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log8.txt
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262 lines (258 loc) · 10.2 KB
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0: Zero (Zero())
1: A (A())
2: Div(Zero, A) (Div(0, 1))
Symbol counts:
A: 0 (0)
MinusOne: 1 (0)
Zero: 2 (0)
Pow: 1 (2)
Div: 1 (2)
Mul: 4 (2)
Final precedence:
Zero: 0
MinusOne: 1
A: 2
Mul: 3
Pow: 4
Div: 5
Rules:
{ Div(a, b) -> Mul(a, Pow(b, MinusOne))
Mul(a, Zero) -> Zero }
Equations:
{ Mul(a, b) = Mul(b, a) }
Original:
Div(Zero, A)
Result:
Mul(Zero, Pow(A, MinusOne))
Iteration 0
DAG:
0: Zero (Zero())
1: A (A())
2: Div(Zero, A) (Div(0, 1))
Simplify DAG.
Apply R-rules
DBG2: Apply rules "Div(a, b)" -> "Mul(a, Pow(b, MinusOne))"
DBG2: Check Id 2
DBG: Match rule "Div(a, b)" -> "Mul(a, Pow(b, MinusOne))" on node 2 (Div(Zero, A))
DBG2: Subst l
DBG2: Subst r
DBG2: Substed: "Div(Zero, A)" -> "Mul(Zero, Pow(A, MinusOne))"
Before Clone
DBG2: After If
DBG2: Check Id 0
DBG2: Check Id 1
DBG: Replace node 2 with new term Mul(Zero, Pow(A, MinusOne)) (previously Div(Zero, A))
DBG2: Apply rules "Mul(a, Zero)" -> "Zero"
DBG2: Check Id 4
DBG2: Check Id 0
DBG2: Check Id 3
DBG2: Check Id 5
DBG2: Check Id 1
Apply E-rules
DBG2: Apply rules "Mul(a, b)" -> "Mul(b, a)"
DBG2: Check Id 4
DBG2: Check Id 0
DBG2: Check Id 3
DBG2: Check Id 5
DBG: Match rule "Mul(a, b)" -> "Mul(b, a)" on node 5 (Mul(Zero, Pow(A, MinusOne)))
DBG2: Subst l
DBG2: Subst r
DBG2: Substed: "Mul(Zero, Pow(A, MinusOne))" -> "Mul(Pow(A, MinusOne), Zero)"
DBG2: After If
DBG2: Check Id 1
DBG2: Apply rules "Mul(b, a)" -> "Mul(a, b)"
DBG2: Check Id 4
DBG2: Check Id 0
DBG2: Check Id 3
DBG2: Check Id 5
DBG: Match rule "Mul(b, a)" -> "Mul(a, b)" on node 5 (Mul(Zero, Pow(A, MinusOne)))
DBG2: Subst l
DBG2: Subst r
DBG2: Substed: "Mul(Zero, Pow(A, MinusOne))" -> "Mul(Pow(A, MinusOne), Zero)"
DBG2: After If
DBG2: Check Id 1
New rules:
{ Div(Zero, A) -> Mul(Zero, Pow(A, MinusOne))
Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne))
Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne)) }
DBG: Critical pair: Div(a, b) -> Mul(a, Pow(b, MinusOne)) with Div(a, b) -> Mul(a, Pow(b, MinusOne))
DBG: OrgCritical pair: Mul(a_1, Pow(b_1, MinusOne)) = Mul(a_1, Pow(b_1, MinusOne))
DBG: OrgCritical pair: Mul(a, Pow(b, MinusOne)) = Mul(a, Pow(b, MinusOne))
DBG: Critical pair: Div(a, b) -> Mul(a, Pow(b, MinusOne)) with Mul(a, Zero) -> Zero
DBG: Critical pair: Div(a, b) -> Mul(a, Pow(b, MinusOne)) with Div(Zero, A) -> Mul(Zero, Pow(A, MinusOne))
DBG: OrgCritical pair: Mul(Zero, Pow(A, MinusOne)) = Mul(Zero, Pow(A, MinusOne))
DBG: Critical pair: Div(a, b) -> Mul(a, Pow(b, MinusOne)) with Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne))
