Walter Pullen's AC(B(A(A)A)A(A)):
-|
AS1 => XS1|A
XN3 => AN3|
CE2 => XE2|C
BE4 => XE4|BC
AS2 => XS2|ABC
AW3 => XW3|AABC
XS2 => AS2|ABC
XS3 => AS3|BC
AW1 => XW1|ABC
XN1 => AN1|BC
XW1 => BW1|C
AE4 => XE4|AC
AS2 => XS2|AAC
XW3 => AW3|AC
XS2 => AS2|C
XS3 => CS3|
+|


Eric's A(A(B(BAA)AA)A(A))B(AA(A))C(AA(A)):
-|
AS1 => XS1|A
AE1 => XE1|AA
BN4 => XN4|BAA
BN1 => XN1|BBAA
XW1 => BW1|BAA
AE4 => XE4|ABAA
XS3 => AS3|BAA
AW1 => XW1|ABAA
XN1 => AN1|BAA
XW1 => BW1|AA
AE4 => XE4|AAA
XS3 => AS3|AA
AW1 => XW1|AAA
XN1 => AN1|AA
XW1 => AW1|A
AS3 => XS3|AA
AS2 => XS2|AAA
XW3 => AW3|AA
XS2 => AS2|A
XE4 => AE4|
BW1 => XW1|B
AN1 => XN1|AB
XW1 => AW1|B
AS3 => XS3|AB
AS2 => XS2|AAB
XW3 => AW3|AB
XW3 => AW3|B
XW3 => BW3|
CW2 => XW2|C
AN1 => XN1|AC
XW1 => AW1|C
AS3 => XS3|AC
AS2 => XS2|AAC
XW3 => AW3|AC
XS2 => AS2|C
XS3 => CS3|
+|


More solutions:

A(B(A(CB(A(A)B))))C:
-|
AS1 => XS1|A
BE3 => XE3|BA
AN3 => XN3|ABA
CN1 => XN1|CABA
XW2 => CW2|ABA
BW3 => XW3|BABA
AW3 => XW3|ABABA
AW3 => XW3|AABABA
XS2 => AS2|ABABA
XE4 => AE4|BABA
BW1 => XW1|BBABA
XN1 => BN1|BABA
XN4 => BN4|ABA
XE1 => AE1|BA
XN3 => BN3|A
XS4 => AS4|
CW4 => XW4|C
XS3 => CS3|
+|


A(A(B(BAA)AA))A(A(A)B(AAB(AA(A))C))C:
-|
AS1 => XS1|A
AE1 => XE1|AA
BN4 => XN4|BAA
BN1 => XN1|BBAA
XW1 => BW1|BAA
AE4 => XE4|ABAA
XS3 => AS3|BAA
AW1 => XW1|ABAA
XN1 => AN1|BAA
XW1 => BW1|AA
AE4 => XE4|AAA
XS3 => AS3|AA
AW1 => XW1|AAA
XN1 => AN1|AA
XN1 => AN1|A
XW1 => AW1|
AS3 => XS3|A
AS2 => XS2|AA
AW3 => XW3|AAA
XS2 => AS2|AA
XE4 => AE4|A
BW1 => XW1|BA
AN1 => XN1|ABA
XW1 => AW1|BA
AS3 => XS3|ABA
XE4 => AE4|BA
BW1 => XW1|BBA
AN1 => XN1|ABBA
XW1 => AW1|BBA
AS3 => XS3|ABBA
AS2 => XS2|AABBA
XW3 => AW3|ABBA
XW3 => AW3|BBA
XW3 => BW3|BA
CW2 => XW2|CBA
XN1 => CN1|BA
XN3 => BN3|A
XS4 => AS4|
CW4 => XW4|C
XS3 => CS3|
+|