diff --git a/src/rsprocess/structure.rs b/src/rsprocess/structure.rs
index 18d3902..81a6d0d 100644
--- a/src/rsprocess/structure.rs
+++ b/src/rsprocess/structure.rs
@@ -41,7 +41,7 @@ impl From<Vec<IdType>> for RSset {
 }
 
 impl RSset {
-    pub fn new() -> Self {
+    pub const fn new() -> Self {
         RSset {
             identifiers: BTreeSet::new(),
         }
diff --git a/src/rsprocess/transitions.rs b/src/rsprocess/transitions.rs
index a2569e4..2c1c09e 100644
--- a/src/rsprocess/transitions.rs
+++ b/src/rsprocess/transitions.rs
@@ -1,11 +1,11 @@
 //! Definitions for simple simulation steps.
 
 use super::structure::{RSchoices,
-		       RSenvironment,
-		       RSlabel,
-		       RSprocess,
-		       RSset,
-		       RSsystem};
+			   RSenvironment,
+			   RSlabel,
+			   RSprocess,
+			   RSset,
+			   RSsystem};
 use super::support_structures::TransitionsIterator;
 use std::rc::Rc;
 
@@ -14,149 +14,216 @@ use std::rc::Rc;
 /// of entities and the continuation.
 /// see unfold
 pub fn unfold(
-    environment: &RSenvironment,
-    context_process: &RSprocess,
-    current_entities: &RSset,
+	environment: &RSenvironment,
+	context_process: &RSprocess,
+	current_entities: &RSset,
 ) -> Result<RSchoices, String> {
-    match context_process {
-        RSprocess::Nill => {
-	    Ok(RSchoices::new())
+	match context_process {
+		RSprocess::Nill => {
+		Ok(RSchoices::new())
 	},
-        RSprocess::RecursiveIdentifier { identifier } => {
-            let newprocess = environment.get(*identifier);
-            if let Some(newprocess) = newprocess {
-                unfold(environment, newprocess, current_entities)
-            } else {
-                Err(format!("Missing symbol in context: {identifier}"))
-            }
-        }
-        RSprocess::EntitySet { entities, next_process, } => {
-	    Ok(RSchoices::from([(
+		RSprocess::RecursiveIdentifier { identifier } => {
+			let newprocess = environment.get(*identifier);
+			if let Some(newprocess) = newprocess {
+				unfold(environment, newprocess, current_entities)
+			} else {
+				Err(format!("Missing symbol in context: {identifier}"))
+			}
+		}
+		RSprocess::EntitySet { entities, next_process, } => {
+		Ok(RSchoices::from([(
 		Rc::new(entities.clone()),
 		Rc::clone(next_process),
-            )]))
+			)]))
 	},
 	RSprocess::Guarded { reaction, next_process } => {
-	    if reaction.enabled(current_entities) {
+		if reaction.enabled(current_entities) {
 		Ok(RSchoices::from([(Rc::new(reaction.products.clone()),
-				     Rc::clone(next_process))]))
-	    } else {
+					 Rc::clone(next_process))]))
+		} else {
 		Ok(RSchoices::new())
-	    }
+		}
 	}
-        RSprocess::WaitEntity { repeat, repeated_process: _, next_process, }
+		RSprocess::WaitEntity { repeat, repeated_process: _, next_process, }
 	if *repeat <= 0 => {
-	    unfold(environment, next_process, current_entities)
+		unfold(environment, next_process, current_entities)
 	},
-        RSprocess::WaitEntity { repeat, repeated_process, next_process, }
+		RSprocess::WaitEntity { repeat, repeated_process, next_process, }
 	if *repeat == 1 => {
-            let mut choices1 = unfold(environment, repeated_process, current_entities)?;
-            choices1.replace(Rc::clone(next_process));
-            Ok(choices1)
-        }
-        RSprocess::WaitEntity { repeat, repeated_process, next_process, } => {
-            let mut choices1 = unfold(environment, repeated_process, current_entities)?;
-            choices1.replace(Rc::new(RSprocess::WaitEntity {
-                repeat: (*repeat - 1),
-                repeated_process: Rc::clone(repeated_process),
-                next_process: Rc::clone(next_process),
-            }));
-            Ok(choices1)
-        }
-        RSprocess::Summation { children } => {
-            // short-circuits with try_fold.
-            children.iter().try_fold(RSchoices::new(), |mut acc, x| {
-                match unfold(environment, x, current_entities) {
-                    Ok(mut choices) => {
-                        acc.append(&mut choices);
-                        Ok(acc)
-                    }
-                    Err(e) => Err(e),
-                }
-            })
-        }
-        RSprocess::NondeterministicChoice { children } => {
-            // short-circuits with try_fold.
-            if children.is_empty() {
-                Ok(RSchoices::from(vec![(
-                    Rc::new(RSset::new()),
-                    Rc::new(RSprocess::Nill),
-                )]))
-            } else {
-                children.iter().try_fold(RSchoices::new(), |mut acc, x| {
-                    acc.shuffle(unfold(environment, x, current_entities)?);
-                    Ok(acc)
-                })
-            }
-        }
-    }
+			let mut choices1 = unfold(environment, repeated_process, current_entities)?;
+			choices1.replace(Rc::clone(next_process));
+			Ok(choices1)
+		}
+		RSprocess::WaitEntity { repeat, repeated_process, next_process, } => {
+			let mut choices1 = unfold(environment, repeated_process, current_entities)?;
+			choices1.replace(Rc::new(RSprocess::WaitEntity {
+				repeat: (*repeat - 1),
+				repeated_process: Rc::clone(repeated_process),
+				next_process: Rc::clone(next_process),
+			}));
+			Ok(choices1)
+		}
+		RSprocess::Summation { children } => {
+			// short-circuits with try_fold.
+			children.iter().try_fold(RSchoices::new(), |mut acc, x| {
+				match unfold(environment, x, current_entities) {
+					Ok(mut choices) => {
+						acc.append(&mut choices);
+						Ok(acc)
+					}
+					Err(e) => Err(e),
+				}
+			})
+		}
+		RSprocess::NondeterministicChoice { children } => {
+			// short-circuits with try_fold.
+			if children.is_empty() {
+				Ok(RSchoices::from(vec![(
+					Rc::new(RSset::new()),
+					Rc::new(RSprocess::Nill),
+				)]))
+			} else {
+				children.iter().try_fold(RSchoices::new(), |mut acc, x| {
+					acc.shuffle(unfold(environment, x, current_entities)?);
+					Ok(acc)
+				})
+			}
+		}
+	}
 }
 
