Certificate for #5827 ⟨a, b | abaaab=baaba

Completion settings:

[1] baaba=abaaab

Axiom: abaaab=baaba.

Flip LHS and RHS.

Referenced by [5].

[2] baa=c

Axiom: baa=c.

Defines rule #4.

Referenced by [6], [8], [9], [11], [13], [14].

[3] ab=d

Axiom: ab=d.

Defines rule #3.

Referenced by [5], [7], [8], [9], [11].

[4] da=e

Axiom: da=e.

Defines rule #2.

Referenced by [5], [7], [9], [10], [11], [12], [13], [15].

[5] baaba=ead

Simplify [1] baaba=abaaab.

Reduce RHS:

[3](ab)aaab
[4](da)aab
[3]ea(ab)
ead

Referenced by [6].

[6] cba=ead

Overlap of [5] baaba=ead with [2] baa=c:

baaba baa

Critical pair: cba=ead.

Referenced by [10].

[7] eb=dd

Overlap of [4] da=e with [3] ab=d:

d a ab

Critical pair: dd=eb.

Flip LHS and RHS.

Defines rule #9.

[8] cb=bad

Overlap of [2] baa=c with [3] ab=d:

ba a ab

Critical pair: bad=cb.

Flip LHS and RHS.

Defines rule #8.

Referenced by [10].

[9] ea=ac

Overlap of [3] ab=d with [2] baa=c:

a b baa

Critical pair: ac=daa.

Reduce RHS:

[4](da)a
ea

Flip LHS and RHS.

Defines rule #1.

Referenced by [10], [13], [16].

[10] acd=bae

Simplify [6] cba=ead.

Reduce LHS:

[8](cb)a
[4]ba(da)
bae

Reduce RHS:

[9](ea)d
acd

Flip LHS and RHS.

Defines rule #7.

Referenced by [11], [12], [13].

[11] ccd=bee

Overlap of [2] baa=c with [10] acd=bae:

ba a acd

Critical pair: babae=ccd.

Reduce LHS:

[3]b(ab)ae
[4]b(da)e
bee

Flip LHS and RHS.

Defines rule #12.

[12] ecd=dbae

Overlap of [4] da=e with [10] acd=bae:

d a acd

Critical pair: dbae=ecd.

Flip LHS and RHS.

Defines rule #13.

[13] ace=cc

Overlap of [10] acd=bae with [4] da=e:

ac d da

Critical pair: ace=baea.

Reduce RHS:

[9]ba(ea)
[2](baa)c
cc

Defines rule #6.

Referenced by [14], [15], [16].

[14] cce=bacc

Overlap of [2] baa=c with [13] ace=cc:

ba a ace

Critical pair: bacc=cce.

Flip LHS and RHS.

Defines rule #10.

[15] ece=dcc

Overlap of [4] da=e with [13] ace=cc:

d a ace

Critical pair: dcc=ece.

Flip LHS and RHS.

Defines rule #11.

[16] cca=acac

Overlap of [13] ace=cc with [9] ea=ac:

ac e ea

Critical pair: acac=cca.

Flip LHS and RHS.

Defines rule #5.