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

WORST_CASE(Omega(n^1),?)