/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__app(X1,X2)) -> app(activate(X1),activate(X2))
            activate(n__from(X)) -> from(activate(X))
            activate(n__nil()) -> nil()
            activate(n__prefix(X)) -> prefix(activate(X))
            activate(n__s(X)) -> s(activate(X))
            activate(n__zWadr(X1,X2)) -> zWadr(activate(X1),activate(X2))
            app(X1,X2) -> n__app(X1,X2)
            app(cons(X,XS),YS) -> cons(X,n__app(activate(XS),YS))
            app(nil(),YS) -> YS
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
            prefix(L) -> cons(nil(),n__zWadr(L,n__prefix(L)))
            prefix(X) -> n__prefix(X)
            s(X) -> n__s(X)
            zWadr(X1,X2) -> n__zWadr(X1,X2)
            zWadr(XS,nil()) -> nil()
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,n__nil())),n__zWadr(activate(XS),activate(YS)))
            zWadr(nil(),YS) -> nil()
        - Signature:
            {activate/1,app/2,from/1,nil/0,prefix/1,s/1,zWadr/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__prefix/1
            ,n__s/1,n__zWadr/2}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,app,from,nil,prefix,s,zWadr} and constructors {cons
            ,n__app,n__from,n__nil,n__prefix,n__s,n__zWadr}
    + 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__app(X1,X2)) -> app(activate(X1),activate(X2))
            activate(n__from(X)) -> from(activate(X))
            activate(n__nil()) -> nil()
            activate(n__prefix(X)) -> prefix(activate(X))
            activate(n__s(X)) -> s(activate(X))
            activate(n__zWadr(X1,X2)) -> zWadr(activate(X1),activate(X2))
            app(X1,X2) -> n__app(X1,X2)
            app(cons(X,XS),YS) -> cons(X,n__app(activate(XS),YS))
            app(nil(),YS) -> YS
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
            prefix(L) -> cons(nil(),n__zWadr(L,n__prefix(L)))
            prefix(X) -> n__prefix(X)
            s(X) -> n__s(X)
            zWadr(X1,X2) -> n__zWadr(X1,X2)
            zWadr(XS,nil()) -> nil()
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,n__nil())),n__zWadr(activate(XS),activate(YS)))
            zWadr(nil(),YS) -> nil()
        - Signature:
            {activate/1,app/2,from/1,nil/0,prefix/1,s/1,zWadr/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__prefix/1
            ,n__s/1,n__zWadr/2}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,app,from,nil,prefix,s,zWadr} and constructors {cons
            ,n__app,n__from,n__nil,n__prefix,n__s,n__zWadr}
    + 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__app(X1,X2)) -> app(activate(X1),activate(X2))
            activate(n__from(X)) -> from(activate(X))
            activate(n__nil()) -> nil()
            activate(n__prefix(X)) -> prefix(activate(X))
            activate(n__s(X)) -> s(activate(X))
            activate(n__zWadr(X1,X2)) -> zWadr(activate(X1),activate(X2))
            app(X1,X2) -> n__app(X1,X2)
            app(cons(X,XS),YS) -> cons(X,n__app(activate(XS),YS))
            app(nil(),YS) -> YS
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
            prefix(L) -> cons(nil(),n__zWadr(L,n__prefix(L)))
            prefix(X) -> n__prefix(X)
            s(X) -> n__s(X)
            zWadr(X1,X2) -> n__zWadr(X1,X2)
            zWadr(XS,nil()) -> nil()
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,n__nil())),n__zWadr(activate(XS),activate(YS)))
            zWadr(nil(),YS) -> nil()
        - Signature:
            {activate/1,app/2,from/1,nil/0,prefix/1,s/1,zWadr/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__prefix/1
            ,n__s/1,n__zWadr/2}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,app,from,nil,prefix,s,zWadr} and constructors {cons
            ,n__app,n__from,n__nil,n__prefix,n__s,n__zWadr}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__app(x,y)} =
            activate(n__app(x,y)) ->^+ app(activate(x),activate(y))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)