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Let $G$ be a 4-chromatic maximal planar graph (MPG) with the minimum degreeof at least 4 and let $C$ be an even-length cycle of $G$.If $|f(C)|=2$ forevery $f$ in some Kempe equivalence class of $G$, then we call $C$ an unchangedbichromatic cycle (UBC) of $G$, and correspondingly $G$ an unchangedbichromatic cycle maximal planar graph (UBCMPG) with respect to $C$, where$f(C)=\{f(v)| v\in V(C)\}$. For an UBCMPG $G$ with respect to an UBC $C$, thesubgraph of $G$ induced by the set of edges belonging to $C$ and its interior(or exterior), denoted by $G^C$, is called a base-module of $G$; in particular,when the length of $C$ is equal to four, we use $C_4$ instead of $C$ and call$G^{C_4}$ a 4-base-module. In this paper, we first study the properties ofUBCMPGs and show that every 4-base-module $G^{C_4}$ contains a 4-coloring underwhich $C_4$ is bichromatic and there are at least two bichromatic paths withdifferent colors between one pair of diagonal vertices of $C_4$ (these pathsare called module-paths). We further prove that every 4-base-module $G^{C_4}$contains a 4-coloring (called decycle coloring) for which the ends of amodule-path are colored by distinct colors. Finally, based on the technique ofthe contracting and extending operations of MPGs, we prove that55-configurations and 56-configurations are reducible by converting thereducibility problem of these two classes of configurations into the decyclecoloring problem of 4-base-modules.

55- and 56-configurations are reducible