/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:
            app(cons(X,XS),YS) -> cons(X,app(XS,YS))
            app(nil(),YS) -> YS
            from(X) -> cons(X,from(s(X)))
            prefix(L) -> cons(nil(),zWadr(L,prefix(L)))
            zWadr(XS,nil()) -> nil()
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,nil())),zWadr(XS,YS))
            zWadr(nil(),YS) -> nil()
        - Signature:
            {app/2,from/1,prefix/1,zWadr/2} / {cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {app,from,prefix,zWadr} and constructors {cons,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(cons(X,XS),YS) -> cons(X,app(XS,YS))
            app(nil(),YS) -> YS
            from(X) -> cons(X,from(s(X)))
            prefix(L) -> cons(nil(),zWadr(L,prefix(L)))
            zWadr(XS,nil()) -> nil()
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,nil())),zWadr(XS,YS))
            zWadr(nil(),YS) -> nil()
        - Signature:
            {app/2,from/1,prefix/1,zWadr/2} / {cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {app,from,prefix,zWadr} and constructors {cons,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(cons(X,XS),YS) -> cons(X,app(XS,YS))
            app(nil(),YS) -> YS
            from(X) -> cons(X,from(s(X)))
            prefix(L) -> cons(nil(),zWadr(L,prefix(L)))
            zWadr(XS,nil()) -> nil()
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,nil())),zWadr(XS,YS))
            zWadr(nil(),YS) -> nil()
        - Signature:
            {app/2,from/1,prefix/1,zWadr/2} / {cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {app,from,prefix,zWadr} and constructors {cons,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          app(y,z){y -> cons(x,y)} =
            app(cons(x,y),z) ->^+ cons(x,app(y,z))
              = C[app(y,z) = app(y,z){}]

WORST_CASE(Omega(n^1),?)