/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 min(x,0()) -> 0()
 min(0(),y) -> 0()
 min(s(x),s(y)) -> s(min(x,y))
 max(x,0()) -> x
 max(0(),y) -> y
 max(s(x),s(y)) -> s(max(x,y))
 minus(x,0()) -> x
 minus(s(x),s(y)) -> s(minus(x,any(y)))
 gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
 any(s(x)) -> s(s(any(x)))
 any(x) -> x

Proof:
 DP Processor:
  DPs:
   min#(s(x),s(y)) -> min#(x,y)
   max#(s(x),s(y)) -> max#(x,y)
   minus#(s(x),s(y)) -> any#(y)
   minus#(s(x),s(y)) -> minus#(x,any(y))
   gcd#(s(x),s(y)) -> min#(x,y)
   gcd#(s(x),s(y)) -> max#(x,y)
   gcd#(s(x),s(y)) -> minus#(max(x,y),min(x,y))
   gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y)))
   any#(s(x)) -> any#(x)
  TRS:
   min(x,0()) -> 0()
   min(0(),y) -> 0()
   min(s(x),s(y)) -> s(min(x,y))
   max(x,0()) -> x
   max(0(),y) -> y
   max(s(x),s(y)) -> s(max(x,y))
   minus(x,0()) -> x
   minus(s(x),s(y)) -> s(minus(x,any(y)))
   gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
   any(s(x)) -> s(s(any(x)))
   any(x) -> x
  TDG Processor:
   DPs:
    min#(s(x),s(y)) -> min#(x,y)
    max#(s(x),s(y)) -> max#(x,y)
    minus#(s(x),s(y)) -> any#(y)
    minus#(s(x),s(y)) -> minus#(x,any(y))
    gcd#(s(x),s(y)) -> min#(x,y)
    gcd#(s(x),s(y)) -> max#(x,y)
    gcd#(s(x),s(y)) -> minus#(max(x,y),min(x,y))
    gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y)))
    any#(s(x)) -> any#(x)
   TRS:
    min(x,0()) -> 0()
    min(0(),y) -> 0()
    min(s(x),s(y)) -> s(min(x,y))
    max(x,0()) -> x
    max(0(),y) -> y
    max(s(x),s(y)) -> s(max(x,y))
    minus(x,0()) -> x
    minus(s(x),s(y)) -> s(minus(x,any(y)))
    gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
    any(s(x)) -> s(s(any(x)))
    any(x) -> x
   graph:
    gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y))) ->
    gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y)))
    gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y))) ->
    gcd#(s(x),s(y)) -> minus#(max(x,y),min(x,y))
    gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y))) ->
    gcd#(s(x),s(y)) -> max#(x,y)
    gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y))) ->
    gcd#(s(x),s(y)) -> min#(x,y)
    gcd#(s(x),s(y)) -> minus#(max(x,y),min(x,y)) ->
    minus#(s(x),s(y)) -> minus#(x,any(y))
    gcd#(s(x),s(y)) -> minus#(max(x,y),min(x,y)) ->
    minus#(s(x),s(y)) -> any#(y)
    gcd#(s(x),s(y)) -> max#(x,y) -> max#(s(x),s(y)) -> max#(x,y)
    gcd#(s(x),s(y)) -> min#(x,y) -> min#(s(x),s(y)) -> min#(x,y)
    any#(s(x)) -> any#(x) -> any#(s(x)) -> any#(x)
    minus#(s(x),s(y)) -> any#(y) -> any#(s(x)) -> any#(x)
    minus#(s(x),s(y)) -> minus#(x,any(y)) ->
    minus#(s(x),s(y)) -> minus#(x,any(y))
    minus#(s(x),s(y)) -> minus#(x,any(y)) ->
    minus#(s(x),s(y)) -> any#(y)
    max#(s(x),s(y)) -> max#(x,y) -> max#(s(x),s(y)) -> max#(x,y)
    min#(s(x),s(y)) -> min#(x,y) -> min#(s(x),s(y)) -> min#(x,y)
   SCC Processor:
    #sccs: 5
    #rules: 5
    #arcs: 14/81
    DPs:
     gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y)))
    TRS:
     min(x,0()) -> 0()
     min(0(),y) -> 0()
     min(s(x),s(y)) -> s(min(x,y))
     max(x,0()) -> x
     max(0(),y) -> y
     max(s(x),s(y)) -> s(max(x,y))
     minus(x,0()) -> x
     minus(s(x),s(y)) -> s(minus(x,any(y)))
     gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
     any(s(x)) -> s(s(any(x)))
     any(x) -> x
    Usable Rule Processor:
     DPs:
      gcd#(s(x),s(y)) -> gcd#(minus(max(x,y),min(x,y)),s(min(x,y)))
     TRS:
      min(x,0()) -> 0()
      min(0(),y) -> 0()
      min(s(x),s(y)) -> s(min(x,y))
      max(x,0()) -> x
      max(0(),y) -> y
      max(s(x),s(y)) -> s(max(x,y))
      minus(x,0()) -> x
      minus(s(x),s(y)) -> s(minus(x,any(y)))
      any(s(x)) -> s(s(any(x)))
      any(x) -> x
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       min(x,0()) -> 0()
       min(0(),y) -> 0()
       min(s(x),s(y)) -> s(min(x,y))
       max(x,0()) -> x
       max(0(),y) -> y
       max(s(x),s(y)) -> s(max(x,y))
       minus(x,0()) -> x
       minus(s(x),s(y)) -> s(minus(x,any(y)))
      interpretation:
       [gcd#](x0, x1) = -3x0 + -5x1 + 0,
       
