/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(?,O(n^1))
* Step 1: Sum.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            add(0(),X) -> X
            add(s(),Y) -> s()
            dbl(0()) -> 0()
            dbl(s()) -> s()
            first(0(),X) -> nil()
            first(s(),cons(Y)) -> cons(Y)
            sqr(0()) -> 0()
            sqr(s()) -> s()
            terms(N) -> cons(recip(sqr(N)))
        - Signature:
            {add/2,dbl/1,first/2,sqr/1,terms/1} / {0/0,cons/1,nil/0,recip/1,s/0}
        - Obligation:
             runtime complexity wrt. defined symbols {add,dbl,first,sqr,terms} and constructors {0,cons,nil,recip,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: ToInnermost.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            add(0(),X) -> X
            add(s(),Y) -> s()
            dbl(0()) -> 0()
            dbl(s()) -> s()
            first(0(),X) -> nil()
            first(s(),cons(Y)) -> cons(Y)
            sqr(0()) -> 0()
            sqr(s()) -> s()
            terms(N) -> cons(recip(sqr(N)))
        - Signature:
            {add/2,dbl/1,first/2,sqr/1,terms/1} / {0/0,cons/1,nil/0,recip/1,s/0}
        - Obligation:
             runtime complexity wrt. defined symbols {add,dbl,first,sqr,terms} and constructors {0,cons,nil,recip,s}
    + Applied Processor:
        ToInnermost
    + Details:
        switch to innermost, as the system is overlay and right linear and does not contain weak rules
* Step 3: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            add(0(),X) -> X
            add(s(),Y) -> s()
            dbl(0()) -> 0()
            dbl(s()) -> s()
            first(0(),X) -> nil()
            first(s(),cons(Y)) -> cons(Y)
            sqr(0()) -> 0()
            sqr(s()) -> s()
            terms(N) -> cons(recip(sqr(N)))
        - Signature:
            {add/2,dbl/1,first/2,sqr/1,terms/1} / {0/0,cons/1,nil/0,recip/1,s/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add,dbl,first,sqr,terms} and constructors {0,cons,nil
            ,recip,s}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 1
          0_0() -> 2
          0_1() -> 1
          0_1() -> 3
          add_0(2,2) -> 1
          cons_0(2) -> 1
          cons_0(2) -> 2
          cons_1(2) -> 1
          dbl_0(2) -> 1
          first_0(2,2) -> 1
          nil_0() -> 1
          nil_0() -> 2
          nil_1() -> 1
          recip_0(2) -> 1
          recip_0(2) -> 2
          recip_1(3) -> 1
          recip_1(3) -> 2
          s_0() -> 1
          s_0() -> 2
          s_1() -> 1
          s_1() -> 3
          sqr_0(2) -> 1
          sqr_1(2) -> 3
          terms_0(2) -> 1
          2 -> 1
* Step 4: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            add(0(),X) -> X
            add(s(),Y) -> s()
            dbl(0()) -> 0()
            dbl(s()) -> s()
            first(0(),X) -> nil()
            first(s(),cons(Y)) -> cons(Y)
            sqr(0()) -> 0()
            sqr(s()) -> s()
            terms(N) -> cons(recip(sqr(N)))
        - Signature:
            {add/2,dbl/1,first/2,sqr/1,terms/1} / {0/0,cons/1,nil/0,recip/1,s/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add,dbl,first,sqr,terms} and constructors {0,cons,nil
            ,recip,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))