/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(c(c(a, y, a), b(x, z), a)) -> b(y, f(c(f(a), z, z)))
   f(b(b(x, f(y)), z)) -> c(z, x, f(b(b(f(a), y), y)))
   c(b(a, a), b(y, z), x) -> b(a, b(z, z))

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(c(c(a, y, a), b(x, z), a)) -> b(y, f(c(f(a), z, z)))
f(b(b(x, f(y)), z)) -> c(z, x, f(b(b(f(a), y), 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:

   c(b(a, a), b(y, z), x) -> b(a, b(z, z))

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:

c(b(a, a), b(x0, x1), x2) ->^* b(a, b(x1, x1))




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(4)
BOUNDS(1, 1)