Certificate for #3482 ⟨a, b | aaabbaaaab=a

Completion settings:

[1] aaabbaaaab=a

Axiom: aaabbaaaab=a.

Referenced by [3].

[2] aaaab=c

Axiom: aaaab=c.

Referenced by [3], [4], [6].

[3] aaabbc=a

Overlap of [1] aaabbaaaab=a with [2] aaaab=c:

aaabb aaaab aaaab

Critical pair: aaabbc=a.

Referenced by [4], [7].

[4] aa=cbc

Overlap of [2] aaaab=c with [3] aaabbc=a:

a aaab aaabbc

Critical pair: aa=cbc.

Defines rule #3.

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

[5] acbc=cbca

Overlap of [4] aa=cbc with [4] aa=cbc:

a a aa

Critical pair: acbc=cbca.

Defines rule #2.

Referenced by [8].

[6] cbccbcb=c

Overlap of [2] aaaab=c with [4] aa=cbc:

aaaab aa

Critical pair: cbcaab=c.

Reduce LHS:

[4]cbc(aa)b
cbccbcb

Defines rule #4.

Referenced by [8], [9], [10], [11], [13], [15].

[7] cbcabbc=a

Overlap of [3] aaabbc=a with [4] aa=cbc:

aaabbc aa

Critical pair: cbcabbc=a.

Defines rule #9.

Referenced by [10], [11], [12], [14], [16].

[8] cbccbcab=ac

Overlap of [5] acbc=cbca with [6] cbccbcb=c:

a cbc cbccbcb

Critical pair: ac=cbcacbcb.

Reduce RHS:

[5]cbc(acbc)b
cbccbcab

Flip LHS and RHS.

Defines rule #8.

Referenced by [15], [16], [17].

[9] cccbcb=cbccbc

Overlap of [6] cbccbcb=c with [6] cbccbcb=c:

cbccb cb cbccbcb

Critical pair: cbccbc=cccbcb.

Flip LHS and RHS.

Defines rule #1.

[10] ccabbc=cbccba

Overlap of [6] cbccbcb=c with [7] cbcabbc=a:

cbccb cb cbcabbc

Critical pair: cbccba=ccabbc.

Flip LHS and RHS.

Defines rule #7.

[11] abccbcb=a

Overlap of [7] cbcabbc=a with [6] cbccbcb=c:

cbcabb c cbccbcb

Critical pair: cbcabbc=abccbcb.

Reduce LHS:

[7](cbcabbc)
a

Flip LHS and RHS.

Defines rule #10.

Referenced by [13], [14], [17].

[12] abcabbc=cbcabba

Overlap of [7] cbcabbc=a with [7] cbcabbc=a:

cbcabb c cbcabbc

Critical pair: cbcabba=abcabbc.

Flip LHS and RHS.

Defines rule #14.

[13] accbcb=abccbc

Overlap of [11] abccbcb=a with [6] cbccbcb=c:

abccb cb cbccbcb

Critical pair: abccbc=accbcb.

Flip LHS and RHS.

Defines rule #6.

[14] acabbc=abccba

Overlap of [11] abccbcb=a with [7] cbcabbc=a:

abccb cb cbcabbc

Critical pair: abccba=acabbc.

Flip LHS and RHS.

Defines rule #12.

[15] cccbcab=cbccbac

Overlap of [6] cbccbcb=c with [8] cbccbcab=ac:

cbccb cb cbccbcab

Critical pair: cbccbac=cccbcab.

Flip LHS and RHS.

Defines rule #5.

[16] abccbcab=cbcabbac

Overlap of [7] cbcabbc=a with [8] cbccbcab=ac:

cbcabb c cbccbcab

Critical pair: cbcabbac=abccbcab.

Flip LHS and RHS.

Defines rule #13.

[17] accbcab=abccbac

Overlap of [11] abccbcb=a with [8] cbccbcab=ac:

abccb cb cbccbcab

Critical pair: abccbac=accbcab.

Flip LHS and RHS.

Defines rule #11.