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


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WORST_CASE(?,O(n^1))
* Step 1: Sum.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__natsFrom(X)) -> natsFrom(X)
            afterNth(N,XS) -> snd(splitAt(N,XS))
            fst(pair(XS,YS)) -> XS
            head(cons(N,XS)) -> N
            natsFrom(N) -> cons(N,n__natsFrom(s(N)))
            natsFrom(X) -> n__natsFrom(X)
            sel(N,XS) -> head(afterNth(N,XS))
            snd(pair(XS,YS)) -> YS
            splitAt(0(),XS) -> pair(nil(),XS)
            splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
            tail(cons(N,XS)) -> activate(XS)
            take(N,XS) -> fst(splitAt(N,XS))
            u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
        - Signature:
            {activate/1,afterNth/2,fst/1,head/1,natsFrom/1,sel/2,snd/1,splitAt/2,tail/1,take/2,u/4} / {0/0,cons/2
            ,n__natsFrom/1,nil/0,pair/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,afterNth,fst,head,natsFrom,sel,snd,splitAt,tail
            ,take,u} and constructors {0,cons,n__natsFrom,nil,pair,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Ara.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__natsFrom(X)) -> natsFrom(X)
            afterNth(N,XS) -> snd(splitAt(N,XS))
            fst(pair(XS,YS)) -> XS
            head(cons(N,XS)) -> N
            natsFrom(N) -> cons(N,n__natsFrom(s(N)))
            natsFrom(X) -> n__natsFrom(X)
            sel(N,XS) -> head(afterNth(N,XS))
            snd(pair(XS,YS)) -> YS
            splitAt(0(),XS) -> pair(nil(),XS)
            splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
            tail(cons(N,XS)) -> activate(XS)
            take(N,XS) -> fst(splitAt(N,XS))
            u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
        - Signature:
            {activate/1,afterNth/2,fst/1,head/1,natsFrom/1,sel/2,snd/1,splitAt/2,tail/1,take/2,u/4} / {0/0,cons/2
            ,n__natsFrom/1,nil/0,pair/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,afterNth,fst,head,natsFrom,sel,snd,splitAt,tail
            ,take,u} and constructors {0,cons,n__natsFrom,nil,pair,s}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 1, araTimeout = 8, araRuleShifting = Just 1, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "0") :: [] -(0)-> "A"(8)
          F (TrsFun "activate") :: ["A"(0)] -(2)-> "A"(0)
          F (TrsFun "afterNth") :: ["A"(8) x "A"(0)] -(3)-> "A"(0)
          F (TrsFun "cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "fst") :: ["A"(0)] -(1)-> "A"(0)
          F (TrsFun "head") :: ["A"(0)] -(1)-> "A"(0)
          F (TrsFun "n__natsFrom") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "natsFrom") :: ["A"(0)] -(1)-> "A"(0)
          F (TrsFun "nil") :: [] -(0)-> "A"(0)
          F (TrsFun "pair") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "s") :: ["A"(8)] -(8)-> "A"(8)
          F (TrsFun "s") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "sel") :: ["A"(8) x "A"(0)] -(5)-> "A"(0)
          F (TrsFun "snd") :: ["A"(0)] -(1)-> "A"(0)
          F (TrsFun "splitAt") :: ["A"(8) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "tail") :: ["A"(0)] -(3)-> "A"(0)
          F (TrsFun "take") :: ["A"(8) x "A"(0)] -(3)-> "A"(0)
          F (TrsFun "u") :: ["A"(0) x "A"(0) x "A"(0) x "A"(0)] -(3)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          activate(X) -> X
          activate(n__natsFrom(X)) -> natsFrom(X)
          afterNth(N,XS) -> snd(splitAt(N,XS))
          fst(pair(XS,YS)) -> XS
          head(cons(N,XS)) -> N
          natsFrom(N) -> cons(N,n__natsFrom(s(N)))
          natsFrom(X) -> n__natsFrom(X)
          sel(N,XS) -> head(afterNth(N,XS))
          snd(pair(XS,YS)) -> YS
          splitAt(0(),XS) -> pair(nil(),XS)
          splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
          tail(cons(N,XS)) -> activate(XS)
          take(N,XS) -> fst(splitAt(N,XS))
          u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
        2. Weak:
          
        

WORST_CASE(?,O(n^1))