       [any](x0) = 1x0 + 1,
       
       [minus](x0, x1) = x0 + -11,
       
       [max](x0, x1) = 2x0 + x1 + -5,
       
       [s](x0) = 3x0 + 4,
       
       [min](x0, x1) = x0 + 0,
       
       [0] = 0
      orientation:
       gcd#(s(x),s(y)) = x + -2y + 1 >= -1x + -3y + 0 = gcd#(minus(max(x,y),min(x,y)),s(min(x,y)))
       
       min(x,0()) = x + 0 >= 0 = 0()
       
       min(0(),y) = 0 >= 0 = 0()
       
       min(s(x),s(y)) = 3x + 4 >= 3x + 4 = s(min(x,y))
       
       max(x,0()) = 2x + 0 >= x = x
       
       max(0(),y) = y + 2 >= y = y
       
       max(s(x),s(y)) = 5x + 3y + 6 >= 5x + 3y + 4 = s(max(x,y))
       
       minus(x,0()) = x + -11 >= x = x
       
       minus(s(x),s(y)) = 3x + 4 >= 3x + 4 = s(minus(x,any(y)))
       
       any(s(x)) = 4x + 5 >= 7x + 7 = s(s(any(x)))
       
       any(x) = 1x + 1 >= x = x
      problem:
       DPs:
        
       TRS:
        min(x,0()) -> 0()
        min(0(),y) -> 0()
        min(s(x),s(y)) -> s(min(x,y))
        max(x,0()) -> x
        max(0(),y) -> y
        max(s(x),s(y)) -> s(max(x,y))
        minus(x,0()) -> x
        minus(s(x),s(y)) -> s(minus(x,any(y)))
        any(s(x)) -> s(s(any(x)))
        any(x) -> x
      Qed
    
    DPs:
     minus#(s(x),s(y)) -> minus#(x,any(y))
    TRS:
     min(x,0()) -> 0()
     min(0(),y) -> 0()
     min(s(x),s(y)) -> s(min(x,y))
     max(x,0()) -> x
     max(0(),y) -> y
     max(s(x),s(y)) -> s(max(x,y))
     minus(x,0()) -> x
     minus(s(x),s(y)) -> s(minus(x,any(y)))
     gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
     any(s(x)) -> s(s(any(x)))
     any(x) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 0
     problem:
      DPs:
       
