Certificate for #275 ⟨a, b | aaaaabba=1⟩

Completion settings:

[1] aaaaabba=1

Axiom: aaaaabba=1.

Referenced by [4].

[2] aaaaaa=c

Axiom: aaaaaa=c.

Defines rule #8.

Referenced by [6], [7], [14].

[3] bb=d

Axiom: bb=d.

Defines rule #1.

Referenced by [4], [5].

[4] aaaaada=1

Overlap of [1] aaaaabba=1 with [3] bb=d:

aaaaa bba bb

Critical pair: aaaaada=1.

Referenced by [7], [8], [9], [11], [12], [13].

[5] db=bd

Overlap of [3] bb=d with [3] bb=d:

b b bb

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #6.

Referenced by [10].

[6] ca=ac

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

a aaaaa aaaaaa

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #2.

[7] cda=a

Overlap of [2] aaaaaa=c with [4] aaaaada=1:

a aaaaa aaaaada

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [9].

[8] aaaada=aaaaad

Overlap of [4] aaaaada=1 with [4] aaaaada=1:

aaaaad a aaaaada

Critical pair: aaaaad=aaaada.

Flip LHS and RHS.

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

[9] cd=1

Overlap of [7] cda=a with [4] aaaaada=1:

cd a aaaaada

Critical pair: cd=aaaaada.

Reduce RHS:

[4](aaaaada)
⇒ 1

Defines rule #4.

Referenced by [10], [14].

[10] cbd=b

Overlap of [9] cd=1 with [5] db=bd:

c d db

Critical pair: cbd=b.

Referenced by [15].

[11] aaada=aaaad

Overlap of [4] aaaaada=1 with [8] aaaada=aaaaad:

aaaaad a aaaada

Critical pair: aaaaadaaaaad=aaada.

Reduce LHS:

[4](aaaaada)aaaad
aaaad

Flip LHS and RHS.

Referenced by [13].

[12] aada=aaad

Overlap of [8] aaaada=aaaaad with [8] aaaada=aaaaad:

aaaad a aaaada

Critical pair: aaaadaaaaad=aaaaadaaada.

Reduce LHS:

[8](aaaada)aaaad
[4](aaaaada)aaad
aaad

Reduce RHS:

[4](aaaaada)aada
aada

Flip LHS and RHS.

Referenced by [13].

[13] da=ad

Overlap of [12] aada=aaad with [8] aaaada=aaaaad:

aad a aaaada

Critical pair: aadaaaaad=aaadaaada.

Reduce LHS:

[12](aada)aaaad
[11](aaada)aaad
[8](aaaada)aad
[4](aaaaada)ad
ad

Reduce RHS:

[11](aaada)aada
[8](aaaada)ada
[4](aaaaada)da
da

Flip LHS and RHS.

Defines rule #5.

Referenced by [14].

[14] dc=1

Overlap of [13] da=ad with [2] aaaaaa=c:

d a aaaaaa

Critical pair: dc=adaaaaa.

Reduce RHS:

[13]a(da)aaaa
[13]aa(da)aaa
[13]aaa(da)aa
[13]aaaa(da)a
[13]aaaaa(da)
[2](aaaaaa)d
[9](cd)
⇒ 1

Defines rule #7.

Referenced by [15].

[15] cb=bc

Overlap of [10] cbd=b with [14] dc=1:

cb d dc

Critical pair: cb=bc.

Defines rule #3.