/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  : [lbl82/17]
1. recursive  : [lbl82_loop_cont/18,lbl92/17]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [stop/9]
4. non_recursive  : [lbl92_loop_cont/10]
5. non_recursive  : [start/9]
6. non_recursive  : [start0/9]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into lbl82/17
1. SCC is partially evaluated into lbl92/17
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into lbl92_loop_cont/10
5. SCC is partially evaluated into start/9
6. SCC is partially evaluated into start0/9

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

### Specialization of cost equations lbl82/17 
* CE 8 is refined into CE [16] 
* CE 6 is refined into CE [17] 
* CE 7 is refined into CE [18] 


### Cost equations --> "Loop" of lbl82/17 
* CEs [18] --> Loop 15 
* CEs [16] --> Loop 16 
* CEs [17] --> Loop 17 

### Ranking functions of CR lbl82(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
* RF of phase [15]: [-B+9,-F+10]

#### Partial ranking functions of CR lbl82(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    -B+9
    -F+10


### Specialization of cost equations lbl92/17 
* CE 13 is refined into CE [19] 
* CE 11 is refined into CE [20,21] 
* CE 15 is refined into CE [22] 
* CE 12 is refined into CE [23] 
* CE 14 is refined into CE [24] 


### Cost equations --> "Loop" of lbl92/17 
* CEs [24] --> Loop 18 
* CEs [23] --> Loop 19 
* CEs [19] --> Loop 20 
* CEs [20,21] --> Loop 21 
* CEs [22] --> Loop 22 

### Ranking functions of CR lbl92(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
* RF of phase [18]: [-D+2,-H+3]
* RF of phase [19]: [-D+4,-H+5]

#### Partial ranking functions of CR lbl92(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
* Partial RF of phase [18]:
  - RF of loop [18:1]:
    -D+2
    -H+3
* Partial RF of phase [19]:
  - RF of loop [19:1]:
    -D+4
    -H+5


### Specialization of cost equations lbl92_loop_cont/10 
* CE 9 is refined into CE [25] 
* CE 10 is refined into CE [26] 


### Cost equations --> "Loop" of lbl92_loop_cont/10 
* CEs [25] --> Loop 23 
* CEs [26] --> Loop 24 

### Ranking functions of CR lbl92_loop_cont(A,B,C,D,E,F,G,H,I,J) 

#### Partial ranking functions of CR lbl92_loop_cont(A,B,C,D,E,F,G,H,I,J) 


### Specialization of cost equations start/9 
* CE 4 is refined into CE [27] 
* CE 5 is refined into CE [28,29,30,31,32,33] 
* CE 2 is refined into CE [34,35] 
* CE 3 is refined into CE [36,37,38,39] 


### Cost equations --> "Loop" of start/9 
* CEs [27] --> Loop 25 
* CEs [30,32] --> Loop 26 
* CEs [29] --> Loop 27 
* CEs [34,35,36] --> Loop 28 
* CEs [39] --> Loop 29 
* CEs [37,38] --> Loop 30 
* CEs [28,31,33] --> Loop 31 

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

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


### Specialization of cost equations start0/9 
* CE 1 is refined into CE [40,41,42,43,44,45,46] 


### Cost equations --> "Loop" of start0/9 
* CEs [46] --> Loop 32 
* CEs [45] --> Loop 33 
* CEs [44] --> Loop 34 
* CEs [43] --> Loop 35 
* CEs [42] --> Loop 36 
* CEs [41] --> Loop 37 
* CEs [40] --> Loop 38 

### Ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 


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

#### Cost of chains of lbl82(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q):
* Chain [[15],17]: 1*it(15)+0
  Such that:it(15) =< -B+9

  with precondition: [I=2,K=9,O=10,F=B+1,A=J,C=L,H=M,E=N,G=P,H+1=Q,9>=F,4>=H,F>=1,H>=3,H>=A] 

* Chain [[15],16]: 1*it(15)+0
  Such that:it(15) =< -F+10

  with precondition: [I=3,F=B+1,9>=F,4>=H,F>=1,H>=3,H>=A] 

* Chain [16]: 0
  with precondition: [I=3,B+1=F,4>=H,B>=0,H>=3,H>=A] 


#### Cost of chains of lbl92(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q):
* Chain [[19],22]: 1*it(19)+1*s(3)+0
  Such that:aux(6) =< -H+5
it(19) =< aux(6)
s(3) =< aux(6)*9

  with precondition: [I=3,D+1=H,3>=D,D>=2,F+10>=5*D,D>=A] 

* Chain [[19],21]: 1*it(19)+1*s(3)+9
  Such that:aux(7) =< 1
aux(8) =< 2
aux(1) =< aux(8)
it(19) =< aux(8)
aux(1) =< aux(7)
it(19) =< aux(7)
s(3) =< aux(1)*9

  with precondition: [D=2,H=3,I=3,2>=A,F>=0] 

* Chain [[19],20]: 1*it(19)+1*s(3)+0
  Such that:aux(9) =< -D+4
it(19) =< aux(9)
s(3) =< aux(9)*9

  with precondition: [I=4,K=9,M=4,O=10,Q=5,D+1=H,A=J,C=L,E=N,G=P,3>=D,D>=2,F+10>=5*D,D>=A] 

