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


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WORST_CASE(?, O(1))
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) DependencyGraphProof [UPPER BOUND(ID), 0 ms]
(2) CpxTRS
(3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
(4) 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:

   2nd(cons(X, n__cons(Y, Z))) -> activate(Y)
   from(X) -> cons(X, n__from(s(X)))
   cons(X1, X2) -> n__cons(X1, X2)
   from(X) -> n__from(X)
   activate(n__cons(X1, X2)) -> cons(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(X) -> X

S is empty.
Rewrite Strategy: FULL
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(1) DependencyGraphProof (UPPER BOUND(ID))
The following rules are not reachable from basic terms in the dependency graph and can be removed:

2nd(cons(X, n__cons(Y, Z))) -> activate(Y)

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(2)
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:

   from(X) -> cons(X, n__from(s(X)))
   cons(X1, X2) -> n__cons(X1, X2)
   from(X) -> n__from(X)
   activate(n__cons(X1, X2)) -> cons(X1, X2)
   activate(n__from(X)) -> from(X)
   activate(X) -> X

S is empty.
Rewrite Strategy: FULL
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(3) 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__from(x0)) ->^* n__from(x0)

activate(n__from(x0)) ->^* n__cons(x0, n__from(s(x0)))

activate(n__cons(x0, x1)) ->^* n__cons(x0, x1)

cons(x0, x1) ->^* n__cons(x0, x1)

from(x0) ->^* n__from(x0)

from(x0) ->^* n__cons(x0, n__from(s(x0)))




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(4)
BOUNDS(1, 1)