/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:
            activate(X) -> X
            activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
            activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2))
            add(X1,X2) -> n__add(X1,X2)
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            fib(N) -> sel(N,fib1(s(0()),s(0())))
            fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y)))
            fib1(X1,X2) -> n__fib1(X1,X2)
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
        - Signature:
            {activate/1,add/2,fib/1,fib1/2,sel/2} / {0/0,cons/2,n__add/2,n__fib1/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,add,fib,fib1,sel} and constructors {0,cons,n__add,n__fib1
            ,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
            activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2))
            add(X1,X2) -> n__add(X1,X2)
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            fib(N) -> sel(N,fib1(s(0()),s(0())))
            fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y)))
            fib1(X1,X2) -> n__fib1(X1,X2)
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
        - Signature:
            {activate/1,add/2,fib/1,fib1/2,sel/2} / {0/0,cons/2,n__add/2,n__fib1/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,add,fib,fib1,sel} and constructors {0,cons,n__add,n__fib1
            ,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
            activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2))
            add(X1,X2) -> n__add(X1,X2)
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            fib(N) -> sel(N,fib1(s(0()),s(0())))
            fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y)))
            fib1(X1,X2) -> n__fib1(X1,X2)
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
        - Signature:
            {activate/1,add/2,fib/1,fib1/2,sel/2} / {0/0,cons/2,n__add/2,n__fib1/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,add,fib,fib1,sel} and constructors {0,cons,n__add,n__fib1
            ,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__add(x,y)} =
            activate(n__add(x,y)) ->^+ add(activate(x),activate(y))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)