DBG: Critical pair: Div(a, b) -> Mul(a, Pow(b, MinusOne)) with Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne))
DBG: Critical pair: Mul(a, Zero) -> Zero with Mul(a, Zero) -> Zero
DBG: OrgCritical pair: Zero = Zero
DBG: Critical pair: Mul(a, Zero) -> Zero with Div(Zero, A) -> Mul(Zero, Pow(A, MinusOne))
DBG: Critical pair: Mul(a, Zero) -> Zero with Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne))
DBG: OrgCritical pair: Mul(Zero, Pow(A, MinusOne)) = Zero
DBG: Simplified critical pair: Mul(Zero, Pow(A, MinusOne)) = Zero
DBG: Critical pair: Mul(a, Zero) -> Zero with Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne))
DBG: OrgCritical pair: Mul(Zero, Pow(A, MinusOne)) = Zero
DBG: Simplified critical pair: Mul(Zero, Pow(A, MinusOne)) = Zero
DBG: Critical pair: Div(Zero, A) -> Mul(Zero, Pow(A, MinusOne)) with Div(Zero, A) -> Mul(Zero, Pow(A, MinusOne))
DBG: OrgCritical pair: Mul(Zero, Pow(A, MinusOne)) = Mul(Zero, Pow(A, MinusOne))
DBG: Critical pair: Div(Zero, A) -> Mul(Zero, Pow(A, MinusOne)) with Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne))
DBG: Critical pair: Div(Zero, A) -> Mul(Zero, Pow(A, MinusOne)) with Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne))
DBG: Critical pair: Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne)) with Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne))
DBG: OrgCritical pair: Mul(Zero, Pow(A, MinusOne)) = Mul(Zero, Pow(A, MinusOne))
DBG: Critical pair: Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne)) with Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne))
DBG: OrgCritical pair: Mul(Zero, Pow(A, MinusOne)) = Mul(Zero, Pow(A, MinusOne))
DBG: Critical pair: Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne)) with Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne))
DBG: OrgCritical pair: Mul(Zero, Pow(A, MinusOne)) = Mul(Zero, Pow(A, MinusOne))
Computed 2 critical pairs
Top 5 critical pairs:
Mul(Zero, Pow(A, MinusOne)) = Zero
Mul(Zero, Pow(A, MinusOne)) = Zero
Rules before KBC:
{ Div(a, b) -> Mul(a, Pow(b, MinusOne))
Mul(a, Zero) -> Zero
Div(Zero, A) -> Mul(Zero, Pow(A, MinusOne))
Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne))
Mul(Pow(A, MinusOne), Zero) -> Mul(Zero, Pow(A, MinusOne)) }
Intermediate State:
Rules:
{ Mul(Zero, Pow(A, MinusOne)) -> Zero
Div(a, b) -> Mul(a, Pow(b, MinusOne))
Mul(a, Zero) -> Zero
Div(Zero, A) -> Zero
Mul(Pow(A, MinusOne), Zero) -> Zero
Mul(Pow(A, MinusOne), Zero) -> Zero }
Equations:
{ Mul(a, b) = Mul(b, a) }
Original:
Div(Zero, A)
Result:
Zero
Extracted term:
Mul(Zero, Pow(A, MinusOne))
Iteration 1
DAG:
0: Zero (Zero())
1: A (A())
3: MinusOne (MinusOne())
4: Pow(A, MinusOne) (Pow(1, 3))
5: Mul(Zero, Pow(A, MinusOne)) (Mul(0, 4))
Simplify DAG.
