test_that("dominates", {
  pr <- as.PowerRelation('12 > 1 > 2')
  expect_true(dominates(pr, 1, 2))
  expect_false(dominates(pr, 2, 1))
  expect_true(dominates(pr, 1, 2, includeEmptySet = FALSE))
  expect_true(dominates(pr, 2, 1, includeEmptySet = FALSE))
  expect_false(dominates(pr, 1, 2, includeEmptySet = FALSE, strictly = TRUE))
  expect_false(dominates(pr, 2, 1, includeEmptySet = FALSE, strictly = TRUE))
  expect_true(pr %:% 1 %>=dom% 2)
  expect_false(pr %:% 2 %>=dom% 1)

  pr <- as.PowerRelation('1 > 2 > 23')
  expect_true(dominates(pr, 1, 1))
  expect_false(dominates(pr, 1, 1, strictly = TRUE))
  expect_true(dominates(pr, 1, 2))
  expect_false(dominates(pr, 2, 1))
  expect_true(dominates(pr, 1, 3))
  expect_true(dominates(pr, 2, 3))
  expect_true(dominates(pr, 1, 2, includeEmptySet = FALSE))
  expect_true(dominates(pr, 2, 1, includeEmptySet = FALSE))
  expect_false(dominates(pr, 1, 2, includeEmptySet = FALSE, strictly = TRUE))
  expect_false(dominates(pr, 2, 1, includeEmptySet = FALSE, strictly = TRUE))

  pr <- as.PowerRelation("123 > (12 ~ 13) > (1 ~ 23 ~ {}) > (2 ~ 3)")
  expect_true(dominates(pr, 2, 3))
  expect_true(dominates(pr, 3, 2))
  expect_true(pr %:% 1 %>=dom% 3)
  expect_true(pr %:% 2 %>=dom% 3)
  expect_true(pr %:% 3 %>=dom% 2)
  expect_true(pr %:% 3 %>=dom% 3)

  expect_true(pr %:% 1 %>dom% 3)
  expect_false(pr %:% 2 %>dom% 3)
  expect_false(pr %:% 3 %>dom% 2)
  expect_false(pr %:% 3 %>dom% 3)

  expect_false(dominates(pr, 2, 3, strictly = TRUE))
  expect_false(dominates(pr, 3, 2, strictly = TRUE))

  expect_true(dominates(pr, 1, 2))
  expect_false(dominates(pr, 2, 1))
  expect_true(dominates(pr, 1, 2, strictly = TRUE))
  expect_false(dominates(pr, 2, 1, strictly = TRUE))

  expect_true(dominates(pr, 1, 3))
  expect_false(dominates(pr, 3, 1))
  expect_true(dominates(pr, 1, 3, strictly = TRUE))
  expect_false(dominates(pr, 3, 1, strictly = TRUE))
})