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


--------------------------------------------------------------------------------


WORST_CASE(?,O(1))  

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

#### Computed strongly connected components 
0. recursive  : [f12/17]
1. non_recursive  : [exit_location/1]
2. recursive  : [f24/17]
3. recursive  : [f36/10]
4. non_recursive  : [f46/20]
5. non_recursive  : [f36_loop_cont/21]
6. non_recursive  : [f24_loop_cont/21]
7. non_recursive  : [f12_loop_cont/21]
8. non_recursive  : [f0/20]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f12/17
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into f24/17
3. SCC is partially evaluated into f36/10
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into f36_loop_cont/21
6. SCC is partially evaluated into f24_loop_cont/21
7. SCC is partially evaluated into f12_loop_cont/21
8. SCC is partially evaluated into f0/20

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

### Specialization of cost equations f12/17 
* CE 3 is refined into CE [17] 
* CE 4 is refined into CE [18] 
* CE 2 is refined into CE [19] 


### Cost equations --> "Loop" of f12/17 
* CEs [19] --> Loop 17 
* CEs [17] --> Loop 18 
* CEs [18] --> Loop 19 

### Ranking functions of CR f12(C,D,E,F,G,H,Q,R,S,U,V,W,X,Y,Z,A1,B1) 
* RF of phase [17]: [-E+3]

#### Partial ranking functions of CR f12(C,D,E,F,G,H,Q,R,S,U,V,W,X,Y,Z,A1,B1) 
* Partial RF of phase [17]:
  - RF of loop [17:1]:
    -E+3


### Specialization of cost equations f24/17 
* CE 8 is refined into CE [20] 
* CE 9 is refined into CE [21] 
* CE 7 is refined into CE [22] 


### Cost equations --> "Loop" of f24/17 
* CEs [22] --> Loop 20 
* CEs [20] --> Loop 21 
* CEs [21] --> Loop 22 

### Ranking functions of CR f24(F,G,H,I,J,K,N,O,P,U,V,W,X,Y,Z,A1,B1) 
* RF of phase [20]: [-G+3]

#### Partial ranking functions of CR f24(F,G,H,I,J,K,N,O,P,U,V,W,X,Y,Z,A1,B1) 
* Partial RF of phase [20]:
  - RF of loop [20:1]:
    -G+3


### Specialization of cost equations f36/10 
* CE 14 is refined into CE [23] 
* CE 13 is refined into CE [24] 
* CE 12 is refined into CE [25] 


### Cost equations --> "Loop" of f36/10 
* CEs [25] --> Loop 23 
* CEs [23] --> Loop 24 
* CEs [24] --> Loop 25 

### Ranking functions of CR f36(I,J,K,L,M,U,V,W,X,Y) 
* RF of phase [23]: [-J+3]

#### Partial ranking functions of CR f36(I,J,K,L,M,U,V,W,X,Y) 
* Partial RF of phase [23]:
  - RF of loop [23:1]:
    -J+3


### Specialization of cost equations f36_loop_cont/21 
* CE 16 is refined into CE [26] 
* CE 15 is refined into CE [27] 


### Cost equations --> "Loop" of f36_loop_cont/21 
* CEs [26] --> Loop 26 
* CEs [27] --> Loop 27 

### Ranking functions of CR f36_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 

#### Partial ranking functions of CR f36_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 


### Specialization of cost equations f24_loop_cont/21 
* CE 11 is refined into CE [28,29,30,31] 
* CE 10 is refined into CE [32] 


### Cost equations --> "Loop" of f24_loop_cont/21 
* CEs [29] --> Loop 28 
* CEs [28,31] --> Loop 29 
* CEs [30] --> Loop 30 
* CEs [32] --> Loop 31 

### Ranking functions of CR f24_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 

#### Partial ranking functions of CR f24_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 


### Specialization of cost equations f12_loop_cont/21 
* CE 6 is refined into CE [33,34,35,36,37,38] 
* CE 5 is refined into CE [39] 


