/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(X1,X2,X3) -> U11(X1,X2,X3)
            a__U11(tt(),M,N) -> a__U12(tt(),M,N)
            a__U12(X1,X2,X3) -> U12(X1,X2,X3)
            a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
            a__plus(N,0()) -> mark(N)
            a__plus(N,s(M)) -> a__U11(tt(),M,N)
            a__plus(X1,X2) -> plus(X1,X2)
            mark(0()) -> 0()
            mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
            mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
            mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
            mark(s(X)) -> s(mark(X))
            mark(tt()) -> tt()
        - Signature:
            {a__U11/3,a__U12/3,a__plus/2,mark/1} / {0/0,U11/3,U12/3,plus/2,s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__U11,a__U12,a__plus,mark} and constructors {0,U11,U12,plus,s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__U11(X1,X2,X3) -> U11(X1,X2,X3)
            a__U11(tt(),M,N) -> a__U12(tt(),M,N)
            a__U12(X1,X2,X3) -> U12(X1,X2,X3)
            a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
            a__plus(N,0()) -> mark(N)
            a__plus(N,s(M)) -> a__U11(tt(),M,N)
            a__plus(X1,X2) -> plus(X1,X2)
            mark(0()) -> 0()
            mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
            mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
            mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
            mark(s(X)) -> s(mark(X))
            mark(tt()) -> tt()
        - Signature:
            {a__U11/3,a__U12/3,a__plus/2,mark/1} / {0/0,U11/3,U12/3,plus/2,s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__U11,a__U12,a__plus,mark} and constructors {0,U11,U12,plus,s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__U11(X1,X2,X3) -> U11(X1,X2,X3)
            a__U11(tt(),M,N) -> a__U12(tt(),M,N)
            a__U12(X1,X2,X3) -> U12(X1,X2,X3)
            a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
            a__plus(N,0()) -> mark(N)
            a__plus(N,s(M)) -> a__U11(tt(),M,N)
            a__plus(X1,X2) -> plus(X1,X2)
            mark(0()) -> 0()
            mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
            mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
            mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
            mark(s(X)) -> s(mark(X))
            mark(tt()) -> tt()
        - Signature:
            {a__U11/3,a__U12/3,a__plus/2,mark/1} / {0/0,U11/3,U12/3,plus/2,s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__U11,a__U12,a__plus,mark} and constructors {0,U11,U12,plus,s,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> U11(x,y,z)} =
            mark(U11(x,y,z)) ->^+ a__U11(mark(x),y,z)
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)