/export/starexec/sandbox2/solver/bin/starexec_run_its /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [lbl81/21]
1. recursive  : [lbl71/21,lbl81_loop_cont/22]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [stop/11]
4. non_recursive  : [lbl71_loop_cont/12]
5. non_recursive  : [start/11]
6. non_recursive  : [start0/11]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into lbl81/21
1. SCC is partially evaluated into lbl71/21
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into lbl71_loop_cont/12
5. SCC is partially evaluated into start/11
6. SCC is partially evaluated into start0/11

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

### Specialization of cost equations lbl81/21 
* CE 9 is refined into CE [15] 
* CE 7 is refined into CE [16] 
* CE 8 is refined into CE [17] 


### Cost equations --> "Loop" of lbl81/21 
* CEs [17] --> Loop 14 
* CEs [15] --> Loop 15 
* CEs [16] --> Loop 16 

### Ranking functions of CR lbl81(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 
* RF of phase [14]: [C-D+1,-D+G+1]

#### Partial ranking functions of CR lbl81(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    C-D+1
    -D+G+1


### Specialization of cost equations lbl71/21 
* CE 14 is refined into CE [18] 
* CE 12 is refined into CE [19] 
* CE 13 is refined into CE [20] 


### Cost equations --> "Loop" of lbl71/21 
* CEs [20] --> Loop 17 
* CEs [18] --> Loop 18 
* CEs [19] --> Loop 19 

### Ranking functions of CR lbl71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 
* RF of phase [17]: [C-D+1,-D+G+1]

#### Partial ranking functions of CR lbl71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 
* Partial RF of phase [17]:
  - RF of loop [17:1]:
    C-D+1
    -D+G+1


### Specialization of cost equations lbl71_loop_cont/12 
* CE 11 is refined into CE [21] 
* CE 10 is refined into CE [22] 


### Cost equations --> "Loop" of lbl71_loop_cont/12 
* CEs [21] --> Loop 20 
* CEs [22] --> Loop 21 

### Ranking functions of CR lbl71_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 

#### Partial ranking functions of CR lbl71_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 


### Specialization of cost equations start/11 
* CE 4 is refined into CE [23] 
* CE 5 is refined into CE [24,25,26,27] 
* CE 6 is refined into CE [28] 
* CE 2 is refined into CE [29,30] 
* CE 3 is refined into CE [31,32] 


### Cost equations --> "Loop" of start/11 
* CEs [23] --> Loop 22 
* CEs [25,27] --> Loop 23 
* CEs [26] --> Loop 24 
* CEs [28] --> Loop 25 
* CEs [30,32] --> Loop 26 
* CEs [29] --> Loop 27 
* CEs [24] --> Loop 28 
* CEs [31] --> Loop 29 

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

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


### Specialization of cost equations start0/11 
* CE 1 is refined into CE [33,34,35,36,37,38,39,40] 


### Cost equations --> "Loop" of start0/11 
* CEs [38] --> Loop 30 
* CEs [37] --> Loop 31 
* CEs [36] --> Loop 32 
* CEs [35] --> Loop 33 
* CEs [34] --> Loop 34 
* CEs [33] --> Loop 35 
* CEs [40] --> Loop 36 
* CEs [39] --> Loop 37 

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

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


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

#### Cost of chains of lbl81(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U):
* Chain [[14],16]: 1*it(14)+0
  Such that:it(14) =< -D+R+1

  with precondition: [E+1=0,K=2,P+1=0,C=G,H=I,A=J,A=L,B=M,C=N,C+1=O,F=Q,C=R,H=S,H=T,A=U,0>=A,D>=B+1,C>=D] 

* Chain [[14],15]: 1*it(14)+0
  Such that:it(14) =< -D+G+1

  with precondition: [E+1=0,K=4,C=G,H=I,A=J,0>=A,D>=B+1,C>=D] 

* Chain [16]: 0
  with precondition: [E+1=0,K=2,P+1=0,J=A,C+1=D,Q=F,C=G,I=H,J=L,B=M,C=N,C+1=O,C=R,I=S,I=T,J=U,0>=J,C>=B] 

