feat: Rebrand Polkadot/Substrate references to PezkuwiChain

This commit systematically rebrands various references from Parity Technologies'
Polkadot/Substrate ecosystem to PezkuwiChain within the kurdistan-sdk.

Key changes include:
- Updated external repository URLs (zombienet-sdk, parity-db, parity-scale-codec, wasm-instrument) to point to pezkuwichain forks.
- Modified internal documentation and code comments to reflect PezkuwiChain naming and structure.
- Replaced direct references to  with  or specific paths within the  for XCM, Pezkuwi, and other modules.
- Cleaned up deprecated  issue and PR references in various  and  files, particularly in  and  modules.
- Adjusted image and logo URLs in documentation to point to PezkuwiChain assets.
- Removed or rephrased comments related to external Polkadot/Substrate PRs and issues.

This is a significant step towards fully customizing the SDK for the PezkuwiChain ecosystem.

bizinikiwi/primitives/npos-elections/fuzzer/.gitignore

@@ -0,0 +1,2 @@
+hfuzz_target
+hfuzz_workspace

bizinikiwi/primitives/npos-elections/fuzzer/Cargo.toml

@@ -0,0 +1,49 @@
+[package]
+name = "pezsp-npos-elections-fuzzer"
+version = "2.0.0-alpha.5"
+authors.workspace = true
+edition.workspace = true
+license = "Apache-2.0"
+homepage.workspace = true
+repository.workspace = true
+description = "Fuzzer for phragmén implementation."
+documentation = "https://docs.rs/pezsp-npos-elections-fuzzer"
+publish = false
+
+[lints]
+workspace = true
+
+[package.metadata.docs.rs]
+targets = ["x86_64-unknown-linux-gnu"]
+
+[[bin]]
+name = "reduce"
+path = "src/reduce.rs"
+
+[[bin]]
+name = "phragmen_balancing"
+path = "src/phragmen_balancing.rs"
+
+[[bin]]
+name = "phragmms_balancing"
+path = "src/phragmms_balancing.rs"
+
+[[bin]]
+name = "phragmen_pjr"
+path = "src/phragmen_pjr.rs"
+
+[dependencies]
+clap = { features = ["derive"], workspace = true }
+honggfuzz = { workspace = true }
+rand = { features = [
+	"small_rng",
+	"std",
+], workspace = true, default-features = true }
+pezsp-npos-elections = { workspace = true, default-features = true }
+pezsp-runtime = { workspace = true, default-features = true }
+
+[features]
+runtime-benchmarks = [
+	"pezsp-npos-elections/runtime-benchmarks",
+	"pezsp-runtime/runtime-benchmarks",
+]

