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(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
*(i(x), x) → 1
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*(1, y) → y
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*(x, 0) → 0
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*(*(x, y), z) → *(x, *(y, z))
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:
*(i(z0), z0) → 1
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*(1, z0) → z0
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*(z0, 0) → 0
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*(*(z0, z1), z2) → *(z0, *(z1, z2))
Tuples:
*'(*(z0, z1), z2) → c3(*'(z0, *(z1, z2)), *'(z1, z2))
S tuples:
*'(*(z0, z1), z2) → c3(*'(z0, *(z1, z2)), *'(z1, z2))
K tuples:none
Defined Rule Symbols:
*
Defined Pair Symbols:
*'
Compound Symbols:
c3
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(3) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
*'(*(z0, z1), z2) → c3(*'(z0, *(z1, z2)), *'(z1, z2))
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(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
*(i(z0), z0) → 1
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*(1, z0) → z0
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*(z0, 0) → 0
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*(*(z0, z1), z2) → *(z0, *(z1, z2))
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
*
Defined Pair Symbols:none
Compound Symbols:none
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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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