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(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(s(x), y, y) → f(y, x, s(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:
f(s(z0), z1, z1) → f(z1, z0, s(z0))
Tuples:
F(s(z0), z1, z1) → c(F(z1, z0, s(z0)))
S tuples:
F(s(z0), z1, z1) → c(F(z1, z0, s(z0)))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c
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(3) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing tuple parts
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(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(s(z0), z1, z1) → f(z1, z0, s(z0))
Tuples:
F(s(z0), z1, z1) → c
S tuples:
F(s(z0), z1, z1) → c
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c
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(5) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing nodes:
F(s(z0), z1, z1) → c
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(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(s(z0), z1, z1) → f(z1, z0, s(z0))
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:none
Compound Symbols:none
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(7) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)
The set S is empty
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(8) BOUNDS(O(1), O(1))
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