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(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
and(not(not(x)), y, not(z)) → and(y, band(x, z), x)
Rewrite Strategy: INNERMOST
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(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
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(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
and(not(not(z0)), z1, not(z2)) → and(z1, band(z0, z2), z0)
Tuples:
AND(not(not(z0)), z1, not(z2)) → c(AND(z1, band(z0, z2), z0))
S tuples:
AND(not(not(z0)), z1, not(z2)) → c(AND(z1, band(z0, z2), z0))
K tuples:none
Defined Rule Symbols:
and
Defined Pair Symbols:
AND
Compound Symbols:
c
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(3) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
AND(not(not(z0)), z1, not(z2)) → c(AND(z1, band(z0, z2), z0))
We considered the (Usable) Rules:none
And the Tuples:
AND(not(not(z0)), z1, not(z2)) → c(AND(z1, band(z0, z2), z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(AND(x1, x2, x3)) = [4]x1 + [4]x2
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POL(band(x1, x2)) = 0
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POL(c(x1)) = x1
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POL(not(x1)) = [4] + x1
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(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
and(not(not(z0)), z1, not(z2)) → and(z1, band(z0, z2), z0)
Tuples:
AND(not(not(z0)), z1, not(z2)) → c(AND(z1, band(z0, z2), z0))
S tuples:none
K tuples:
AND(not(not(z0)), z1, not(z2)) → c(AND(z1, band(z0, z2), z0))
Defined Rule Symbols:
and
Defined Pair Symbols:
AND
Compound Symbols:
c
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(5) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)
The set S is empty
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(6) BOUNDS(O(1), O(1))
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