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tokens: time like Fig. 2 , we can conclude that the bending in period B must exist from the observational data about the periatron time T N in both periods A and C. It is possible to judge whether KL-oscillation had happened or not by using our analysis without the observational data in highly eccentric state. One may be worried about the spin evolution of the pulsar because the spin–orbit coupling appears in GR (Barker, O’Connell 1975 ), which may change the direction of the pulsar rotation axis. If the beaming direction of pulse signal is changed, the pulsar will disappear in stage B. However, following Liu Lai ( 2017 ), we find that the adiabaticity, which measures the ratio of the KL oscillation time-scale to the presession time-scale, is very small in the present system. It means that the spin of the inner binary evolves ‘non-adiabatically’ even when the KL-oscillation occurs. As a result, the spin will be parallelly transported just as Newtonian case, and then the beaming direction will not change so much even in the KL-oscillation stage and the whole period (A, B, and C) will be observed. Finally we shall discuss the possible parameter range that the bending of the cumulative-shift curve occurs within our lifetime. In addition to the model given in Table 1 , we have performed our calculation for 19 200 models by changing the outer semimajor axis () and the mass of the third body (10M ⊙ ≦ m 3 ≦90M ⊙ ) and analysed in which parameter ranges the above bending will occur within 100 yr. In order that such phenomenon occurs within 100 yr, the KL time-scale should be less than 100 yr. So we investigate how many years are required for the deviation of Δ P from Δ P 1 to become large enough. For 19 200 models with different m 3 and a out , we calculate Δ P and judge the deviation simply by the relative difference between Δ P and Δ P 1 , i.e. (Δ P − Δ P 1 )/Δ P 1 > 1. We define T d as the time when this criterion is satisfied. Fig. 3 shows the colour contour map of T d . The black region in the bottom-right corner of Fig. 3 corresponds to T d > 100 yr. The white dotted line shows the critical curve used by the Newtonian formula T KL = 100 yr given by equation ( 3 ). It is also found that the dependence of T d on a out and m 3 is consistent with the Newtonian formula T KL . This is because the semimajor axis in the present model is large and 1PN effect is quite small. The top-left white region in a out 15 au and m 3 > 30M ⊙ shows that the system becomes unstable if the initial parameters are in the region. The yellow solid line is the empirical criterion for the instability given by Blaes et al. ( 2002 ): From Fig. 3 , we find that if this binary has the third companion with m 3 = 10–100M ⊙ and , we may be able to see the bending of the cumulative-shift curve within 100 yr through the observation of radio pulse. Figure 3. The parameter range of third body with which the bending of cumulative-shift curve occurs within 100 yr. The horizontal and