/export/starexec/sandbox2/solver/bin/starexec_run_C /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^1))  

Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. recursive  : [eval_t62_2/6,eval_t62_3/7,eval_t62_bb2_in/5,eval_t62_bb3_in/6]
1. recursive  : [eval_t62_6/6,eval_t62_7/7,eval_t62__critedge_in/5,eval_t62_bb4_in/6]
2. recursive  : [eval_t62__critedge3_in/7,eval_t62__critedge_in_loop_cont/8,eval_t62_bb1_in/3,eval_t62_bb2_in_loop_cont/7]
3. non_recursive  : [eval_t62_stop/1]
4. non_recursive  : [eval_t62_bb5_in/1]
5. non_recursive  : [eval_t62_bb1_in_loop_cont/2]
6. non_recursive  : [eval_t62_bb0_in/3]
7. non_recursive  : [eval_t62_start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_t62_bb2_in/5
1. SCC is partially evaluated into eval_t62__critedge_in/5
2. SCC is partially evaluated into eval_t62_bb1_in/3
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is completely evaluated into other SCCs
6. SCC is partially evaluated into eval_t62_bb0_in/3
7. SCC is partially evaluated into eval_t62_start/3

Control-Flow Refinement of Cost Relations
=====================================

### Specialization of cost equations eval_t62_bb2_in/5 
* CE 6 is refined into CE [12] 
* CE 8 is refined into CE [13] 
* CE 7 is refined into CE [14] 


### Cost equations --> "Loop" of eval_t62_bb2_in/5 
* CEs [14] --> Loop 12 
* CEs [12] --> Loop 13 
* CEs [13] --> Loop 14 

### Ranking functions of CR eval_t62_bb2_in(V__01,V__1,B,C,D) 
* RF of phase [12]: [V__01-V__1-1]

#### Partial ranking functions of CR eval_t62_bb2_in(V__01,V__1,B,C,D) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    V__01-V__1-1


### Specialization of cost equations eval_t62__critedge_in/5 
* CE 11 is refined into CE [15] 
* CE 9 is refined into CE [16] 
* CE 10 is refined into CE [17] 


### Cost equations --> "Loop" of eval_t62__critedge_in/5 
* CEs [17] --> Loop 15 
* CEs [15] --> Loop 16 
* CEs [16] --> Loop 17 

### Ranking functions of CR eval_t62__critedge_in(V_1,V__12,B,C,D) 
* RF of phase [15]: [-V_1+V__12-1]

#### Partial ranking functions of CR eval_t62__critedge_in(V_1,V__12,B,C,D) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    -V_1+V__12-1


### Specialization of cost equations eval_t62_bb1_in/3 
* CE 5 is refined into CE [18,19,20,21,22,23] 
* CE 4 is refined into CE [24,25,26,27] 


### Cost equations --> "Loop" of eval_t62_bb1_in/3 
* CEs [27] --> Loop 18 
* CEs [25] --> Loop 19 
* CEs [26] --> Loop 20 
* CEs [24] --> Loop 21 
* CEs [22] --> Loop 22 
* CEs [20,23] --> Loop 23 
* CEs [19] --> Loop 24 
* CEs [21] --> Loop 25 
* CEs [18] --> Loop 26 

### Ranking functions of CR eval_t62_bb1_in(V__01,V__0,B) 
* RF of phase [18,19,20,21]: [V__01/2-V__0/2-1]

#### Partial ranking functions of CR eval_t62_bb1_in(V__01,V__0,B) 
* Partial RF of phase [18,19,20,21]:
  - RF of loop [18:1]:
    V__01/4-V__0/4-1
  - RF of loop [19:1,20:1]:
    V__01/3-V__0/3-1
  - RF of loop [21:1]:
    V__01/2-V__0/2-1


### Specialization of cost equations eval_t62_bb0_in/3 
* CE 2 is refined into CE [28] 
* CE 3 is refined into CE [29,30,31,32,33,34,35] 