bizinikiwi/primitives/npos-elections/fuzzer/src/common.rs

@@ -0,0 +1,170 @@
+// This file is part of Bizinikiwi.
+
+// Copyright (C) Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! Common fuzzing utils.
+
+// Each function will be used based on which fuzzer binary is being used.
+#![allow(dead_code)]
+
+use rand::{self, seq::SliceRandom, Rng, RngCore};
+use pezsp_npos_elections::{phragmms, seq_phragmen, BalancingConfig, ElectionResult, VoteWeight};
+use pezsp_runtime::Perbill;
+use std::collections::{BTreeMap, HashSet};
+
+/// converts x into the range [a, b] in a pseudo-fair way.
+pub fn to_range(x: usize, a: usize, b: usize) -> usize {
+	// does not work correctly if b < 2 * a
+	assert!(b >= 2 * a);
+	let collapsed = x % b;
+	if collapsed >= a {
+		collapsed
+	} else {
+		collapsed + a
+	}
+}
+
+pub enum ElectionType {
+	Phragmen(Option<BalancingConfig>),
+	Phragmms(Option<BalancingConfig>),
+}
+
+pub type AccountId = u64;
+
+/// Generate a set of inputs suitable for fuzzing an election algorithm
+///
+/// Given parameters governing how many candidates and voters should exist, generates a voting
+/// scenario suitable for fuzz-testing an election algorithm.
+///
+/// The returned candidate list is sorted. This sorting property should not affect the result of the
+/// calculation.
+///
+/// The returned voters list is sorted. This enables binary searching for a particular voter by
+/// account id. This sorting property should not affect the results of the calculation.
+///
+/// Each voter's selection of candidates to vote for is sorted.
+///
+/// Note that this does not generate balancing parameters.
+pub fn generate_random_npos_inputs(
+	candidate_count: usize,
+	voter_count: usize,
+	mut rng: impl Rng,
+) -> (usize, Vec<AccountId>, Vec<(AccountId, VoteWeight, Vec<AccountId>)>) {
+	// cache for fast generation of unique candidate and voter ids
+	let mut used_ids = HashSet::with_capacity(candidate_count + voter_count);
+
+	// always generate a sensible desired number of candidates: elections are uninteresting if we
+	// desire 0 candidates, or a number of candidates >= the actual number of candidates present
+	let rounds = rng.gen_range(1..candidate_count);
+
+	// candidates are easy: just a completely random set of IDs
+	let mut candidates: Vec<AccountId> = Vec::with_capacity(candidate_count);
+	for _ in 0..candidate_count {
+		let mut id = rng.gen();
+		// insert returns `false` when the value was already present
+		while !used_ids.insert(id) {
+			id = rng.gen();
+		}
+		candidates.push(id);
+	}
+	candidates.sort();
+	candidates.dedup();
+	assert_eq!(candidates.len(), candidate_count);
+
+	let mut voters = Vec::with_capacity(voter_count);
+	for _ in 0..voter_count {
+		let mut id = rng.gen();
+		// insert returns `false` when the value was already present
+		while !used_ids.insert(id) {
+			id = rng.gen();
+		}
+
+		let vote_weight = rng.gen();
+
+		// it's not interesting if a voter chooses 0 or all candidates, so rule those cases out.
+		let n_candidates_chosen = rng.gen_range(1..candidates.len());
+
+		let mut chosen_candidates = Vec::with_capacity(n_candidates_chosen);
+		chosen_candidates.extend(candidates.choose_multiple(&mut rng, n_candidates_chosen));
+		chosen_candidates.sort();
+		voters.push((id, vote_weight, chosen_candidates));
+	}
+
+	voters.sort();
+	voters.dedup_by_key(|(id, _weight, _chosen_candidates)| *id);
+	assert_eq!(voters.len(), voter_count);
+
+	(rounds, candidates, voters)
+}
+
+pub fn generate_random_npos_result(
+	voter_count: u64,
+	target_count: u64,
+	to_elect: usize,
+	mut rng: impl RngCore,
+	election_type: ElectionType,
+) -> (
+	ElectionResult<AccountId, Perbill>,
+	Vec<AccountId>,
+	Vec<(AccountId, VoteWeight, Vec<AccountId>)>,
+	BTreeMap<AccountId, VoteWeight>,
+) {
+	let prefix = 100_000;
+	// Note, it is important that stakes are always bigger than ed.
+	let base_stake: u64 = 1_000_000_000_000;
+	let ed: u64 = base_stake;
+
+	let mut candidates = Vec::with_capacity(target_count as usize);
+	let mut stake_of: BTreeMap<AccountId, VoteWeight> = BTreeMap::new();
+
+	(1..=target_count).for_each(|acc| {
+		candidates.push(acc);
+		let stake_var = rng.gen_range(ed..100 * ed);
+		stake_of.insert(acc, base_stake + stake_var);
+	});
+
+	let mut voters = Vec::with_capacity(voter_count as usize);
+	(prefix..=(prefix + voter_count)).for_each(|acc| {
+		let edge_per_this_voter = rng.gen_range(1..candidates.len());
+		// all possible targets
+		let mut all_targets = candidates.clone();
+		// we remove and pop into `targets` `edge_per_this_voter` times.
+		let targets = (0..edge_per_this_voter)
+			.map(|_| {
+				let upper = all_targets.len() - 1;
+				let idx = rng.gen_range(0..upper);
+				all_targets.remove(idx)
+			})
+			.collect::<Vec<AccountId>>();
+
+		let stake_var = rng.gen_range(ed..100 * ed);
+		let stake = base_stake + stake_var;
+		stake_of.insert(acc, stake);
+		voters.push((acc, stake, targets));
+	});
+
+	(
+		match election_type {
+			ElectionType::Phragmen(conf) =>
+				seq_phragmen(to_elect, candidates.clone(), voters.clone(), conf).unwrap(),
+			ElectionType::Phragmms(conf) =>
+				phragmms(to_elect, candidates.clone(), voters.clone(), conf).unwrap(),
+		},
+		candidates,
+		voters,
+		stake_of,
+	)
+}

