Certificate for #4719 ⟨a, b | aabbbaab=baa

Completion settings:

[1] aabbbaab=baa

Axiom: aabbbaab=baa.

Referenced by [4].

[2] aa=c

Axiom: aa=c.

Defines rule #9.

Referenced by [4], [5], [7].

[3] bbbc=d

Axiom: bbbc=d.

Referenced by [5], [6].

[4] aabbbaab=bc

Simplify [1] aabbbaab=baa.

Reduce RHS:

[2]b(aa)
bc

Referenced by [5].

[5] bc=cdb

Overlap of [4] aabbbaab=bc with [2] aa=c:

aabbbaab aa

Critical pair: cbbbaab=bc.

Reduce LHS:

[2]cbbb(aa)b
[3]c(bbbc)b
cdb

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [8], [9], [10], [11], [12], [15].

[6] cdbdbdb=d

Overlap of [3] bbbc=d with [5] bc=cdb:

bb bc bc

Critical pair: bbcdb=d.

Reduce LHS:

[5]b(bc)db
[5](bc)dbdb
cdbdbdb

Defines rule #2.

Referenced by [10], [11], [13], [14], [15], [16].

[7] ca=ac

Overlap of [2] aa=c with [2] aa=c:

a a aa

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #6.

Referenced by [8].

[8] cdba=bac

Overlap of [5] bc=cdb with [7] ca=ac:

b c ca

Critical pair: bac=cdba.

Flip LHS and RHS.

Defines rule #7.

Referenced by [9].

[9] cdbdba=bbac

Overlap of [5] bc=cdb with [8] cdba=bac:

b c cdba

Critical pair: bbac=cdbdba.

Flip LHS and RHS.

Defines rule #8.

Referenced by [15].

[10] ddb=bd

Overlap of [5] bc=cdb with [6] cdbdbdb=d:

b c cdbdbdb

Critical pair: bd=cdbdbdbdb.

Reduce RHS:

[6](cdbdbdb)db
ddb

Flip LHS and RHS.

Defines rule #1.

Referenced by [12], [16].

[11] cdbdbdcdb=dc

Overlap of [6] cdbdbdb=d with [5] bc=cdb:

cdbdbd b bc

Critical pair: cdbdbdcdb=dc.

Referenced by [16].

[12] ddcdb=bdc

Overlap of [10] ddb=bd with [5] bc=cdb:

dd b bc

Critical pair: ddcdb=bdc.

Referenced by [13], [14].

[13] bdcdbdb=ddd

Overlap of [12] ddcdb=bdc with [6] cdbdbdb=d:

dd cdb cdbdbdb

Critical pair: ddd=bdcdbdb.

Flip LHS and RHS.

Referenced by [14].

[14] bdcdb=cdbdbdddd

Overlap of [6] cdbdbdb=d with [13] bdcdbdb=ddd:

cdbdbd b bdcdbdb

Critical pair: cdbdbdddd=ddcdbdb.

Reduce RHS:

[12](ddcdb)db
bdcdb

Flip LHS and RHS.

Referenced by [16].

[15] da=bbbac

Overlap of [5] bc=cdb with [9] cdbdba=bbac:

b c cdbdba

Critical pair: bbbac=cdbdbdba.

Reduce RHS:

[6](cdbdbdb)a
da

Flip LHS and RHS.

Defines rule #5.

[16] dc=cdddddddd

Overlap of [11] cdbdbdcdb=dc with [14] bdcdb=cdbdbdddd:

cdbd bdcdb bdcdb

Critical pair: cdbdcdbdbdddd=dc.

Reduce LHS:

[14]cd(bdcdb)dbdddd
[10]cdcdbdbddd(ddb)dddd
[10]cdcdbdbd(ddb)ddddd
[6]cd(cdbdbdb)dddddd
cdddddddd

Flip LHS and RHS.

Defines rule #4.