YES(O(1), O(n^1)) 0.00/0.72 YES(O(1), O(n^1)) 0.00/0.73 0.00/0.73 0.00/0.73 0.00/0.73 0.00/0.73 0.00/0.73 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 0.00/0.73 0.00/0.73 0.00/0.73
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(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

revapp(Cons(x, xs), rest) → revapp(xs, Cons(x, rest)) 0.00/0.73
revapp(Nil, rest) → rest 0.00/0.73
goal(xs, ys) → revapp(xs, ys)

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:

revapp(Cons(z0, z1), z2) → revapp(z1, Cons(z0, z2)) 0.00/0.73
revapp(Nil, z0) → z0 0.00/0.73
goal(z0, z1) → revapp(z0, z1)
Tuples:

REVAPP(Cons(z0, z1), z2) → c(REVAPP(z1, Cons(z0, z2))) 0.00/0.73
GOAL(z0, z1) → c2(REVAPP(z0, z1))
S tuples:

REVAPP(Cons(z0, z1), z2) → c(REVAPP(z1, Cons(z0, z2))) 0.00/0.73
GOAL(z0, z1) → c2(REVAPP(z0, z1))
K tuples:none
Defined Rule Symbols:

revapp, goal

Defined Pair Symbols:

REVAPP, GOAL

Compound Symbols:

c, c2

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(3) CdtLeafRemovalProof (ComplexityIfPolyImplication transformation)

Removed 1 leading nodes:

GOAL(z0, z1) → c2(REVAPP(z0, z1))
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(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

revapp(Cons(z0, z1), z2) → revapp(z1, Cons(z0, z2)) 0.00/0.73
revapp(Nil, z0) → z0 0.00/0.73
goal(z0, z1) → revapp(z0, z1)
Tuples:

REVAPP(Cons(z0, z1), z2) → c(REVAPP(z1, Cons(z0, z2)))
S tuples:

REVAPP(Cons(z0, z1), z2) → c(REVAPP(z1, Cons(z0, z2)))
K tuples:none
Defined Rule Symbols:

revapp, goal

Defined Pair Symbols:

REVAPP

Compound Symbols:

c

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(5) 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.

REVAPP(Cons(z0, z1), z2) → c(REVAPP(z1, Cons(z0, z2)))
We considered the (Usable) Rules:none
And the Tuples:

REVAPP(Cons(z0, z1), z2) → c(REVAPP(z1, Cons(z0, z2)))
The order we found is given by the following interpretation:
Polynomial interpretation : 0.00/0.73

POL(Cons(x1, x2)) = [4] + x1 + x2    0.00/0.73
POL(REVAPP(x1, x2)) = [4]x1    0.00/0.73
POL(c(x1)) = x1   
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(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

revapp(Cons(z0, z1), z2) → revapp(z1, Cons(z0, z2)) 0.00/0.73
revapp(Nil, z0) → z0 0.00/0.73
goal(z0, z1) → revapp(z0, z1)
Tuples:

REVAPP(Cons(z0, z1), z2) → c(REVAPP(z1, Cons(z0, z2)))
S tuples:none
K tuples:

REVAPP(Cons(z0, z1), z2) → c(REVAPP(z1, Cons(z0, z2)))
Defined Rule Symbols:

revapp, goal

Defined Pair Symbols:

REVAPP

Compound Symbols:

c

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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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0.00/0.73 EOF