Certificate for #131 ⟨a, b | aaaabba=1⟩

Completion settings:

[1] aaaabba=1

Axiom: aaaabba=1.

Referenced by [4].

[2] aaaaa=c

Axiom: aaaaa=c.

Defines rule #8.

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

[3] bb=d

Axiom: bb=d.

Defines rule #1.

Referenced by [4], [5].

[4] aaaada=1

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

aaaa bba bb

Critical pair: aaaada=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] aaaaa=c with [2] aaaaa=c:

a aaaa aaaaa

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #2.

[7] cda=a

Overlap of [2] aaaaa=c with [4] aaaada=1:

a aaaa aaaada

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [9].

[8] aaada=aaaad

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

aaaad a aaaada

Critical pair: aaaad=aaada.

Flip LHS and RHS.

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

[9] cd=1

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

cd a aaaada

Critical pair: cd=aaaada.

Reduce RHS:

[4](aaaada)
⇒ 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] aada=aaad

Overlap of [4] aaaada=1 with [8] aaada=aaaad:

aaaad a aaada

Critical pair: aaaadaaaad=aada.

Reduce LHS:

[4](aaaada)aaad
aaad

Flip LHS and RHS.

Referenced by [13].

[12] ada=aad

Overlap of [8] aaada=aaaad with [8] aaada=aaaad:

aaad a aaada

Critical pair: aaadaaaad=aaaadaada.

Reduce LHS:

[8](aaada)aaad
[4](aaaada)aad
aad

Reduce RHS:

[4](aaaada)ada
ada

Flip LHS and RHS.

Referenced by [13].

[13] da=ad

Overlap of [12] ada=aad with [4] aaaada=1:

ad a aaaada

Critical pair: ad=aadaaada.

Reduce RHS:

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

Flip LHS and RHS.

Defines rule #5.

Referenced by [14].

[14] dc=1

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

d a aaaaa

Critical pair: dc=adaaaa.

Reduce RHS:

[13]a(da)aaa
[13]aa(da)aa
[13]aaa(da)a
[13]aaaa(da)
[2](aaaaa)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.