bizinikiwi/primitives/npos-elections/fuzzer/src/phragmen_balancing.rs

@@ -0,0 +1,96 @@
+// This file is part of Bizinikiwi.
+
+// Copyright (C) Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! Fuzzing for sequential phragmen with potential balancing.
+
+mod common;
+
+use common::*;
+use honggfuzz::fuzz;
+use rand::{self, SeedableRng};
+use pezsp_npos_elections::{
+	assignment_ratio_to_staked_normalized, seq_phragmen, to_supports, BalancingConfig,
+	ElectionResult, EvaluateSupport, VoteWeight,
+};
+
+fn main() {
+	loop {
+		fuzz!(|data: (usize, usize, usize, usize, u64)| {
+			let (mut target_count, mut voter_count, mut iterations, mut to_elect, seed) = data;
+			let rng = rand::rngs::SmallRng::seed_from_u64(seed);
+			target_count = to_range(target_count, 100, 200);
+			voter_count = to_range(voter_count, 100, 200);
+			iterations = to_range(iterations, 0, 30);
+			to_elect = to_range(to_elect, 25, target_count);
+
+			println!(
+				"++ [voter_count: {} / target_count:{} / to_elect:{} / iterations:{}]",
+				voter_count, target_count, to_elect, iterations,
+			);
+			let (unbalanced, candidates, voters, stake_of_tree) = generate_random_npos_result(
+				voter_count as u64,
+				target_count as u64,
+				to_elect,
+				rng,
+				ElectionType::Phragmen(None),
+			);
+
+			let stake_of = |who: &AccountId| -> VoteWeight { *stake_of_tree.get(who).unwrap() };
+
+			let unbalanced_score = {
+				let staked =
+					assignment_ratio_to_staked_normalized(unbalanced.assignments, &stake_of)
+						.unwrap();
+				let score = to_supports(staked.as_ref()).evaluate();
+
+				if score.minimal_stake == 0 {
+					// such cases cannot be improved by balancing.
+					return;
+				}
+				score
+			};
+
+			if iterations > 0 {
+				let config = BalancingConfig { iterations, tolerance: 0 };
+				let balanced: ElectionResult<AccountId, pezsp_runtime::Perbill> =
+					seq_phragmen(to_elect, candidates, voters, Some(config)).unwrap();
+
+				let balanced_score = {
+					let staked =
+						assignment_ratio_to_staked_normalized(balanced.assignments, &stake_of)
+							.unwrap();
+					to_supports(staked.as_ref()).evaluate()
+				};
+
+				let enhance = balanced_score.strict_better(unbalanced_score);
+
+				println!(
+					"iter = {} // {:?} -> {:?} [{}]",
+					iterations, unbalanced_score, balanced_score, enhance,
+				);
+
+				// The only guarantee of balancing is such that the first and third element of the
+				// score cannot decrease.
+				assert!(
+					balanced_score.minimal_stake >= unbalanced_score.minimal_stake &&
+						balanced_score.sum_stake == unbalanced_score.sum_stake &&
+						balanced_score.sum_stake_squared <= unbalanced_score.sum_stake_squared
+				);
+			}
+		});
+	}
+}