### Cost equations --> "Loop" of eval_t62_bb0_in/3 
* CEs [28] --> Loop 27 
* CEs [35] --> Loop 28 
* CEs [34] --> Loop 29 
* CEs [33] --> Loop 30 
* CEs [32] --> Loop 31 
* CEs [31] --> Loop 32 
* CEs [30] --> Loop 33 
* CEs [29] --> Loop 34 

### Ranking functions of CR eval_t62_bb0_in(V_l,V_h,B) 

#### Partial ranking functions of CR eval_t62_bb0_in(V_l,V_h,B) 


### Specialization of cost equations eval_t62_start/3 
* CE 1 is refined into CE [36,37,38,39,40,41,42,43] 


### Cost equations --> "Loop" of eval_t62_start/3 
* CEs [43] --> Loop 35 
* CEs [42] --> Loop 36 
* CEs [41] --> Loop 37 
* CEs [40] --> Loop 38 
* CEs [39] --> Loop 39 
* CEs [38] --> Loop 40 
* CEs [36] --> Loop 41 
* CEs [37] --> Loop 42 

### Ranking functions of CR eval_t62_start(V_l,V_h,B) 

#### Partial ranking functions of CR eval_t62_start(V_l,V_h,B) 


Computing Bounds
=====================================

#### Cost of chains of eval_t62_bb2_in(V__01,V__1,B,C,D):
* Chain [[12],14]: 1*it(12)+0
  Such that:it(12) =< V__01-V__1

  with precondition: [B=3,V__01=C+1,V__01=D,V__01>=V__1+2] 

* Chain [[12],13]: 1*it(12)+0
  Such that:it(12) =< -V__1+C

  with precondition: [B=3,C+1=D,C>=V__1+1,V__01>=C+2] 

* Chain [14]: 0
  with precondition: [B=3,V__01=V__1+1,V__01=C+1,V__01=D] 

* Chain [13]: 0
  with precondition: [B=3,V__1=C,V__1+1=D,V__01>=V__1+2] 


#### Cost of chains of eval_t62__critedge_in(V_1,V__12,B,C,D):
* Chain [[15],17]: 1*it(15)+0
  Such that:it(15) =< V__12-C

  with precondition: [B=2,C=D+1,C>=V_1+2,V__12>=C+1] 

* Chain [[15],16]: 1*it(15)+0
  Such that:it(15) =< -V_1+V__12

  with precondition: [B=2,V_1+1=C,V_1=D,V__12>=V_1+2] 

* Chain [17]: 0
  with precondition: [B=2,V__12=C,V__12=D+1,V__12>=V_1+2] 

* Chain [16]: 0
  with precondition: [B=2,V__12=C,V__12=D+1,V_1+1>=V__12] 


#### Cost of chains of eval_t62_bb1_in(V__01,V__0,B):
* Chain [[18,19,20,21],26]: 1*it(18)+2*it(19)+1*it(21)+4*s(9)+0
  Such that:it(18) =< V__01/4-V__0/4
aux(7) =< V__01-V__0
aux(8) =< V__01/2-V__0/2
aux(9) =< V__01/3-V__0/3
it(19) =< aux(7)
it(21) =< aux(7)
s(9) =< aux(7)
it(18) =< aux(8)
it(19) =< aux(8)
it(21) =< aux(8)
it(19) =< aux(9)

  with precondition: [B=4,V__01>=V__0+3] 

* Chain [[18,19,20,21],25]: 1*it(18)+2*it(19)+1*it(21)+4*s(9)+0
  Such that:it(18) =< V__01/4-V__0/4
aux(10) =< V__01-V__0
aux(11) =< V__01/2-V__0/2
aux(12) =< V__01/3-V__0/3
it(19) =< aux(10)
it(21) =< aux(10)
s(9) =< aux(10)
it(18) =< aux(11)
it(19) =< aux(11)
it(21) =< aux(11)
it(19) =< aux(12)

  with precondition: [B=4,V__01>=V__0+4] 

