Runti Compl Inner Rewri 22807 pair #381904934

details

property	value
status	complete
benchmark	4.18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n046.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	1.49057197571 seconds
cpu usage	1.927581091
max memory	3.11296E7

stage attributes

key	value
output-size	4343
starexec-result	WORST_CASE(?,O(1))

output

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


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WORST_CASE(?,O(1))
* Step 1: Sum WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            gcd(x,0()) -> x
            gcd(0(),y) -> y
            gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))
        - Signature:
            {gcd/2} / {-/2,0/0,</2,if/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {gcd} and constructors {-,0,<,if,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            gcd(x,0()) -> x
            gcd(0(),y) -> y
            gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))
        - Signature:
            {gcd/2} / {-/2,0/0,</2,if/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {gcd} and constructors {-,0,<,if,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          gcd#(x,0()) -> c_1()
          gcd#(0(),y) -> c_2()
          gcd#(s(x),s(y)) -> c_3(gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: PredecessorEstimation WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            gcd#(x,0()) -> c_1()
            gcd#(0(),y) -> c_2()
            gcd#(s(x),s(y)) -> c_3(gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
        - Weak TRS:
            gcd(x,0()) -> x
            gcd(0(),y) -> y
            gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))
        - Signature:
            {gcd/2,gcd#/2} / {-/2,0/0,</2,if/3,s/1,c_1/0,c_2/0,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {gcd#} and constructors {-,0,<,if,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,3}
        by application of
          Pre({1,2,3}) = {}.
        Here rules are labelled as follows:
          1: gcd#(x,0()) -> c_1()
          2: gcd#(0(),y) -> c_2()
          3: gcd#(s(x),s(y)) -> c_3(gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
* Step 4: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            gcd#(x,0()) -> c_1()
            gcd#(0(),y) -> c_2()
            gcd#(s(x),s(y)) -> c_3(gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
        - Weak TRS:
            gcd(x,0()) -> x
            gcd(0(),y) -> y
            gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y)))
        - Signature:
            {gcd/2,gcd#/2} / {-/2,0/0,</2,if/3,s/1,c_1/0,c_2/0,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {gcd#} and constructors {-,0,<,if,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:gcd#(x,0()) -> c_1()
             
          
          2:W:gcd#(0(),y) -> c_2()
             
          
          3:W:gcd#(s(x),s(y)) -> c_3(gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: gcd#(s(x),s(y)) -> c_3(gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y)))
          2: gcd#(0(),y) -> c_2()
          1: gcd#(x,0()) -> c_1()

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