Runti Compl Full Rewri 10127 pair #381903624

details

property	value
status	complete
benchmark	Ex1_2_AEL03_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n041.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	78.1493349075 seconds
cpu usage	350.66681749
max memory	2.158379008E9

stage attributes

key	value
output-size	329882
starexec-result	WORST_CASE(Omega(n^1),O(n^3))

output

/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1),O(n^3))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^3))
    + Considered Problem:
        - Strict TRS:
            2ndsneg(0(),Z) -> rnil()
            2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
            2ndspos(0(),Z) -> rnil()
            2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            pi(X) -> 2ndspos(X,from(0()))
            plus(0(),Y) -> Y
            plus(s(X),Y) -> s(plus(X,Y))
            square(X) -> times(X,X)
            times(0(),Y) -> 0()
            times(s(X),Y) -> plus(Y,times(X,Y))
        - Signature:
            {2ndsneg/2,2ndspos/2,activate/1,cons/2,from/1,pi/1,plus/2,square/1,times/2} / {0/0,n__cons/2,n__from/1
            ,negrecip/1,posrecip/1,rcons/2,rnil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2ndsneg,2ndspos,activate,cons,from,pi,plus,square
            ,times} and constructors {0,n__cons,n__from,negrecip,posrecip,rcons,rnil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            2ndsneg(0(),Z) -> rnil()
            2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
            2ndspos(0(),Z) -> rnil()
            2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            pi(X) -> 2ndspos(X,from(0()))
            plus(0(),Y) -> Y
            plus(s(X),Y) -> s(plus(X,Y))
            square(X) -> times(X,X)
            times(0(),Y) -> 0()
            times(s(X),Y) -> plus(Y,times(X,Y))
        - Signature:
            {2ndsneg/2,2ndspos/2,activate/1,cons/2,from/1,pi/1,plus/2,square/1,times/2} / {0/0,n__cons/2,n__from/1
            ,negrecip/1,posrecip/1,rcons/2,rnil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2ndsneg,2ndspos,activate,cons,from,pi,plus,square
            ,times} and constructors {0,n__cons,n__from,negrecip,posrecip,rcons,rnil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          plus(x,y){x -> s(x)} =
            plus(s(x),y) ->^+ s(plus(x,y))
              = C[plus(x,y) = plus(x,y){}]

** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            2ndsneg(0(),Z) -> rnil()
            2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
            2ndspos(0(),Z) -> rnil()
            2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            pi(X) -> 2ndspos(X,from(0()))
            plus(0(),Y) -> Y
            plus(s(X),Y) -> s(plus(X,Y))
            square(X) -> times(X,X)
            times(0(),Y) -> 0()
            times(s(X),Y) -> plus(Y,times(X,Y))
        - Signature:
            {2ndsneg/2,2ndspos/2,activate/1,cons/2,from/1,pi/1,plus/2,square/1,times/2} / {0/0,n__cons/2,n__from/1
            ,negrecip/1,posrecip/1,rcons/2,rnil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2ndsneg,2ndspos,activate,cons,from,pi,plus,square
            ,times} and constructors {0,n__cons,n__from,negrecip,posrecip,rcons,rnil,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = WIDP}
    + Details:
        We add the following weak dependency pairs:
        
        Strict DPs

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