Certificate for #5333 ⟨a, b | abaabba=baba⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(c) = 0; deg(b) = deg(a) = 1, b < a
• Auxiliary generators:
  1. aabb=c

Axiom: abaabba=baba.

Referenced by [3].

Axiom: aabb=c.

Defines rule #4.

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

Overlap of [1] abaabba=baba with [2] aabb=c:

Critical pair: abca=baba.

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [2] aabb=c with [3] baba=abca:

Critical pair: aababca=caba.

Referenced by [9].

Overlap of [3] baba=abca with [2] aabb=c:

Critical pair: babc=abcaabb.

Reduce RHS:

Defines rule #1.

Referenced by [7], [8], [9], [10], [11], [13], [14].

Overlap of [3] baba=abca with [3] baba=abca:

Critical pair: baabca=abcaba.

Flip LHS and RHS.

Defines rule #7.

Referenced by [13], [14], [15].

Overlap of [2] aabb=c with [5] babc=abcc:

Critical pair: aababcc=cabc.

Reduce LHS:

Defines rule #5.

Overlap of [3] baba=abca with [5] babc=abcc:

Critical pair: baabcc=abcabc.

Flip LHS and RHS.

Defines rule #3.

Referenced by [10], [11], [12], [15].

Simplify [4] aababca=caba.

Reduce LHS:

Defines rule #8.

Referenced by [10], [13].

Overlap of [9] aaabcca=caba with [8] abcabc=baabcc:

Critical pair: aaabccbaabcc=cababcabc.

Reduce RHS:

Defines rule #12.

Overlap of [5] babc=abcc with [8] abcabc=baabcc:

Critical pair: bbaabcc=abccabc.

Defines rule #6.

Overlap of [8] abcabc=baabcc with [8] abcabc=baabcc:

Critical pair: abcbaabcc=baabccabc.

Defines rule #10.

Overlap of [9] aaabcca=caba with [6] abcaba=baabca:

Critical pair: aaabccbaabca=cababcaba.

Reduce RHS:

Defines rule #13.

Overlap of [5] babc=abcc with [6] abcaba=baabca:

Critical pair: bbaabca=abccaba.

Defines rule #9.

Overlap of [8] abcabc=baabcc with [6] abcaba=baabca:

Critical pair: abcbaabca=baabccaba.

Defines rule #11.