### Cost equations --> "Loop" of f12_loop_cont/21 
* CEs [37,38] --> Loop 32 
* CEs [34,35,36] --> Loop 33 
* CEs [33] --> Loop 34 
* CEs [39] --> Loop 35 

### Ranking functions of CR f12_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 

#### Partial ranking functions of CR f12_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 


### Specialization of cost equations f0/20 
* CE 1 is refined into CE [40,41,42,43] 


### Cost equations --> "Loop" of f0/20 
* CEs [40,41,42,43] --> Loop 36 

### Ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,U) 

#### Partial ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,U) 


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

#### Cost of chains of f12(C,D,E,F,G,H,Q,R,S,U,V,W,X,Y,Z,A1,B1):
* Chain [[17],19]: 1*it(17)+0
  Such that:it(17) =< -E+3

  with precondition: [C=3,U=3,2>=E,E>=0] 

* Chain [[17],18]: 1*it(17)+0
  Such that:it(17) =< -E+3

  with precondition: [C=3,U=5,W=3,X=0,Y=1,V=Z,V=A1,2>=E,E>=0] 

* Chain [19]: 0
  with precondition: [C=3,U=3,E>=0] 


#### Cost of chains of f24(F,G,H,I,J,K,N,O,P,U,V,W,X,Y,Z,A1,B1):
* Chain [[20],22]: 1*it(20)+0
  Such that:it(20) =< -G+3

  with precondition: [F=3,U=3,2>=G] 

* Chain [[20],21]: 1*it(20)+0
  Such that:it(20) =< -G+3

  with precondition: [F=3,U=4,V=3,X=0,Y=1,W=Z,W=A1,2>=G] 

* Chain [22]: 0
  with precondition: [F=3,U=3] 

* Chain [21]: 0
  with precondition: [F=3,U=4,X=0,Y=1,G=V,H=W,H=Z,H=A1,G>=3] 


#### Cost of chains of f36(I,J,K,L,M,U,V,W,X,Y):
* Chain [[23],25]: 1*it(23)+0
  Such that:it(23) =< -J+3

  with precondition: [I=3,U=2,V=3,W=X,W=Y,2>=J] 

* Chain [[23],24]: 1*it(23)+0
  Such that:it(23) =< -J+3

  with precondition: [I=3,U=3,2>=J] 

* Chain [25]: 0
  with precondition: [I=3,U=2,J=V,K=W,K=X,K=Y,J>=3] 

* Chain [24]: 0
  with precondition: [I=3,U=3] 


#### Cost of chains of f36_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U):
* Chain [27]: 0
  with precondition: [A=2,B=3,D=3,G=3,J=3] 

* Chain [26]: 0
  with precondition: [A=3,B=3,D=3,G=3,J=3] 


#### Cost of chains of f24_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U):
* Chain [31]: 0
  with precondition: [A=3,B=3,D=3,G=3,J=3] 

* Chain [30]: 0
  with precondition: [A=4,B=3,D=3,G=3,J=3] 

* Chain [29]: 2*s(1)+0
  Such that:aux(1) =< -K+3
s(1) =< aux(1)

  with precondition: [A=4,B=3,D=3,G=3,J=3,2>=K] 

* Chain [28]: 0
  with precondition: [A=4,B=3,D=3,G=3,J=3,K>=3] 


#### Cost of chains of f12_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U):
* Chain [35]: 0
  with precondition: [A=3,B=3,D=3,G=3] 

* Chain [34]: 0
  with precondition: [A=5,B=3,D=3,G=3] 

* Chain [33]: 3*s(3)+2*s(7)+0
  Such that:s(6) =< 3
aux(2) =< -H+3
s(3) =< aux(2)
s(7) =< s(6)

  with precondition: [A=5,B=3,D=3,G=3,2>=H] 

* Chain [32]: 6
  with precondition: [A=5,B=3,D=3,G=3,H>=3] 


#### Cost of chains of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,U):
* Chain [36]: 24
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,U): 
-------------------------------------
* Chain [36] with precondition: [] 
    - Upper bound: 24 
    - Complexity: constant 

### Maximum cost of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,U): 24 
Asymptotic class: constant 
* Total analysis performed in 522 ms.