bizinikiwi/primitives/npos-elections/fuzzer/src/phragmen_pjr.rs

@@ -0,0 +1,118 @@
+// This file is part of Bizinikiwi.
+
+// Copyright (C) Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! Fuzzing which ensures that running unbalanced sequential phragmen always produces a result
+//! which satisfies our PJR checker.
+//!
+//! ## Running a single iteration
+//!
+//! Honggfuzz shuts down each individual loop iteration after a configurable time limit.
+//! It can be helpful to run a single iteration on your hardware to help benchmark how long that
+//! time limit should reasonably be. Simply run the program without the `fuzzing` configuration to
+//! run a single iteration: `cargo run --bin phragmen_pjr`.
+//!
+//! ## Running
+//!
+//! Run with `HFUZZ_RUN_ARGS="-t 10" cargo hfuzz run phragmen_pjr`.
+//!
+//! Note the environment variable: by default, `cargo hfuzz` shuts down each iteration after 1
+//! second of runtime. We significantly increase that to ensure that the fuzzing gets a chance to
+//! complete. Running a single iteration can help determine an appropriate value for this parameter.
+//!
+//! ## Debugging a panic
+//!
+//! Once a panic is found, it can be debugged with
+//! `HFUZZ_RUN_ARGS="-t 10" cargo hfuzz run-debug phragmen_pjr hfuzz_workspace/phragmen_pjr/*.fuzz`.
+
+#[cfg(fuzzing)]
+use honggfuzz::fuzz;
+
+#[cfg(not(fuzzing))]
+use clap::Parser;
+
+mod common;
+use common::{generate_random_npos_inputs, to_range};
+use rand::{self, SeedableRng};
+use pezsp_npos_elections::{pjr_check_core, seq_phragmen_core, setup_inputs, standard_threshold};
+
+type AccountId = u64;
+
+const MIN_CANDIDATES: usize = 250;
+const MAX_CANDIDATES: usize = 1000;
+const MIN_VOTERS: usize = 500;
+const MAX_VOTERS: usize = 2500;
+
+#[cfg(fuzzing)]
+fn main() {
+	loop {
+		fuzz!(|data: (usize, usize, u64)| {
+			let (candidate_count, voter_count, seed) = data;
+			iteration(candidate_count, voter_count, seed);
+		});
+	}
+}
+
+#[cfg(not(fuzzing))]
+#[derive(Debug, Parser)]
+#[command(author, version, about)]
+struct Opt {
+	/// How many candidates participate in this election
+	#[arg(short, long)]
+	candidates: Option<usize>,
+
+	/// How many voters participate in this election
+	#[arg(short, long)]
+	voters: Option<usize>,
+
+	/// Random seed to use in this election
+	#[arg(long)]
+	seed: Option<u64>,
+}
+
+#[cfg(not(fuzzing))]
+fn main() {
+	let opt = Opt::parse();
+	// candidates and voters by default use the maxima, which turn out to be one less than
+	// the constant.
+	iteration(
+		opt.candidates.unwrap_or(MAX_CANDIDATES - 1),
+		opt.voters.unwrap_or(MAX_VOTERS - 1),
+		opt.seed.unwrap_or_default(),
+	);
+}
+
+fn iteration(mut candidate_count: usize, mut voter_count: usize, seed: u64) {
+	let rng = rand::rngs::SmallRng::seed_from_u64(seed);
+	candidate_count = to_range(candidate_count, MIN_CANDIDATES, MAX_CANDIDATES);
+	voter_count = to_range(voter_count, MIN_VOTERS, MAX_VOTERS);
+
+	let (rounds, candidates, voters) =
+		generate_random_npos_inputs(candidate_count, voter_count, rng);
+
+	let (candidates, voters) = setup_inputs(candidates, voters);
+
+	// Run seq-phragmen
+	let (candidates, voters) = seq_phragmen_core::<AccountId>(rounds, candidates, voters)
+		.expect("seq_phragmen must succeed");
+
+	let threshold = standard_threshold(rounds, voters.iter().map(|voter| voter.budget()));
+
+	assert!(
+		pjr_check_core(&candidates, &voters, threshold).is_ok(),
+		"unbalanced sequential phragmen must satisfy PJR",
+	);
+}

