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


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


WORST_CASE(?,O(1))  

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

#### Computed strongly connected components 
0. recursive  : [f9/46]
1. non_recursive  : [exit_location/1]
2. recursive  : [f5/35]
3. non_recursive  : [f0/28]
4. non_recursive  : [f12/28]
5. non_recursive  : [f5_loop_cont/29]
6. non_recursive  : [f9_loop_cont/29]
7. non_recursive  : [f6/28]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f9/46
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into f5/35
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into f5_loop_cont/29
6. SCC is partially evaluated into f9_loop_cont/29
7. SCC is partially evaluated into f6/28

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

### Specialization of cost equations f9/46 
* CE 3 is refined into CE [26] 
* CE 7 is refined into CE [27] 
* CE 5 is refined into CE [28] 
* CE 9 is refined into CE [29] 
* CE 4 is refined into CE [30] 
* CE 8 is refined into CE [31] 
* CE 6 is refined into CE [32] 
* CE 10 is refined into CE [33] 
* CE 11 is refined into CE [34] 
* CE 2 is refined into CE [35] 


### Cost equations --> "Loop" of f9/46 
* CEs [35] --> Loop 26 
* CEs [26] --> Loop 27 
* CEs [27] --> Loop 28 
* CEs [28] --> Loop 29 
* CEs [29] --> Loop 30 
* CEs [30] --> Loop 31 
* CEs [31] --> Loop 32 
* CEs [32] --> Loop 33 
* CEs [33] --> Loop 34 
* CEs [34] --> Loop 35 

### Ranking functions of CR f9(A,B,C,D,E,F,G,H,I,J,K,L,P,Q,R,S,T,U,W,X,Y,Z,A1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2) 
* RF of phase [26]: [-B+17,-C+16]

#### Partial ranking functions of CR f9(A,B,C,D,E,F,G,H,I,J,K,L,P,Q,R,S,T,U,W,X,Y,Z,A1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2) 
* Partial RF of phase [26]:
  - RF of loop [26:1]:
    -B+17
    -C+16


### Specialization of cost equations f5/35 
* CE 22 is refined into CE [36] 
* CE 14 is refined into CE [37] 
* CE 15 is refined into CE [38] 
* CE 20 is refined into CE [39] 
* CE 21 is refined into CE [40] 
* CE 16 is refined into CE [41] 
* CE 18 is refined into CE [42] 
* CE 17 is refined into CE [43] 
* CE 19 is refined into CE [44] 


### Cost equations --> "Loop" of f5/35 
* CEs [41] --> Loop 36 
* CEs [42] --> Loop 37 
* CEs [43] --> Loop 38 
* CEs [44] --> Loop 39 
* CEs [36] --> Loop 40 
* CEs [37] --> Loop 41 
* CEs [38] --> Loop 42 
* CEs [39] --> Loop 43 
* CEs [40] --> Loop 44 

### Ranking functions of CR f5(G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2) 
* RF of phase [36,37,38,39]: [G+1]

#### Partial ranking functions of CR f5(G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2) 
* Partial RF of phase [36,37,38,39]:
  - RF of loop [36:1,37:1,38:1,39:1]:
    G+1


### Specialization of cost equations f5_loop_cont/29 
* CE 25 is refined into CE [45] 
* CE 24 is refined into CE [46] 
* CE 23 is refined into CE [47] 


### Cost equations --> "Loop" of f5_loop_cont/29 
* CEs [45] --> Loop 45 
* CEs [46] --> Loop 46 
* CEs [47] --> Loop 47 

### Ranking functions of CR f5_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1) 

#### Partial ranking functions of CR f5_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1) 


### Specialization of cost equations f9_loop_cont/29 
* CE 13 is refined into CE [48,49,50,51,52,53,54,55,56,57] 
* CE 12 is refined into CE [58] 


### Cost equations --> "Loop" of f9_loop_cont/29 
* CEs [56] --> Loop 48 
* CEs [55] --> Loop 49 
* CEs [50,51,52,53] --> Loop 50 
* CEs [54] --> Loop 51 
* CEs [49] --> Loop 52 
* CEs [48] --> Loop 53 
* CEs [57] --> Loop 54 
* CEs [58] --> Loop 55 

### Ranking functions of CR f9_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1) 

#### Partial ranking functions of CR f9_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1) 


### Specialization of cost equations f6/28 
* CE 1 is refined into CE [59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100] 


