MAYBE

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

Proof:
 DP Processor:
  DPs:
   a__f#(b(),X,c()) -> a__c#()
   a__f#(b(),X,c()) -> a__f#(X,a__c(),X)
   mark#(f(X1,X2,X3)) -> mark#(X2)
   mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3)
   mark#(c()) -> a__c#()
  TRS:
   a__f(b(),X,c()) -> a__f(X,a__c(),X)
   a__c() -> b()
   mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
   mark(c()) -> a__c()
   mark(b()) -> b()
   a__f(X1,X2,X3) -> f(X1,X2,X3)
   a__c() -> c()
  TDG Processor:
   DPs:
    a__f#(b(),X,c()) -> a__c#()
    a__f#(b(),X,c()) -> a__f#(X,a__c(),X)
    mark#(f(X1,X2,X3)) -> mark#(X2)
    mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3)
    mark#(c()) -> a__c#()
   TRS:
    a__f(b(),X,c()) -> a__f(X,a__c(),X)
    a__c() -> b()
    mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
    mark(c()) -> a__c()
    mark(b()) -> b()
    a__f(X1,X2,X3) -> f(X1,X2,X3)
    a__c() -> c()
   graph:
    mark#(f(X1,X2,X3)) -> mark#(X2) -> mark#(c()) -> a__c#()
    mark#(f(X1,X2,X3)) -> mark#(X2) ->
    mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3)
    mark#(f(X1,X2,X3)) -> mark#(X2) ->
    mark#(f(X1,X2,X3)) -> mark#(X2)
    mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3) ->
    a__f#(b(),X,c()) -> a__f#(X,a__c(),X)
    mark#(f(X1,X2,X3)) -> a__f#(X1,mark(X2),X3) ->
    a__f#(b(),X,c()) -> a__c#()
    a__f#(b(),X,c()) -> a__f#(X,a__c(),X) ->
    a__f#(b(),X,c()) -> a__f#(X,a__c(),X)
    a__f#(b(),X,c()) -> a__f#(X,a__c(),X) -> a__f#(b(),X,c()) -> a__c#()
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 7/25
    DPs:
     mark#(f(X1,X2,X3)) -> mark#(X2)
    TRS:
     a__f(b(),X,c()) -> a__f(X,a__c(),X)
     a__c() -> b()
     mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
     mark(c()) -> a__c()
     mark(b()) -> b()
     a__f(X1,X2,X3) -> f(X1,X2,X3)
     a__c() -> c()
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [mark#](x0) = x0,
      
      [mark](x0) = 4x0,
      
      [f](x0, x1, x2) = x1 + 1,
      
      [a__c] = 0,
      
      [a__f](x0, x1, x2) = x1 + 1,
      
      [c] = 0,
      
      [b] = 0
     orientation:
      mark#(f(X1,X2,X3)) = X2 + 1 >= X2 = mark#(X2)
      
      a__f(b(),X,c()) = X + 1 >= 1 = a__f(X,a__c(),X)
      
      a__c() = 0 >= 0 = b()
      
      mark(f(X1,X2,X3)) = 4X2 + 4 >= 4X2 + 1 = a__f(X1,mark(X2),X3)
      
      mark(c()) = 0 >= 0 = a__c()
      
      mark(b()) = 0 >= 0 = b()
      
      a__f(X1,X2,X3) = X2 + 1 >= X2 + 1 = f(X1,X2,X3)
      
      a__c() = 0 >= 0 = c()
     problem:
      DPs:
       
      TRS:
       a__f(b(),X,c()) -> a__f(X,a__c(),X)
       a__c() -> b()
       mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
       mark(c()) -> a__c()
       mark(b()) -> b()
       a__f(X1,X2,X3) -> f(X1,X2,X3)
       a__c() -> c()
     Qed
    
    DPs:
     a__f#(b(),X,c()) -> a__f#(X,a__c(),X)
    TRS:
     a__f(b(),X,c()) -> a__f(X,a__c(),X)
     a__c() -> b()
     mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
     mark(c()) -> a__c()
     mark(b()) -> b()
     a__f(X1,X2,X3) -> f(X1,X2,X3)
     a__c() -> c()
    Open