diff --git a/three-style-lib/src/commutator/finder.rs b/three-style-lib/src/commutator/finder.rs
index e273a08..bdb8d6f 100644
--- a/three-style-lib/src/commutator/finder.rs
+++ b/three-style-lib/src/commutator/finder.rs
@@ -6,6 +6,8 @@ use crate::{
 };
 use std::{fmt, ops::Not};
 
+/// Tracks the state of a moving facelet position,
+/// used for detecting interchange and insertions.
 #[derive(Debug, PartialEq, Clone)]
 struct Slot {
     initial_position: Facelet,
@@ -108,7 +110,7 @@ impl CommutatorFinder {
     fn find_interchange(&mut self, params: SearchParams) {
         let threshold = match self.search_type {
             SearchType::Corner => 4,
-            SearchType::Edge => 2,
+            SearchType::Edge => 2, // possible four movers
         };
 
         if self.max_depth - params.depth < threshold {
@@ -134,14 +136,15 @@ impl CommutatorFinder {
 
     fn check_interchange(&self, params: &SearchParams, state: &FaceletCube) -> Option<Insertion> {
         for slot in &params.slots {
-            let current = state[slot.current_position];
+            let next_value = state[slot.current_position];
 
-            if slot.value != current && params.inside_cycle(current) {
-                let source = params.get_remaining_slot(slot.value, current);
+            if slot.value != next_value && params.inside_cycle(next_value) {
+                let other = params.get_remaining_slot(slot.value, next_value);
+                let outside_interchage = state[other.current_position] == other.value;
 
-                if state[source.current_position] == source.value {
+                if outside_interchage {
                     return Some(Insertion {
-                        source,
+                        source: other,
                         target: slot.clone(),
                     });
                 }
diff --git a/three-style-lib/src/commutator/types.rs b/three-style-lib/src/commutator/types.rs
index 512bd55..d7fd918 100644
--- a/three-style-lib/src/commutator/types.rs
+++ b/three-style-lib/src/commutator/types.rs
@@ -5,6 +5,7 @@ use crate::{
 };
 use std::fmt;
 
+/// Represents a 3-cycle commutator.
 #[derive(Debug, Clone, PartialEq)]
 #[allow(clippy::len_without_is_empty)]
 pub struct Commutator {
@@ -15,14 +16,17 @@ pub struct Commutator {
 }
 
 impl Commutator {
+    /// Returns `true` if the commutator has no setup moves.
     pub fn is_pure(&self) -> bool {
         self.setup.is_none()
     }
 
+    /// Returns the length og the commutator in its notation form.
     pub fn len(&self) -> usize {
         self.setup.as_ref().map_or(0, |s| s.len()) + self.insertion.len() + 1
     }
 
+    /// Returns the non-reduced expanded algorithm.
     pub fn expand(&self) -> Alg {
         let interchange = Alg::new([self.interchange]);
         let (first, second) = if self.insertion_first {
@@ -59,6 +63,7 @@ impl fmt::Display for Commutator {
     }
 }
 
+/// Wrapper around 3-cycle targets (stickers).
 #[derive(Debug, Clone, Copy, PartialEq)]
 pub struct Cycle<T> {
     targets: [T; 3],
diff --git a/three-style-lib/src/facelet/moves.rs b/three-style-lib/src/facelet/moves.rs
index 06b2090..0fa2478 100644
--- a/three-style-lib/src/facelet/moves.rs
+++ b/three-style-lib/src/facelet/moves.rs
@@ -2,6 +2,9 @@ use super::{types::DEFAULT_STATE, Facelet, FaceletCube, FaceletState};
 use crate::moves::Move;
 use std::ops::Index;
 
+/// State of the cube at the facelet level
+/// in the "is carried to" representation.
+/// It is used to know where facelets will land on
 #[derive(Debug, PartialEq, Clone)]
 pub struct FaceletPermutation(FaceletState);
 
diff --git a/three-style-lib/src/facelet/state.rs b/three-style-lib/src/facelet/state.rs
index 224c202..e40d6a5 100644
--- a/three-style-lib/src/facelet/state.rs
+++ b/three-style-lib/src/facelet/state.rs
@@ -14,6 +14,9 @@ use std::{
     ops::{Index, IndexMut, Mul},
 };
 
+/// State of the cube at the facelet level
+/// in the "is replaced by" representation.
+/// See https://kociemba.org/cube.htm for more details
 #[derive(Debug, PartialEq, Eq, Clone, Hash)]
 pub struct FaceletCube(FaceletState);
 
@@ -421,7 +424,7 @@ mod tests {
         let cube = FaceletCube::default().cycle(cycle).unwrap();
 
         #[rustfmt::skip]
-        let expecte = FaceletCube([
+        let expected = FaceletCube([
             F::U0, F::U7, F::U2, F::U3, F::U4, F::U5, F::U6, F::F3, F::U8,
             F::R0, F::R1, F::R2, F::R3, F::R4, F::R5, F::R6, F::R7, F::R8,
             F::F0, F::L5, F::F2, F::U1, F::F4, F::F5, F::F6, F::F7, F::F8,
@@ -430,7 +433,7 @@ mod tests {
             F::B0, F::F1, F::B2, F::B3, F::B4, F::B5, F::B6, F::B7, F::B8,
         ]);
 
-        assert_eq!(expecte, cube);
+        assert_eq!(expected, cube);
 
         let cube = cube.cycle(cycle.inverse()).unwrap();
 
@@ -443,7 +446,7 @@ mod tests {
         let cube = FaceletCube::default().cycle(cycle).unwrap();
 