### Cost equations --> "Loop" of f6/28 
* CEs [59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100] --> Loop 56 

### Ranking functions of CR f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,J1) 

#### Partial ranking functions of CR f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,J1) 


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

#### Cost of chains of f9(A,B,C,D,E,F,G,H,I,J,K,L,P,Q,R,S,T,U,W,X,Y,Z,A1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2):
* Chain [[26],35]: 1*it(26)+0
  Such that:it(26) =< -B+17

  with precondition: [A=17,J1=4,C+1=B,D=E,D=F,15>=C,C>=0] 

* Chain [[26],34]: 1*it(26)+0
  Such that:it(26) =< -B+17

  with precondition: [A=17,J1=5,K1=17,L1=16,P1=13,R1=1,S1=0,Z1=1,A2=13,D2=14,C+1=B,D=E,D=F,M1=N1,M1=O1,Q1=W1,M1=B2,M1=C2,15>=C,0>=M1+1,0>=Q1+1,0>=X1+1,C>=0,E2>=F2] 

* Chain [[26],33]: 1*it(26)+0
  Such that:it(26) =< -B+17

  with precondition: [A=17,J1=5,K1=17,L1=16,P1=13,R1=1,S1=0,Z1=1,A2=13,D2=14,C+1=B,D=E,D=F,M1=N1,M1=O1,Q1=W1,M1=B2,M1=C2,15>=C,0>=M1+1,0>=Q1+1,C>=0,X1>=1,E2>=F2] 

* Chain [[26],32]: 1*it(26)+0
  Such that:it(26) =< -B+17

  with precondition: [A=17,J1=5,K1=17,L1=16,P1=13,R1=1,S1=0,Z1=1,A2=13,D2=14,C+1=B,D=E,D=F,M1=N1,M1=O1,Q1=W1,M1=B2,M1=C2,15>=C,0>=M1+1,0>=X1+1,C>=0,Q1>=1,E2>=F2] 

* Chain [[26],31]: 1*it(26)+0
  Such that:it(26) =< -B+17

  with precondition: [A=17,J1=5,K1=17,L1=16,P1=13,R1=1,S1=0,Z1=1,A2=13,D2=14,C+1=B,D=E,D=F,M1=N1,M1=O1,Q1=W1,M1=B2,M1=C2,15>=C,0>=M1+1,C>=0,Q1>=1,X1>=1,E2>=F2] 

* Chain [[26],30]: 1*it(26)+0
  Such that:it(26) =< -B+17

  with precondition: [A=17,J1=5,K1=17,L1=16,P1=13,R1=1,S1=0,Z1=1,A2=13,D2=14,C+1=B,D=E,D=F,M1=N1,M1=O1,Q1=W1,M1=B2,M1=C2,15>=C,0>=Q1+1,0>=X1+1,C>=0,M1>=1,E2>=F2] 

* Chain [[26],29]: 1*it(26)+0
  Such that:it(26) =< -B+17

  with precondition: [A=17,J1=5,K1=17,L1=16,P1=13,R1=1,S1=0,Z1=1,A2=13,D2=14,C+1=B,D=E,D=F,M1=N1,M1=O1,Q1=W1,M1=B2,M1=C2,15>=C,0>=Q1+1,C>=0,M1>=1,X1>=1,E2>=F2] 

* Chain [[26],28]: 1*it(26)+0
  Such that:it(26) =< -B+17

  with precondition: [A=17,J1=5,K1=17,L1=16,P1=13,R1=1,S1=0,Z1=1,A2=13,D2=14,C+1=B,D=E,D=F,M1=N1,M1=O1,Q1=W1,M1=B2,M1=C2,15>=C,0>=X1+1,C>=0,M1>=1,Q1>=1,E2>=F2] 

* Chain [[26],27]: 1*it(26)+0
  Such that:it(26) =< -B+17

  with precondition: [A=17,J1=5,K1=17,L1=16,P1=13,R1=1,S1=0,Z1=1,A2=13,D2=14,C+1=B,D=E,D=F,M1=N1,M1=O1,Q1=W1,M1=B2,M1=C2,15>=C,C>=0,M1>=1,Q1>=1,X1>=1,E2>=F2] 

* Chain [35]: 0
  with precondition: [A=17,J1=4,B=C+1,D=E,D=F,B>=1] 


#### Cost of chains of f5(G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2):
* Chain [[36,37,38,39],44]: 4*it(36)+0
  Such that:aux(2) =< -I+X1
aux(1) =< -I+X1+Y1+1
it(36) =< aux(1)
it(36) =< aux(2)

  with precondition: [J=0,J1=3,N1=0,T1=0,M=Q1,O=S1,U1=V1,K1=Y1,G+I=K1+M1,G+I=K1+X1,G+I=K1+Z1,0>=L1+1,I>=0,K1>=0,G>=K1+1,M>=R1] 

