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


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x,y,z) -> loop(x,double(y),s(z))
            if(true(),x,y,z) -> z
            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)
        - Signature:
            {double/1,if/4,le/2,log/1,loop/3} / {0/0,false/0,logError/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {double,if,le,log,loop} and constructors {0,false,logError,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x,y,z) -> loop(x,double(y),s(z))
            if(true(),x,y,z) -> z
            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)
        - Signature:
            {double/1,if/4,le/2,log/1,loop/3} / {0/0,false/0,logError/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {double,if,le,log,loop} and constructors {0,false,logError,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x,y,z) -> loop(x,double(y),s(z))
            if(true(),x,y,z) -> z
            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)
        - Signature:
            {double/1,if/4,le/2,log/1,loop/3} / {0/0,false/0,logError/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {double,if,le,log,loop} and constructors {0,false,logError,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),?)