/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:
            app(add(n,x),y) -> add(n,app(x,y))
            app(nil(),y) -> y
            high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x))
            high(n,nil()) -> nil()
            if_high(false(),n,add(m,x)) -> add(m,high(n,x))
            if_high(true(),n,add(m,x)) -> high(n,x)
            if_low(false(),n,add(m,x)) -> low(n,x)
            if_low(true(),n,add(m,x)) -> add(m,low(n,x))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x))
            low(n,nil()) -> nil()
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            quicksort(add(n,x)) -> app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))
            quicksort(nil()) -> nil()
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {app/2,high/2,if_high/3,if_low/3,le/2,low/2,minus/2,quicksort/1,quot/2} / {0/0,add/2,false/0,nil/0,s/1
            ,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,high,if_high,if_low,le,low,minus,quicksort
            ,quot} and constructors {0,add,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(add(n,x),y) -> add(n,app(x,y))
            app(nil(),y) -> y
            high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x))
            high(n,nil()) -> nil()
            if_high(false(),n,add(m,x)) -> add(m,high(n,x))
            if_high(true(),n,add(m,x)) -> high(n,x)
            if_low(false(),n,add(m,x)) -> low(n,x)
            if_low(true(),n,add(m,x)) -> add(m,low(n,x))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x))
            low(n,nil()) -> nil()
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            quicksort(add(n,x)) -> app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))
            quicksort(nil()) -> nil()
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {app/2,high/2,if_high/3,if_low/3,le/2,low/2,minus/2,quicksort/1,quot/2} / {0/0,add/2,false/0,nil/0,s/1
            ,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,high,if_high,if_low,le,low,minus,quicksort
            ,quot} and constructors {0,add,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(add(n,x),y) -> add(n,app(x,y))
            app(nil(),y) -> y
            high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x))
            high(n,nil()) -> nil()
            if_high(false(),n,add(m,x)) -> add(m,high(n,x))
            if_high(true(),n,add(m,x)) -> high(n,x)
            if_low(false(),n,add(m,x)) -> low(n,x)
            if_low(true(),n,add(m,x)) -> add(m,low(n,x))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x))
            low(n,nil()) -> nil()
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            quicksort(add(n,x)) -> app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))
            quicksort(nil()) -> nil()
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {app/2,high/2,if_high/3,if_low/3,le/2,low/2,minus/2,quicksort/1,quot/2} / {0/0,add/2,false/0,nil/0,s/1
            ,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,high,if_high,if_low,le,low,minus,quicksort
            ,quot} and constructors {0,add,false,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          app(y,z){y -> add(x,y)} =
            app(add(x,y),z) ->^+ add(x,app(y,z))
              = C[app(y,z) = app(y,z){}]

WORST_CASE(Omega(n^1),?)