* Chain [[36,37,38,39],43]: 4*it(36)+0
  Such that:aux(2) =< -I+X1
aux(1) =< -I+X1+Y1+1
it(36) =< aux(1)
it(36) =< aux(2)

  with precondition: [J=0,J1=3,N1=0,T1=0,M=Q1,O=S1,U1=V1,K1=Y1,G+I=K1+M1,G+I=K1+X1,G+I=K1+Z1,I>=0,K1>=0,L1>=1,G>=K1+1,M>=R1] 

* Chain [[36,37,38,39],42]: 4*it(36)+0
  Such that:aux(1) =< G+1
aux(2) =< G-K1
it(36) =< aux(1)
it(36) =< aux(2)

  with precondition: [J=0,J1=2,N1=U1,K1=Y1,W=A2,G+I=K1+M1,G+I=K1+X1,G+I=K1+Z1+1,0>=N1+1,I>=0,K1>=0,G>=K1+1,R1>=Q1+1] 

* Chain [[36,37,38,39],41]: 4*it(36)+0
  Such that:aux(1) =< G+1
aux(2) =< G-Y1
it(36) =< aux(1)
it(36) =< aux(2)

  with precondition: [J=0,J1=2,N1=U1,K1=Y1,W=A2,G+I=K1+M1,G+I=K1+X1,G+I=K1+Z1+1,I>=0,K1>=0,N1>=1,G>=K1+1,R1>=Q1+1] 

* Chain [[36,37,38,39],40]: 4*it(36)+0
  Such that:aux(3) =< G+1
it(36) =< aux(3)

  with precondition: [J=0,J1=4,G>=0,I>=0] 

* Chain [44]: 0
  with precondition: [J=0,P=0,J1=3,N1=0,T1=0,S1=O,W1=S,X1=T,Y1=U,G=K1,H=L1,I=M1,M=Q1,R=U1,R=V1,I=Z1,0>=H+1,G>=0,I>=0,M>=R1] 

* Chain [43]: 0
  with precondition: [J=0,P=0,J1=3,N1=0,T1=0,S1=O,W1=S,X1=T,Y1=U,G=K1,H=L1,I=M1,M=Q1,R=U1,R=V1,I=Z1,G>=0,H>=1,I>=0,M>=R1] 

* Chain [42]: 0
  with precondition: [J1=2,T1=P,U1=Q,V1=R,W1=S,X1=T,Y1=U,Z1=V,A2=W,G=K1,I=M1,H=N1,0>=H+1,G>=0,I>=1,R1>=Q1+1] 

* Chain [41]: 0
  with precondition: [J1=2,T1=P,U1=Q,V1=R,W1=S,X1=T,Y1=U,Z1=V,A2=W,G=K1,I=M1,H=N1,G>=0,H>=1,I>=1,R1>=Q1+1] 

* Chain [40]: 0
  with precondition: [J1=4] 


#### Cost of chains of f5_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1):
* Chain [47]: 0
  with precondition: [A=2,B=17] 

* Chain [46]: 0
  with precondition: [A=3,B=17] 

* Chain [45]: 0
  with precondition: [A=4,B=17] 


#### Cost of chains of f9_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1):
* Chain [55]: 0
  with precondition: [A=4,B=17] 

* Chain [54]: 0
  with precondition: [A=5,B=17] 

* Chain [53]: 0
  with precondition: [A=5,B=17,K=0,Q=0,0>=I+1,H>=0,J>=0] 

* Chain [52]: 0
  with precondition: [A=5,B=17,K=0,Q=0,H>=0,I>=1,J>=0] 

* Chain [51]: 4*s(2)+0
  Such that:s(1) =< H+1
s(2) =< s(1)

  with precondition: [A=5,B=17,K=0,H>=0,J>=0] 

* Chain [50]: 16*s(5)+0
  Such that:aux(4) =< H
aux(5) =< H+1
s(5) =< aux(5)
s(5) =< aux(4)

  with precondition: [A=5,B=17,K=0,H>=1,J>=0] 

* Chain [49]: 0
  with precondition: [A=5,B=17,0>=I+1,H>=0,J>=1] 

* Chain [48]: 0
  with precondition: [A=5,B=17,H>=0,I>=1,J>=1] 


#### Cost of chains of f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,J1):
* Chain [56]: 2896
  with precondition: [] 


Closed-form bounds of f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,J1): 
-------------------------------------
* Chain [56] with precondition: [] 
    - Upper bound: 2896 
    - Complexity: constant 

### Maximum cost of f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,J1): 2896 
Asymptotic class: constant 
* Total analysis performed in 3398 ms.