  A tree search algorithm called successive cancellation ordered search (SCOS)
is proposed for $\boldsymbol{G}_N$-coset codes that implements
maximum-likelihood (ML) decoding with adaptive complexity for transmission over
binary-input AWGN channels. Unlike bit-flip decoders, no outer code is needed
to terminate decoding; therefore, SCOS also applies to $\boldsymbol{G}_N$-coset
codes modified with dynamic frozen bits. The average complexity is close to
that of successive cancellation (SC) decoding at practical frame error rates
(FERs) for codes with wide ranges of rate and lengths up to $512$ bits, which
perform within $0.25$ dB or less from the random coding union bound and
outperform Reed--Muller codes under ML decoding by up to $0.5$ dB. Simulations
illustrate simultaneous gains for SCOS over SC-Fano, SC stack (SCS) and SC list
(SCL) decoding in FER and the average complexity at various SNR regimes. SCOS
is further extended by forcing it to look for candidates satisfying a
threshold, thereby outperforming basic SCOS under complexity constraints. The
modified SCOS enables strong error-detection capability without the need for an
outer code. In particular, the $(128, 64)$ polarization-adjusted convolutional
code under modified SCOS provides gains in overall and undetected FER compared
to CRC-aided polar codes under SCL/dynamic SC flip decoding at high SNR.
