Experimentally, in bash:
$ strace -tttfe execve bash -c 'sleep 5 <(sleep 6)' 1522025733.188859 execve("/bin/bash", ["bash", "-c", "sleep 5 <(sleep 6)"], [/* 41 vars */]) = 0 strace: Process 24248 attached [pid 24247] 1522025733.215188 execve("/bin/sleep", ["sleep", "5", "/dev/fd/63"], [/* 41 vars */]) = 0 strace: Process 24249 attached [pid 24249] 1522025733.218331 execve("/bin/sleep", ["sleep", "6"], [/* 41 vars */]) = 0 sleep: invalid time interval ‘/dev/fd/63’ Try 'sleep --help' for more information. [pid 24247] 1522025733.227459 +++ exited with 1 +++ [pid 24249] 1522025739.230933 +++ exited with 0 +++ 1522025739.232270 --- SIGCHLD {si_signo=SIGCHLD, si_code=CLD_EXITED, si_pid=24249, si_uid=1000, si_status=0, si_utime=0, si_stime=0} --- 1522025739.233169 +++ exited with 0 +++ $ strace -tttfe execve bash -c 'sleep 5 >(sleep 6)' 1522025752.162876 execve("/bin/bash", ["bash", "-c", "sleep 5 >(sleep 6)"], [/* 41 vars */]) = 0 strace: Process 24253 attached [pid 24252] 1522025752.188413 execve("/bin/sleep", ["sleep", "5", "/dev/fd/63"], [/* 41 vars */]) = 0 strace: Process 24254 attached [pid 24254] 1522025752.191032 execve("/bin/sleep", ["sleep", "6"], [/* 41 vars */]) = 0 sleep: invalid time interval ‘/dev/fd/63’ Try 'sleep --help' for more information. [pid 24252] 1522025752.197213 +++ exited with 1 +++ [pid 24254] 1522025758.197114 +++ exited with 0 +++ 1522025758.197959 --- SIGCHLD {si_signo=SIGCHLD, si_code=CLD_EXITED, si_pid=24254, si_uid=1000, si_status=0, si_utime=0, si_stime=0} --- 1522025758.198820 +++ exited with 0 +++
command1 and command3 start after command2 and command4 respectively.
They exit whenever their conditions for exiting or being killed are met.
makefifo fifo1; prog2 < fifo1 &; prog1 > fifo1; and makefifo fifo2; prog3 > fifo12 &; prog2 < fifo2; are syntax errors, at least in bash. Even if it weren't, I don't see anything in the redirections that would cause a different execution order from without redirections.
