/export/starexec/sandbox/solver/bin/starexec_run_its /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [evalbinsearchStepSize2bb10in/18,evalbinsearchStepSize2bb12in/18,evalbinsearchStepSize2bb13in/18,evalbinsearchStepSize2bb1in/18,evalbinsearchStepSize2bb2in/18,evalbinsearchStepSize2bb3in/18,evalbinsearchStepSize2bb4in/18,evalbinsearchStepSize2bb6in/18,evalbinsearchStepSize2bb7in/18,evalbinsearchStepSize2bb9in/18,evalbinsearchStepSize2bbin/18]
1. non_recursive  : [evalbinsearchStepSize2stop/10]
2. non_recursive  : [evalbinsearchStepSize2returnin/10]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [evalbinsearchStepSize2bbin_loop_cont/11]
5. non_recursive  : [evalbinsearchStepSize2entryin/10]
6. non_recursive  : [evalbinsearchStepSize2start/10]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into evalbinsearchStepSize2bbin/18
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into evalbinsearchStepSize2bbin_loop_cont/11
5. SCC is partially evaluated into evalbinsearchStepSize2entryin/10
6. SCC is partially evaluated into evalbinsearchStepSize2start/10

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

### Specialization of cost equations evalbinsearchStepSize2bbin/18 
* CE 64 is refined into CE [67] 
* CE 8 is refined into CE [68] 
* CE 34 is refined into CE [69] 
* CE 4 is discarded (unfeasible) 
* CE 30 is discarded (unfeasible) 
* CE 10 is discarded (unfeasible) 
* CE 36 is discarded (unfeasible) 
* CE 6 is discarded (unfeasible) 
* CE 32 is discarded (unfeasible) 
* CE 57 is refined into CE [70] 
* CE 55 is discarded (unfeasible) 
* CE 58 is discarded (unfeasible) 
* CE 56 is discarded (unfeasible) 
* CE 63 is refined into CE [71] 
* CE 59 is discarded (unfeasible) 
* CE 60 is discarded (unfeasible) 
* CE 12 is discarded (unfeasible) 
* CE 38 is discarded (unfeasible) 
* CE 14 is discarded (unfeasible) 
* CE 40 is discarded (unfeasible) 
* CE 61 is refined into CE [72] 
* CE 62 is discarded (unfeasible) 
* CE 45 is discarded (unfeasible) 
* CE 19 is refined into CE [73] 
* CE 53 is discarded (unfeasible) 
* CE 27 is discarded (unfeasible) 
* CE 20 is refined into CE [74] 
* CE 28 is discarded (unfeasible) 
* CE 46 is refined into CE [75] 
* CE 54 is discarded (unfeasible) 
* CE 41 is refined into CE [76] 
* CE 48 is discarded (unfeasible) 
* CE 47 is discarded (unfeasible) 
* CE 15 is refined into CE [77] 
* CE 22 is discarded (unfeasible) 
* CE 21 is discarded (unfeasible) 
* CE 7 is refined into CE [78] 
* CE 3 is discarded (unfeasible) 
* CE 9 is discarded (unfeasible) 
* CE 5 is discarded (unfeasible) 
* CE 33 is refined into CE [79] 
* CE 29 is discarded (unfeasible) 
* CE 35 is discarded (unfeasible) 
* CE 31 is discarded (unfeasible) 
* CE 11 is discarded (unfeasible) 
* CE 13 is discarded (unfeasible) 
* CE 37 is discarded (unfeasible) 
* CE 39 is discarded (unfeasible) 
* CE 17 is refined into CE [80] 
* CE 25 is discarded (unfeasible) 
* CE 18 is refined into CE [81] 
* CE 26 is discarded (unfeasible) 
* CE 43 is discarded (unfeasible) 
* CE 51 is discarded (unfeasible) 
* CE 44 is refined into CE [82] 
* CE 52 is discarded (unfeasible) 
* CE 42 is refined into CE [83] 
* CE 50 is discarded (unfeasible) 
* CE 49 is discarded (unfeasible) 
* CE 16 is refined into CE [84] 
* CE 24 is discarded (unfeasible) 
* CE 23 is discarded (unfeasible) 


### Cost equations --> "Loop" of evalbinsearchStepSize2bbin/18 
* CEs [78] --> Loop 67 
* CEs [79] --> Loop 68 
* CEs [82] --> Loop 69 
* CEs [80] --> Loop 70 
* CEs [83] --> Loop 71 
* CEs [84] --> Loop 72 
* CEs [81] --> Loop 73 
* CEs [67] --> Loop 74 
* CEs [69] --> Loop 75 
* CEs [70] --> Loop 76 
* CEs [71] --> Loop 77 
* CEs [72] --> Loop 78 
* CEs [75] --> Loop 79 
* CEs [68] --> Loop 80 
* CEs [76] --> Loop 81 
* CEs [73] --> Loop 82 
* CEs [77] --> Loop 83 
* CEs [74] --> Loop 84 

