/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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me>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U81</name></sharp><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>U91</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>U121</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U141</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U151</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U161</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U171</name></sharp><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>z</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U181</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U191</name></sharp><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U91</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U121</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U141</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U151</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>union</name></sharp><arg><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>union</name></sharp><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>union</name></sharp><arg><funapp><name>union</name><arg><funapp><name>empty</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>union</name></sharp><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><extensions><rules><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><funapp><name>empty</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>X</var></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></extensions><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U172</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>prod</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U171</name></sharp><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U171</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>U172</name></sharp><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U172</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>prod</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acMonoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U171</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U172</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>prod</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U171</name></sharp><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>empty</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U101</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U102</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U102</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U112</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U112</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U131</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U132</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U132</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U142</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U142</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U152</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U152</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U161</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U171</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>U172</name><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U172</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>prod</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>prod</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U181</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U191</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>U192</name><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U192</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>sum</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>sum</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U52</name><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U91</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funa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p></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U22</name><arg><funapp><name>isBag</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U52</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U81</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U62</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U171</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>U172</name></sharp><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U172</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>prod</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U172</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>prod</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></acDepGraphProc></acDPTerminationProof></acMonoRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>U172</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>prod</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>prod</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U102</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U102</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U112</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U112</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>3</degree></polynomial></type><interpret><sharp><name>mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U91</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U112</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U111</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U111</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U102</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U101</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U101</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U132</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U112</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U142</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U152</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U151</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U102</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>isBag</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U22</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U131</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U132</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U62</name><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U112</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U142</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U22</name><arg><funapp><name>isBag</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U152</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U52</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U132</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U102</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U112</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U81</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U142</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U101</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U102</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U91</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U81</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U52</name><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U152</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U62</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U112</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U112</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U102</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U102</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>3</degree></polynomial></type><interpret><sharp><name>mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U91</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U101</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U102</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U101</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U132</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U102</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U142</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U111</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U112</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U152</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U151</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U22</name><arg><funapp><name>isBag</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U81</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBin</name><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U132</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isBag</name><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U101</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U102</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U142</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U142</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U112</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U91</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U152</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U131</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U132</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U112</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U22</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U62</name><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U62</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U52</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U52</name><arg><funapp><name>isBin</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U102</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U81</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U152</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U102</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U102</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U91</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U101</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U132</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U151</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U152</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U142</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U111</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U112</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U102</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U131</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U132</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U152</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U142</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U91</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U152</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U132</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U142</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U112</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U112</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U102</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U101</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U102</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U101</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U102</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U111</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U91</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U112</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U142</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U151</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U152</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U132</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U102</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U101</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U102</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U112</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U112</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U142</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U142</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U152</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U152</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U131</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U132</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U132</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U91</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><var>x</var></arg><arg><funapp><name>mult</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acRedPairProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component></acDepGraphProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component></acDepGraphProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>U101</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U102</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U111</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U112</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U112</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U192</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>A</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U191</name></sharp><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U191</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>U192</name></sharp><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U192</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acMonoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U192</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>sum</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U191</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>U192</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U191</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>U192</name></sharp><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U191</name></sharp><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U192</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>sum</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>empty</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U101</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U102</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U102</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U112</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U112</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U131</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U132</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U132</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U142</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U142</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U152</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U152</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U161</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U171</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>U172</name><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U172</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>prod</name><arg><var>A</var></arg></funapp></arg><arg><funa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><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U141</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U151</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U152</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>U152</name></sharp><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>plus</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U151</name></sharp><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U131</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U141</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U142</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U132</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U121</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U151</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U132</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U152</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U142</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>U152</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U152</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U141</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U141</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U132</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U152</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U142</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U131</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U132</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U152</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U142</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U132</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U132</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U141</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U142</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U142</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>plus</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U151</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U152</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U132</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U142</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U152</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U131</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U132</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U152</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U132</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U142</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U142</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>plus</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U142</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U152</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U132</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U151</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U142</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U152</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U131</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U132</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U152</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U132</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U142</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>plus</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U141</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U142</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U121</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U132</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U151</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U152</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U131</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U142</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U132</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U152</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U131</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U132</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U152</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U142</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z'</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>x</var></arg><arg><funapp><name>plus</name><arg><var>y</var></arg><arg><var>z'</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acRedPairProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>U151</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U151</name></sharp><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U151</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>U152</name></sharp><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></acDepGraphProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>U131</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U132</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U141</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U151</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>Y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U152</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U171</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U191</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>B</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>prod</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>sum</name></sharp><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>A</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acMonoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U81</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBag</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>isBin</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U51</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U61</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U62</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>z</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U52</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prod</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U71</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>union</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>singl</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sum</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U51</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>isBin</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U61</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>U21</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>isBag</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>0</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>singl</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>prod</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>1</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>sum</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>isBag</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBin</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBin</name></sharp><arg><funapp><name>mult</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>isBin</name><arg><var>V1</var></arg></funapp></arg><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isBag</name></sharp><arg><funapp><name>union</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isBag</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>empty</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></lhs><rhs><funapp><name>z</name></funapp></rhs></rule><rule><lhs><funapp><name>U101</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U102</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U102</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U111</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U112</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U112</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>0</name><arg><funapp><name>mult</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U121</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U131</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U132</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U132</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U141</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U142</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U142</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U151</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>U152</name><arg><funapp><name>isBin</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U152</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>plus</name><arg><funapp><name>plus</name><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U161</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U171</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>U172</name><arg><funapp><name>isBag</name><arg><var>B</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U172</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>prod</name><arg><var>A</var></arg></funapp></arg><arg><funapp><name>prod</name><arg><var>B</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U181</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule><rule><lhs><funapp><name>U191</name><arg><funapp><name>tt</name></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></lhs><rhs><funapp><name>U192</name><arg><funapp><name>isBag</name>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var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>prod</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>1</name><arg><funapp><name>z</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prod</name><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U161</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>prod</name><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U171</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>sum</name><arg><funapp><name>empty</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name><arg><funapp><name>z</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sum</name><arg><funapp><name>singl</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U181</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>sum</name><arg><funapp><name>union</name><arg><var>A</var></arg><arg><var>B</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U191</name><arg><funapp><name>isBag</name><arg><var>A</var></arg></funapp></arg><arg><var>A</var></arg><arg><var>B</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U91</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U101</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><funapp><name>mult</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>mult</name><arg><funapp><name>U111</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>z</name></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U121</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>0</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U131</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>0</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U141</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><funapp><name>plus</name><arg><funapp><name>1</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>1</name><arg><var>Y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>U151</name><arg><funapp><name>isBin</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg><arg><var>Y</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>union</name><arg><funapp><name>union</name><arg><var>X</var></arg><arg><funapp><name>empty</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>union</name><arg><var>X</var></arg><arg><va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Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished
</version><strategy>Statistics for single proof: 100.00 % (24 real / 0 unknown / 0 assumptions / 24 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem>