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While glacial remnants in the form of viscous flow features in the mid-latitudes of Mars are considered to be cold-based in the present-day, an increasing amount of geomorphic evidence suggests that at least some flow features were previously wet-based or had a mixed thermal state (polythermal) at during their evolution. Many of the viscous flow features known as glacier-like forms have been observed to emerge from alcoves that appear similar to cirques on Earth. Terrestrial cirques are typically characterized by a concave basin connected to a steep backwall. Cirques are expected to form from depressions in mountainsides that fill with snow/ice and over time support active glaciers that deepen the depressions by wet-based glacial erosion. To assess which alcoves on Mars are most "cirque-like", we mapped a population of ~2000 alcoves in Deuteronilus Mensae, a region in the mid-latitudes of Mars characterized by mesas encompassed by glacial remnants. Based on visual characteristics and morphometrics, we refined our dataset to 386 "cirque-like alcoves", which is five times the amount of glacier-like forms in the region, and used this to assess the past extent and style of glaciation on Mars. Using high resolution imagery, we find geomorphic evidence for glacial occupation associated with the cirque-like alcoves, including crevasse-like features, surface lineations, polygonal terrain, and moraine-like ridges. We propose that the cirque-like alcoves with icy remnants similar to rock glaciers on Earth represent a late stage of glacier-like form evolution. We also outline stages of cirque-like alcove evolution, linking a potential early stage of cirque-like alcoves to gully activity. On a population-wide scale, the cirque-like alcoves have a south to southeastward aspect bias, which may indicate a requirement for increased insolation for melting to occur and a connection to gullies on Mars. While the alcoves also have similarities to other features such as landslide scarps and amphitheater-headed valleys, the cirque-like alcoves have unique morphologies and morphometrics that differentiate their origin. Assuming warm-based erosion rates, the cirque-like alcoves have timescales consistent with both glacier-like forms and other viscous flow features like lobate debris aprons, whereas cold-based erosion rates would only allow the older timescales of lobate debris aprons. We propose that based on the geomorphic features and southward aspect, cirque-like alcove formation is more consistent with warm-based glaciation. [ABSTRACT FROM AUTHOR]