/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:
            help(x,s(y),c) -> if(le(c,x),x,s(y),c)
            if(false(),x,s(y),c) -> minus(x,minus(c,s(y)))
            if(true(),x,s(y),c) -> help(x,s(y),plus(c,s(y)))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(0(),s(y)) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            mod(x,s(y)) -> help(x,s(y),0())
            mod(s(x),0()) -> 0()
            plus(x,0()) -> x
            plus(x,s(y)) -> s(plus(x,y))
        - Signature:
            {help/3,if/4,le/2,minus/2,mod/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {help,if,le,minus,mod,plus} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            help(x,s(y),c) -> if(le(c,x),x,s(y),c)
            if(false(),x,s(y),c) -> minus(x,minus(c,s(y)))
            if(true(),x,s(y),c) -> help(x,s(y),plus(c,s(y)))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(0(),s(y)) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            mod(x,s(y)) -> help(x,s(y),0())
            mod(s(x),0()) -> 0()
            plus(x,0()) -> x
            plus(x,s(y)) -> s(plus(x,y))
        - Signature:
            {help/3,if/4,le/2,minus/2,mod/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {help,if,le,minus,mod,plus} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            help(x,s(y),c) -> if(le(c,x),x,s(y),c)
            if(false(),x,s(y),c) -> minus(x,minus(c,s(y)))
            if(true(),x,s(y),c) -> help(x,s(y),plus(c,s(y)))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(0(),s(y)) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            mod(x,s(y)) -> help(x,s(y),0())
            mod(s(x),0()) -> 0()
            plus(x,0()) -> x
            plus(x,s(y)) -> s(plus(x,y))
        - Signature:
            {help/3,if/4,le/2,minus/2,mod/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {help,if,le,minus,mod,plus} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          le(x,y){x -> s(x),y -> s(y)} =
            le(s(x),s(y)) ->^+ le(x,y)
              = C[le(x,y) = le(x,y){}]

WORST_CASE(Omega(n^1),?)