      TRS:
       min(x,0()) -> 0()
       min(0(),y) -> 0()
       min(s(x),s(y)) -> s(min(x,y))
       max(x,0()) -> x
       max(0(),y) -> y
       max(s(x),s(y)) -> s(max(x,y))
       minus(x,0()) -> x
       minus(s(x),s(y)) -> s(minus(x,any(y)))
       gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
       any(s(x)) -> s(s(any(x)))
       any(x) -> x
     Qed
    
    DPs:
     any#(s(x)) -> any#(x)
    TRS:
     min(x,0()) -> 0()
     min(0(),y) -> 0()
     min(s(x),s(y)) -> s(min(x,y))
     max(x,0()) -> x
     max(0(),y) -> y
     max(s(x),s(y)) -> s(max(x,y))
     minus(x,0()) -> x
     minus(s(x),s(y)) -> s(minus(x,any(y)))
     gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
     any(s(x)) -> s(s(any(x)))
     any(x) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(any#) = 0
     problem:
      DPs:
       
      TRS:
       min(x,0()) -> 0()
       min(0(),y) -> 0()
       min(s(x),s(y)) -> s(min(x,y))
       max(x,0()) -> x
       max(0(),y) -> y
       max(s(x),s(y)) -> s(max(x,y))
       minus(x,0()) -> x
       minus(s(x),s(y)) -> s(minus(x,any(y)))
       gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
       any(s(x)) -> s(s(any(x)))
       any(x) -> x
     Qed
    
    DPs:
     max#(s(x),s(y)) -> max#(x,y)
    TRS:
     min(x,0()) -> 0()
     min(0(),y) -> 0()
     min(s(x),s(y)) -> s(min(x,y))
     max(x,0()) -> x
     max(0(),y) -> y
     max(s(x),s(y)) -> s(max(x,y))
     minus(x,0()) -> x
     minus(s(x),s(y)) -> s(minus(x,any(y)))
     gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
     any(s(x)) -> s(s(any(x)))
     any(x) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(max#) = 0
     problem:
      DPs:
       
      TRS:
       min(x,0()) -> 0()
       min(0(),y) -> 0()
       min(s(x),s(y)) -> s(min(x,y))
       max(x,0()) -> x
       max(0(),y) -> y
       max(s(x),s(y)) -> s(max(x,y))
       minus(x,0()) -> x
       minus(s(x),s(y)) -> s(minus(x,any(y)))
       gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
       any(s(x)) -> s(s(any(x)))
       any(x) -> x
     Qed
    
    DPs:
     min#(s(x),s(y)) -> min#(x,y)
    TRS:
     min(x,0()) -> 0()
     min(0(),y) -> 0()
     min(s(x),s(y)) -> s(min(x,y))
     max(x,0()) -> x
     max(0(),y) -> y
     max(s(x),s(y)) -> s(max(x,y))
     minus(x,0()) -> x
     minus(s(x),s(y)) -> s(minus(x,any(y)))
     gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
     any(s(x)) -> s(s(any(x)))
     any(x) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(min#) = 0
     problem:
      DPs:
       
      TRS:
       min(x,0()) -> 0()
       min(0(),y) -> 0()
       min(s(x),s(y)) -> s(min(x,y))
       max(x,0()) -> x
       max(0(),y) -> y
       max(s(x),s(y)) -> s(max(x,y))
       minus(x,0()) -> x
       minus(s(x),s(y)) -> s(minus(x,any(y)))
       gcd(s(x),s(y)) -> gcd(minus(max(x,y),min(x,y)),s(min(x,y)))
       any(s(x)) -> s(s(any(x)))
       any(x) -> x
     Qed