Abs program loaded in 3 ms.

Rule based representation generated in 1 ms.

Rule based representation stored in /tmp/costabs/rbr.rbr

RBR properties stored in /tmp/costabs/rbr.properties

Class invariants generated and loaded in 1 ms.
Size abstraction not supported for native

Abstract compilation performed in 0 ms.
sabu_memo_table_1(case_0,[A,B],[1*B=1,1*A=1],0,0)
sabu_memo_table_1(flip,[A,B],[1*A=1,1*B=1],0,0)
sabu_memo_table_1(case_0,[A,B],[-1*A>= -2,-1*A+1*B>=0,1*A>=1],1,1)
sabu_memo_table_1(flip,[A,B],[-1*A>= -2,-1*A+1*B>=0,1*A>=1],2,1)
sabu_memo_table_1(case_0,[A,B],[-1*A>= -3,1*A>=1,-1*A+1*B>=0],3,2)
sabu_memo_table_1(flip,[A,B],[-1*A>= -3,1*A>=1,-1*A+1*B>=0],4,2)
sabu_memo_table_1(case_0,[A,B],[-1*A>= -4,1*A>=1,-1*A+1*B>=0],5,3)
sabu_memo_table_1(flip,[A,B],[-1*A>= -4,1*A>=1,-1*A+1*B>=0],6,3)
sabu_memo_table_1(case_0,[A,B],[-1*A+1*B>=0,1*A>=1],7,0)
sabu_memo_table_1(flip,[A,B],[-1*A+1*B>=0,1*A>=1],8,0)
sabu_memo_table_1(start,[A,B],[1*A>=1,-1*A+1*B>=0],0,0)
sabu_memo_table_1(start,[A,B],[],0,1)
:- dynamic sabu_memo_table_1/5.

sabu_memo_table_1(case_0, [A, B], [-1*A+1*B>=0, 1*A>=1], 7, 0).
sabu_memo_table_1(flip, [A, B], [-1*A+1*B>=0, 1*A>=1], 8, 0).
sabu_memo_table_1(start, [_, _], [], 0, 1).


Size analysis performed in 4 ms.

Cost relation system stored in /tmp/costabs/crs.crs

Generated 28 equations 

Cost relation system solved by PUBS in 8 ms.

Method start terminates?: YES

UB for start(w) = nat(w)


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

#### Computed strongly connected components 
0. recursive  : [case_0/1,flip/1]
1. non_recursive  : [start/1]
Warning: the following predicates are never called:[and_op/2,eq/2,geq/2,gt/2,leq/2,lt/2,maxNorm/2,neg/1,neq/2,or/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into flip/1
1. SCC is partially evaluated into start/1

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

### Specialization of cost equations flip/1 
* CE 5 is refined into CE [6] 
* CE 4 is refined into CE [7] 
* CE 3 is refined into CE [8] 


#### Refined cost equations flip/1 
* CE 6: flip(A) = 6+ flip(B)
     [A>=2,A=B+1] 
* CE 7: flip(A) = 5+ flip(B)
     [A>=2,A=B+1] 
* CE 8: flip(A) = 3
     [A=1] 

### Cost equations --> "Loop" of flip/1 
* CEs [8] --> Loop 6 
* CEs [7] --> Loop 7 
* CEs [6] --> Loop 8 

#### Loops of flip/1 
* Loop 6: flip(A) [A=1] 
* Loop 7: flip(A)->  flip(A')
                  [A>=2,A=A'+1] 
* Loop 8: flip(A)->  flip(A')
                  [A>=2,A=A'+1] 

### Ranking functions of CR flip(A) 
* RF of phase [7,8]: [A-1]

#### Partial ranking functions of CR flip(A) 
* Partial RF of phase [7,8]:
  - RF of loop [7:1,8:1]:
    A-1


### Resulting Chains:flip(A) 
* [[7,8],6]
* [6]


### Specialization of cost equations start/1 
* CE 2 is refined into CE [9,10] 
* CE 1 is refined into CE [11] 


#### Refined cost equations start/1 
* CE 9: start(A) = 1+ flip(A):[[7,8],6]
     [A>=2] 
* CE 10: start(A) = 1+ flip(B):[6]
     [B=1,A=1] 
* CE 11: start(A) = 1
     [] 

### Cost equations --> "Loop" of start/1 
* CEs [9] --> Loop 9 
* CEs [10] --> Loop 10 
* CEs [11] --> Loop 11 

#### Loops of start/1 
* Loop 9: start(A) [A>=2] 
* Loop 10: start(A) [A=1] 
* Loop 11: start(A) [] 

### Ranking functions of CR start(A) 

#### Partial ranking functions of CR start(A) 


### Resulting Chains:start(A) 
* [11]
* [10]
* [9]


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

#### Cost of loops [7,8] 

 * loop 7:flip(A) -> [flip(A')] 
5
 * loop 8:flip(A) -> [flip(A')] 
6
#### Cost of phase [7,8]:flip(A) -> [flip(A')] 
5*it(7)+6*it(8)+0
  Such that:it(7)+it(8) =< A-1
it(7)+it(8) =< A-A'
it(7)+it(8) >= A-A'

#### Cost of chains of flip(A):
* Chain [[7,8],6]: 5*it(7)+6*it(8)+3
  Such that:it(7)+it(8) =< A-1
it(7)+it(8) >= A-1

  with precondition: [A>=2] 

* Chain [6]: 3
  with precondition: [A=1] 


#### Cost of chains of start(A):
* Chain [11]: 1
  with precondition: [] 

* Chain [10]: 4
  with precondition: [A=1] 

* Chain [9]: 5*s(1)+6*s(2)+4
  Such that:s(1)+s(2) =< A-1
s(1)+s(2) >= A-1

  with precondition: [A>=2] 


Closed-form bounds of start(A): 
-------------------------------------
* Chain [11] with precondition: [] 
    - Lower bound: 1 
    - Complexity: constant
 * Chain [10] with precondition: [A=1] 
    - Lower bound: 4 
    - Complexity: constant
 * Chain [9] with precondition: [A>=2] 
    - Lower bound: 5*A-1 
    - Complexity: n
 
### Partitioned lower bound of start(A): 
* 1 
 if []
Possible lower bounds : [1]
Maximum lower bound complexity: constant
* Total analysis performed in 20 ms.