(31) =< s(28)
0.06/0.31	s(31) =< s(26)
0.06/0.31	s(32) =< s(26)
0.06/0.31	s(32) =< s(31)-1/2
0.06/0.31	s(30) =< s(31)
0.06/0.31	s(33) =< s(26)
0.06/0.31	s(34) =< s(29)*s(31)
0.06/0.31	s(35) =< s(29)*s(31)
0.06/0.31	s(36) =< s(29)*s(26)
0.06/0.31	s(37) =< s(29)*s(26)
0.06/0.31	s(38) =< s(29)*s(32)
0.06/0.31	s(39) =< s(29)*s(32)
0.06/0.31	s(40) =< s(29)*s(30)
0.06/0.31	s(35) =< s(29)*s(30)
0.06/0.31	s(41) =< s(29)*s(33)
0.06/0.31	s(39) =< s(29)*s(33)
0.06/0.31	s(37) =< s(29)*s(33)
0.06/0.31	s(42) =< s(34)
0.06/0.31	s(43) =< s(36)
0.06/0.31	s(44) =< s(38)
0.06/0.31	s(42) =< s(40)
0.06/0.31	s(44) =< s(41)
0.06/0.31	s(43) =< s(41)
0.06/0.31	s(45) =< s(35)+s(24)
0.06/0.31	s(45) =< s(39)+s(27)
0.06/0.31	s(45) =< s(37)+s(25)
0.06/0.31	s(45) =< s(42)+s(27)
0.06/0.31	s(45) =< s(44)+s(27)
0.06/0.31	s(45) =< s(43)+s(27)
0.06/0.31	
0.06/0.31	  with precondition: [V_r>=0] 
0.06/0.31	
0.06/0.31	
0.06/0.31	#### Cost of chains of eval_foo_start(V_r,V_da,V_db,V_temp,B):
0.06/0.31	* Chain [15]: 0
0.06/0.31	  with precondition: [0>=V_r+1] 
0.06/0.31	
0.06/0.31	* Chain [14]: 1*s(51)+1*s(67)+0
0.06/0.31	  Such that:s(46) =< V_r
0.06/0.31	s(47) =< V_r+1
0.06/0.31	s(48) =< V_r+1/2
0.06/0.31	s(49) =< 2*V_r
0.06/0.31	s(50) =< 2*V_r+1
0.06/0.31	s(51) =< s(47)
0.06/0.31	s(52) =< s(49)
0.06/0.31	s(53) =< s(49)
0.06/0.31	s(53) =< s(46)
0.06/0.31	s(54) =< s(46)
0.06/0.31	s(54) =< s(53)-1/2
0.06/0.31	s(52) =< s(53)
0.06/0.31	s(55) =< s(46)
0.06/0.31	s(56) =< s(51)*s(53)
0.06/0.31	s(57) =< s(51)*s(53)
0.06/0.31	s(58) =< s(51)*s(46)
0.06/0.31	s(59) =< s(51)*s(46)
0.06/0.31	s(60) =< s(51)*s(54)
0.06/0.31	s(61) =< s(51)*s(54)
0.06/0.31	s(62) =< s(51)*s(52)
0.06/0.31	s(57) =< s(51)*s(52)
0.06/0.31	s(63) =< s(51)*s(55)
0.06/0.31	s(61) =< s(51)*s(55)
0.06/0.31	s(59) =< s(51)*s(55)
0.06/0.31	s(64) =< s(56)
0.06/0.31	s(65) =< s(58)
0.06/0.31	s(66) =< s(60)
0.06/0.31	s(64) =< s(62)
0.06/0.31	s(66) =< s(63)
0.06/0.31	s(65) =< s(63)
0.06/0.31	s(67) =< s(57)+s(48)
0.06/0.31	s(67) =< s(61)+s(47)
0.06/0.31	s(67) =< s(59)+s(50)
0.06/0.31	s(67) =< s(64)+s(47)
0.06/0.31	s(67) =< s(66)+s(47)
0.06/0.31	s(67) =< s(65)+s(47)
0.06/0.31	
0.06/0.31	  with precondition: [V_r>=0] 
0.06/0.31	
0.06/0.31	
0.06/0.31	Closed-form bounds of eval_foo_start(V_r,V_da,V_db,V_temp,B): 
0.06/0.31	-------------------------------------
0.06/0.31	* Chain [15] with precondition: [0>=V_r+1] 
0.06/0.31	    - Upper bound: 0 
0.06/0.31	    - Complexity: constant 
0.06/0.31	* Chain [14] with precondition: [V_r>=0] 
0.06/0.31	    - Upper bound: V_r+1+(V_r+1)*(2*V_r)+(V_r+1/2) 
0.06/0.31	    - Complexity: n^2 
0.06/0.31	
0.06/0.31	### Maximum cost of eval_foo_start(V_r,V_da,V_db,V_temp,B): nat(V_r+1)*nat(2*V_r)+nat(V_r+1)+nat(V_r+1/2) 
0.06/0.31	Asymptotic class: n^2 
0.06/0.31	* Total analysis performed in 218 ms.
0.06/0.31	
0.06/0.41	EOF