/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:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            <=(0(),y) -> true()
            <=(s(x),0()) -> false()
            <=(s(x),s(y)) -> <=(x,y)
            f(0(),y,0(),u) -> true()
            f(0(),y,s(z),u) -> false()
            f(s(x),0(),z,u) -> f(x,u,-(z,s(x)),u)
            f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u))
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            perfectp(0()) -> false()
            perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
        - Signature:
            {-/2,<=/2,f/4,if/3,perfectp/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {-,<=,f,if,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:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            <=(0(),y) -> true()
            <=(s(x),0()) -> false()
            <=(s(x),s(y)) -> <=(x,y)
            f(0(),y,0(),u) -> true()
            f(0(),y,s(z),u) -> false()
            f(s(x),0(),z,u) -> f(x,u,-(z,s(x)),u)
            f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u))
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            perfectp(0()) -> false()
            perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
        - Signature:
            {-/2,<=/2,f/4,if/3,perfectp/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {-,<=,f,if,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:
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            <=(0(),y) -> true()
            <=(s(x),0()) -> false()
            <=(s(x),s(y)) -> <=(x,y)
            f(0(),y,0(),u) -> true()
            f(0(),y,s(z),u) -> false()
            f(s(x),0(),z,u) -> f(x,u,-(z,s(x)),u)
            f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u))
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            perfectp(0()) -> false()
            perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
        - Signature:
            {-/2,<=/2,f/4,if/3,perfectp/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {-,<=,f,if,perfectp} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          -(x,y){x -> s(x),y -> s(y)} =
            -(s(x),s(y)) ->^+ -(x,y)
              = C[-(x,y) = -(x,y){}]

WORST_CASE(Omega(n^1),?)