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

WORST_CASE(Omega(n^1),?)