Apply R-rules
DBG2: Apply rules "Mul(Zero, Pow(A, MinusOne))" -> "Zero"
DBG2: Check Id 4
DBG2: Check Id 0
DBG2: Check Id 3
DBG2: Check Id 5
DBG: Match rule "Mul(Zero, Pow(A, MinusOne))" -> "Zero" on node 5 (Mul(Zero, Pow(A, MinusOne)))
DBG2: Subst l
DBG2: Subst r
DBG2: Substed: "Mul(Zero, Pow(A, MinusOne))" -> "Zero"
Before Clone
DBG2: After If
DBG2: Check Id 1
DBG: Replace node 5 with new term Zero (previously Mul(Zero, Pow(A, MinusOne)))
DBG2: Apply rules "Div(a, b)" -> "Mul(a, Pow(b, MinusOne))"
DBG2: Check Id 4
DBG2: Check Id 0
DBG2: Check Id 3
DBG2: Check Id 1
DBG2: Apply rules "Mul(a, Zero)" -> "Zero"
DBG2: Check Id 4
DBG2: Check Id 0
DBG2: Check Id 3
DBG2: Check Id 1
DBG2: Apply rules "Div(Zero, A)" -> "Zero"
DBG2: Check Id 4
DBG2: Check Id 0
DBG2: Check Id 3
DBG2: Check Id 1
DBG2: Apply rules "Mul(Pow(A, MinusOne), Zero)" -> "Zero"
DBG2: Check Id 4
DBG2: Check Id 0
DBG2: Check Id 3
DBG2: Check Id 1
DBG2: Apply rules "Mul(Pow(A, MinusOne), Zero)" -> "Zero"
DBG2: Check Id 4
DBG2: Check Id 0
DBG2: Check Id 3
DBG2: Check Id 1
Apply E-rules
DBG2: Apply rules "Mul(a, b)" -> "Mul(b, a)"
DBG2: Check Id 4
DBG2: Check Id 0
DBG2: Check Id 3
DBG2: Check Id 1
DBG2: Apply rules "Mul(b, a)" -> "Mul(a, b)"
DBG2: Check Id 4
DBG2: Check Id 0
DBG2: Check Id 3
DBG2: Check Id 1
New rules:
{ Mul(Zero, Pow(A, MinusOne)) -> Zero }
DBG: Critical pair: Mul(Zero, Pow(A, MinusOne)) -> Zero with Mul(Zero, Pow(A, MinusOne)) -> Zero
DBG: OrgCritical pair: Zero = Zero
DBG: Critical pair: Mul(Zero, Pow(A, MinusOne)) -> Zero with Div(a, b) -> Mul(a, Pow(b, MinusOne))
DBG: Critical pair: Mul(Zero, Pow(A, MinusOne)) -> Zero with Mul(a, Zero) -> Zero
DBG: Critical pair: Mul(Zero, Pow(A, MinusOne)) -> Zero with Div(Zero, A) -> Zero
DBG: Critical pair: Mul(Zero, Pow(A, MinusOne)) -> Zero with Mul(Pow(A, MinusOne), Zero) -> Zero
DBG: Critical pair: Mul(Zero, Pow(A, MinusOne)) -> Zero with Mul(Pow(A, MinusOne), Zero) -> Zero
DBG: Critical pair: Mul(Zero, Pow(A, MinusOne)) -> Zero with Mul(Zero, Pow(A, MinusOne)) -> Zero
DBG: OrgCritical pair: Zero = Zero
DBG: Critical pair: Div(a, b) -> Mul(a, Pow(b, MinusOne)) with Div(a, b) -> Mul(a, Pow(b, MinusOne))
DBG: OrgCritical pair: Mul(a_1, Pow(b_1, MinusOne)) = Mul(a_1, Pow(b_1, MinusOne))
DBG: OrgCritical pair: Mul(a, Pow(b, MinusOne)) = Mul(a, Pow(b, MinusOne))
DBG: Critical pair: Div(a, b) -> Mul(a, Pow(b, MinusOne)) with Mul(a, Zero) -> Zero
DBG: Critical pair: Div(a, b) -> Mul(a, Pow(b, MinusOne)) with Div(Zero, A) -> Zero
DBG: OrgCritical pair: Zero = Mul(Zero, Pow(A, MinusOne))
