/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__add(X1,X2) -> add(X1,X2)
            a__add(0(),X) -> mark(X)
            a__add(s(X),Y) -> s(a__add(mark(X),mark(Y)))
            a__fib(N) -> a__sel(mark(N),a__fib1(s(0()),s(0())))
            a__fib(X) -> fib(X)
            a__fib1(X,Y) -> cons(mark(X),fib1(Y,add(X,Y)))
            a__fib1(X1,X2) -> fib1(X1,X2)
            a__sel(X1,X2) -> sel(X1,X2)
            a__sel(0(),cons(X,XS)) -> mark(X)
            a__sel(s(N),cons(X,XS)) -> a__sel(mark(N),mark(XS))
            mark(0()) -> 0()
            mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(fib(X)) -> a__fib(mark(X))
            mark(fib1(X1,X2)) -> a__fib1(mark(X1),mark(X2))
            mark(s(X)) -> s(mark(X))
            mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
        - Signature:
            {a__add/2,a__fib/1,a__fib1/2,a__sel/2,mark/1} / {0/0,add/2,cons/2,fib/1,fib1/2,s/1,sel/2}
        - Obligation:
             runtime complexity wrt. defined symbols {a__add,a__fib,a__fib1,a__sel,mark} and constructors {0,add,cons
            ,fib,fib1,s,sel}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__add(X1,X2) -> add(X1,X2)
            a__add(0(),X) -> mark(X)
            a__add(s(X),Y) -> s(a__add(mark(X),mark(Y)))
            a__fib(N) -> a__sel(mark(N),a__fib1(s(0()),s(0())))
            a__fib(X) -> fib(X)
            a__fib1(X,Y) -> cons(mark(X),fib1(Y,add(X,Y)))
            a__fib1(X1,X2) -> fib1(X1,X2)
            a__sel(X1,X2) -> sel(X1,X2)
            a__sel(0(),cons(X,XS)) -> mark(X)
            a__sel(s(N),cons(X,XS)) -> a__sel(mark(N),mark(XS))
            mark(0()) -> 0()
            mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(fib(X)) -> a__fib(mark(X))
            mark(fib1(X1,X2)) -> a__fib1(mark(X1),mark(X2))
            mark(s(X)) -> s(mark(X))
            mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
        - Signature:
            {a__add/2,a__fib/1,a__fib1/2,a__sel/2,mark/1} / {0/0,add/2,cons/2,fib/1,fib1/2,s/1,sel/2}
        - Obligation:
             runtime complexity wrt. defined symbols {a__add,a__fib,a__fib1,a__sel,mark} and constructors {0,add,cons
            ,fib,fib1,s,sel}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__add(X1,X2) -> add(X1,X2)
            a__add(0(),X) -> mark(X)
            a__add(s(X),Y) -> s(a__add(mark(X),mark(Y)))
            a__fib(N) -> a__sel(mark(N),a__fib1(s(0()),s(0())))
            a__fib(X) -> fib(X)
            a__fib1(X,Y) -> cons(mark(X),fib1(Y,add(X,Y)))
            a__fib1(X1,X2) -> fib1(X1,X2)
            a__sel(X1,X2) -> sel(X1,X2)
            a__sel(0(),cons(X,XS)) -> mark(X)
            a__sel(s(N),cons(X,XS)) -> a__sel(mark(N),mark(XS))
            mark(0()) -> 0()
            mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(fib(X)) -> a__fib(mark(X))
            mark(fib1(X1,X2)) -> a__fib1(mark(X1),mark(X2))
            mark(s(X)) -> s(mark(X))
            mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
        - Signature:
            {a__add/2,a__fib/1,a__fib1/2,a__sel/2,mark/1} / {0/0,add/2,cons/2,fib/1,fib1/2,s/1,sel/2}
        - Obligation:
             runtime complexity wrt. defined symbols {a__add,a__fib,a__fib1,a__sel,mark} and constructors {0,add,cons
            ,fib,fib1,s,sel}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> add(x,y)} =
            mark(add(x,y)) ->^+ a__add(mark(x),mark(y))
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)