Certificate for #3698 ⟨a, b | abaaaaaaab=b⟩

Completion settings:

[1] abaaaaaaab=b

Axiom: abaaaaaaab=b.

Referenced by [2], [3], [4], [5], [6], [7], [8], [9].

[2] baaaaaaab=abaaaaaab

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

abaaaaaa ab abaaaaaaab

Critical pair: abaaaaaab=baaaaaaab.

Flip LHS and RHS.

Referenced by [3], [9], [10].

[3] baaaaaab=abaaaaab

Overlap of [2] baaaaaaab=abaaaaaab with [1] abaaaaaaab=b:

baaaaaa ab abaaaaaaab

Critical pair: baaaaaab=abaaaaaabaaaaaaab.

Reduce RHS:

[1]abaaaaa(abaaaaaaab)
⇒ abaaaaab

Referenced by [4], [9], [10], [11].

[4] baaaaab=abaaaab

Overlap of [3] baaaaaab=abaaaaab with [1] abaaaaaaab=b:

baaaaa ab abaaaaaaab

Critical pair: baaaaab=abaaaaabaaaaaaab.

Reduce RHS:

[1]abaaaa(abaaaaaaab)
⇒ abaaaab

Referenced by [5], [9], [10], [11], [12].

[5] baaaab=abaaab

Overlap of [4] baaaaab=abaaaab with [1] abaaaaaaab=b:

baaaa ab abaaaaaaab

Critical pair: baaaab=abaaaabaaaaaaab.

Reduce RHS:

[1]abaaa(abaaaaaaab)
⇒ abaaab

Referenced by [6], [9], [10], [11], [12], [13].

[6] baaab=abaab

Overlap of [5] baaaab=abaaab with [1] abaaaaaaab=b:

baaa ab abaaaaaaab

Critical pair: baaab=abaaabaaaaaaab.

Reduce RHS:

[1]abaa(abaaaaaaab)
⇒ abaab

Referenced by [7], [9], [10], [11], [12], [13], [14].

[7] baab=abab

Overlap of [6] baaab=abaab with [1] abaaaaaaab=b:

baa ab abaaaaaaab

Critical pair: baab=abaabaaaaaaab.

Reduce RHS:

[1]aba(abaaaaaaab)
⇒ abab

Referenced by [8], [9], [10], [11], [12], [13], [14], [15].

[8] bab=abb

Overlap of [7] baab=abab with [1] abaaaaaaab=b:

ba ab abaaaaaaab

Critical pair: bab=ababaaaaaaab.

Reduce RHS:

[1]ab(abaaaaaaab)
⇒ abb

Defines rule #1.

Referenced by [9], [10], [11], [12], [13], [14], [15].

[9] aaaaaaaabb=b

Overlap of [1] abaaaaaaab=b with [2] baaaaaaab=abaaaaaab:

a baaaaaaab baaaaaaab

Critical pair: aabaaaaaab=b.

Reduce LHS:

[3]aa(baaaaaab)
[4]⇒ aaa(baaaaab)
[5]⇒ aaaa(baaaab)
[6]⇒ aaaaa(baaab)
[7]⇒ aaaaaa(baab)
[8]⇒ aaaaaaa(bab)
⇒ aaaaaaaabb

Defines rule #8.

[10] baaaaaaab=aaaaaaabb

Simplify [2] baaaaaaab=abaaaaaab.

Reduce RHS:

[3]a(baaaaaab)
[4]⇒ aa(baaaaab)
[5]⇒ aaa(baaaab)
[6]⇒ aaaa(baaab)
[7]⇒ aaaaa(baab)
[8]⇒ aaaaaa(bab)
⇒ aaaaaaabb

Defines rule #7.

[11] baaaaaab=aaaaaabb

Simplify [3] baaaaaab=abaaaaab.

Reduce RHS:

[4]a(baaaaab)
[5]⇒ aa(baaaab)
[6]⇒ aaa(baaab)
[7]⇒ aaaa(baab)
[8]⇒ aaaaa(bab)
⇒ aaaaaabb

Defines rule #6.

[12] baaaaab=aaaaabb

Simplify [4] baaaaab=abaaaab.

Reduce RHS:

[5]a(baaaab)
[6]⇒ aa(baaab)
[7]⇒ aaa(baab)
[8]⇒ aaaa(bab)
⇒ aaaaabb

Defines rule #5.

[13] baaaab=aaaabb

Simplify [5] baaaab=abaaab.

Reduce RHS:

[6]a(baaab)
[7]⇒ aa(baab)
[8]⇒ aaa(bab)
⇒ aaaabb

Defines rule #4.

[14] baaab=aaabb

Simplify [6] baaab=abaab.

Reduce RHS:

[7]a(baab)
[8]⇒ aa(bab)
⇒ aaabb

Defines rule #3.

[15] baab=aabb

Simplify [7] baab=abab.

Reduce RHS:

[8]a(bab)
⇒ aabb

Defines rule #2.