DBG: Critical pair: Div(a, b) -> Mul(a, Pow(b, MinusOne)) with Mul(Pow(A, MinusOne), Zero) -> Zero
DBG: Critical pair: Div(a, b) -> Mul(a, Pow(b, MinusOne)) with Mul(Pow(A, MinusOne), Zero) -> Zero
DBG: Critical pair: Div(a, b) -> Mul(a, Pow(b, MinusOne)) with Mul(Zero, Pow(A, MinusOne)) -> Zero
DBG: Critical pair: Mul(a, Zero) -> Zero with Mul(a, Zero) -> Zero
DBG: OrgCritical pair: Zero = Zero
DBG: Critical pair: Mul(a, Zero) -> Zero with Div(Zero, A) -> Zero
DBG: Critical pair: Mul(a, Zero) -> Zero with Mul(Pow(A, MinusOne), Zero) -> Zero
DBG: OrgCritical pair: Zero = Zero
DBG: Critical pair: Mul(a, Zero) -> Zero with Mul(Pow(A, MinusOne), Zero) -> Zero
DBG: OrgCritical pair: Zero = Zero
DBG: Critical pair: Mul(a, Zero) -> Zero with Mul(Zero, Pow(A, MinusOne)) -> Zero
DBG: Critical pair: Div(Zero, A) -> Zero with Div(Zero, A) -> Zero
DBG: OrgCritical pair: Zero = Zero
DBG: Critical pair: Div(Zero, A) -> Zero with Mul(Pow(A, MinusOne), Zero) -> Zero
DBG: Critical pair: Div(Zero, A) -> Zero with Mul(Pow(A, MinusOne), Zero) -> Zero
DBG: Critical pair: Div(Zero, A) -> Zero with Mul(Zero, Pow(A, MinusOne)) -> Zero
DBG: Critical pair: Mul(Pow(A, MinusOne), Zero) -> Zero with Mul(Pow(A, MinusOne), Zero) -> Zero
DBG: OrgCritical pair: Zero = Zero
DBG: Critical pair: Mul(Pow(A, MinusOne), Zero) -> Zero with Mul(Pow(A, MinusOne), Zero) -> Zero
DBG: OrgCritical pair: Zero = Zero
DBG: Critical pair: Mul(Pow(A, MinusOne), Zero) -> Zero with Mul(Zero, Pow(A, MinusOne)) -> Zero
DBG: Critical pair: Mul(Pow(A, MinusOne), Zero) -> Zero with Mul(Pow(A, MinusOne), Zero) -> Zero
DBG: OrgCritical pair: Zero = Zero
DBG: Critical pair: Mul(Pow(A, MinusOne), Zero) -> Zero with Mul(Zero, Pow(A, MinusOne)) -> Zero
DBG: Critical pair: Mul(Zero, Pow(A, MinusOne)) -> Zero with Mul(Zero, Pow(A, MinusOne)) -> Zero
DBG: OrgCritical pair: Zero = Zero
Computed 0 critical pairs
Top 5 critical pairs:
Rules before KBC:
{ Mul(Zero, Pow(A, MinusOne)) -> Zero
Div(a, b) -> Mul(a, Pow(b, MinusOne))
Mul(a, Zero) -> Zero
Div(Zero, A) -> Zero
Mul(Pow(A, MinusOne), Zero) -> Zero
Mul(Pow(A, MinusOne), Zero) -> Zero
Mul(Zero, Pow(A, MinusOne)) -> Zero }
Intermediate State:
Rules:
{ Mul(Zero, Pow(A, MinusOne)) -> Zero
Div(a, b) -> Mul(a, Pow(b, MinusOne))
Mul(a, Zero) -> Zero
Div(Zero, A) -> Zero
Mul(Pow(A, MinusOne), Zero) -> Zero
Mul(Pow(A, MinusOne), Zero) -> Zero
Mul(Zero, Pow(A, MinusOne)) -> Zero }
Equations:
{ Mul(a, b) = Mul(b, a) }
Original:
Div(Zero, A)
Result:
Zero
Extracted term:
Zero