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


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            2ndsneg(0(),Z) -> rnil()
            2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z))
            2ndspos(0(),Z) -> rnil()
            2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,Z))
            from(X) -> cons(X,from(s(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,from/1,pi/1,plus/2,square/1,times/2} / {0/0,cons/2,negrecip/1,posrecip/1,rcons/2,rnil/0
            ,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2ndsneg,2ndspos,from,pi,plus,square,times} and constructors {0
            ,cons,negrecip,posrecip,rcons,rnil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            2ndsneg(0(),Z) -> rnil()
            2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z))
            2ndspos(0(),Z) -> rnil()
            2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,Z))
            from(X) -> cons(X,from(s(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,from/1,pi/1,plus/2,square/1,times/2} / {0/0,cons/2,negrecip/1,posrecip/1,rcons/2,rnil/0
            ,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2ndsneg,2ndspos,from,pi,plus,square,times} and constructors {0
            ,cons,negrecip,posrecip,rcons,rnil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            2ndsneg(0(),Z) -> rnil()
            2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z))
            2ndspos(0(),Z) -> rnil()
            2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,Z))
            from(X) -> cons(X,from(s(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,from/1,pi/1,plus/2,square/1,times/2} / {0/0,cons/2,negrecip/1,posrecip/1,rcons/2,rnil/0
            ,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2ndsneg,2ndspos,from,pi,plus,square,times} and constructors {0
            ,cons,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){}]

WORST_CASE(Omega(n^1),?)