diff --git a/razor-chase/Cargo.toml b/razor-chase/Cargo.toml
index cb2ee24..fbcff72 100644
--- a/razor-chase/Cargo.toml
+++ b/razor-chase/Cargo.toml
@@ -22,10 +22,10 @@ serde_derive = "1.0.93"
 either = "1.6.1"
 thiserror = "^1.0"
 razor-fol = { path = "../razor-fol", version = "0.1.0" }
-codd = { path = "../../codd/core", version = "^0.1" }
+codd = "^0.1"
 
 [dev-dependencies]
-codd = { path = "../../codd/core", features = ["unstable"], version = "^0.1" }
+codd = { version = "^0.1", features = ["unstable"] }
 
 [lib]
 name = "razor_chase"
diff --git a/razor-chase/src/chase/impl/relational/equation_rewrite.rs b/razor-chase/src/chase/impl/relational/equation_rewrite.rs
new file mode 100644
index 0000000..c59eb32
--- /dev/null
+++ b/razor-chase/src/chase/impl/relational/equation_rewrite.rs
@@ -0,0 +1,186 @@
+use std::{collections::HashMap, hash::Hash};
+
+pub(super) struct Rewrite<T>
+where
+    T: PartialEq + Eq + Clone + Hash,
+{
+    rules: HashMap<T, T>,
+}
+
+impl<T> Rewrite<T>
+where
+    T: PartialEq + Eq + Clone + Hash,
+{
+    pub fn new() -> Self {
+        Self {
+            rules: HashMap::new(),
+        }
+    }
+
+    pub fn add(&mut self, left: &T, right: &T) {
+        if self.equals(left, right) == Some(true) {
+            return;
+        }
+
+        let left = self
+            .rules
+            .entry(left.clone())
+            .or_insert(right.clone())
+            .clone();
+        let right = self
+            .rules
+            .entry(right.clone())
+            .or_insert(right.clone())
+            .clone();
+
+        self.rules.iter_mut().for_each(|(_, v)| {
+            if *v == left {
+                *v = right.clone()
+            }
+        });
+    }
+
+    pub fn equals(&self, left: &T, right: &T) -> Option<bool> {
+        let left = self.rules.get(left)?;
+        let right = self.rules.get(right)?;
+
+        Some(left == right)
+    }
+
+    pub fn canonical(&self, item: &T) -> Option<&T> {
+        self.rules.get(item)
+    }
+
+    pub fn canonicals(&self) -> Vec<&T> {
+        use itertools::Itertools;
+        self.rules.values().unique().collect()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_basic() {
+        let mut rewrite = Rewrite::new();
+        rewrite.add(&1, &11);
+        rewrite.add(&2, &22);
+
+        assert_eq!(Some(true), rewrite.equals(&1, &11));
+        assert_eq!(Some(false), rewrite.equals(&2, &11));
+        assert_eq!(None, rewrite.equals(&2, &3));
+
+        assert_eq!(Some(&11), rewrite.canonical(&1));
+        assert_eq!(Some(&22), rewrite.canonical(&22));
+        assert_eq!(None, rewrite.canonical(&3));
+    }
+
+    #[test]
+    fn test_merge_classes() {
+        {
+            let mut rewrite = Rewrite::new();
+            rewrite.add(&1, &11);
+            rewrite.add(&1, &111);
+
+            assert_eq!(Some(true), rewrite.equals(&1, &11));
+            assert_eq!(Some(true), rewrite.equals(&1, &111));
+            assert_eq!(Some(true), rewrite.equals(&11, &111));
+
+            assert_eq!(Some(&111), rewrite.canonical(&1));
+            assert_eq!(Some(&111), rewrite.canonical(&11));
+            assert_eq!(Some(&111), rewrite.canonical(&111));
+        }
+        {
+            let mut rewrite = Rewrite::new();
+            rewrite.add(&1, &11);
+            rewrite.add(&11, &111);
+
+            assert_eq!(Some(true), rewrite.equals(&1, &11));
+            assert_eq!(Some(true), rewrite.equals(&1, &111));
+            assert_eq!(Some(true), rewrite.equals(&11, &111));
+
+            assert_eq!(Some(&111), rewrite.canonical(&1));
+            assert_eq!(Some(&111), rewrite.canonical(&11));
+            assert_eq!(Some(&111), rewrite.canonical(&111));
+        }
+        {
+            let mut rewrite = Rewrite::new();
+            rewrite.add(&1, &11);
+            rewrite.add(&2, &22);
+            rewrite.add(&11, &111);
