Deterministic Rabin-Automaton according to improved Muller/Schupp:

13 states:
k 0: 
     [1|0]-

k 1: 1
     [1|0,1]-

k 2: 10
     [1|0,2]-

k 3: 100
     [1|0,4]-

k 4: 101
     [1|0,1,3]-
      +-> [2|3]+
      +-> [3|0,1]-

k 5: 1010
     [1|0,2,4]-
      +-> [2|4]0
      +-> [3|0,2]-

k 6: 10100
     [1|0,4]-
      +-> [2|4]0
      +-> [3|0]-

k 7: 10101
     [1|0,1,3]-
      +-> [2|1]0
      +-> [3|0,3]-
           +-> [4|3]+
           +-> [5|0]-

k 8: 101001
     [1|0,1]-
      +-> [2|1]0
      +-> [3|0]-

k 9: 101010
     [1|0,2,4]-
      +-> [2|2]0
      +-> [3|0,4]-
           +-> [4|4]0
           +-> [5|0]-

k10: 1010010
     [1|0,2]-
      +-> [2|2]0
      +-> [3|0]-

k11: 1010101
     [1|0,1,3]-
      +-> [2|3]+
      +-> [3|0,1]-
           +-> [4|1]0
           +-> [5|0]-

k12: 10101010
     [1|0,2,4]-
      +-> [2|4]0
      +-> [3|0,2]-
           +-> [4|2]0
           +-> [5|0]-

Transition table:
       0    1    
k 0  k 0  k 1  
k 1  k 2  k 1  
k 2  k 3  k 4  
k 3  k 3  k 1  
k 4  k 5  k 1  
k 5  k 6  k 7  
k 6  k 6  k 8  
k 7  k 9  k 1  
k 8  k10  k 1  
k 9  k 6  k11  
k10  k 6  k 4  
k11  k12  k 1  
k12  k 6  k 7  

Acceptance pairs:
Pair for vertex 2 (sizes: 4, 2):
({k0,k1,k2,k3},
 {k4,k11})

Pair for vertex 4 (sizes: 9, 1):
({k0,k1,k2,k3,k4,k5,k6,k8,k10},
 {k7})

Overall: 2 pair(s) with non-empty accepting set