The phrase 'complying pension' is usually reserved for special types of pensions that in most circumstances cannot be rolled-back to an accumulation (non-pension) account. Pensions payable from SMSFs that fall into this category are:
In some cases these pensions are also asset-test exempt income streams. Asset-test exemption is granted to these pensions by the provisions of the Social Security Act 1991 under sections 9A, 9B and 9BA, respectively.
In the SMSF industry these pensions are also collectively referred to as legacy pensions. The lifetime and life expectancy types are no longer available to SMSFs, except as annuities prescribed by SIS Reg 1.05, from a life office. Market-linked pensions can be started in SMSFs only from the commutation of an already existing complying pension.
If it is asset-test exempt for social security (age pension assessment) purposes then, generally, no it isn't, except for special circumstances. Be very careful. Those circumstances are described here.
Otherwise, yes, the SIS Act does permit the commutation of complying pensions. But not to an accumulation benefit.
There is a simple rule-of-thumb: a complying pension can be commuted to another type of complying pension. Only. This means you can start one of the following pensions using the lump-sum equivalent of the original pension:
The lump-sum commutation value of lifetime pensions is discussed here.
The lump-sum commutation value of life expectancy pensions is discussed here.
The lump-sum commutation value of market-linked pensions will normally be the full account balance.
If the lump-sum value of the original pension is less than the account balance then the left-over capital remains in an unallocated reserve in the SMSF. Unallocated reserves are discussed here.