Certificate for #4015 ⟨a, b | aaabbaaba=ab⟩

Completion settings:

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

Axiom: aaabbaaba=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #5.

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

Overlap of [1] aaabbaaba=ab with [2] abb=c:

Critical pair: aacaaba=ab.

Defines rule #2.

Referenced by [4], [5], [6], [7], [8].

Overlap of [3] aacaaba=ab with [2] abb=c:

Critical pair: aacaabc=abbb.

Reduce RHS:

Defines rule #3.

Referenced by [6], [8], [9], [12], [14], [15], [16], [17], [18], [19].

Overlap of [3] aacaaba=ab with [3] aacaaba=ab:

Critical pair: aacaabab=abacaaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

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

Overlap of [3] aacaaba=ab with [4] aacaabc=cb:

Critical pair: aacaabcb=abacaabc.

Reduce LHS:

Defines rule #8.

Overlap of [3] aacaaba=ab with [5] abacaaba=c:

Critical pair: aacac=abcaaba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [15], [16].

Overlap of [3] aacaaba=ab with [5] abacaaba=c:

Critical pair: aacaabc=abbacaaba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [12], [13].

Overlap of [5] abacaaba=c with [4] aacaabc=cb:

Critical pair: abacaabcb=cacaabc.

Defines rule #15.

Overlap of [5] abacaaba=c with [5] abacaaba=c:

Critical pair: abacac=ccaaba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [14].

Overlap of [5] abacaaba=c with [5] abacaaba=c:

Critical pair: abacaabc=cbacaaba.

Flip LHS and RHS.

Defines rule #11.

Referenced by [19].

Overlap of [8] cacaaba=cb with [4] aacaabc=cb:

Critical pair: cacaabcb=cbacaabc.

Defines rule #13.

Overlap of [8] cacaaba=cb with [5] abacaaba=c:

Critical pair: cacac=cbcaaba.

Flip LHS and RHS.

Defines rule #10.

Referenced by [17].

Overlap of [10] ccaaba=abacac with [4] aacaabc=cb:

Critical pair: ccaabcb=abacacacaabc.

Defines rule #12.

Overlap of [4] aacaabc=cb with [7] abcaaba=aacac:

Critical pair: aacaaacac=cbaaba.

Flip LHS and RHS.

Defines rule #9.

Referenced by [18].

Overlap of [7] abcaaba=aacac with [4] aacaabc=cb:

Critical pair: abcaabcb=aacacacaabc.

Defines rule #14.

Overlap of [13] cbcaaba=cacac with [4] aacaabc=cb:

Critical pair: cbcaabcb=cacacacaabc.

Defines rule #17.

Overlap of [15] cbaaba=aacaaacac with [4] aacaabc=cb:

Critical pair: cbaabcb=aacaaacacacaabc.

Defines rule #16.

Overlap of [11] cbacaaba=abacaabc with [4] aacaabc=cb:

Critical pair: cbacaabcb=abacaabcacaabc.

Defines rule #18.