* Chain [[18,19,20,21],24]: 1*it(18)+2*it(19)+1*it(21)+5*s(9)+0
  Such that:it(18) =< V__01/4-V__0/4
aux(13) =< V__01-V__0
aux(14) =< V__01/2-V__0/2
aux(15) =< V__01/3-V__0/3
aux(4) =< aux(13)
aux(6) =< aux(13)
it(18) =< aux(13)
s(9) =< aux(13)
aux(4) =< aux(14)
aux(6) =< aux(15)
it(19) =< aux(13)
it(21) =< aux(13)
it(18) =< aux(14)
it(19) =< aux(14)
it(21) =< aux(14)
it(18) =< aux(4)
it(19) =< aux(4)
it(21) =< aux(4)
it(19) =< aux(15)
it(19) =< aux(6)

  with precondition: [B=4,V__01>=V__0+4] 

* Chain [[18,19,20,21],23]: 1*it(18)+2*it(19)+1*it(21)+6*s(9)+0
  Such that:it(18) =< V__01/4-V__0/4
aux(17) =< V__01-V__0
aux(18) =< V__01/2-V__0/2
aux(19) =< V__01/3-V__0/3
aux(4) =< aux(17)
aux(6) =< aux(17)
it(18) =< aux(17)
aux(4) =< aux(18)
aux(6) =< aux(19)
s(9) =< aux(17)
it(19) =< aux(17)
it(21) =< aux(17)
it(18) =< aux(18)
it(19) =< aux(18)
it(21) =< aux(18)
it(18) =< aux(4)
it(19) =< aux(4)
it(21) =< aux(4)
it(19) =< aux(19)
it(19) =< aux(6)

  with precondition: [B=4,V__01>=V__0+5] 

* Chain [[18,19,20,21],22]: 1*it(18)+2*it(19)+1*it(21)+6*s(9)+0
  Such that:it(18) =< V__01/4-V__0/4
aux(21) =< V__01-V__0
aux(22) =< V__01/2-V__0/2
aux(23) =< V__01/3-V__0/3
aux(4) =< aux(21)
aux(6) =< aux(21)
it(18) =< aux(21)
aux(4) =< aux(22)
aux(6) =< aux(23)
s(9) =< aux(21)
it(19) =< aux(21)
it(21) =< aux(21)
it(18) =< aux(22)
it(19) =< aux(22)
it(21) =< aux(22)
it(18) =< aux(4)
it(19) =< aux(4)
it(21) =< aux(4)
it(19) =< aux(23)
it(19) =< aux(6)

  with precondition: [B=4,V__01>=V__0+6] 

* Chain [26]: 0
  with precondition: [B=4,V__0+1=V__01] 

* Chain [25]: 0
  with precondition: [B=4,V__0+2=V__01] 

* Chain [24]: 1*s(13)+0
  Such that:s(13) =< V__01-V__0

  with precondition: [B=4,V__01>=V__0+2] 

* Chain [23]: 2*s(14)+0
  Such that:aux(16) =< V__01-V__0
s(14) =< aux(16)

  with precondition: [B=4,V__01>=V__0+3] 

* Chain [22]: 2*s(16)+0
  Such that:aux(20) =< V__01-V__0
s(16) =< aux(20)

  with precondition: [B=4,V__01>=V__0+4] 


#### Cost of chains of eval_t62_bb0_in(V_l,V_h,B):
* Chain [34]: 0
  with precondition: [V_h=V_l+2] 

* Chain [33]: 0
  with precondition: [V_h=V_l+1] 

* Chain [32]: 1*s(45)+0
  Such that:s(45) =< -V_l+V_h

  with precondition: [V_h>=V_l+2] 

