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3.14/1.24
(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
+(1, x) → +(+(0, 1), x)
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+(0, x) → 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:
+(1, z0) → +(+(0, 1), z0)
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+(0, z0) → z0
Tuples:
+'(1, z0) → c(+'(+(0, 1), z0), +'(0, 1))
S tuples:
+'(1, z0) → c(+'(+(0, 1), z0), +'(0, 1))
K tuples:none
Defined Rule Symbols:
+
Defined Pair Symbols:
+'
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:
+(1, z0) → +(+(0, 1), z0)
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+(0, z0) → z0
Tuples:
+'(1, z0) → c(+'(+(0, 1), z0))
S tuples:
+'(1, z0) → c(+'(+(0, 1), z0))
K tuples:none
Defined Rule Symbols:
+
Defined Pair Symbols:
+'
Compound Symbols:
c
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(5) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
+'(
1,
z0) →
c(
+'(
+(
0,
1),
z0)) by
+'(1, x0) → c(+'(1, x0))
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3.14/1.24
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
+(1, z0) → +(+(0, 1), z0)
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+(0, z0) → z0
Tuples:
+'(1, x0) → c(+'(1, x0))
S tuples:
+'(1, x0) → c(+'(1, x0))
K tuples:none
Defined Rule Symbols:
+
Defined Pair Symbols:
+'
Compound Symbols:
c
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