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(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(x, x) → a
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f(g(x), y) → f(x, y)
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:
f(z0, z0) → a
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f(g(z0), z1) → f(z0, z1)
Tuples:
F(g(z0), z1) → c1(F(z0, z1))
S tuples:
F(g(z0), z1) → c1(F(z0, z1))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1
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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.
F(g(z0), z1) → c1(F(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
F(g(z0), z1) → c1(F(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(F(x1, x2)) = [3]x1
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POL(c1(x1)) = x1
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POL(g(x1)) = [1] + x1
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(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, z0) → a
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f(g(z0), z1) → f(z0, z1)
Tuples:
F(g(z0), z1) → c1(F(z0, z1))
S tuples:none
K tuples:
F(g(z0), z1) → c1(F(z0, z1))
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1
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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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