+
+            assert_eq!(Some(false), rewrite.equals(&1, &22));
+            assert_eq!(Some(false), rewrite.equals(&11, &22));
+            assert_eq!(Some(false), rewrite.equals(&11, &22));
+        }
+    }
+
+    #[test]
+    fn test_merge_multiple_classes() {
+        {
+            let mut rewrite = Rewrite::new();
+            rewrite.add(&1, &11);
+            rewrite.add(&2, &22);
+            rewrite.add(&1, &2);
+
+            assert_eq!(Some(true), rewrite.equals(&1, &11));
+            assert_eq!(Some(true), rewrite.equals(&1, &22));
+            assert_eq!(Some(true), rewrite.equals(&2, &11));
+            assert_eq!(Some(true), rewrite.equals(&2, &22));
+            assert_eq!(Some(true), rewrite.equals(&1, &2));
+            assert_eq!(Some(true), rewrite.equals(&11, &22));
+        }
+        {
+            let mut rewrite = Rewrite::new();
+            rewrite.add(&1, &11);
+            rewrite.add(&2, &22);
+            rewrite.add(&1, &22);
+
+            assert_eq!(Some(true), rewrite.equals(&1, &11));
+            assert_eq!(Some(true), rewrite.equals(&1, &22));
+            assert_eq!(Some(true), rewrite.equals(&2, &11));
+            assert_eq!(Some(true), rewrite.equals(&2, &22));
+            assert_eq!(Some(true), rewrite.equals(&1, &2));
+            assert_eq!(Some(true), rewrite.equals(&11, &22));
+        }
+        {
+            let mut rewrite = Rewrite::new();
+            rewrite.add(&1, &11);
+            rewrite.add(&2, &22);
+            rewrite.add(&2, &1);
+
+            assert_eq!(Some(true), rewrite.equals(&1, &11));
+            assert_eq!(Some(true), rewrite.equals(&1, &22));
+            assert_eq!(Some(true), rewrite.equals(&2, &11));
+            assert_eq!(Some(true), rewrite.equals(&2, &22));
+            assert_eq!(Some(true), rewrite.equals(&1, &2));
+            assert_eq!(Some(true), rewrite.equals(&11, &22));
+        }
+        {
+            let mut rewrite = Rewrite::new();
+            rewrite.add(&1, &11);
+            rewrite.add(&2, &22);
+            rewrite.add(&2, &11);
+
+            assert_eq!(Some(true), rewrite.equals(&1, &11));
+            assert_eq!(Some(true), rewrite.equals(&1, &22));
+            assert_eq!(Some(true), rewrite.equals(&2, &11));
+            assert_eq!(Some(true), rewrite.equals(&2, &22));
+            assert_eq!(Some(true), rewrite.equals(&1, &2));
+            assert_eq!(Some(true), rewrite.equals(&11, &22));
+        }
+        {
+            let mut rewrite = Rewrite::new();
+            rewrite.add(&1, &11);
+            rewrite.add(&2, &22);
+            rewrite.add(&11, &111);
+            rewrite.add(&2, &222);
+            rewrite.add(&1, &2);
+
+            assert_eq!(Some(true), rewrite.equals(&1, &2));
+            assert_eq!(Some(true), rewrite.equals(&11, &22));
+            assert_eq!(Some(true), rewrite.equals(&111, &222));
+        }
+    }
+}
diff --git a/razor/src/main.rs b/razor/src/main.rs
index d4fb378..9f07c98 100644
--- a/razor/src/main.rs
+++ b/razor/src/main.rs
@@ -208,7 +208,7 @@ fn process_solve(
     println!();
     println!();
 
-    let pre_processor = PreProcessor::new(true);
+    let pre_processor = PreProcessor::new(false);
     let (sequents, init_model) = pre_processor.pre_process(&theory);
 
     let evaluator = Evaluator;
@@ -239,10 +239,10 @@ fn process_solve(
                 &mut scheduler,
                 &evaluator,
                 bounder.as_ref(),
-                |m| print_model(m, color, &mut complete_count),
+                |m| print_model(m.finalize(), color, &mut complete_count),
                 |m| {
                     if show_incomplete {
-                        print_model(m, color, &mut incomplete_count);
+                        print_model(m.finalize(), color, &mut incomplete_count);
                     }
                 },
             )