Certificate for #832 ⟨a, b | abaaaaab=b

Completion settings:

[1] abaaaaab=b

Axiom: abaaaaab=b.

Referenced by [2], [3], [4], [5], [6], [7].

[2] baaaaab=abaaaab

Overlap of [1] abaaaaab=b with [1] abaaaaab=b:

abaaaa ab abaaaaab

Critical pair: abaaaab=baaaaab.

Flip LHS and RHS.

Referenced by [3], [7], [8].

[3] baaaab=abaaab

Overlap of [2] baaaaab=abaaaab with [1] abaaaaab=b:

baaaa ab abaaaaab

Critical pair: baaaab=abaaaabaaaaab.

Reduce RHS:

[1]abaaa(abaaaaab)
abaaab

Referenced by [4], [7], [8], [9].

[4] baaab=abaab

Overlap of [3] baaaab=abaaab with [1] abaaaaab=b:

baaa ab abaaaaab

Critical pair: baaab=abaaabaaaaab.

Reduce RHS:

[1]abaa(abaaaaab)
abaab

Referenced by [5], [7], [8], [9], [10].

[5] baab=abab

Overlap of [4] baaab=abaab with [1] abaaaaab=b:

baa ab abaaaaab

Critical pair: baab=abaabaaaaab.

Reduce RHS:

[1]aba(abaaaaab)
abab

Referenced by [6], [7], [8], [9], [10], [11].

[6] bab=abb

Overlap of [5] baab=abab with [1] abaaaaab=b:

ba ab abaaaaab

Critical pair: bab=ababaaaaab.

Reduce RHS:

[1]ab(abaaaaab)
abb

Defines rule #1.

Referenced by [7], [8], [9], [10], [11].

[7] aaaaaabb=b

Overlap of [1] abaaaaab=b with [2] baaaaab=abaaaab:

a baaaaab baaaaab

Critical pair: aabaaaab=b.

Reduce LHS:

[3]aa(baaaab)
[4]aaa(baaab)
[5]aaaa(baab)
[6]aaaaa(bab)
aaaaaabb

Defines rule #6.

[8] baaaaab=aaaaabb

Simplify [2] baaaaab=abaaaab.

Reduce RHS:

[3]a(baaaab)
[4]aa(baaab)
[5]aaa(baab)
[6]aaaa(bab)
aaaaabb

Defines rule #5.

[9] baaaab=aaaabb

Simplify [3] baaaab=abaaab.

Reduce RHS:

[4]a(baaab)
[5]aa(baab)
[6]aaa(bab)
aaaabb

Defines rule #4.

[10] baaab=aaabb

Simplify [4] baaab=abaab.

Reduce RHS:

[5]a(baab)
[6]aa(bab)
aaabb

Defines rule #3.

[11] baab=aabb

Simplify [5] baab=abab.

Reduce RHS:

[6]a(bab)
aabb

Defines rule #2.