Certificate for #5152 ⟨a, b | aab=ab, bbab=a⟩

Completion settings:

• Reduction order:
  • Right-to-left recursive path with deg(b) = 0; deg(a) = 1

Axiom: aab=ab.

Referenced by [4], [5], [7].

Axiom: bbab=a.

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

Overlap of [2] bbab=a with [2] bbab=a:

Critical pair: bbaa=abab.

Flip LHS and RHS.

Referenced by [5], [7].

Overlap of [1] aab=ab with [2] bbab=a:

Critical pair: aaa=abbab.

Reduce RHS:

Referenced by [6].

Overlap of [3] abab=bbaa with [2] bbab=a:

Critical pair: abaa=bbaabab.

Reduce RHS:

Referenced by [6], [7].

Overlap of [2] bbab=a with [5] abaa=ab:

Critical pair: bbab=aaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

Overlap of [5] abaa=ab with [1] aab=ab:

Critical pair: abab=abb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [2] bbab=a with [7] abb=bba:

Critical pair: bbbba=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [9].

Overlap of [2] bbab=a with [8] ab=bbbba:

Critical pair: bbbbbba=a.

Defines rule #1.