Certificate for #4334 ⟨a, b | abbaabaab=ba

Completion settings:

[1] abbaabaab=ba

Axiom: abbaabaab=ba.

Referenced by [4].

[2] baa=c

Axiom: baa=c.

Referenced by [4], [5].

[3] ab=d

Axiom: ab=d.

Defines rule #26.

Referenced by [4], [6], [7], [10].

[4] ba=dccb

Overlap of [1] abbaabaab=ba with [3] ab=d:

abbaabaab ab

Critical pair: dbaabaab=ba.

Reduce LHS:

[2]d(baa)baab
[2]dc(baa)b
dccb

Flip LHS and RHS.

Defines rule #29.

Referenced by [5], [6], [7], [8].

[5] dccdccb=c

Overlap of [2] baa=c with [4] ba=dccb:

baa ba

Critical pair: dccba=c.

Reduce LHS:

[4]dcc(ba)
dccdccb

Defines rule #3.

Referenced by [8], [9], [11], [15], [16], [21].

[6] da=adccb

Overlap of [3] ab=d with [4] ba=dccb:

a b ba

Critical pair: adccb=da.

Flip LHS and RHS.

Defines rule #28.

[7] dccbb=bd

Overlap of [4] ba=dccb with [3] ab=d:

b a ab

Critical pair: bd=dccbb.

Flip LHS and RHS.

Defines rule #11.

Referenced by [9], [12], [22].

[8] ca=dccc

Overlap of [5] dccdccb=c with [4] ba=dccb:

dccdcc b ba

Critical pair: dccdccdccb=ca.

Reduce LHS:

[5]dcc(dccdccb)
dccc

Flip LHS and RHS.

Defines rule #27.

Referenced by [10].

[9] dccbd=cb

Overlap of [5] dccdccb=c with [7] dccbb=bd:

dcc dccb dccbb

Critical pair: dccbd=cb.

Defines rule #1.

Referenced by [11], [12], [13], [14], [23].

[10] dcccb=cd

Overlap of [8] ca=dccc with [3] ab=d:

c a ab

Critical pair: cd=dcccb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [14], [19], [24].

[11] cbccdccb=dccbc

Overlap of [9] dccbd=cb with [5] dccdccb=c:

dccb d dccdccb

Critical pair: dccbc=cbccdccb.

Flip LHS and RHS.

Defines rule #7.

Referenced by [16], [17], [18], [27].

[12] cbccbb=bdd

Overlap of [9] dccbd=cb with [7] dccbb=bd:

dccb d dccbb

Critical pair: dccbbd=cbccbb.

Reduce LHS:

[7](dccbb)d
bdd

Flip LHS and RHS.

Defines rule #23.

Referenced by [15], [28].

[13] dccbcb=cbccbd

Overlap of [9] dccbd=cb with [9] dccbd=cb:

dccb d dccbd

Critical pair: dccbcb=cbccbd.

Defines rule #12.

Referenced by [28].

[14] cbcccb=dccbcd

Overlap of [9] dccbd=cb with [10] dcccb=cd:

dccb d dcccb

Critical pair: dccbcd=cbcccb.

Flip LHS and RHS.

Defines rule #6.

Referenced by [18], [20], [29], [31].

[15] cccbb=dccdcbdd

Overlap of [5] dccdccb=c with [12] cbccbb=bdd:

dccdc cb cbccbb

Critical pair: dccdcbdd=cccbb.

Flip LHS and RHS.

Defines rule #10.

Referenced by [19], [20].

[16] dccdcdccbc=cccdccb

Overlap of [5] dccdccb=c with [11] cbccdccb=dccbc:

dccdc cb cbccdccb

Critical pair: dccdcdccbc=cccdccb.

Defines rule #5.

Referenced by [27], [28], [29], [30].

[17] dccbcccdccb=cbccdcdccbc

Overlap of [11] cbccdccb=dccbc with [11] cbccdccb=dccbc:

cbccdc cb cbccdccb

Critical pair: cbccdcdccbc=dccbcccdccb.

Flip LHS and RHS.

Defines rule #15.