bizinikiwi/primitives/npos-elections/fuzzer/src/phragmms_balancing.rs

@@ -0,0 +1,94 @@
+// This file is part of Bizinikiwi.
+
+// Copyright (C) Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! Fuzzing for phragmms.
+
+mod common;
+
+use common::*;
+use honggfuzz::fuzz;
+use rand::{self, SeedableRng};
+use pezsp_npos_elections::{
+	assignment_ratio_to_staked_normalized, phragmms, to_supports, BalancingConfig, ElectionResult,
+	EvaluateSupport, VoteWeight,
+};
+use pezsp_runtime::Perbill;
+
+fn main() {
+	loop {
+		fuzz!(|data: (usize, usize, usize, usize, u64)| {
+			let (mut target_count, mut voter_count, mut iterations, mut to_elect, seed) = data;
+			let rng = rand::rngs::SmallRng::seed_from_u64(seed);
+			target_count = to_range(target_count, 100, 200);
+			voter_count = to_range(voter_count, 100, 200);
+			iterations = to_range(iterations, 5, 30);
+			to_elect = to_range(to_elect, 25, target_count);
+
+			println!(
+				"++ [voter_count: {} / target_count:{} / to_elect:{} / iterations:{}]",
+				voter_count, target_count, to_elect, iterations,
+			);
+			let (unbalanced, candidates, voters, stake_of_tree) = generate_random_npos_result(
+				voter_count as u64,
+				target_count as u64,
+				to_elect,
+				rng,
+				ElectionType::Phragmms(None),
+			);
+
+			let stake_of = |who: &AccountId| -> VoteWeight { *stake_of_tree.get(who).unwrap() };
+
+			let unbalanced_score = {
+				let staked =
+					assignment_ratio_to_staked_normalized(unbalanced.assignments, &stake_of)
+						.unwrap();
+				let score = to_supports(&staked).evaluate();
+
+				if score.minimal_stake == 0 {
+					// such cases cannot be improved by balancing.
+					return;
+				}
+				score
+			};
+
+			let config = BalancingConfig { iterations, tolerance: 0 };
+			let balanced: ElectionResult<AccountId, Perbill> =
+				phragmms(to_elect, candidates, voters, Some(config)).unwrap();
+
+			let balanced_score = {
+				let staked =
+					assignment_ratio_to_staked_normalized(balanced.assignments, &stake_of).unwrap();
+				to_supports(staked.as_ref()).evaluate()
+			};
+
+			let enhance = balanced_score.strict_better(unbalanced_score);
+
+			println!(
+				"iter = {} // {:?} -> {:?} [{}]",
+				iterations, unbalanced_score, balanced_score, enhance,
+			);
+
+			// The only guarantee of balancing is such that the first and third element of the score
+			// cannot decrease.
+			assert!(
+				balanced_score.minimal_stake >= unbalanced_score.minimal_stake &&
+					balanced_score.sum_stake == unbalanced_score.sum_stake &&
+					balanced_score.sum_stake_squared <= unbalanced_score.sum_stake_squared
+			);
+		});
+	}
+}

