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


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

WORST_CASE(Omega(n^1),?)