### Ranking functions of CR evalbinsearchStepSize2bbin(A,B,C,D,E,F,G,H,I,K,L,M,N,O,P,Q,R,S) 
* RF of phase [69]: [D/4-3/4]
* RF of phase [70]: [-D/4+63]

#### Partial ranking functions of CR evalbinsearchStepSize2bbin(A,B,C,D,E,F,G,H,I,K,L,M,N,O,P,Q,R,S) 
* Partial RF of phase [69]:
  - RF of loop [69:1]:
    D/4-3/4
* Partial RF of phase [70]:
  - RF of loop [70:1]:
    -D/4+63


### Specialization of cost equations evalbinsearchStepSize2bbin_loop_cont/11 
* CE 66 is refined into CE [85] 
* CE 65 is refined into CE [86] 


### Cost equations --> "Loop" of evalbinsearchStepSize2bbin_loop_cont/11 
* CEs [85] --> Loop 85 
* CEs [86] --> Loop 86 

### Ranking functions of CR evalbinsearchStepSize2bbin_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 

#### Partial ranking functions of CR evalbinsearchStepSize2bbin_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 


### Specialization of cost equations evalbinsearchStepSize2entryin/10 
* CE 2 is refined into CE [87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117] 


### Cost equations --> "Loop" of evalbinsearchStepSize2entryin/10 
* CEs [109] --> Loop 87 
* CEs [112] --> Loop 88 
* CEs [88] --> Loop 89 
* CEs [107,108,110,111,113,116] --> Loop 90 
* CEs [99] --> Loop 91 
* CEs [91] --> Loop 92 
* CEs [98] --> Loop 93 
* CEs [114] --> Loop 94 
* CEs [90,93,96,97,101,106] --> Loop 95 
* CEs [105] --> Loop 96 
* CEs [104] --> Loop 97 
* CEs [94] --> Loop 98 
* CEs [89] --> Loop 99 
* CEs [92,100,103] --> Loop 100 
* CEs [95,102] --> Loop 101 
* CEs [87] --> Loop 102 
* CEs [115,117] --> Loop 103 

### Ranking functions of CR evalbinsearchStepSize2entryin(A,B,C,D,E,F,G,H,I,K) 

#### Partial ranking functions of CR evalbinsearchStepSize2entryin(A,B,C,D,E,F,G,H,I,K) 


### Specialization of cost equations evalbinsearchStepSize2start/10 
* CE 1 is refined into CE [118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134] 


### Cost equations --> "Loop" of evalbinsearchStepSize2start/10 
* CEs [134] --> Loop 104 
* CEs [133] --> Loop 105 
* CEs [132] --> Loop 106 
* CEs [131] --> Loop 107 
* CEs [130] --> Loop 108 
* CEs [129] --> Loop 109 
* CEs [128] --> Loop 110 
* CEs [127] --> Loop 111 
* CEs [126] --> Loop 112 
* CEs [125] --> Loop 113 
* CEs [124] --> Loop 114 
* CEs [123] --> Loop 115 
* CEs [122] --> Loop 116 
* CEs [121] --> Loop 117 
* CEs [120] --> Loop 118 
* CEs [119] --> Loop 119 
* CEs [118] --> Loop 120 

### Ranking functions of CR evalbinsearchStepSize2start(A,B,C,D,E,F,G,H,I,K) 

#### Partial ranking functions of CR evalbinsearchStepSize2start(A,B,C,D,E,F,G,H,I,K) 


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

#### Cost of chains of evalbinsearchStepSize2bbin(A,B,C,D,E,F,G,H,I,K,L,M,N,O,P,Q,R,S):
* Chain [[69],83]: 1*it(69)+0
  Such that:it(69) =< D/4-O/4

  with precondition: [B=0,C=4,K=2,L=1,M=0,N=4,Q=4,R=1,1>=A,2>=S,A>=0,2*S>=3,P>=G+1,D>=O+4,O+S>=256] 

* Chain [[69],79]: 1*it(69)+0
  Such that:it(69) =< D/4-O/4

  with precondition: [B=0,C=4,K=2,L=1,M=0,N=4,Q=4,R=0,S=4,1>=A,3>=O,A>=0,O>=0,D>=O+4,G>=P+1] 

