Certificate for #6525 ⟨a, b | aba=b, bbbbb=b

Completion settings:

[1] aba=b

Axiom: aba=b.

Referenced by [4], [5], [7], [9], [13].

[2] bbbbb=b

Axiom: bbbbb=b.

Defines rule #3.

Referenced by [11], [12].

[3] baa=c

Axiom: baa=c.

Referenced by [5], [6].

[4] bba=abb

Overlap of [1] aba=b with [1] aba=b:

ab a aba

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [10], [11].

[5] ba=ac

Overlap of [1] aba=b with [3] baa=c:

a ba baa

Critical pair: ac=ba.

Flip LHS and RHS.

Defines rule #5.

Referenced by [6], [7], [10], [11], [13], [14], [15].

[6] aca=c

Overlap of [3] baa=c with [5] ba=ac:

baa ba

Critical pair: aca=c.

Referenced by [7], [9], [10], [14].

[7] cc=bb

Overlap of [5] ba=ac with [1] aba=b:

b a aba

Critical pair: bb=acba.

Reduce RHS:

[5]ac(ba)
[6](aca)c
cc

Flip LHS and RHS.

Defines rule #1.

Referenced by [8], [10], [14], [15].

[8] cbb=bbc

Overlap of [7] cc=bb with [7] cc=bb:

c c cc

Critical pair: cbb=bbc.

Defines rule #2.

Referenced by [12].

[9] bca=abc

Overlap of [1] aba=b with [6] aca=c:

ab a aca

Critical pair: abc=bca.

Flip LHS and RHS.

Referenced by [14], [15].

[10] aabb=bc

Overlap of [5] ba=ac with [6] aca=c:

b a aca

Critical pair: bc=acca.

Reduce RHS:

[7]a(cc)a
[4]a(bba)
aabb

Flip LHS and RHS.

Referenced by [12].

[11] abbbbc=ac

Overlap of [2] bbbbb=b with [5] ba=ac:

bbbb b ba

Critical pair: bbbbac=ba.

Reduce LHS:

[4]bb(bba)c
[4](bba)bbc
abbbbc

Reduce RHS:

[5](ba)
ac

Referenced by [14].

[12] aab=bbbcb

Overlap of [10] aabb=bc with [2] bbbbb=b:

aa bb bbbbb

Critical pair: aab=bcbbb.

Reduce RHS:

[8]b(cbb)b
bbbcb

Defines rule #7.

[13] aac=b

Overlap of [1] aba=b with [5] ba=ac:

a ba ba

Critical pair: aac=b.

Defines rule #8.

Referenced by [14].

[14] bbbbc=c

Overlap of [11] abbbbc=ac with [9] bca=abc:

abbb bc bca

Critical pair: abbbabc=aca.

Reduce LHS:

[5]abb(ba)bc
[5]ab(ba)cbc
[5]a(ba)ccbc
[13](aac)ccbc
[7]b(cc)bc
bbbbc

Reduce RHS:

[6](aca)
c

Defines rule #4.

Referenced by [15].

[15] ca=abbcbc

Overlap of [14] bbbbc=c with [9] bca=abc:

bbb bc bca

Critical pair: bbbabc=ca.

Reduce LHS:

[5]bb(ba)bc
[5]b(ba)cbc
[5](ba)ccbc
[7]a(cc)cbc
abbcbc

Flip LHS and RHS.

Defines rule #6.