/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__U11(X) -> U11(X)
            a__U11(tt()) -> a__U12(tt())
            a__U12(X) -> U12(X)
            a__U12(tt()) -> tt()
            a____(X,nil()) -> mark(X)
            a____(X1,X2) -> __(X1,X2)
            a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
            a____(nil(),X) -> mark(X)
            a__isNePal(X) -> isNePal(X)
            a__isNePal(__(I,__(P,I))) -> a__U11(tt())
            mark(U11(X)) -> a__U11(mark(X))
            mark(U12(X)) -> a__U12(mark(X))
            mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
            mark(isNePal(X)) -> a__isNePal(mark(X))
            mark(nil()) -> nil()
            mark(tt()) -> tt()
        - Signature:
            {a__U11/1,a__U12/1,a____/2,a__isNePal/1,mark/1} / {U11/1,U12/1,__/2,isNePal/1,nil/0,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__U11,a__U12,a____,a__isNePal,mark} and constructors {U11,U12,__
            ,isNePal,nil,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__U11(X) -> U11(X)
            a__U11(tt()) -> a__U12(tt())
            a__U12(X) -> U12(X)
            a__U12(tt()) -> tt()
            a____(X,nil()) -> mark(X)
            a____(X1,X2) -> __(X1,X2)
            a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
            a____(nil(),X) -> mark(X)
            a__isNePal(X) -> isNePal(X)
            a__isNePal(__(I,__(P,I))) -> a__U11(tt())
            mark(U11(X)) -> a__U11(mark(X))
            mark(U12(X)) -> a__U12(mark(X))
            mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
            mark(isNePal(X)) -> a__isNePal(mark(X))
            mark(nil()) -> nil()
            mark(tt()) -> tt()
        - Signature:
            {a__U11/1,a__U12/1,a____/2,a__isNePal/1,mark/1} / {U11/1,U12/1,__/2,isNePal/1,nil/0,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__U11,a__U12,a____,a__isNePal,mark} and constructors {U11,U12,__
            ,isNePal,nil,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__U11(X) -> U11(X)
            a__U11(tt()) -> a__U12(tt())
            a__U12(X) -> U12(X)
            a__U12(tt()) -> tt()
            a____(X,nil()) -> mark(X)
            a____(X1,X2) -> __(X1,X2)
            a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
            a____(nil(),X) -> mark(X)
            a__isNePal(X) -> isNePal(X)
            a__isNePal(__(I,__(P,I))) -> a__U11(tt())
            mark(U11(X)) -> a__U11(mark(X))
            mark(U12(X)) -> a__U12(mark(X))
            mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
            mark(isNePal(X)) -> a__isNePal(mark(X))
            mark(nil()) -> nil()
            mark(tt()) -> tt()
        - Signature:
            {a__U11/1,a__U12/1,a____/2,a__isNePal/1,mark/1} / {U11/1,U12/1,__/2,isNePal/1,nil/0,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__U11,a__U12,a____,a__isNePal,mark} and constructors {U11,U12,__
            ,isNePal,nil,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> U11(x)} =
            mark(U11(x)) ->^+ a__U11(mark(x))
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)