* Chain [[18],[19],22]: 1*it(18)+1*it(19)+1*s(3)+0
  Such that:aux(6) =< 2
it(18) =< -H+3
it(19) =< aux(6)
s(3) =< aux(6)*9

  with precondition: [I=3,H=D+1,2>=H,F>=0,H>=A+1] 

* Chain [[18],[19],21]: 1*it(18)+1*it(19)+1*s(3)+9
  Such that:aux(7) =< 1
aux(8) =< 2
it(18) =< -D+2
aux(1) =< aux(8)
it(19) =< aux(8)
aux(1) =< aux(7)
it(19) =< aux(7)
s(3) =< aux(1)*9

  with precondition: [I=3,H=D+1,2>=H,F>=0,H>=A+1] 

* Chain [[18],[19],20]: 1*it(18)+1*it(19)+1*s(3)+0
  Such that:aux(9) =< 2
it(18) =< -D+2
it(19) =< aux(9)
s(3) =< aux(9)*9

  with precondition: [I=4,K=9,M=4,O=10,Q=5,H=D+1,A=J,C=L,E=N,G=P,2>=H,F>=0,H>=A+1] 

* Chain [[18],22]: 1*it(18)+0
  Such that:it(18) =< -H+3

  with precondition: [I=3,H=D+1,2>=H,F>=0,H>=A+1] 

* Chain [[18],21]: 1*it(18)+9
  Such that:it(18) =< -H+3

  with precondition: [I=3,H=D+1,2>=H,F>=0,H>=A+1] 

* Chain [22]: 0
  with precondition: [I=3] 

* Chain [21]: 9
  with precondition: [I=3,D+1=H,3>=D,D>=2,F+10>=5*D,D>=A] 

* Chain [20]: 0
  with precondition: [I=4,K=B,L=C,N=E,P=G,D+1=H,A=J,D=M,F=O,D+1=Q,D>=4,F+10>=5*D,D>=A] 


#### Cost of chains of lbl92_loop_cont(A,B,C,D,E,F,G,H,I,J):
* Chain [24]: 0
  with precondition: [A=3] 

* Chain [23]: 0
  with precondition: [A=4] 


#### Cost of chains of start(A,B,C,D,E,F,G,H,I):
* Chain [31]: 69
  with precondition: [A=2,H=2,C=B,E=D,G=F] 

* Chain [30]: 48
  with precondition: [A=3,H=3,C=B,E=D,G=F] 

* Chain [29]: 1*s(39)+1
  Such that:s(39) =< 9

  with precondition: [A=4,H=4,C=B,E=D,G=F] 

* Chain [28]: 19
  with precondition: [H=A,C=B,E=D,G=F,4>=H,H>=3] 

* Chain [27]: 0
  with precondition: [H=A,C=B,E=D,G=F,2>=H] 

* Chain [26]: 4*s(43)+1*s(48)+1*s(49)+2*s(50)+2*s(51)+1*s(53)+9
  Such that:s(42) =< 1
s(53) =< -A+2
aux(16) =< -H+2
aux(17) =< 2
s(43) =< aux(16)
s(47) =< aux(17)
s(48) =< aux(17)
s(47) =< s(42)
s(48) =< s(42)
s(49) =< s(47)*9
s(50) =< aux(17)
s(51) =< aux(17)*9

  with precondition: [H=A,C=B,E=D,G=F,1>=H] 

* Chain [25]: 0
  with precondition: [H=A,C=B,E=D,G=F,H>=5] 


#### Cost of chains of start0(A,B,C,D,E,F,G,H,I):
* Chain [38]: 69
  with precondition: [A=2] 

* Chain [37]: 48
  with precondition: [A=3] 

* Chain [36]: 1*s(56)+1
  Such that:s(56) =< 9

  with precondition: [A=4] 

* Chain [35]: 19
  with precondition: [4>=A,A>=3] 

* Chain [34]: 0
  with precondition: [2>=A] 

* Chain [33]: 5*s(58)+1*s(63)+1*s(64)+2*s(65)+2*s(66)+9
  Such that:s(57) =< 1
s(60) =< 2
aux(18) =< -A+2
s(58) =< aux(18)
s(62) =< s(60)
s(63) =< s(60)
s(62) =< s(57)
s(63) =< s(57)
s(64) =< s(62)*9
s(65) =< s(60)
s(66) =< s(60)*9

  with precondition: [1>=A] 

* Chain [32]: 0
  with precondition: [A>=5] 


Closed-form bounds of start0(A,B,C,D,E,F,G,H,I): 
-------------------------------------
* Chain [38] with precondition: [A=2] 
    - Upper bound: 69 
    - Complexity: constant 
* Chain [37] with precondition: [A=3] 
    - Upper bound: 48 
    - Complexity: constant 
* Chain [36] with precondition: [A=4] 
    - Upper bound: 10 
    - Complexity: constant 
* Chain [35] with precondition: [4>=A,A>=3] 
    - Upper bound: 19 
    - Complexity: constant 
* Chain [34] with precondition: [2>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [33] with precondition: [1>=A] 
    - Upper bound: -5*A+79 
    - Complexity: n 
* Chain [32] with precondition: [A>=5] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of start0(A,B,C,D,E,F,G,H,I): max([69,nat(-A+2)*5+69]) 
Asymptotic class: n 
* Total analysis performed in 768 ms.