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


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


WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(0(),y,0(),u) -> true()
            f(0(),y,s(z),u) -> false()
            f(s(x),0(),z,u) -> f(x,u,minus(z,s(x)),u)
            f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(0(),y) -> 0()
            minus(s(x),0()) -> s(x)
            minus(s(x),s(y)) -> minus(x,y)
            perfectp(0()) -> false()
            perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
        - Signature:
            {f/4,if/3,le/2,minus/2,perfectp/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {f,if,le,minus,perfectp} 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:
            f(0(),y,0(),u) -> true()
            f(0(),y,s(z),u) -> false()
            f(s(x),0(),z,u) -> f(x,u,minus(z,s(x)),u)
            f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(0(),y) -> 0()
            minus(s(x),0()) -> s(x)
            minus(s(x),s(y)) -> minus(x,y)
            perfectp(0()) -> false()
            perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
        - Signature:
            {f/4,if/3,le/2,minus/2,perfectp/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {f,if,le,minus,perfectp} 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:
            f(0(),y,0(),u) -> true()
            f(0(),y,s(z),u) -> false()
            f(s(x),0(),z,u) -> f(x,u,minus(z,s(x)),u)
            f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(0(),y) -> 0()
            minus(s(x),0()) -> s(x)
            minus(s(x),s(y)) -> minus(x,y)
            perfectp(0()) -> false()
            perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
        - Signature:
            {f/4,if/3,le/2,minus/2,perfectp/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {f,if,le,minus,perfectp} 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),?)