/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),O(n^1))
* Step 1: Sum.  WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            merge(x,nil()) -> x
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
             runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            merge(x,nil()) -> x
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
             runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            merge(x,nil()) -> x
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
             runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          merge(y,++(u(),v())){y -> ++(x,y)} =
            merge(++(x,y),++(u(),v())) ->^+ ++(x,merge(y,++(u(),v())))
              = C[merge(y,++(u(),v())) = merge(y,++(u(),v())){}]

** Step 1.b:1: ToInnermost.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            merge(x,nil()) -> x
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
             runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
    + Applied Processor:
        ToInnermost
    + Details:
        switch to innermost, as the system is overlay and right linear and does not contain weak rules
** Step 1.b:2: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            merge(x,nil()) -> x
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          ++_0(2,2) -> 1
          ++_0(2,2) -> 2
          ++_1(2,2) -> 8
          ++_1(2,3) -> 1
          ++_1(2,3) -> 3
          ++_1(5,6) -> 3
          ++_1(5,6) -> 4
          ++_1(5,7) -> 1
          ++_1(5,7) -> 3
          merge_0(2,2) -> 1
          merge_1(2,4) -> 3
          merge_1(8,6) -> 7
          nil_0() -> 1
          nil_0() -> 2
          u_0() -> 1
          u_0() -> 2
          u_1() -> 5
          v_0() -> 1
          v_0() -> 2
          v_1() -> 6
          2 -> 1
          4 -> 3
** Step 1.b:3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            merge(x,nil()) -> x
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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