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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

   f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))
   f(x, y, y) -> y
   f(x, y, g(y)) -> x
   f(x, x, y) -> x
   f(g(x), x, y) -> y

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:

f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))

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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:

   f(x, y, y) -> y
   f(x, y, g(y)) -> x
   f(x, x, y) -> x
   f(g(x), x, y) -> y

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:

f(x0, x1, x2) ->^* f(x0, x1, x2)




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(4)
BOUNDS(1, 1)