* Chain [[69],78]: 1*it(69)+0
  Such that:it(69) =< D/4-O/4

  with precondition: [B=0,C=4,K=2,L=1,M=0,N=4,Q=4,R=0,S=4,G=P,1>=A,A>=0,O>=0,D>=O+4] 

* Chain [[69],74]: 1*it(69)+0
  Such that:it(69) =< D/4

  with precondition: [B=0,C=4,K=3,1>=A,A>=0,D>=4] 

* Chain [[69],72,80]: 1*it(69)+1
  Such that:it(69) =< D/4

  with precondition: [B=0,C=4,K=2,L=2,M=1,N=2,O=255,Q=1,R=1,S=1,1>=A,A>=0,D>=257,P>=G+1] 

* Chain [[69],72,76]: 1*it(69)+1
  Such that:it(69) =< D/4-O/4+1/2

  with precondition: [B=0,C=4,K=2,L=2,M=1,N=2,R=1,S=2,G=P,1>=A,255>=O,1>=Q,A>=0,O>=2,2*Q>=1,D>=O+2] 

* Chain [[69],72,74]: 1*it(69)+1
  Such that:it(69) =< D/4

  with precondition: [B=0,C=4,K=3,1>=A,A>=0,D>=4] 

* Chain [[69],72,68,77]: 1*it(69)+2
  Such that:it(69) =< D/4-O/4+1/4

  with precondition: [B=0,C=4,K=2,L=1,M=1,N=1,Q=1,R=1,S=1,1>=A,254>=O,A>=0,O>=1,D>=O+3,G>=P+1] 

* Chain [[69],72,68,74]: 1*it(69)+2
  Such that:it(69) =< D/4

  with precondition: [B=0,C=4,K=3,1>=A,A>=0,D>=4] 

* Chain [[69],72,67,77]: 1*it(69)+2
  Such that:it(69) =< D/4-O/4+3/4

  with precondition: [B=0,C=4,K=2,L=2,M=1,N=1,Q=1,R=1,S=1,1>=A,255>=O,A>=0,O>=3,P>=G+1,D>=O+1] 

* Chain [[69],72,67,74]: 1*it(69)+2
  Such that:it(69) =< D/4

  with precondition: [B=0,C=4,K=3,1>=A,A>=0,D>=4] 

* Chain [84]: 0
  with precondition: [A=0,B=0,C=4,K=2,L=0,M=0,N=4,Q=4,R=0,S=4,D=O,D>=252,P>=G+1] 

* Chain [79]: 0
  with precondition: [B=0,C=4,K=2,M=0,N=4,Q=4,R=0,S=4,A=L,D=O,1>=A,3>=D,A>=0,G>=P+1] 

* Chain [78]: 0
  with precondition: [B=0,C=4,K=2,M=0,N=4,Q=4,O=D,P=G,R=H,S=I,A=L,2>=A,A>=0] 

* Chain [74]: 0
  with precondition: [K=3,2>=A,1>=B,4>=2*B+C,A>=B,2*C+7*B>=8] 

* Chain [73,[70],82]: 1*it(70)+1
  Such that:it(70) =< -D/4+62

  with precondition: [A=0,B=0,C=4,K=2,L=2,M=0,N=4,Q=4,R=0,S=4,255>=O,O>=252,O>=D+8,P>=G+1] 

* Chain [73,[70],81]: 1*it(70)+1
  Such that:it(70) =< -D/4+O/4

  with precondition: [A=0,B=0,C=4,K=2,L=2,M=0,N=4,Q=4,R=1,2>=S,2*S>=3,O>=D+8,S>=O+1,G>=P+1] 

* Chain [73,[70],78]: 1*it(70)+1
  Such that:it(70) =< -D/4+62
it(70) =< -D/4+O/4

  with precondition: [A=0,B=0,C=4,K=2,L=2,M=0,N=4,Q=4,R=0,S=4,G=P,255>=O,O>=D+8] 

* Chain [73,[70],74]: 1*it(70)+1
  Such that:it(70) =< -D/4+62

  with precondition: [A=0,B=0,C=4,K=3,247>=D] 

* Chain [73,[70],71,76]: 1*it(70)+2
  Such that:it(70) =< -D/4+62
it(70) =< -D/4+O/4

  with precondition: [A=0,B=0,C=4,K=2,L=1,M=1,N=2,R=1,S=2,G=P,253>=O,1>=Q,O>=0,2*Q>=1,O>=D+6] 

* Chain [73,[70],71,75]: 1*it(70)+2
  Such that:it(70) =< -D/4

  with precondition: [A=0,B=0,C=4,K=2,L=1,M=1,N=2,O=0,Q=1,R=1,S=1,0>=D+6,G>=P+1] 

