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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

   not(x) -> xor(x, true)
   implies(x, y) -> xor(and(x, y), xor(x, true))
   or(x, y) -> xor(and(x, y), xor(x, y))
   =(x, y) -> xor(x, xor(y, true))

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:

=(x0, x1) ->^* xor(x0, xor(x1, true))

or(x0, x1) ->^* xor(and(x0, x1), xor(x0, x1))

implies(x0, x1) ->^* xor(and(x0, x1), xor(x0, true))

not(x0) ->^* xor(x0, true)




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(2)
BOUNDS(1, 1)