/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum.  WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            dfsAcc#3(Leaf(x8),x16) -> Cons(x8,x16)
            dfsAcc#3(Node(x6,x4),x2) -> dfsAcc#3(x4,dfsAcc#3(x6,x2))
            main(x1) -> revApp#2(dfsAcc#3(x1,Nil()),Nil())
            revApp#2(Cons(x6,x4),x2) -> revApp#2(x4,Cons(x6,x2))
            revApp#2(Nil(),x16) -> x16
        - Signature:
            {dfsAcc#3/2,main/1,revApp#2/2} / {Cons/2,Leaf/1,Nil/0,Node/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dfsAcc#3,main,revApp#2} and constructors {Cons,Leaf,Nil
            ,Node}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            dfsAcc#3(Leaf(x8),x16) -> Cons(x8,x16)
            dfsAcc#3(Node(x6,x4),x2) -> dfsAcc#3(x4,dfsAcc#3(x6,x2))
            main(x1) -> revApp#2(dfsAcc#3(x1,Nil()),Nil())
            revApp#2(Cons(x6,x4),x2) -> revApp#2(x4,Cons(x6,x2))
            revApp#2(Nil(),x16) -> x16
        - Signature:
            {dfsAcc#3/2,main/1,revApp#2/2} / {Cons/2,Leaf/1,Nil/0,Node/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dfsAcc#3,main,revApp#2} and constructors {Cons,Leaf,Nil
            ,Node}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            dfsAcc#3(Leaf(x8),x16) -> Cons(x8,x16)
            dfsAcc#3(Node(x6,x4),x2) -> dfsAcc#3(x4,dfsAcc#3(x6,x2))
            main(x1) -> revApp#2(dfsAcc#3(x1,Nil()),Nil())
            revApp#2(Cons(x6,x4),x2) -> revApp#2(x4,Cons(x6,x2))
            revApp#2(Nil(),x16) -> x16
        - Signature:
            {dfsAcc#3/2,main/1,revApp#2/2} / {Cons/2,Leaf/1,Nil/0,Node/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dfsAcc#3,main,revApp#2} and constructors {Cons,Leaf,Nil
            ,Node}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          dfsAcc#3(y,z){y -> Node(x,y)} =
            dfsAcc#3(Node(x,y),z) ->^+ dfsAcc#3(y,dfsAcc#3(x,z))
              = C[dfsAcc#3(y,dfsAcc#3(x,z)) = dfsAcc#3(y,z){z -> dfsAcc#3(x,z)}]

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            dfsAcc#3(Leaf(x8),x16) -> Cons(x8,x16)
            dfsAcc#3(Node(x6,x4),x2) -> dfsAcc#3(x4,dfsAcc#3(x6,x2))
            main(x1) -> revApp#2(dfsAcc#3(x1,Nil()),Nil())
            revApp#2(Cons(x6,x4),x2) -> revApp#2(x4,Cons(x6,x2))
            revApp#2(Nil(),x16) -> x16
        - Signature:
            {dfsAcc#3/2,main/1,revApp#2/2} / {Cons/2,Leaf/1,Nil/0,Node/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dfsAcc#3,main,revApp#2} and constructors {Cons,Leaf,Nil
            ,Node}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          Cons_0(2,2) -> 1
          Cons_0(2,2) -> 2
          Cons_1(2,1) -> 1
          Cons_1(2,2) -> 1
          Cons_1(2,2) -> 3
          Cons_1(2,3) -> 1
          Cons_1(2,3) -> 3
          Cons_1(2,4) -> 4
          Cons_1(2,6) -> 4
          Cons_2(2,5) -> 1
          Cons_2(2,5) -> 7
          Cons_2(2,7) -> 1
          Cons_2(2,7) -> 7
          Leaf_0(2) -> 1
          Leaf_0(2) -> 2
          Nil_0() -> 1
          Nil_0() -> 2
          Nil_1() -> 5
          Nil_1() -> 6
          Node_0(2,2) -> 1
          Node_0(2,2) -> 2
          dfsAcc#3_0(2,2) -> 1
          dfsAcc#3_1(2,2) -> 3
          dfsAcc#3_1(2,3) -> 1
          dfsAcc#3_1(2,3) -> 3
          dfsAcc#3_1(2,4) -> 4
          dfsAcc#3_1(2,6) -> 4
          main_0(2) -> 1
          revApp#2_0(2,2) -> 1
          revApp#2_1(2,1) -> 1
          revApp#2_1(4,5) -> 1
          revApp#2_2(4,7) -> 1
          revApp#2_2(6,7) -> 1
          2 -> 1
          7 -> 1
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            dfsAcc#3(Leaf(x8),x16) -> Cons(x8,x16)
            dfsAcc#3(Node(x6,x4),x2) -> dfsAcc#3(x4,dfsAcc#3(x6,x2))
            main(x1) -> revApp#2(dfsAcc#3(x1,Nil()),Nil())
            revApp#2(Cons(x6,x4),x2) -> revApp#2(x4,Cons(x6,x2))
            revApp#2(Nil(),x16) -> x16
        - Signature:
            {dfsAcc#3/2,main/1,revApp#2/2} / {Cons/2,Leaf/1,Nil/0,Node/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dfsAcc#3,main,revApp#2} and constructors {Cons,Leaf,Nil
            ,Node}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))