/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:
            a() -> b()
            a() -> c()
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            droplast(cons(x,cons(y,xs))) -> cons(x,droplast(cons(y,xs)))
            droplast(cons(x,nil())) -> nil()
            droplast(nil()) -> nil()
            if(false(),x,y,z) -> loop(x,double(y),s(z))
            if(true(),x,y,z) -> z
            ifmap(false(),xs,ys) -> mapIter(droplast(xs),cons(log(last(xs)),ys))
            ifmap(true(),xs,ys) -> ys
            isempty(cons(x,xs)) -> false()
            isempty(nil()) -> true()
            last(cons(x,cons(y,xs))) -> last(cons(y,xs))
            last(cons(x,nil())) -> x
            last(nil()) -> error()
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(0()) -> logError()
            log(s(x)) -> loop(s(x),s(0()),0())
            loop(x,s(y),z) -> if(le(x,s(y)),x,s(y),z)
            mapIter(xs,ys) -> ifmap(isempty(xs),xs,ys)
            maplog(xs) -> mapIter(xs,nil())
        - Signature:
            {a/0,double/1,droplast/1,if/4,ifmap/3,isempty/1,last/1,le/2,log/1,loop/3,mapIter/2,maplog/1} / {0/0,b/0,c/0
            ,cons/2,error/0,false/0,logError/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a,double,droplast,if,ifmap,isempty,last,le,log,loop,mapIter
            ,maplog} and constructors {0,b,c,cons,error,false,logError,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a() -> b()
            a() -> c()
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            droplast(cons(x,cons(y,xs))) -> cons(x,droplast(cons(y,xs)))
            droplast(cons(x,nil())) -> nil()
            droplast(nil()) -> nil()
            if(false(),x,y,z) -> loop(x,double(y),s(z))
            if(true(),x,y,z) -> z
            ifmap(false(),xs,ys) -> mapIter(droplast(xs),cons(log(last(xs)),ys))
            ifmap(true(),xs,ys) -> ys
            isempty(cons(x,xs)) -> false()
            isempty(nil()) -> true()
            last(cons(x,cons(y,xs))) -> last(cons(y,xs))
            last(cons(x,nil())) -> x
            last(nil()) -> error()
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(0()) -> logError()
            log(s(x)) -> loop(s(x),s(0()),0())
            loop(x,s(y),z) -> if(le(x,s(y)),x,s(y),z)
            mapIter(xs,ys) -> ifmap(isempty(xs),xs,ys)
            maplog(xs) -> mapIter(xs,nil())
        - Signature:
            {a/0,double/1,droplast/1,if/4,ifmap/3,isempty/1,last/1,le/2,log/1,loop/3,mapIter/2,maplog/1} / {0/0,b/0,c/0
            ,cons/2,error/0,false/0,logError/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a,double,droplast,if,ifmap,isempty,last,le,log,loop,mapIter
            ,maplog} and constructors {0,b,c,cons,error,false,logError,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a() -> b()
            a() -> c()
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            droplast(cons(x,cons(y,xs))) -> cons(x,droplast(cons(y,xs)))
            droplast(cons(x,nil())) -> nil()
            droplast(nil()) -> nil()
            if(false(),x,y,z) -> loop(x,double(y),s(z))
            if(true(),x,y,z) -> z
            ifmap(false(),xs,ys) -> mapIter(droplast(xs),cons(log(last(xs)),ys))
            ifmap(true(),xs,ys) -> ys
            isempty(cons(x,xs)) -> false()
            isempty(nil()) -> true()
            last(cons(x,cons(y,xs))) -> last(cons(y,xs))
            last(cons(x,nil())) -> x
            last(nil()) -> error()
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(0()) -> logError()
            log(s(x)) -> loop(s(x),s(0()),0())
            loop(x,s(y),z) -> if(le(x,s(y)),x,s(y),z)
            mapIter(xs,ys) -> ifmap(isempty(xs),xs,ys)
            maplog(xs) -> mapIter(xs,nil())
        - Signature:
            {a/0,double/1,droplast/1,if/4,ifmap/3,isempty/1,last/1,le/2,log/1,loop/3,mapIter/2,maplog/1} / {0/0,b/0,c/0
            ,cons/2,error/0,false/0,logError/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a,double,droplast,if,ifmap,isempty,last,le,log,loop,mapIter
            ,maplog} and constructors {0,b,c,cons,error,false,logError,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          double(x){x -> s(x)} =
            double(s(x)) ->^+ s(s(double(x)))
              = C[double(x) = double(x){}]

WORST_CASE(Omega(n^1),?)