Certificate for #3976 ⟨a, b | aaabaabba=ab⟩

Completion settings:

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

Axiom: aaabaabba=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #4.

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

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

Critical pair: aaabaca=ab.

Defines rule #1.

Referenced by [4], [5], [6], [7], [10].

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

Critical pair: aaabacc=abbb.

Reduce RHS:

Defines rule #3.

Referenced by [6], [7], [8], [12], [15].

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

Critical pair: aaabacab=abaabaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

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

Overlap of [3] aaabaca=ab with [4] aaabacc=cb:

Critical pair: aaabaccb=abaabacc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [8], [9].

Overlap of [3] aaabaca=ab with [5] abaabaca=c:

Critical pair: aaabacc=abbaabaca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [11], [12], [13], [14], [16].

Overlap of [5] abaabaca=c with [4] aaabacc=cb:

Critical pair: abaabaccb=caabacc.

Reduce LHS:

Defines rule #11.

Referenced by [17].

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

Critical pair: abaabacc=cbaabaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [15], [16], [17].

Overlap of [3] aaabaca=ab with [7] caabaca=cb:

Critical pair: aaabacb=ababaca.

Flip LHS and RHS.

Defines rule #5.

Referenced by [17].

Overlap of [5] abaabaca=c with [7] caabaca=cb:

Critical pair: abaabacb=cabaca.

Defines rule #12.

Overlap of [7] caabaca=cb with [4] aaabacc=cb:

Critical pair: caabaccb=cbaabacc.

Flip LHS and RHS.

Defines rule #10.

Referenced by [15].

Overlap of [7] caabaca=cb with [5] abaabaca=c:

Critical pair: caabacc=cbbaabaca.

Flip LHS and RHS.

Defines rule #14.

Overlap of [7] caabaca=cb with [7] caabaca=cb:

Critical pair: caabacb=cbabaca.

Flip LHS and RHS.

Defines rule #6.

Overlap of [9] cbaabaca=cbb with [4] aaabacc=cb:

Critical pair: cbaabaccb=cbbaabacc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.

Overlap of [9] cbaabaca=cbb with [7] caabaca=cb:

Critical pair: cbaabacb=cbbabaca.

Flip LHS and RHS.

Defines rule #13.

Overlap of [9] cbaabaca=cbb with [10] ababaca=aaabacb:

Critical pair: cbaabacaaabacb=cbbbabaca.

Reduce LHS:

Reduce RHS:

Defines rule #16.