An important feature of a melt of long polymers is that the bonds of the chains cannot cross each other. This seemingly simple fact has a great impact on the long time dynamics and rheology of the material. In this paper an algorithm is described that explicitly detects and prevents bond crossings in mesoscopic simulations of polymers. The central idea is to view the bonds as slippery elastic bands which can become entangled. The method is applied to a simulation of a coarse-grained melt of C120H242, in which each chain is represented by six blobs. The long time dynamics and zero-shear rate rheology are investigated and the relative importance of uncrossability and chain stiffness is established. As a result of the uncrossability of the chains, we observe a subdiffusive exponent in the mean square displacement of the chains, a stretching of the exponential decay of the Rouse mode relaxations, an increase of relaxation times associated with large scales, and a slowing down of the relaxation of the dynamic structure factor. These results are in agreement with results from previous microscopic molecular dynamics simulations. Finally, an increased viscosity as compared to the Rouse model is observed, which is attributed to slowly decaying interchain stress components.