/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(NON_POLY, ?)
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).

(0) CpxTRS
(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(2) TRS for Loop Detection
(3) InfiniteLowerBoundProof [FINISHED, 38 ms]
(4) BOUNDS(INF, INF)


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(0)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).


The TRS R consists of the following rules:

   pairNs -> cons(0, n__incr(oddNs))
   oddNs -> incr(pairNs)
   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
   take(0, XS) -> nil
   take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS)))
   zip(nil, XS) -> nil
   zip(X, nil) -> nil
   zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
   tail(cons(X, XS)) -> activate(XS)
   repItems(nil) -> nil
   repItems(cons(X, XS)) -> cons(X, n__cons(X, n__repItems(activate(XS))))
   incr(X) -> n__incr(X)
   take(X1, X2) -> n__take(X1, X2)
   zip(X1, X2) -> n__zip(X1, X2)
   cons(X1, X2) -> n__cons(X1, X2)
   repItems(X) -> n__repItems(X)
   activate(n__incr(X)) -> incr(X)
   activate(n__take(X1, X2)) -> take(X1, X2)
   activate(n__zip(X1, X2)) -> zip(X1, X2)
   activate(n__cons(X1, X2)) -> cons(X1, X2)
   activate(n__repItems(X)) -> repItems(X)
   activate(X) -> X

S is empty.
Rewrite Strategy: FULL
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(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
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(2)
Obligation:
Analyzing the following TRS for decreasing loops:

The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).


The TRS R consists of the following rules:

   pairNs -> cons(0, n__incr(oddNs))
   oddNs -> incr(pairNs)
   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
   take(0, XS) -> nil
   take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS)))
   zip(nil, XS) -> nil
   zip(X, nil) -> nil
   zip(cons(X, XS), cons(Y, YS)) -> cons(pair(X, Y), n__zip(activate(XS), activate(YS)))
   tail(cons(X, XS)) -> activate(XS)
   repItems(nil) -> nil
   repItems(cons(X, XS)) -> cons(X, n__cons(X, n__repItems(activate(XS))))
   incr(X) -> n__incr(X)
   take(X1, X2) -> n__take(X1, X2)
   zip(X1, X2) -> n__zip(X1, X2)
   cons(X1, X2) -> n__cons(X1, X2)
   repItems(X) -> n__repItems(X)
   activate(n__incr(X)) -> incr(X)
   activate(n__take(X1, X2)) -> take(X1, X2)
   activate(n__zip(X1, X2)) -> zip(X1, X2)
   activate(n__cons(X1, X2)) -> cons(X1, X2)
   activate(n__repItems(X)) -> repItems(X)
   activate(X) -> X

S is empty.
Rewrite Strategy: FULL
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(3) InfiniteLowerBoundProof (FINISHED)
The following loop proves infinite runtime complexity:

The rewrite sequence

oddNs ->^+ incr(cons(0, n__incr(oddNs)))

gives rise to a decreasing loop by considering the right hand sides subterm at position [0,1,0].

The pumping substitution is [ ].

The result substitution is [ ].




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(4)
BOUNDS(INF, INF)