 pub fn iterator_transitions<'a>(
-    system: &'a RSsystem
+	system: &'a RSsystem
 ) -> Result<TransitionsIterator<'a>, String> {
-    TransitionsIterator::from(system)
+	TransitionsIterator::from(system)
 }
 
 /// see oneTransition, transition, smartTransition, smartOneTransition
 pub fn one_transition(
-    system: &RSsystem
+	system: &RSsystem
 ) -> Result<Option<(RSlabel, RSsystem)>, String> {
-    let mut tr = TransitionsIterator::from(system)?;
-    Ok(tr.next())
+	let mut tr = TransitionsIterator::from(system)?;
+	Ok(tr.next())
 }
 
 /// see allTransitions, smartAllTransitions
 pub fn all_transitions(
-    system: &RSsystem
+	system: &RSsystem
 ) -> Result<Vec<(RSlabel, RSsystem)>, String> {
-    let tr = TransitionsIterator::from(system)?;
-    Ok(tr.collect::<Vec<_>>())
+	let tr = TransitionsIterator::from(system)?;
+	Ok(tr.collect::<Vec<_>>())
 }
 
 /// see oneTarget, smartOneTarget, target, smartTarget
 pub fn target(
-    system: &RSsystem
+	system: &RSsystem
 ) -> Result<(i64, RSset), String> {
-    let current = one_transition(system)?;
-    if current.is_none() {
-        return Ok((0, system.available_entities.clone()));
-    }
-    let mut n = 1;
-    let mut current = current.unwrap().1;
-    while let Some((_, next)) = one_transition(&current)? {
-        current = next;
-        n += 1;
-    }
-    Ok((n, current.available_entities.clone()))
+	let current = one_transition(system)?;
+	if current.is_none() {
+		return Ok((0, system.available_entities.clone()));
+	}
+	let mut n = 1;
+	let mut current = current.unwrap().1;
+	while let Some((_, next)) = one_transition(&current)? {
+		current = next;
+		n += 1;
+	}
+	Ok((n, current.available_entities.clone()))
 }
 
