It works for the original dataset pretty well. Here's what comes out:

> summary(model1 <- lmer(score ~ nstates_amp_and_freq_n:phase_order:phase ++                    (1 | id) , data=all, REML=F))fixed-effect model matrix is rank deficient so dropping 4 columns / coefficientsfixed-effect model matrix is rank deficient so dropping 4 columns / coefficientsfixed-effect model matrix is rank deficient so dropping 4 columns / coefficientsfixed-effect model matrix is rank deficient so dropping 4 columns / coefficientsLinear mixed model fit by maximum likelihood  t-tests use  Satterthwaite approximations to degrees of freedom ['merModLmerTest']Formula: score ~ nstates_amp_and_freq_n:phase_order:phase + (1 | id)   Data: all
AIC BIC logLik deviance df.resid  -12.3 5.3 14.1 -28.3 58
Scaled residuals:  Min 1Q Median 3Q Max -2.1345 -0.7098 -0.1321 0.7379 1.9288
Random effects: Groups Name Variance Std.Dev. id (Intercept) 0.01448 0.1203  Residual 0.02791 0.1671 Number of obs: 66, groups: id, 22
Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 6.402e-01 3.506e-02 2.606e+01 18.260 2.22e-16 ***nstates_amp_and_freq_n:phase_order0:phase0 7.747e-02 3.836e-02 5.587e+01 2.020 0.048236 * nstates_amp_and_freq_n:phase_order1:phase1 1.934e-01 8.274e-02 6.110e+01 2.338 0.022698 * nstates_amp_and_freq_n:phase_order2:phase1 5.329e-02 6.533e-02 6.363e+01 0.816 0.417712 nstates_amp_and_freq_n:phase_order1:phase2 8.565e-04 4.749e-02 6.113e+01 0.018 0.985668 nstates_amp_and_freq_n:phase_order2:phase2 2.412e-01 6.279e-02 5.894e+01 3.842 0.000301 ***---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects: (Intr) n____:_0 n____:_1:1 n____:_2:1 n____:_1:2ns____:_0:0 0.255 ns____:_1:1 -0.044 0.021 ns____:_2:1 -0.011 0.114 0.005 ns____:_1:2 -0.148 0.033 0.009 0.190 ns____:_2:2 -0.207 -0.112 0.161 -0.005 0.026 fit warnings:fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients

Here are the coefficients represented graphically:

Note how the two conditions behave in markedly different ways. The lower coefficients (which is the second condition) indicate the second condition allows better compression than the first condition. The first condition shows a gradual increase in the number of states (although the increase from 2 to 3 is not significant), whereas the second shows an immediate and significant decrease in the number of states, followed by a non-significant increase.

Finally, $$R^2 = 0.6159172$$.

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