/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:
            implies(x,or(y,z)) -> or(y,implies(x,z))
            implies(not(x),y) -> or(x,y)
            implies(not(x),or(y,z)) -> implies(y,or(x,z))
        - Signature:
            {implies/2} / {not/1,or/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {implies} and constructors {not,or}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            implies(x,or(y,z)) -> or(y,implies(x,z))
            implies(not(x),y) -> or(x,y)
            implies(not(x),or(y,z)) -> implies(y,or(x,z))
        - Signature:
            {implies/2} / {not/1,or/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {implies} and constructors {not,or}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          implies(x,z){z -> or(y,z)} =
            implies(x,or(y,z)) ->^+ or(y,implies(x,z))
              = C[implies(x,z) = implies(x,z){}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            implies(x,or(y,z)) -> or(y,implies(x,z))
            implies(not(x),y) -> or(x,y)
            implies(not(x),or(y,z)) -> implies(y,or(x,z))
        - Signature:
            {implies/2} / {not/1,or/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {implies} and constructors {not,or}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          implies :: ["A"(15) x "A"(15)] -(15)-> "A"(3)
          not :: ["A"(15)] -(15)-> "A"(15)
          or :: ["A"(15) x "A"(15)] -(15)-> "A"(15)
          or :: ["A"(3) x "A"(3)] -(3)-> "A"(3)
          or :: ["A"(10) x "A"(10)] -(10)-> "A"(10)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "not_A" :: ["A"(1)] -(1)-> "A"(1)
          "or_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
        

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