Certificate for #4062 ⟨a, b | aabaaaaab=ab

Completion settings:

[1] aabaaaaab=ab

Axiom: aabaaaaab=ab.

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

[2] abaaaaab=aabaaaab

Overlap of [1] aabaaaaab=ab with [1] aabaaaaab=ab:

aabaaa aab aabaaaaab

Critical pair: aabaaaab=abaaaaab.

Flip LHS and RHS.

Referenced by [3], [6], [7].

[3] abaaaab=aabaaab

Overlap of [2] abaaaaab=aabaaaab with [1] aabaaaaab=ab:

abaaa aab aabaaaaab

Critical pair: abaaaab=aabaaaabaaaaab.

Reduce RHS:

[1]aabaa(aabaaaaab)
aabaaab

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

[4] abaaab=aabaab

Overlap of [3] abaaaab=aabaaab with [1] aabaaaaab=ab:

abaa aab aabaaaaab

Critical pair: abaaab=aabaaabaaaaab.

Reduce RHS:

[1]aaba(aabaaaaab)
aabaab

Referenced by [5], [6], [7], [8], [9].

[5] abaab=aabab

Overlap of [4] abaaab=aabaab with [1] aabaaaaab=ab:

aba aab aabaaaaab

Critical pair: abaab=aabaabaaaaab.

Reduce RHS:

[1]aab(aabaaaaab)
aabab

Defines rule #1.

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

[6] aaaaaabab=ab

Overlap of [1] aabaaaaab=ab with [2] abaaaaab=aabaaaab:

a abaaaaab abaaaaab

Critical pair: aaabaaaab=ab.

Reduce LHS:

[3]aa(abaaaab)
[4]aaa(abaaab)
[5]aaaa(abaab)
aaaaaabab

Defines rule #5.

[7] abaaaaab=aaaaabab

Simplify [2] abaaaaab=aabaaaab.

Reduce RHS:

[3]a(abaaaab)
[4]aa(abaaab)
[5]aaa(abaab)
aaaaabab

Defines rule #4.

[8] abaaaab=aaaabab

Simplify [3] abaaaab=aabaaab.

Reduce RHS:

[4]a(abaaab)
[5]aa(abaab)
aaaabab

Defines rule #3.

[9] abaaab=aaabab

Simplify [4] abaaab=aabaab.

Reduce RHS:

[5]a(abaab)
aaabab

Defines rule #2.