Certificate for #1571 ⟨a, b | aaaaabbaa=a

Completion settings:

[1] aaaaabbaa=a

Axiom: aaaaabbaa=a.

Referenced by [2], [3], [4], [5], [6].

[2] aaaabbaa=aaaaabba

Overlap of [1] aaaaabbaa=a with [1] aaaaabbaa=a:

aaaaabb aa aaaaabbaa

Critical pair: aaaaabba=aaaabbaa.

Flip LHS and RHS.

Referenced by [3], [4], [5], [6].

[3] aaabbaa=aaaabba

Overlap of [1] aaaaabbaa=a with [2] aaaabbaa=aaaaabba:

aaaaabb aa aaaabbaa

Critical pair: aaaaabbaaaaabba=aaabbaa.

Reduce LHS:

[1](aaaaabbaa)aaabba
aaaabba

Flip LHS and RHS.

Referenced by [5].

[4] aabbaa=aaabba

Overlap of [2] aaaabbaa=aaaaabba with [2] aaaabbaa=aaaaabba:

aaaabb aa aaaabbaa

Critical pair: aaaabbaaaaabba=aaaaabbaaabbaa.

Reduce LHS:

[2](aaaabbaa)aaabba
[1](aaaaabbaa)aabba
aaabba

Reduce RHS:

[1](aaaaabbaa)abbaa
aabbaa

Flip LHS and RHS.

Referenced by [5].

[5] abbaa=aabba

Overlap of [4] aabbaa=aaabba with [1] aaaaabbaa=a:

aabb aa aaaaabbaa

Critical pair: aabba=aaabbaaaabbaa.

Reduce RHS:

[3](aaabbaa)aabbaa
[2](aaaabbaa)abbaa
[1](aaaaabbaa)bbaa
abbaa

Flip LHS and RHS.

Defines rule #1.

[6] aaaaaabba=a

Overlap of [1] aaaaabbaa=a with [2] aaaabbaa=aaaaabba:

a aaaabbaa aaaabbaa

Critical pair: aaaaaabba=a.

Defines rule #2.