MAYBE

Problem:
 a__f(a(),b(),X) -> a__f(X,X,mark(X))
 a__c() -> a()
 a__c() -> b()
 mark(f(X1,X2,X3)) -> a__f(X1,X2,mark(X3))
 mark(c()) -> a__c()
 mark(a()) -> a()
 mark(b()) -> b()
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 a__c() -> c()

Proof:
 DP Processor:
  DPs:
   a__f#(a(),b(),X) -> mark#(X)
   a__f#(a(),b(),X) -> a__f#(X,X,mark(X))
   mark#(f(X1,X2,X3)) -> mark#(X3)
   mark#(f(X1,X2,X3)) -> a__f#(X1,X2,mark(X3))
   mark#(c()) -> a__c#()
  TRS:
   a__f(a(),b(),X) -> a__f(X,X,mark(X))
   a__c() -> a()
   a__c() -> b()
   mark(f(X1,X2,X3)) -> a__f(X1,X2,mark(X3))
   mark(c()) -> a__c()
   mark(a()) -> a()
   mark(b()) -> b()
   a__f(X1,X2,X3) -> f(X1,X2,X3)
   a__c() -> c()
  TDG Processor:
   DPs:
    a__f#(a(),b(),X) -> mark#(X)
    a__f#(a(),b(),X) -> a__f#(X,X,mark(X))
    mark#(f(X1,X2,X3)) -> mark#(X3)
    mark#(f(X1,X2,X3)) -> a__f#(X1,X2,mark(X3))
    mark#(c()) -> a__c#()
   TRS:
    a__f(a(),b(),X) -> a__f(X,X,mark(X))
    a__c() -> a()
    a__c() -> b()
    mark(f(X1,X2,X3)) -> a__f(X1,X2,mark(X3))
    mark(c()) -> a__c()
    mark(a()) -> a()
    mark(b()) -> b()
    a__f(X1,X2,X3) -> f(X1,X2,X3)
    a__c() -> c()
   graph:
    mark#(f(X1,X2,X3)) -> mark#(X3) -> mark#(c()) -> a__c#()
    mark#(f(X1,X2,X3)) -> mark#(X3) ->
    mark#(f(X1,X2,X3)) -> a__f#(X1,X2,mark(X3))
    mark#(f(X1,X2,X3)) -> mark#(X3) ->
    mark#(f(X1,X2,X3)) -> mark#(X3)
    mark#(f(X1,X2,X3)) -> a__f#(X1,X2,mark(X3)) ->
    a__f#(a(),b(),X) -> a__f#(X,X,mark(X))
    mark#(f(X1,X2,X3)) -> a__f#(X1,X2,mark(X3)) ->
    a__f#(a(),b(),X) -> mark#(X)
    a__f#(a(),b(),X) -> mark#(X) -> mark#(c()) -> a__c#()
    a__f#(a(),b(),X) -> mark#(X) ->
    mark#(f(X1,X2,X3)) -> a__f#(X1,X2,mark(X3))
    a__f#(a(),b(),X) -> mark#(X) ->
    mark#(f(X1,X2,X3)) -> mark#(X3)
    a__f#(a(),b(),X) -> a__f#(X,X,mark(X)) ->
    a__f#(a(),b(),X) -> a__f#(X,X,mark(X))
    a__f#(a(),b(),X) -> a__f#(X,X,mark(X)) -> a__f#(a(),b(),X) -> mark#(X)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 10/25
    DPs:
     mark#(f(X1,X2,X3)) -> mark#(X3)
     mark#(f(X1,X2,X3)) -> a__f#(X1,X2,mark(X3))
     a__f#(a(),b(),X) -> mark#(X)
     a__f#(a(),b(),X) -> a__f#(X,X,mark(X))
    TRS:
     a__f(a(),b(),X) -> a__f(X,X,mark(X))
     a__c() -> a()
     a__c() -> b()
     mark(f(X1,X2,X3)) -> a__f(X1,X2,mark(X3))
     mark(c()) -> a__c()
     mark(a()) -> a()
     mark(b()) -> b()
     a__f(X1,X2,X3) -> f(X1,X2,X3)
     a__c() -> c()
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [mark#](x0) = x0 + 0,
      
      [a__f#](x0, x1, x2) = x1 + 1x2 + 1,
      
      [c] = 5,
      
      [f](x0, x1, x2) = x0 + 2x1 + 2x2 + 2,
      
      [a__c] = 5,
      
      [mark](x0) = x0 + 0,
      
      [a__f](x0, x1, x2) = x0 + 2x1 + 2x2 + 2,
      
      [b] = 0,
      
      [a] = 2
     orientation:
      mark#(f(X1,X2,X3)) = X1 + 2X2 + 2X3 + 2 >= X3 + 0 = mark#(X3)
      
      mark#(f(X1,X2,X3)) = X1 + 2X2 + 2X3 + 2 >= X2 + 1X3 + 1 = a__f#(X1,X2,mark(X3))
      
      a__f#(a(),b(),X) = 1X + 1 >= X + 0 = mark#(X)
      
      a__f#(a(),b(),X) = 1X + 1 >= 1X + 1 = a__f#(X,X,mark(X))
      
      a__f(a(),b(),X) = 2X + 2 >= 2X + 2 = a__f(X,X,mark(X))
      
      a__c() = 5 >= 2 = a()
      
      a__c() = 5 >= 0 = b()
      
      mark(f(X1,X2,X3)) = X1 + 2X2 + 2X3 + 2 >= X1 + 2X2 + 2X3 + 2 = a__f(X1,X2,mark(X3))
      
      mark(c()) = 5 >= 5 = a__c()
      
      mark(a()) = 2 >= 2 = a()
      
      mark(b()) = 0 >= 0 = b()
      
      a__f(X1,X2,X3) = X1 + 2X2 + 2X3 + 2 >= X1 + 2X2 + 2X3 + 2 = f(X1,X2,X3)
      
      a__c() = 5 >= 5 = c()
     problem:
      DPs:
       a__f#(a(),b(),X) -> a__f#(X,X,mark(X))
      TRS:
       a__f(a(),b(),X) -> a__f(X,X,mark(X))
       a__c() -> a()
       a__c() -> b()
       mark(f(X1,X2,X3)) -> a__f(X1,X2,mark(X3))
       mark(c()) -> a__c()
       mark(a()) -> a()
       mark(b()) -> b()
       a__f(X1,X2,X3) -> f(X1,X2,X3)
       a__c() -> c()
     Open