* Chain [31]: 1*s(48)+6*s(50)+2*s(51)+1*s(52)+0
  Such that:s(49) =< -V_l+V_h
s(46) =< -V_l/2+V_h/2
s(47) =< -V_l/3+V_h/3
s(48) =< -V_l/4+V_h/4
s(50) =< s(49)
s(51) =< s(49)
s(52) =< s(49)
s(48) =< s(46)
s(51) =< s(46)
s(52) =< s(46)
s(51) =< s(47)

  with precondition: [V_h>=V_l+3] 

* Chain [30]: 1*s(57)+1*s(58)+11*s(59)+2*s(62)+1*s(63)+2*s(64)+1*s(65)+0
  Such that:s(53) =< -V_l+V_h
s(54) =< -V_l/2+V_h/2
s(55) =< -V_l/3+V_h/3
s(56) =< -V_l/4+V_h/4
s(57) =< s(56)
s(58) =< s(56)
s(59) =< s(53)
s(60) =< s(53)
s(61) =< s(53)
s(57) =< s(53)
s(60) =< s(54)
s(61) =< s(55)
s(62) =< s(53)
s(63) =< s(53)
s(57) =< s(54)
s(62) =< s(54)
s(63) =< s(54)
s(57) =< s(60)
s(62) =< s(60)
s(63) =< s(60)
s(62) =< s(55)
s(62) =< s(61)
s(64) =< s(53)
s(65) =< s(53)
s(58) =< s(54)
s(64) =< s(54)
s(65) =< s(54)
s(64) =< s(55)

  with precondition: [V_h>=V_l+4] 

* Chain [29]: 1*s(66)+6*s(72)+2*s(73)+1*s(74)+0
  Such that:s(67) =< -V_l+V_h
s(68) =< -V_l/2+V_h/2
s(69) =< -V_l/3+V_h/3
s(66) =< -V_l/4+V_h/4
s(70) =< s(67)
s(71) =< s(67)
s(66) =< s(67)
s(70) =< s(68)
s(71) =< s(69)
s(72) =< s(67)
s(73) =< s(67)
s(74) =< s(67)
s(66) =< s(68)
s(73) =< s(68)
s(74) =< s(68)
s(66) =< s(70)
s(73) =< s(70)
s(74) =< s(70)
s(73) =< s(69)
s(73) =< s(71)

  with precondition: [V_h>=V_l+5] 

* Chain [28]: 1*s(75)+6*s(81)+2*s(82)+1*s(83)+0
  Such that:s(76) =< -V_l+V_h
s(77) =< -V_l/2+V_h/2
s(78) =< -V_l/3+V_h/3
s(75) =< -V_l/4+V_h/4
s(79) =< s(76)
s(80) =< s(76)
s(75) =< s(76)
s(79) =< s(77)
s(80) =< s(78)
s(81) =< s(76)
s(82) =< s(76)
s(83) =< s(76)
s(75) =< s(77)
s(82) =< s(77)
s(83) =< s(77)
s(75) =< s(79)
s(82) =< s(79)
s(83) =< s(79)
s(82) =< s(78)
s(82) =< s(80)

  with precondition: [V_h>=V_l+6] 

* Chain [27]: 0
  with precondition: [V_l>=V_h] 


#### Cost of chains of eval_t62_start(V_l,V_h,B):
* Chain [42]: 0
  with precondition: [V_h=V_l+2] 

* Chain [41]: 0
  with precondition: [V_h=V_l+1] 

* Chain [40]: 1*s(84)+0
  Such that:s(84) =< -V_l+V_h

  with precondition: [V_h>=V_l+2] 

* Chain [39]: 1*s(88)+6*s(89)+2*s(90)+1*s(91)+0
  Such that:s(85) =< -V_l+V_h
s(86) =< -V_l/2+V_h/2
s(87) =< -V_l/3+V_h/3
s(88) =< -V_l/4+V_h/4
s(89) =< s(85)
s(90) =< s(85)
s(91) =< s(85)
s(88) =< s(86)
s(90) =< s(86)
s(91) =< s(86)
s(90) =< s(87)

  with precondition: [V_h>=V_l+3] 