* Chain [15]: 0
  with precondition: [E+1=0,K=4,J=A,G=C,I=H,0>=J,D>=B+1,G+1>=D] 


#### Cost of chains of lbl71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U):
* Chain [[17],19]: 1*it(17)+0
  Such that:it(17) =< -D+R+1

  with precondition: [E=1,K=2,P=1,C=G,H=I,A=J,A=L,B=M,C=N,C+1=O,F=Q,C=R,H=S,H=T,A=U,A>=1,D>=B+1,C>=D] 

* Chain [[17],18]: 1*it(17)+0
  Such that:it(17) =< C-D+1

  with precondition: [E=1,K=4,C=G,H=I,A=J,A>=1,D>=B+1,C>=D] 

* Chain [19]: 0
  with precondition: [E=1,K=2,P=1,J=A,C+1=D,Q=F,C=G,I=H,J=L,B=M,C=N,C+1=O,C=R,I=S,I=T,J=U,J>=1,C>=B] 

* Chain [18]: 0
  with precondition: [E=1,K=4,J=A,G=C,I=H,J>=1,D>=B+1,G+1>=D] 


#### Cost of chains of lbl71_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L):
* Chain [21]: 0
  with precondition: [A=2] 

* Chain [20]: 0
  with precondition: [A=4] 


#### Cost of chains of start(A,B,C,D,E,F,G,H,I,J,K):
* Chain [29]: 0
  with precondition: [J=A,B=C,B=D,F=E,B=G,I=H,0>=J] 

* Chain [28]: 0
  with precondition: [J=A,B=C,B=D,F=E,B=G,I=H,J>=1] 

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

* Chain [26]: 2*s(1)+0
  Such that:aux(1) =< -B+G
s(1) =< aux(1)

  with precondition: [J=A,D=B,G=C,F=E,I=H,0>=J,G>=D+1] 

* Chain [25]: 0
  with precondition: [J=A,D=B,G=C,F=E,I=H,0>=J,D>=G+1] 

* Chain [24]: 0
  with precondition: [J=A,D=B,G=C,F=E,I=H,J>=1,G>=D] 

* Chain [23]: 2*s(3)+0
  Such that:aux(2) =< -B+G
s(3) =< aux(2)

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

* Chain [22]: 0
  with precondition: [J=A,D=B,G=C,F=E,I=H,J>=1,D>=G+1] 


#### Cost of chains of start0(A,B,C,D,E,F,G,H,I,J,K):
* Chain [37]: 0
  with precondition: [C=B,0>=A] 

* Chain [36]: 0
  with precondition: [C=B,A>=1] 

* Chain [35]: 0
  with precondition: [0>=A,C>=B] 

* Chain [34]: 2*s(6)+0
  Such that:s(5) =< -B+C
s(6) =< s(5)

  with precondition: [0>=A,C>=B+1] 

* Chain [33]: 0
  with precondition: [0>=A,B>=C+1] 

* Chain [32]: 0
  with precondition: [A>=1,C>=B] 

* Chain [31]: 2*s(8)+0
  Such that:s(7) =< -B+C
s(8) =< s(7)

  with precondition: [A>=1,C>=B+1] 

* Chain [30]: 0
  with precondition: [A>=1,B>=C+1] 


Closed-form bounds of start0(A,B,C,D,E,F,G,H,I,J,K): 
-------------------------------------
* Chain [37] with precondition: [C=B,0>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [36] with precondition: [C=B,A>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [35] with precondition: [0>=A,C>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [34] with precondition: [0>=A,C>=B+1] 
    - Upper bound: -2*B+2*C 
    - Complexity: n 
* Chain [33] with precondition: [0>=A,B>=C+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [32] with precondition: [A>=1,C>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [31] with precondition: [A>=1,C>=B+1] 
    - Upper bound: -2*B+2*C 
    - Complexity: n 
* Chain [30] with precondition: [A>=1,B>=C+1] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of start0(A,B,C,D,E,F,G,H,I,J,K): nat(-B+C)*2 
Asymptotic class: n 
* Total analysis performed in 662 ms.