/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /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:
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
            f(C(x1,x2)) -> C(f(x1),f(x2))
            f(Z()) -> Z()
            first(C(x1,x2)) -> x1
            g(x) -> x
            second(C(x1,x2)) -> x2
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
        - Signature:
            {and/2,eqZList/2,f/1,first/1,g/1,second/1} / {C/2,False/0,True/0,Z/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,eqZList,f,first,g,second} and constructors {C,False
            ,True,Z}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
            f(C(x1,x2)) -> C(f(x1),f(x2))
            f(Z()) -> Z()
            first(C(x1,x2)) -> x1
            g(x) -> x
            second(C(x1,x2)) -> x2
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
        - Signature:
            {and/2,eqZList/2,f/1,first/1,g/1,second/1} / {C/2,False/0,True/0,Z/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,eqZList,f,first,g,second} and constructors {C,False
            ,True,Z}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
            f(C(x1,x2)) -> C(f(x1),f(x2))
            f(Z()) -> Z()
            first(C(x1,x2)) -> x1
            g(x) -> x
            second(C(x1,x2)) -> x2
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
        - Signature:
            {and/2,eqZList/2,f/1,first/1,g/1,second/1} / {C/2,False/0,True/0,Z/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,eqZList,f,first,g,second} and constructors {C,False
            ,True,Z}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          eqZList(x,z){x -> C(x,y),z -> C(z,u)} =
            eqZList(C(x,y),C(z,u)) ->^+ and(eqZList(x,z),eqZList(y,u))
              = C[eqZList(x,z) = eqZList(x,z){}]

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
            f(C(x1,x2)) -> C(f(x1),f(x2))
            f(Z()) -> Z()
            first(C(x1,x2)) -> x1
            g(x) -> x
            second(C(x1,x2)) -> x2
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
        - Signature:
            {and/2,eqZList/2,f/1,first/1,g/1,second/1} / {C/2,False/0,True/0,Z/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,eqZList,f,first,g,second} and constructors {C,False
            ,True,Z}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          C_0(2,2) -> 1
          C_0(2,2) -> 2
          C_1(5,6) -> 1
          C_1(6,6) -> 5
          C_1(6,6) -> 6
          False_0() -> 1
          False_0() -> 2
          False_1() -> 1
          False_1() -> 3
          False_1() -> 4
          True_0() -> 1
          True_0() -> 2
          True_1() -> 1
          True_1() -> 3
          True_1() -> 4
          Z_0() -> 1
          Z_0() -> 2
          Z_1() -> 1
          Z_1() -> 5
          Z_1() -> 6
          and_0(2,2) -> 1
          and_1(3,4) -> 1
          and_1(4,4) -> 3
          and_1(4,4) -> 4
          eqZList_0(2,2) -> 1
          eqZList_1(2,2) -> 3
          eqZList_1(2,2) -> 4
          f_0(2) -> 1
          f_1(2) -> 5
          f_1(2) -> 6
          first_0(2) -> 1
          g_0(2) -> 1
          second_0(2) -> 1
          2 -> 1
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
            eqZList(C(x1,x2),C(y1,y2)) -> and(eqZList(x1,y1),eqZList(x2,y2))
            eqZList(C(x1,x2),Z()) -> False()
            eqZList(Z(),C(y1,y2)) -> False()
            eqZList(Z(),Z()) -> True()
            f(C(x1,x2)) -> C(f(x1),f(x2))
            f(Z()) -> Z()
            first(C(x1,x2)) -> x1
            g(x) -> x
            second(C(x1,x2)) -> x2
        - Signature:
            {and/2,eqZList/2,f/1,first/1,g/1,second/1} / {C/2,False/0,True/0,Z/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,eqZList,f,first,g,second} and constructors {C,False
            ,True,Z}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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