* Chain [38]: 1*s(96)+1*s(97)+11*s(98)+2*s(101)+1*s(102)+2*s(103)+1*s(104)+0
  Such that:s(92) =< -V_l+V_h
s(93) =< -V_l/2+V_h/2
s(94) =< -V_l/3+V_h/3
s(95) =< -V_l/4+V_h/4
s(96) =< s(95)
s(97) =< s(95)
s(98) =< s(92)
s(99) =< s(92)
s(100) =< s(92)
s(96) =< s(92)
s(99) =< s(93)
s(100) =< s(94)
s(101) =< s(92)
s(102) =< s(92)
s(96) =< s(93)
s(101) =< s(93)
s(102) =< s(93)
s(96) =< s(99)
s(101) =< s(99)
s(102) =< s(99)
s(101) =< s(94)
s(101) =< s(100)
s(103) =< s(92)
s(104) =< s(92)
s(97) =< s(93)
s(103) =< s(93)
s(104) =< s(93)
s(103) =< s(94)

  with precondition: [V_h>=V_l+4] 

* Chain [37]: 1*s(108)+6*s(111)+2*s(112)+1*s(113)+0
  Such that:s(105) =< -V_l+V_h
s(106) =< -V_l/2+V_h/2
s(107) =< -V_l/3+V_h/3
s(108) =< -V_l/4+V_h/4
s(109) =< s(105)
s(110) =< s(105)
s(108) =< s(105)
s(109) =< s(106)
s(110) =< s(107)
s(111) =< s(105)
s(112) =< s(105)
s(113) =< s(105)
s(108) =< s(106)
s(112) =< s(106)
s(113) =< s(106)
s(108) =< s(109)
s(112) =< s(109)
s(113) =< s(109)
s(112) =< s(107)
s(112) =< s(110)

  with precondition: [V_h>=V_l+5] 

* Chain [36]: 1*s(117)+6*s(120)+2*s(121)+1*s(122)+0
  Such that:s(114) =< -V_l+V_h
s(115) =< -V_l/2+V_h/2
s(116) =< -V_l/3+V_h/3
s(117) =< -V_l/4+V_h/4
s(118) =< s(114)
s(119) =< s(114)
s(117) =< s(114)
s(118) =< s(115)
s(119) =< s(116)
s(120) =< s(114)
s(121) =< s(114)
s(122) =< s(114)
s(117) =< s(115)
s(121) =< s(115)
s(122) =< s(115)
s(117) =< s(118)
s(121) =< s(118)
s(122) =< s(118)
s(121) =< s(116)
s(121) =< s(119)

  with precondition: [V_h>=V_l+6] 

* Chain [35]: 0
  with precondition: [V_l>=V_h] 


Closed-form bounds of eval_t62_start(V_l,V_h,B): 
-------------------------------------
* Chain [42] with precondition: [V_h=V_l+2] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [41] with precondition: [V_h=V_l+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [40] with precondition: [V_h>=V_l+2] 
    - Upper bound: -V_l+V_h 
    - Complexity: n 
* Chain [39] with precondition: [V_h>=V_l+3] 
    - Upper bound: -37/4*V_l+37/4*V_h 
    - Complexity: n 
* Chain [38] with precondition: [V_h>=V_l+4] 
    - Upper bound: -35/2*V_l+35/2*V_h 
    - Complexity: n 
* Chain [37] with precondition: [V_h>=V_l+5] 
    - Upper bound: -37/4*V_l+37/4*V_h 
    - Complexity: n 
* Chain [36] with precondition: [V_h>=V_l+6] 
    - Upper bound: -37/4*V_l+37/4*V_h 
    - Complexity: n 
* Chain [35] with precondition: [V_l>=V_h] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_t62_start(V_l,V_h,B): nat(-V_l+V_h)*8+nat(-V_l/4+V_h/4)+(nat(-V_l+V_h)*8+nat(-V_l/4+V_h/4))+nat(-V_l+V_h) 
Asymptotic class: n 
* Total analysis performed in 422 ms.