* Chain [73,[70],71,74]: 1*it(70)+2
  Such that:it(70) =< -D/4+62

  with precondition: [A=0,B=0,C=4,K=3,247>=D] 

* Chain [73,[70],71,68,77]: 1*it(70)+3
  Such that:it(70) =< -D/4+62
it(70) =< -D/4+O/4

  with precondition: [A=0,B=0,C=4,K=2,L=1,M=1,N=1,Q=1,R=1,S=1,252>=O,O>=0,O>=D+5,G>=P+1] 

* Chain [73,[70],71,68,74]: 1*it(70)+3
  Such that:it(70) =< -D/4+62

  with precondition: [A=0,B=0,C=4,K=3,247>=D] 

* Chain [73,[70],71,67,77]: 1*it(70)+3
  Such that:it(70) =< -D/4+62
it(70) =< -D/4+O/4

  with precondition: [A=0,B=0,C=4,K=2,L=2,M=1,N=1,Q=1,R=1,S=1,254>=O,O>=1,O>=D+7,P>=G+1] 

* Chain [73,[70],71,67,74]: 1*it(70)+3
  Such that:it(70) =< -D/4+62

  with precondition: [A=0,B=0,C=4,K=3,247>=D] 

* Chain [73,82]: 1
  with precondition: [A=0,B=0,C=4,K=2,L=2,M=0,N=4,Q=4,R=0,S=4,O=D+4,255>=O,O>=252,P>=G+1] 

* Chain [73,81]: 1
  with precondition: [A=0,B=0,C=4,K=2,L=2,M=0,N=4,Q=4,R=1,O=D+4,2>=S,2*S>=3,S>=O+1,G>=P+1] 

* Chain [73,78]: 1
  with precondition: [A=0,B=0,C=4,K=2,L=2,M=0,N=4,Q=4,R=0,S=4,D+4=O,G=P,251>=D] 

* Chain [73,74]: 1
  with precondition: [A=0,B=0,C=4,K=3,251>=D] 

* Chain [73,71,76]: 2
  with precondition: [A=0,B=0,C=4,K=2,L=1,M=1,N=2,R=1,S=2,O=D+2,G=P,253>=O,1>=Q,O>=0,2*Q>=1] 

* Chain [73,71,75]: 2
  with precondition: [A=0,B=0,C=4,D+2=0,K=2,L=1,M=1,N=2,O=0,Q=1,R=1,S=1,G>=P+1] 

* Chain [73,71,74]: 2
  with precondition: [A=0,B=0,C=4,K=3,251>=D,2*D+5>=0] 

* Chain [73,71,68,77]: 3
  with precondition: [A=0,B=0,C=4,K=2,L=1,M=1,N=1,Q=1,R=1,S=1,O=D+1,252>=O,O>=0,G>=P+1] 

* Chain [73,71,68,74]: 3
  with precondition: [A=0,B=0,C=4,K=3,251>=D,2*D+3>=0] 

* Chain [73,71,67,77]: 3
  with precondition: [A=0,B=0,C=4,K=2,L=2,M=1,N=1,Q=1,R=1,S=1,O=D+3,254>=O,O>=1,P>=G+1] 

* Chain [73,71,67,74]: 3
  with precondition: [A=0,B=0,C=4,K=3,251>=D,D+2>=0] 


#### Cost of chains of evalbinsearchStepSize2bbin_loop_cont(A,B,C,D,E,F,G,H,I,J,K):
* Chain [86]: 0
  with precondition: [A=2] 

* Chain [85]: 0
  with precondition: [A=3] 


#### Cost of chains of evalbinsearchStepSize2entryin(A,B,C,D,E,F,G,H,I,K):
* Chain [103]: 0
  with precondition: [] 

* Chain [102]: 2
  with precondition: [A+2=0] 

* Chain [101]: 1
  with precondition: [251>=A] 

* Chain [100]: 3
  with precondition: [251>=A,A+2>=0] 

* Chain [99]: 3
  with precondition: [251>=A,A+1>=0] 

* Chain [98]: 1
  with precondition: [251>=A,A>=248] 

* Chain [97]: 2
  with precondition: [251>=A,2*A+5>=0] 

* Chain [96]: 3
  with precondition: [251>=A,2*A+3>=0] 

* Chain [95]: 9*s(9)+3
  Such that:aux(3) =< -A/4+62
s(9) =< aux(3)

  with precondition: [247>=A] 

* Chain [94]: 0
  with precondition: [3>=A] 

