/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 a(a(y,0()),0()) -> y
 c(c(y)) -> y
 c(a(c(c(y)),x)) -> a(c(c(c(a(x,0())))),y)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [a](x0, x1) = x0 + x1,
   
   [0] = 0,
   
   [c](x0) = x0 + 2
  orientation:
   a(a(y,0()),0()) = y >= y = y
   
   c(c(y)) = y + 4 >= y = y
   
   c(a(c(c(y)),x)) = x + y + 6 >= x + y + 6 = a(c(c(c(a(x,0())))),y)
  problem:
   a(a(y,0()),0()) -> y
   c(a(c(c(y)),x)) -> a(c(c(c(a(x,0())))),y)
  DP Processor:
   DPs:
    c#(a(c(c(y)),x)) -> a#(x,0())
    c#(a(c(c(y)),x)) -> c#(a(x,0()))
    c#(a(c(c(y)),x)) -> c#(c(a(x,0())))
    c#(a(c(c(y)),x)) -> c#(c(c(a(x,0()))))
    c#(a(c(c(y)),x)) -> a#(c(c(c(a(x,0())))),y)
   TRS:
    a(a(y,0()),0()) -> y
    c(a(c(c(y)),x)) -> a(c(c(c(a(x,0())))),y)
   TDG Processor:
    DPs:
     c#(a(c(c(y)),x)) -> a#(x,0())
     c#(a(c(c(y)),x)) -> c#(a(x,0()))
     c#(a(c(c(y)),x)) -> c#(c(a(x,0())))
     c#(a(c(c(y)),x)) -> c#(c(c(a(x,0()))))
     c#(a(c(c(y)),x)) -> a#(c(c(c(a(x,0())))),y)
    TRS:
     a(a(y,0()),0()) -> y
     c(a(c(c(y)),x)) -> a(c(c(c(a(x,0())))),y)
    graph:
     c#(a(c(c(y)),x)) -> c#(c(c(a(x,0())))) ->
     c#(a(c(c(y)),x)) -> a#(c(c(c(a(x,0())))),y)
     c#(a(c(c(y)),x)) -> c#(c(c(a(x,0())))) ->
     c#(a(c(c(y)),x)) -> c#(c(c(a(x,0()))))
     c#(a(c(c(y)),x)) -> c#(c(c(a(x,0())))) ->
     c#(a(c(c(y)),x)) -> c#(c(a(x,0())))
     c#(a(c(c(y)),x)) -> c#(c(c(a(x,0())))) ->
     c#(a(c(c(y)),x)) -> c#(a(x,0()))
     c#(a(c(c(y)),x)) -> c#(c(c(a(x,0())))) ->
     c#(a(c(c(y)),x)) -> a#(x,0())
     c#(a(c(c(y)),x)) -> c#(c(a(x,0()))) ->
     c#(a(c(c(y)),x)) -> a#(c(c(c(a(x,0())))),y)
     c#(a(c(c(y)),x)) -> c#(c(a(x,0()))) ->
     c#(a(c(c(y)),x)) -> c#(c(c(a(x,0()))))
     c#(a(c(c(y)),x)) -> c#(c(a(x,0()))) ->
     c#(a(c(c(y)),x)) -> c#(c(a(x,0())))
     c#(a(c(c(y)),x)) -> c#(c(a(x,0()))) ->
     c#(a(c(c(y)),x)) -> c#(a(x,0()))
     c#(a(c(c(y)),x)) -> c#(c(a(x,0()))) ->
     c#(a(c(c(y)),x)) -> a#(x,0())
     c#(a(c(c(y)),x)) -> c#(a(x,0())) ->
     c#(a(c(c(y)),x)) -> a#(c(c(c(a(x,0())))),y)
     c#(a(c(c(y)),x)) -> c#(a(x,0())) ->
     c#(a(c(c(y)),x)) -> c#(c(c(a(x,0()))))
     c#(a(c(c(y)),x)) -> c#(a(x,0())) ->
     c#(a(c(c(y)),x)) -> c#(c(a(x,0())))
     c#(a(c(c(y)),x)) -> c#(a(x,0())) ->
     c#(a(c(c(y)),x)) -> c#(a(x,0()))
     c#(a(c(c(y)),x)) -> c#(a(x,0())) -> c#(a(c(c(y)),x)) -> a#(x,0())
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 15/25
     DPs:
      c#(a(c(c(y)),x)) -> c#(c(c(a(x,0()))))
      c#(a(c(c(y)),x)) -> c#(a(x,0()))
      c#(a(c(c(y)),x)) -> c#(c(a(x,0())))
     TRS:
      a(a(y,0()),0()) -> y
      c(a(c(c(y)),x)) -> a(c(c(c(a(x,0())))),y)
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       a(a(y,0()),0()) -> y
       c(a(c(c(y)),x)) -> a(c(c(c(a(x,0())))),y)
      interpretation:
       [c#](x0) = x0 + 0,
       
       [a](x0, x1) = x0 + 2x1 + 0,
       
       [0] = 2,
       
       [c](x0) = 1x0 + 5
      orientation:
       c#(a(c(c(y)),x)) = 2x + 2y + 6 >= 2x + 6 = c#(c(c(a(x,0()))))
       
       c#(a(c(c(y)),x)) = 2x + 2y + 6 >= x + 4 = c#(a(x,0()))
       
       c#(a(c(c(y)),x)) = 2x + 2y + 6 >= 1x + 5 = c#(c(a(x,0())))
       
       a(a(y,0()),0()) = y + 4 >= y = y
       
       c(a(c(c(y)),x)) = 3x + 3y + 7 >= 3x + 2y + 7 = a(c(c(c(a(x,0())))),y)
      problem:
       DPs:
        c#(a(c(c(y)),x)) -> c#(c(c(a(x,0()))))
       TRS:
        a(a(y,0()),0()) -> y
        c(a(c(c(y)),x)) -> a(c(c(c(a(x,0())))),y)
      Restore Modifier:
       DPs:
        c#(a(c(c(y)),x)) -> c#(c(c(a(x,0()))))
       TRS:
        a(a(y,0()),0()) -> y
        c(a(c(c(y)),x)) -> a(c(c(c(a(x,0())))),y)
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(a(y,0()),0()) -> y
         c(a(c(c(y)),x)) -> a(c(c(c(a(x,0())))),y)
        interpretation:
         [c#](x0) = [0  -&]x0 + [0],
         
                       [-& 0 ]     [0  2 ]     [0]
         [a](x0, x1) = [0  1 ]x0 + [-& 2 ]x1 + [2],
         
               [0 ]
         [0] = [-&],
         
                   [-& 0 ]     [1]
         [c](x0) = [1  -&]x0 + [0]
        orientation:
         c#(a(c(c(y)),x)) = [0 2]x + [-& 1 ]y + [2] >= [-& 1 ]x + [1] = c#(c(c(a(x,0()))))
         
                           [0 1]    [2]         
         a(a(y,0()),0()) = [1 2]y + [3] >= y = y
         
                           [-& 2 ]    [1  2 ]    [3]    [-& 2 ]    [0  2 ]    [2]                         
         c(a(c(c(y)),x)) = [1  3 ]x + [-& 2 ]y + [3] >= [1  3 ]x + [-& 2 ]y + [3] = a(c(c(c(a(x,0())))),y)
        problem:
         DPs:
          
         TRS:
          a(a(y,0()),0()) -> y
          c(a(c(c(y)),x)) -> a(c(c(c(a(x,0())))),y)
        Qed