/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(?,O(n^1))
* Step 1: Sum.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(X,X) -> c(X)
            f(X,c(X)) -> f(s(X),X)
            f(s(X),X) -> f(X,a(X))
        - Signature:
            {f/2} / {a/1,c/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {a,c,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: NaturalPI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(X,X) -> c(X)
            f(X,c(X)) -> f(s(X),X)
            f(s(X),X) -> f(X,a(X))
        - Signature:
            {f/2} / {a/1,c/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {a,c,s}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(a) = x1
          p(c) = 7 
          p(f) = 15
          p(s) = 1 
        
        Following rules are strictly oriented:
        f(X,X) = 15  
               > 7   
               = c(X)
        
        
        Following rules are (at-least) weakly oriented:
        f(X,c(X)) =  15       
                  >= 15       
                  =  f(s(X),X)
        
        f(s(X),X) =  15       
                  >= 15       
                  =  f(X,a(X))
        
* Step 3: NaturalPI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(X,c(X)) -> f(s(X),X)
            f(s(X),X) -> f(X,a(X))
        - Weak TRS:
            f(X,X) -> c(X)
        - Signature:
            {f/2} / {a/1,c/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {a,c,s}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(a) = 0            
          p(c) = 1 + x1       
          p(f) = 1 + x1 + 8*x2
          p(s) = 1            
        
        Following rules are strictly oriented:
        f(X,c(X)) = 9 + 9*X  
                  > 2 + 8*X  
                  = f(s(X),X)
        
        f(s(X),X) = 2 + 8*X  
                  > 1 + X    
                  = f(X,a(X))
        
        
        Following rules are (at-least) weakly oriented:
        f(X,X) =  1 + 9*X
               >= 1 + X  
               =  c(X)   
        
* Step 4: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(X,X) -> c(X)
            f(X,c(X)) -> f(s(X),X)
            f(s(X),X) -> f(X,a(X))
        - Signature:
            {f/2} / {a/1,c/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {a,c,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))