/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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:

   h(c(x, y), c(s(z), z), t(w)) -> h(z, c(y, x), t(t(c(x, c(y, t(w))))))
   h(x, c(y, z), t(w)) -> h(c(s(y), x), z, t(c(t(w), w)))
   h(c(s(x), c(s(0), y)), z, t(x)) -> h(y, c(s(0), c(x, z)), t(t(c(x, s(x)))))
   t(t(x)) -> t(c(t(x), x))
   t(x) -> x
   t(x) -> c(0, c(0, c(0, c(0, c(0, 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:

h(c(x, y), c(s(z), z), t(w)) -> h(z, c(y, x), t(t(c(x, c(y, t(w))))))
h(x, c(y, z), t(w)) -> h(c(s(y), x), z, t(c(t(w), w)))
h(c(s(x), c(s(0), y)), z, t(x)) -> h(y, c(s(0), c(x, z)), t(t(c(x, s(x)))))
t(t(x)) -> t(c(t(x), x))

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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:

   t(x) -> x
   t(x) -> c(0, c(0, c(0, c(0, c(0, 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:

t(x0) ->^* c(0, c(0, c(0, c(0, c(0, x0)))))




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(4)
BOUNDS(1, 1)