Runti Compl Inner Rewri 22807 pair #381904520

details

property	value
status	complete
benchmark	inssort.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n026.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	6.27513289452 seconds
cpu usage	22.901207365
max memory	7.1716864E7

stage attributes

key	value
output-size	29791
starexec-result	WORST_CASE(Omega(n^1),O(n^2))

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(Omega(n^1),O(n^2))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^2))
    + Considered Problem:
        - Strict TRS:
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            inssort(xs) -> isort(xs,Nil())
            isort(Cons(x,xs),r) -> isort(xs,insert(x,r))
            isort(Nil(),r) -> Nil()
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            {</2,insert/2,insert[Ite]/3,inssort/1,isort/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {<,insert,insert[Ite],inssort,isort} and constructors {0
            ,Cons,False,Nil,S,True}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            inssort(xs) -> isort(xs,Nil())
            isort(Cons(x,xs),r) -> isort(xs,insert(x,r))
            isort(Nil(),r) -> Nil()
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            {</2,insert/2,insert[Ite]/3,inssort/1,isort/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {<,insert,insert[Ite],inssort,isort} and constructors {0
            ,Cons,False,Nil,S,True}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          isort(y,z){y -> Cons(x,y)} =
            isort(Cons(x,y),z) ->^+ isort(y,insert(x,z))
              = C[isort(y,insert(x,z)) = isort(y,z){z -> insert(x,z)}]

** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            inssort(xs) -> isort(xs,Nil())
            isort(Cons(x,xs),r) -> isort(xs,insert(x,r))
            isort(Nil(),r) -> Nil()
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            {</2,insert/2,insert[Ite]/3,inssort/1,isort/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {<,insert,insert[Ite],inssort,isort} and constructors {0
            ,Cons,False,Nil,S,True}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x))
          inssort#(xs) -> c_2(isort#(xs,Nil()))
          isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
          isort#(Nil(),r) -> c_4()
        Weak DPs
          <#(x,0()) -> c_5()
          <#(0(),S(y)) -> c_6()
          <#(S(x),S(y)) -> c_7(<#(x,y))
          insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
          insert[Ite]#(True(),x,r) -> c_9()
        
        and mark the set of starting terms.
** Step 1.b:2: PredecessorEstimation WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x))
            inssort#(xs) -> c_2(isort#(xs,Nil()))
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
            isort#(Nil(),r) -> c_4()
        - Weak DPs:
            <#(x,0()) -> c_5()

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