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

** Step 1.b:1: ToInnermost.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            h(x,c(y,z)) -> h(c(s(y),x),z)
            h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z)))
        - Signature:
            {h/2} / {0/0,c/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {h} and constructors {0,c,s}
    + 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:
            h(x,c(y,z)) -> h(c(s(y),x),z)
            h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z)))
        - Signature:
            {h/2} / {0/0,c/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h} and constructors {0,c,s}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 2
          0_1() -> 8
          c_0(2,2) -> 2
          c_1(2,2) -> 7
          c_1(2,5) -> 7
          c_1(4,2) -> 3
          c_1(4,3) -> 3
          c_1(4,11) -> 3
          c_1(6,5) -> 5
          c_1(6,7) -> 5
          c_2(10,2) -> 9
          c_2(10,3) -> 9
          c_2(10,9) -> 9
          c_2(10,11) -> 9
          c_2(12,9) -> 11
          h_0(2,2) -> 1
          h_1(2,5) -> 1
          h_1(3,2) -> 1
          h_1(3,5) -> 1
          h_1(9,5) -> 1
          h_1(11,5) -> 1
          h_2(9,5) -> 1
          h_2(9,7) -> 1
          h_2(11,2) -> 1
          h_2(11,5) -> 1
          s_0(2) -> 2
          s_1(2) -> 4
          s_1(8) -> 6
          s_2(2) -> 12
          s_2(6) -> 10
** Step 1.b:3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            h(x,c(y,z)) -> h(c(s(y),x),z)
            h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z)))
        - Signature:
            {h/2} / {0/0,c/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h} and constructors {0,c,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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