fix: Ignore no_predicates in brillig functions (#5012)

# Description

## Problem\*

Resolves #5010

## Summary\*

Ignores no predicates for brillig functions to avoid trying to convert
to brillig flattened functions.

## Additional Context



## Documentation\*

Check one:
- [x] No documentation needed.
- [ ] Documentation included in this PR.
- [ ] **[For Experimental Features]** Documentation to be submitted in a
separate PR.

# PR Checklist\*

- [x] I have tested the changes locally.
- [x] I have formatted the changes with [Prettier](https://prettier.io/)
and/or `cargo fmt` on default settings.

compiler/noirc_evaluator/src/ssa/opt/inlining.rs

@@ -11,7 +11,7 @@ use crate::ssa::{
     ir::{
         basic_block::BasicBlockId,
         dfg::{CallStack, InsertInstructionResult},
-        function::{Function, FunctionId},
+        function::{Function, FunctionId, RuntimeType},
         instruction::{Instruction, InstructionId, TerminatorInstruction},
         value::{Value, ValueId},
     },
@@ -392,10 +392,11 @@ impl<'function> PerFunctionContext<'function> {
                     Some(func_id) => {
                         let function = &ssa.functions[&func_id];
                         // If we have not already finished the flattening pass, functions marked
-                        // to not have predicates should be marked as entry points.
+                        // to not have predicates should be marked as entry points unless we are inlining into brillig.
                         let no_predicates_is_entry_point =
                             self.context.no_predicates_is_entry_point
-                                && function.is_no_predicates();
+                                && function.is_no_predicates()
+                                && !matches!(self.source_function.runtime(), RuntimeType::Brillig);
                         if function.runtime().is_entry_point() || no_predicates_is_entry_point {
                             self.push_instruction(*id);
                         } else {

test_programs/execution_success/no_predicates_brillig/Nargo.toml

@@ -0,0 +1,7 @@
+[package]
+name = "no_predicates_brillig"
+type = "bin"
+authors = [""]
+compiler_version = ">=0.27.0"
+
+[dependencies]

test_programs/execution_success/no_predicates_brillig/Prover.toml

@@ -0,0 +1,2 @@
+x = "10"
+y = "20"

test_programs/execution_success/no_predicates_brillig/src/main.nr

@@ -0,0 +1,12 @@
+unconstrained fn main(x: u32, y: pub u32) {
+    basic_checks(x, y);
+}
+
+#[no_predicates]
+fn basic_checks(x: u32, y: u32) {
+    if x > y {
+        assert(x == 10);
+    } else {
+        assert(y == 20);
+    }
+}