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

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
            f(a(x),a(y)) -> a(f(x,y))
            f(b(x),b(y)) -> b(f(x,y))
        - Signature:
            {a/1,f/2} / {b/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a,f} and constructors {b}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          a_0(2) -> 1
          b_0(2) -> 2
          b_1(3) -> 1
          b_1(3) -> 3
          f_0(2,2) -> 1
          f_1(2,2) -> 3
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
            f(a(x),a(y)) -> a(f(x,y))
            f(b(x),b(y)) -> b(f(x,y))
        - Signature:
            {a/1,f/2} / {b/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a,f} and constructors {b}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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