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

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            minus(f(x,y)) -> f(minus(y),minus(x))
            minus(h(x)) -> h(minus(x))
            minus(minus(x)) -> x
        - Signature:
            {minus/1} / {f/2,h/1}
        - Obligation:
             runtime complexity wrt. defined symbols {minus} and constructors {f,h}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          f_0(2,2) -> 2
          f_1(3,4) -> 1
          f_1(4,4) -> 3
          f_1(4,4) -> 4
          h_0(2) -> 2
          h_1(4) -> 1
          h_1(4) -> 3
          h_1(4) -> 4
          minus_0(2) -> 1
          minus_1(2) -> 3
          minus_1(2) -> 4
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            minus(f(x,y)) -> f(minus(y),minus(x))
            minus(h(x)) -> h(minus(x))
            minus(minus(x)) -> x
        - Signature:
            {minus/1} / {f/2,h/1}
        - Obligation:
             runtime complexity wrt. defined symbols {minus} and constructors {f,h}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))