Certificate for #22284 ⟨a, b | aaa=1, abbbab=bb⟩

Completion settings:

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

Axiom: aaa=1.

Defines rule #9.

Referenced by [3], [14].

Axiom: abbbab=bb.

Defines rule #5.

Referenced by [3], [4], [5], [6], [14].

Overlap of [1] aaa=1 with [2] abbbab=bb:

Critical pair: aabb=bbbab.

Defines rule #7.

Referenced by [5], [14].

Overlap of [2] abbbab=bb with [2] abbbab=bb:

Critical pair: abbbbb=bbbbab.

Defines rule #3.

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

Overlap of [3] aabb=bbbab with [2] abbbab=bb:

Critical pair: abb=bbbabbab.

Flip LHS and RHS.

Referenced by [6], [7], [8], [9], [11], [12], [13].

Overlap of [5] bbbabbab=abb with [2] abbbab=bb:

Critical pair: bbbabbbb=abbbbab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [7], [8].

Overlap of [5] bbbabbab=abb with [6] abbbbab=bbbabbbb:

Critical pair: bbbabbbbbabbbb=abbbbbab.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [6] abbbbab=bbbabbbb with [5] bbbabbab=abb:

Critical pair: ababb=bbbabbbbbab.

Reduce RHS:

Defines rule #8.

Referenced by [9], [10].

Overlap of [5] bbbabbab=abb with [8] ababb=bbbbbbbabab:

Critical pair: bbbabbbbbbbbbabab=abbabb.

Reduce LHS:

Referenced by [12].

Simplify [7] bbbbbbbababbbb=bbbbabab.

Reduce LHS:

Referenced by [11], [12].

Overlap of [4] abbbbb=bbbbab with [10] bbbbbbbbbbbbbbbbbbbbbbbbbbbbabab=bbbbabab:

Critical pair: abbbbbbabab=bbbbabbbbbbbbbbbbbbbbbbbbbbbbbbabab.

Reduce LHS:

Reduce RHS:

Referenced by [13], [16].

Overlap of [10] bbbbbbbbbbbbbbbbbbbbbbbbbbbbabab=bbbbabab with [9] bbbbbbbbbbbababab=abbabb:

Critical pair: bbbbbbbbbbbbbbbbbabbabb=bbbbababab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15].

Overlap of [5] bbbabbab=abb with [11] babbab=bbbbbbbbbbbbbbbbbbbbbbabb:

Critical pair: bbbbbbbbbbbbbbbbbbbbbbbbabb=abb.

Defines rule #2.

Referenced by [14], [16].

Overlap of [3] aabb=bbbab with [13] bbbbbbbbbbbbbbbbbbbbbbbbabb=abb:

Critical pair: aaabb=bbbabbbbbbbbbbbbbbbbbbbbbbbabb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [15], [16].

Overlap of [14] bbbbbbbbbbbbbbbbbbbbbbbbbb=bb with [12] bbbbababab=bbbbbbbbbbbbbbabbb:

Critical pair: bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbb=bbababab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Overlap of [13] bbbbbbbbbbbbbbbbbbbbbbbbabb=abb with [11] babbab=bbbbbbbbbbbbbbbbbbbbbbabb:

Critical pair: bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabb=abbab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.