Certificate for #2257 ⟨a, b | aabbaab=baa

Completion settings:

[1] aabbaab=baa

Axiom: aabbaab=baa.

Referenced by [4].

[2] aa=c

Axiom: aa=c.

Defines rule #8.

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

[3] bbc=d

Axiom: bbc=d.

Referenced by [5], [6].

[4] aabbaab=bc

Simplify [1] aabbaab=baa.

Reduce RHS:

[2]b(aa)
bc

Referenced by [5].

[5] bc=cdb

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

aabbaab aa

Critical pair: cbbaab=bc.

Reduce LHS:

[2]cbb(aa)b
[3]c(bbc)b
cdb

Flip LHS and RHS.

Defines rule #3.

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

[6] cdbdb=d

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

b bc bc

Critical pair: bcdb=d.

Reduce LHS:

[5](bc)db
cdbdb

Defines rule #2.

Referenced by [9], [10], [12], [13], [14], [15].

[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 [12].

[9] ddb=bd

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

b c cdbdb

Critical pair: bd=cdbdbdb.

Reduce RHS:

[6](cdbdb)db
ddb

Flip LHS and RHS.

Defines rule #1.

Referenced by [11], [15].

[10] cdbdcdb=dc

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

cdbd b bc

Critical pair: cdbdcdb=dc.

Referenced by [15].

[11] ddcdb=bdc

Overlap of [9] ddb=bd with [5] bc=cdb:

dd b bc

Critical pair: ddcdb=bdc.

Referenced by [13], [14].

[12] da=bbac

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

b c cdba

Critical pair: bbac=cdbdba.

Reduce RHS:

[6](cdbdb)a
da

Flip LHS and RHS.

Defines rule #5.

[13] bdcdb=ddd

Overlap of [11] ddcdb=bdc with [6] cdbdb=d:

dd cdb cdbdb

Critical pair: ddd=bdcdb.

Flip LHS and RHS.

Referenced by [14].

[14] bdc=cdbdddd

Overlap of [6] cdbdb=d with [13] bdcdb=ddd:

cdbd b bdcdb

Critical pair: cdbdddd=ddcdb.

Reduce RHS:

[11](ddcdb)
bdc

Flip LHS and RHS.

Referenced by [15].

[15] dc=cdddd

Simplify [10] cdbdcdb=dc.

Reduce LHS:

[14]cd(bdc)db
[9]cdcdbddd(ddb)
[9]cdcdbd(ddb)d
[6]cd(cdbdb)dd
cdddd

Flip LHS and RHS.

Defines rule #4.