| Back: | ⟨a, b | abbabbbba=ba⟩ |
|---|
Completion settings:
Axiom: abbabbbba=ba.
Referenced by [3], [4], [5], [6], [13].
Axiom: bbbbbba=c.
Referenced by [4], [6], [7], [8], [14].
Overlap of [1] abbabbbba=ba with [1] abbabbbba=ba:
Critical pair: abbabbbbba=babbabbbba.
Reduce RHS:
| [1] | b(abbabbbba) |
| ⇒ bba |
Referenced by [6], [7], [8], [9], [15].
Overlap of [2] bbbbbba=c with [1] abbabbbba=ba:
Critical pair: bbbbbbba=cbbabbbba.
Reduce LHS:
| [2] | b(bbbbbba) |
| ⇒ bc |
Flip LHS and RHS.
Referenced by [5], [8], [10], [11], [16].
Overlap of [4] cbbabbbba=bc with [1] abbabbbba=ba:
Critical pair: cbbabbbbba=bcbbabbbba.
Reduce RHS:
| [4] | b(cbbabbbba) |
| ⇒ bbc |
Overlap of [1] abbabbbba=ba with [3] abbabbbbba=bba:
Critical pair: abbabbbbbba=babbabbbbba.
Reduce LHS:
| [2] | abba(bbbbbba) |
| ⇒ abbac |
Reduce RHS:
| [3] | b(abbabbbbba) |
| ⇒ bbba |
Flip LHS and RHS.
Defines rule #1.
Referenced by [7], [9], [12], [13], [14], [15], [16].
Overlap of [3] abbabbbbba=bba with [3] abbabbbbba=bba:
Critical pair: abbabbbbbbba=bbabbabbbbba.
Reduce LHS:
| [2] | abbab(bbbbbba) |
| ⇒ abbabc |
Reduce RHS:
| [3] | bb(abbabbbbba) |
| [6] | ⇒ b(bbba) |
| ⇒ babbac |
Defines rule #3.
Overlap of [4] cbbabbbba=bc with [3] abbabbbbba=bba:
Critical pair: cbbabbbbbba=bcbbabbbbba.
Reduce LHS:
| [2] | cbba(bbbbbba) |
| ⇒ cbbac |
Reduce RHS:
| [5] | b(cbbabbbbba) |
| ⇒ bbbc |
Flip LHS and RHS.
Defines rule #2.
Referenced by [10].
Overlap of [6] bbba=abbac with [3] abbabbbbba=bba:
Critical pair: bbbbba=abbacbbabbbbba.
Reduce LHS:
| [6] | bb(bbba) |
| ⇒ bbabbac |
Reduce RHS:
| [5] | abba(cbbabbbbba) |
| ⇒ abbabbc |
Flip LHS and RHS.
Defines rule #5.
Overlap of [8] bbbc=cbbac with [4] cbbabbbba=bc:
Critical pair: bbbbc=cbbacbbabbbba.
Reduce LHS:
| [8] | b(bbbc) |
| ⇒ bcbbac |
Reduce RHS:
| [4] | cbba(cbbabbbba) |
| ⇒ cbbabc |
Flip LHS and RHS.
Defines rule #4.
Referenced by [11].
Overlap of [10] cbbabc=bcbbac with [4] cbbabbbba=bc:
Critical pair: cbbabbc=bcbbacbbabbbba.
Reduce RHS:
| [4] | bcbba(cbbabbbba) |
| [10] | ⇒ b(cbbabc) |
| ⇒ bbcbbac |
Defines rule #7.
Simplify [5] cbbabbbbba=bbc.
Reduce LHS:
| [6] | cbbabb(bbba) |
| ⇒ cbbabbabbac |
Defines rule #11.
Overlap of [1] abbabbbba=ba with [6] bbba=abbac:
Critical pair: abbababbac=ba.
Defines rule #8.
Overlap of [2] bbbbbba=c with [6] bbba=abbac:
Critical pair: bbbabbac=c.
Reduce LHS:
| [6] | (bbba)bbac |
| ⇒ abbacbbac |
Defines rule #6.
Overlap of [3] abbabbbbba=bba with [6] bbba=abbac:
Critical pair: abbabbabbac=bba.
Defines rule #10.
Overlap of [4] cbbabbbba=bc with [6] bbba=abbac:
Critical pair: cbbababbac=bc.
Defines rule #9.