[18] dccbccccb=cbccdcdccbcd

Overlap of [11] cbccdccb=dccbc with [14] cbcccb=dccbcd:

cbccdc cb cbcccb

Critical pair: cbccdcdccbcd=dccbccccb.

Flip LHS and RHS.

Defines rule #14.

[19] ddccdcbdd=cdb

Overlap of [10] dcccb=cd with [15] cccbb=dccdcbdd:

d cccb cccbb

Critical pair: ddccdcbdd=cdb.

Defines rule #4.

Referenced by [21], [22], [23], [24], [25], [26], [30].

[20] dccbcdb=cbdccdcbdd

Overlap of [14] cbcccb=dccbcd with [15] cccbb=dccdcbdd:

cb cccb cccbb

Critical pair: cbdccdcbdd=dccbcdb.

Flip LHS and RHS.

Defines rule #13.

[21] cdbccdccb=ddccdcbdc

Overlap of [19] ddccdcbdd=cdb with [5] dccdccb=c:

ddccdcbd d dccdccb

Critical pair: ddccdcbdc=cdbccdccb.

Flip LHS and RHS.

Defines rule #9.

Referenced by [31].

[22] cdbccbb=ddccdcbdbd

Overlap of [19] ddccdcbdd=cdb with [7] dccbb=bd:

ddccdcbd d dccbb

Critical pair: ddccdcbdbd=cdbccbb.

Flip LHS and RHS.

Defines rule #24.

[23] ddccdcbdcb=cdbccbd

Overlap of [19] ddccdcbdd=cdb with [9] dccbd=cb:

ddccdcbd d dccbd

Critical pair: ddccdcbdcb=cdbccbd.

Defines rule #19.

[24] cdbcccb=ddccdcbdcd

Overlap of [19] ddccdcbdd=cdb with [10] dcccb=cd:

ddccdcbd d dcccb

Critical pair: ddccdcbdcd=cdbcccb.

Flip LHS and RHS.

Defines rule #8.

[25] ddccdcbcdb=cdbccdcbdd

Overlap of [19] ddccdcbdd=cdb with [19] ddccdcbdd=cdb:

ddccdcb dd ddccdcbdd

Critical pair: ddccdcbcdb=cdbccdcbdd.

Defines rule #18.

[26] ddccdcbdcdb=cdbdccdcbdd

Overlap of [19] ddccdcbdd=cdb with [19] ddccdcbdd=cdb:

ddccdcbd d ddccdcbdd

Critical pair: ddccdcbdcdb=cdbdccdcbdd.

Defines rule #20.

[27] cccdccbcdccb=dccdcdcdccbc

Overlap of [16] dccdcdccbc=cccdccb with [11] cbccdccb=dccbc:

dccdcdc cbc cbccdccb

Critical pair: dccdcdcdccbc=cccdccbcdccb.

Flip LHS and RHS.

Defines rule #17.

[28] ccccbccbdb=dccdcdcbdd

Overlap of [16] dccdcdccbc=cccdccb with [12] cbccbb=bdd:

dccdcdc cbc cbccbb

Critical pair: dccdcdcbdd=cccdccbcbb.

Reduce RHS:

[13]ccc(dccbcb)b
ccccbccbdb

Flip LHS and RHS.

Defines rule #25.

[29] cccdccbccb=dccdcdcdccbcd

Overlap of [16] dccdcdccbc=cccdccb with [14] cbcccb=dccbcd:

dccdcdc cbc cbcccb

Critical pair: dccdcdcdccbcd=cccdccbccb.

Flip LHS and RHS.

Defines rule #16.

[30] ddccdcbdcccdccb=cdbccdcdccbc

Overlap of [19] ddccdcbdd=cdb with [16] dccdcdccbc=cccdccb:

ddccdcbd d dccdcdccbc

Critical pair: ddccdcbdcccdccb=cdbccdcdccbc.

Defines rule #22.

[31] ddccdcbdccccb=cdbccdcdccbcd

Overlap of [21] cdbccdccb=ddccdcbdc with [14] cbcccb=dccbcd:

cdbccdc cb cbcccb

Critical pair: cdbccdcdccbcd=ddccdcbdccccb.

Flip LHS and RHS.

Defines rule #21.