 /// see oneRun, run, smartOneRunEK, smartRunEK
 pub fn run(system: RSsystem) -> Result<Vec<Rc<RSsystem>>, String> {
-    let mut res = vec![Rc::new(system)];
-    while let Some((_, next_sys)) = one_transition(res.last().unwrap())? {
-        res.push(Rc::new(next_sys));
-    }
-    Ok(res)
+	let mut res = vec![Rc::new(system)];
+	while let Some((_, next_sys)) = one_transition(res.last().unwrap())? {
+		res.push(Rc::new(next_sys));
+	}
+	Ok(res)
 }
 
 /// see smartOneRunECT, smartRunECT
 pub fn run_separated(
-    system: &RSsystem
+	system: &RSsystem
 ) -> Result<Vec<(RSset, RSset, RSset)>, String> {
-    let mut res = vec![];
-    let current = one_transition(system)?;
-    if current.is_none() {
-        return Ok(res);
-    }
-    let current = current.unwrap();
-    let (available_entities, context, t) = current.0.get_context();
-    res.push((available_entities.clone(), context.clone(), t.clone()));
-    let mut current = current.1;
-    while let Some((label, next)) = one_transition(&current)? {
-        current = next;
+	let mut res = vec![];
+	let current = one_transition(system)?;
+	if current.is_none() {
+		return Ok(res);
+	}
+	let current = current.unwrap();
+	let (available_entities, context, t) = current.0.get_context();
+	res.push((available_entities.clone(), context.clone(), t.clone()));
+	let mut current = current.1;
+	while let Some((label, next)) = one_transition(&current)? {
+		current = next;
 	let (available_entities, context, t) = label.get_context();
-        res.push((available_entities.clone(), context.clone(), t.clone()));
-    }
-    Ok(res)
+		res.push((available_entities.clone(), context.clone(), t.clone()));
+	}
+	Ok(res)
+}
+
+
+
+fn nth_transition(
+	system: &RSsystem,
+	n: usize,
+) -> Result<Option<(RSlabel, RSsystem)>, String> {
+	let mut tr = TransitionsIterator::from(system)?;
+	Ok(tr.nth(n))
+}
+
+type Trace = Vec<(Option<Rc<RSlabel>>, Rc<RSsystem>)>;
+
+pub fn traces(
+	system: RSsystem,
+	n: usize,
+) -> Result<Vec<Trace>, String> {
+	if n == 0 {
+		return Ok(vec![])
+	}
+
+	let mut n = n;
+	let mut res : Vec<Trace> = vec![];
+	let mut current_trace: Trace = vec![(None, Rc::new(system))];
+	let mut branch = vec![0];
+	let mut depth = 0;
+	let mut new_branch = true;
+
+	loop {
+		let next_sys = nth_transition(&current_trace[depth].1,
+									  branch[depth])?;
+
+		if let Some((current_label, next_sys)) = next_sys {
+			depth += 1;
+			if depth >= branch.len() {
+				branch.push(0);
+				current_trace.push((Some(Rc::new(current_label)),
+									Rc::new(next_sys)));
+			} else {
+				branch[depth] = 0;
+				current_trace[depth] = (Some(Rc::new(current_label)),
+										Rc::new(next_sys));
+			}
+			new_branch = true;
+		} else {
+			// at the bottom of a trace, we save to res, then backtrack until
+			// we find another possible path.
+			if new_branch {
+				res.push(current_trace[0..depth].to_vec());
+				new_branch = false;
+				n -= 1;
+			}
+			if n == 0 {
+				break;
+			}
+
+			if depth == 0 {
+				break;
+			}
+
+			depth -= 1;
+			branch[depth] += 1;
+		}
+	}
+
+	Ok(res)
 }