bizinikiwi/primitives/npos-elections/fuzzer/src/reduce.rs

@@ -0,0 +1,143 @@
+// This file is part of Bizinikiwi.
+
+// Copyright (C) Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! Fuzzing for the reduce algorithm.
+//!
+//! It that reduce always return a new set og edges in which the bound is kept (`edges_after <= m +
+//! n,`) and the result must effectively be the same, meaning that the same support map should be
+//! computable from both.
+//!
+//! # Running
+//!
+//! Run with `cargo hfuzz run reduce`. `honggfuzz`.
+//!
+//! # Debugging a panic
+//!
+//! Once a panic is found, it can be debugged with
+//! `cargo hfuzz run-debug reduce hfuzz_workspace/reduce/*.fuzz`.
+
+use honggfuzz::fuzz;
+
+mod common;
+use common::to_range;
+use rand::{self, Rng, RngCore, SeedableRng};
+use pezsp_npos_elections::{reduce, to_support_map, ExtendedBalance, StakedAssignment};
+
+type Balance = u128;
+type AccountId = u64;
+
+/// Or any other token type.
+const KSM: Balance = 1_000_000_000_000;
+
+fn main() {
+	loop {
+		fuzz!(|data: (usize, usize, u64)| {
+			let (mut voter_count, mut target_count, seed) = data;
+			let rng = rand::rngs::SmallRng::seed_from_u64(seed);
+			target_count = to_range(target_count, 100, 1000);
+			voter_count = to_range(voter_count, 100, 2000);
+			let (assignments, winners) =
+				generate_random_phragmen_assignment(voter_count, target_count, 8, 8, rng);
+			reduce_and_compare(&assignments, &winners);
+		});
+	}
+}
+
+fn generate_random_phragmen_assignment(
+	voter_count: usize,
+	target_count: usize,
+	avg_edge_per_voter: usize,
+	edge_per_voter_var: usize,
+	mut rng: impl RngCore,
+) -> (Vec<StakedAssignment<AccountId>>, Vec<AccountId>) {
+	// prefix to distinguish the voter and target account ranges.
+	let target_prefix = 1_000_000;
+	assert!(voter_count < target_prefix);
+
+	let mut assignments = Vec::with_capacity(voter_count as usize);
+	let mut winners: Vec<AccountId> = Vec::new();
+
+	let all_targets = (target_prefix..(target_prefix + target_count))
+		.map(|a| a as AccountId)
+		.collect::<Vec<AccountId>>();
+
+	(1..=voter_count).for_each(|acc| {
+		let mut targets_to_chose_from = all_targets.clone();
+		let targets_to_chose = if edge_per_voter_var > 0 {
+			rng.gen_range(
+				avg_edge_per_voter - edge_per_voter_var..avg_edge_per_voter + edge_per_voter_var,
+			)
+		} else {
+			avg_edge_per_voter
+		};
+
+		let distribution = (0..targets_to_chose)
+			.map(|_| {
+				let target =
+					targets_to_chose_from.remove(rng.gen_range(0..targets_to_chose_from.len()));
+				if winners.iter().all(|w| *w != target) {
+					winners.push(target);
+				}
+				(target, rng.gen_range(1 * KSM..100 * KSM))
+			})
+			.collect::<Vec<(AccountId, ExtendedBalance)>>();
+
+		assignments.push(StakedAssignment { who: (acc as AccountId), distribution });
+	});
+
+	(assignments, winners)
+}
+
+fn assert_assignments_equal(
+	ass1: &Vec<StakedAssignment<AccountId>>,
+	ass2: &Vec<StakedAssignment<AccountId>>,
+) {
+	let support_1 = to_support_map::<AccountId>(ass1);
+	let support_2 = to_support_map::<AccountId>(ass2);
+	for (who, support) in support_1.iter() {
+		assert_eq!(support.total, support_2.get(who).unwrap().total);
+	}
+}
+
+fn reduce_and_compare(assignment: &Vec<StakedAssignment<AccountId>>, winners: &Vec<AccountId>) {
+	let mut altered_assignment = assignment.clone();
+	let n = assignment.len() as u32;
+	let m = winners.len() as u32;
+
+	let edges_before = assignment_len(assignment);
+	let num_changed = reduce(&mut altered_assignment);
+	let edges_after = edges_before - num_changed;
+
+	assert!(
+		edges_after <= m + n,
+		"reduce bound not satisfied. n = {}, m = {}, edges after reduce = {} (removed {})",
+		n,
+		m,
+		edges_after,
+		num_changed,
+	);
+
+	assert_assignments_equal(&assignment, &altered_assignment);
+}
+
+fn assignment_len(assignments: &[StakedAssignment<AccountId>]) -> u32 {
+	let mut counter = 0;
+	assignments
+		.iter()
+		.for_each(|x| x.distribution.iter().for_each(|_| counter += 1));
+	counter
+}