/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(?, O(1))
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(1, 1).

(0) CpxTRS
(1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
(2) BOUNDS(1, 1)


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(0)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).


The TRS R consists of the following rules:

   f(0) -> cons(0, n__f(s(0)))
   f(s(0)) -> f(p(s(0)))
   p(s(0)) -> 0
   f(X) -> n__f(X)
   activate(n__f(X)) -> f(X)
   activate(X) -> X

S is empty.
Rewrite Strategy: FULL
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(1) NarrowingOnBasicTermsTerminatesProof (FINISHED)
Constant runtime complexity proven by termination of constructor-based narrowing.

The maximal most general narrowing sequences give rise to the following rewrite sequences:

activate(n__f(x0)) ->^* n__f(x0)

activate(n__f(s(0))) ->^* n__f(0)

activate(n__f(s(0))) ->^* cons(0, n__f(s(0)))

activate(n__f(0)) ->^* cons(0, n__f(s(0)))

p(s(0)) ->^* 0

f(x0) ->^* n__f(x0)

f(s(0)) ->^* n__f(0)

f(s(0)) ->^* cons(0, n__f(s(0)))

f(0) ->^* cons(0, n__f(s(0)))




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(2)
BOUNDS(1, 1)