What is the meaning of "Ha'ashimem"?
Radak #1: The root is Shemamah (destruction). Asham and Shemam are the same matter.
Radak #2: It refers to Asham (guilt). Convict their counsel, that they will not succeed to do what they plotted about me. Asham [refers to failure,] like "v'Lo Yachati" (Shoftim 20:16).
Malbim: Their verdict will be Ashemim (guilty), for two reasons. (a) They sinned via counsel of the intellect ("mi'Mo'atzoseihem", not due to lust or error). (b) They repeat their sin until they became Mumarim (wanton sinners - "b'Rov Pish'eihem"). This is like it says about Dor ha'Mabul - "Rabah Ra'as ha'Adam ba'Aretz v'Chol Yetzer Machshevos Libo Rak Ra Kol ha'Yom" (Bereishis 6:5).
What are "Mo'atzoseihem"?
Rashi: It is their counsel about Yisrael. [When they fall from this,] all who trust in You will rejoice (verse 12).
Malbim: Their evil counsel will be the reason for their fall; they will fall from their counsel to the ground. The prefix Mem "mi'Mo'atzoseihem" refers to place. Their sin will punish them; the Midah they meted to others will be meted to them.
How did they rebel against You?
Radak: You commanded that I will be king; they rebelled against Your words. "Maru" is like "Merisem Pi" (Bamidbar 27:14).
Malbim: They calmly act to anger You.