/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(1))
* Step 1: Sum.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
            f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
            f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
        - Signature:
            {c/3,f/1} / {a/0,b/2}
        - Obligation:
             runtime complexity wrt. defined symbols {c,f} and constructors {a,b}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
            f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
            f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
        - Signature:
            {c/3,f/1} / {a/0,b/2}
        - Obligation:
             runtime complexity wrt. defined symbols {c,f} and constructors {a,b}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following weak dependency pairs:
        
        Strict DPs
          c#(b(a(),a()),b(y,z),x) -> c_1(z,z)
          f#(b(b(x,f(y)),z)) -> c_2(c#(z,x,f(b(b(f(a()),y),y))))
          f#(c(c(a(),y,a()),b(x,z),a())) -> c_3(y,f#(c(f(a()),z,z)))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            c#(b(a(),a()),b(y,z),x) -> c_1(z,z)
            f#(b(b(x,f(y)),z)) -> c_2(c#(z,x,f(b(b(f(a()),y),y))))
            f#(c(c(a(),y,a()),b(x,z),a())) -> c_3(y,f#(c(f(a()),z,z)))
        - Strict TRS:
            c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
            f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
            f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
        - Signature:
            {c/3,f/1,c#/3,f#/1} / {a/0,b/2,c_1/2,c_2/1,c_3/2}
        - Obligation:
             runtime complexity wrt. defined symbols {c#,f#} and constructors {a,b}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          c#(b(a(),a()),b(y,z),x) -> c_1(z,z)
* Step 4: WeightGap.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            c#(b(a(),a()),b(y,z),x) -> c_1(z,z)
        - Signature:
            {c/3,f/1,c#/3,f#/1} / {a/0,b/2,c_1/2,c_2/1,c_3/2}
        - Obligation:
             runtime complexity wrt. defined symbols {c#,f#} and constructors {a,b}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
          The following argument positions are considered usable:
            none
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
              p(a) = [0] 
              p(b) = [0] 
              p(c) = [0] 
              p(f) = [0] 
             p(c#) = [11]
             p(f#) = [0] 
            p(c_1) = [0] 
            p(c_2) = [0] 
            p(c_3) = [0] 
          
          Following rules are strictly oriented:
          c#(b(a(),a()),b(y,z),x) = [11]    
                                  > [0]     
                                  = c_1(z,z)
          
          
          Following rules are (at-least) weakly oriented:
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 5: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            c#(b(a(),a()),b(y,z),x) -> c_1(z,z)
        - Signature:
            {c/3,f/1,c#/3,f#/1} / {a/0,b/2,c_1/2,c_2/1,c_3/2}
        - Obligation:
             runtime complexity wrt. defined symbols {c#,f#} and constructors {a,b}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))