         #[rustfmt::skip]
-        let expecte = FaceletCube([
+        let expected = FaceletCube([
             F::U0, F::U1, F::U2, F::U3, F::U4, F::U5, F::U8, F::U7, F::R6,
             F::D2, F::R1, F::R2, F::R3, F::R4, F::R5, F::U6, F::R7, F::R8,
             F::R0, F::F1, F::F8, F::F3, F::F4, F::F5, F::F6, F::F7, F::L2,
@@ -452,7 +455,7 @@ mod tests {
             F::B0, F::B1, F::B2, F::B3, F::B4, F::B5, F::B6, F::B7, F::B8,
         ]);
 
-        assert_eq!(expecte, cube);
+        assert_eq!(expected, cube);
 
         let cube = cube.cycle(cycle.inverse()).unwrap();
 
diff --git a/three-style-lib/src/facelet/types.rs b/three-style-lib/src/facelet/types.rs
index a9c6b23..ddc9912 100644
--- a/three-style-lib/src/facelet/types.rs
+++ b/three-style-lib/src/facelet/types.rs
@@ -39,6 +39,7 @@ pub trait FaceletTarget {
     }
 }
 
+/// Represents all the facelets of a cube in the`URFDLB` order.
 pub type FaceletState = [Facelet; 54];
 
 #[rustfmt::skip]
@@ -51,15 +52,9 @@ pub const DEFAULT_STATE: FaceletState = [
     F::B0, F::B1, F::B2, F::B3, F::B4, F::B5, F::B6, F::B7, F::B8,
 ];
 
+#[rustfmt::skip]
 #[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
-pub enum Color {
-    U,
-    R,
-    F,
-    D,
-    L,
-    B,
-}
+pub enum Color { U, R, F, D, L, B }
 
 impl fmt::Display for Color {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
diff --git a/three-style-lib/src/moves/alg.rs b/three-style-lib/src/moves/alg.rs
index 012c671..4e1712f 100644
--- a/three-style-lib/src/moves/alg.rs
+++ b/three-style-lib/src/moves/alg.rs
@@ -15,23 +15,30 @@ impl Alg {
         Self(moves.into_iter().collect())
     }
 
+    /// Returns the number of moves of the algorithm.
     pub fn len(&self) -> usize {
         self.0.len()
     }
 
+    /// Returns `true` if the algorithm has no moves.
     pub fn is_empty(&self) -> bool {
-        self.len() == 0
+        self.0.is_empty()
     }
 
+    /// Returns an iterator over moves.
     pub fn iter(&self) -> impl Iterator<Item = &Move> {
         self.0.iter()
     }
 
+    /// Reduces the algorithm by applying cancellations rules.
+    /// Example: `U2 D U' R M'` -> `U D r`
     pub fn reduce(self) -> Self {
         let mut moves = Vec::new();
         let mut stack = Vec::new();
         let mut group: BTreeMap<MoveKind, Move> = BTreeMap::new();
 
+        // First pass, moves should constantly be re-evaluated
+        // as long as parallelism isn't broken
         for m in self.0 {
             let prev_value = group.remove(&m.kind);
             let has_prev_value = prev_value.is_some();
@@ -48,6 +55,7 @@ impl Alg {
                 continue;
             }
 
+            // parallelism has been broken so commit the current moves
             while let Some((_, m)) = group.pop_first() {
                 moves.push(m);
             }
@@ -57,16 +65,17 @@ impl Alg {
 
         moves.extend(group.into_values());
 
+        // Second pass, search wide moves generators and reductions
+        // by trying to reduce move pairs successively
         for m in moves {
-            if let Some(&last) = stack.last() {
-                if let Some(result) = last * m {
-                    stack.pop();
-                    stack.push(result);
-                    continue;
-                }
-            }
+            let result = stack.last().and_then(|&l| l * m);
 
-            stack.push(m);
+            if let Some(result) = result {
+                stack.pop();
+                stack.push(result);
+            } else {
+                stack.push(m);
+            }
         }
 
         Alg::new(stack)
diff --git a/three-style-lib/src/moves/core.rs b/three-style-lib/src/moves/core.rs
index dae83a5..4a77755 100644
--- a/three-style-lib/src/moves/core.rs
+++ b/three-style-lib/src/moves/core.rs
@@ -226,7 +226,7 @@ impl Mul<Move> for Move {
     type Output = Option<Move>;
 
     fn mul(self, rhs: Move) -> Self::Output {
-        self.reduce(rhs).or(rhs.reduce(self))
+        self.reduce(rhs).or(rhs.reduce(self)) // reduce is not commutative
     }
 }
 
diff --git a/three-style-lib/src/sticker/mod.rs b/three-style-lib/src/sticker/mod.rs
index f6d6726..cc128ce 100644
--- a/three-style-lib/src/sticker/mod.rs
+++ b/three-style-lib/src/sticker/mod.rs
@@ -7,6 +7,7 @@ use crate::{
 use constants::{CORNER_FACELET_MAP, EDGE_FACELET_MAP};
 use std::{fmt, str::FromStr};
 
+/// Layer based representation of corner stickers.
 #[rustfmt::skip]
 #[derive(Debug, PartialEq, Clone, Copy)]
 pub enum Corner {
@@ -66,6 +67,7 @@ impl fmt::Display for Corner {
     }
 }
 
+/// Layer based representation of edge stickers.
 #[rustfmt::skip]
 #[derive(Debug, PartialEq, Clone, Copy)]
 pub enum Edge {