We investigate the relaxation dynamics in the melt of entangled binary mixtures comprising a small fraction of short polybutadiene, polyisoprene and polystyrene chains in a high molecular weight (MW) matrix. In this way, we create model environments of quasi-permanent entanglements for probe chains, where tube motions are suppressed at the time scale of the probe chains reptation, while contour length fluctuations remain unaffected. The relaxation of a probe in its matrix presents several important features, which are independent of polymer species. Because of the absence of tube motions, the probe chains terminal peak is narrower, with a G''(omega) similar to omega(-1/2) high-frequency slope, in agreement with the prediction of pure reptation theory. Moreover, the position of the G'' peak, omega(max) (rad/s), shifts to lower frequencies, which means that the longest relaxation time of the probe chains is increased, as compared to a melt of pure probe chains. Unambiguous and quantitative comparisons between the terminal times of probe chains in a matrix or self-melt environments are obtained with the help of an iso-free-volume correction. In this way, we clarify for the first time contributions from tube motions to the terminal relaxation. The retardation factor for the terminal relaxation time is independent of the number of entanglements Z above 100 but increases steadily below that threshold as Z(-0.3). The Z dependence of the retardation factor leads to different scalings for the terminal relaxation time of probe chains in self-melt or matrix environments. The observed scaling exponent of 3.1 in the matrix is very close to the prediction of the original reptation model. Our results hence indicate that the motions of surrounding chains have a dominant influence on the 3.4 exponent for terminal relaxation times and zero shear viscosity. This is in sharp contrast with the conventional view attributing the nonreptation scalings entirely to fluctuations but is in agreement with existing literature on tracer (probe) chains and self-diffusion.