Certificate for #1850 ⟨a, b | aaaabaaa=aa

Completion settings:

[1] aaaabaaa=aa

Axiom: aaaabaaa=aa.

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

[2] aaabaaa=aaaabaa

Overlap of [1] aaaabaaa=aa with [1] aaaabaaa=aa:

aaaab aaa aaaabaaa

Critical pair: aaaabaa=aaabaaa.

Flip LHS and RHS.

Referenced by [3], [4].

[3] aabaaa=aaabaa

Overlap of [1] aaaabaaa=aa with [2] aaabaaa=aaaabaa:

aaaab aaa aaabaaa

Critical pair: aaaabaaaabaa=aabaaa.

Reduce LHS:

[1](aaaabaaa)abaa
aaabaa

Flip LHS and RHS.

Defines rule #1.

[4] aaaaabaa=aa

Overlap of [1] aaaabaaa=aa with [2] aaabaaa=aaaabaa:

aaaabaa a aaabaaa

Critical pair: aaaabaaaaaabaa=aaaabaaa.

Reduce LHS:

[1](aaaabaaa)aaabaa
aaaaabaa

Reduce RHS:

[1](aaaabaaa)
aa

Defines rule #2.