Certificate for #5362 ⟨a, b | aab=aa, baa=ab

Completion settings:

[1] aab=aa

Axiom: aab=aa.

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

[2] baa=ab

Axiom: baa=ab.

Referenced by [3], [4], [5], [6], [7], [8].

[3] abb=ab

Overlap of [2] baa=ab with [1] aab=aa:

b aa aab

Critical pair: baa=abb.

Reduce LHS:

[2](baa)
ab

Flip LHS and RHS.

Referenced by [5].

[4] abab=aba

Overlap of [2] baa=ab with [1] aab=aa:

ba a aab

Critical pair: baaa=abab.

Reduce LHS:

[2](baa)a
aba

Flip LHS and RHS.

Referenced by [5].

[5] aba=aa

Overlap of [3] abb=ab with [2] baa=ab:

ab b baa

Critical pair: abab=abaa.

Reduce LHS:

[4](abab)
aba

Reduce RHS:

[2]a(baa)
[1](aab)
aa

Referenced by [6], [7].

[6] aaa=aa

Overlap of [5] aba=aa with [2] baa=ab:

a ba baa

Critical pair: aab=aaa.

Reduce LHS:

[1](aab)
aa

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

[7] ab=aa

Overlap of [2] baa=ab with [6] aaa=aa:

b aa aaa

Critical pair: baa=aba.

Reduce LHS:

[2](baa)
ab

Reduce RHS:

[5](aba)
aa

Defines rule #1.

Referenced by [8].

[8] baa=aa

Simplify [2] baa=ab.

Reduce RHS:

[7](ab)
aa

Defines rule #3.