* Chain [93]: 1
  with precondition: [0>=A+3] 

* Chain [92]: 1*s(16)+2
  Such that:s(16) =< -A/4

  with precondition: [0>=A+6] 

* Chain [91]: 1*s(17)+1
  Such that:s(17) =< -A/4+1/4

  with precondition: [0>=A+7] 

* Chain [90]: 9*s(18)+2
  Such that:aux(4) =< A/4
s(18) =< aux(4)

  with precondition: [A>=4] 

* Chain [89]: 0
  with precondition: [A>=252] 

* Chain [88]: 1*s(25)+1
  Such that:s(25) =< A/4

  with precondition: [A>=257] 

* Chain [87]: 1*s(26)+0
  Such that:s(26) =< A/4

  with precondition: [A>=258] 


#### Cost of chains of evalbinsearchStepSize2start(A,B,C,D,E,F,G,H,I,K):
* Chain [120]: 0
  with precondition: [] 

* Chain [119]: 2
  with precondition: [A+2=0] 

* Chain [118]: 1
  with precondition: [251>=A] 

* Chain [117]: 3
  with precondition: [251>=A,A+2>=0] 

* Chain [116]: 3
  with precondition: [251>=A,A+1>=0] 

* Chain [115]: 1
  with precondition: [251>=A,A>=248] 

* Chain [114]: 2
  with precondition: [251>=A,2*A+5>=0] 

* Chain [113]: 3
  with precondition: [251>=A,2*A+3>=0] 

* Chain [112]: 9*s(28)+3
  Such that:s(27) =< -A/4+62
s(28) =< s(27)

  with precondition: [247>=A] 

* Chain [111]: 0
  with precondition: [3>=A] 

* Chain [110]: 1
  with precondition: [0>=A+3] 

* Chain [109]: 1*s(29)+2
  Such that:s(29) =< -A/4

  with precondition: [0>=A+6] 

* Chain [108]: 1*s(30)+1
  Such that:s(30) =< -A/4+1/4

  with precondition: [0>=A+7] 

* Chain [107]: 9*s(32)+2
  Such that:s(31) =< A/4
s(32) =< s(31)

  with precondition: [A>=4] 

* Chain [106]: 0
  with precondition: [A>=252] 

* Chain [105]: 1*s(33)+1
  Such that:s(33) =< A/4

  with precondition: [A>=257] 

* Chain [104]: 1*s(34)+0
  Such that:s(34) =< A/4

  with precondition: [A>=258] 


Closed-form bounds of evalbinsearchStepSize2start(A,B,C,D,E,F,G,H,I,K): 
-------------------------------------
* Chain [120] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [119] with precondition: [A+2=0] 
    - Upper bound: 2 
    - Complexity: constant 
* Chain [118] with precondition: [251>=A] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [117] with precondition: [251>=A,A+2>=0] 
    - Upper bound: 3 
    - Complexity: constant 
* Chain [116] with precondition: [251>=A,A+1>=0] 
    - Upper bound: 3 
    - Complexity: constant 
* Chain [115] with precondition: [251>=A,A>=248] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [114] with precondition: [251>=A,2*A+5>=0] 
    - Upper bound: 2 
    - Complexity: constant 
* Chain [113] with precondition: [251>=A,2*A+3>=0] 
    - Upper bound: 3 
    - Complexity: constant 
* Chain [112] with precondition: [247>=A] 
    - Upper bound: -9/4*A+561 
    - Complexity: n 
* Chain [111] with precondition: [3>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [110] with precondition: [0>=A+3] 
    - Upper bound: 1 
    - Complexity: constant 
* Chain [109] with precondition: [0>=A+6] 
    - Upper bound: -A/4+2 
    - Complexity: n 
* Chain [108] with precondition: [0>=A+7] 
    - Upper bound: -A/4+5/4 
    - Complexity: n 
* Chain [107] with precondition: [A>=4] 
    - Upper bound: 9/4*A+2 
    - Complexity: n 
* Chain [106] with precondition: [A>=252] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [105] with precondition: [A>=257] 
    - Upper bound: A/4+1 
    - Complexity: n 
* Chain [104] with precondition: [A>=258] 
    - Upper bound: A/4 
    - Complexity: n 

### Maximum cost of evalbinsearchStepSize2start(A,B,C,D,E,F,G,H,I,K): max([max([3,nat(-A/4+1/4)+1,nat(-A/4)+2,nat(-A/4+62)*9+3]),nat(A/4)+max([1,nat(A/4)*8+2])]) 
Asymptotic class: n 
* Total analysis performed in 6319 ms.