Reduction of Cycle Unification of Type Cpg+r

In this paper a class of cycle unification problems called type Cpg+r is studied, and an intuitive representation method, called the position supergraph, is presented to analyze or reduce the cycle problem. A typical case of Cpg+r problems is considered and an algorithm is given, which transforms the original problem of Cpg+r that is of the exponential complexity into a new one that is of the linear complexity when using SLD resolution method. These results are of importance for practice and theory.