MAYBE

Problem:
 a__f(a(),b(),X) -> a__f(mark(X),X,mark(X))
 a__c() -> a()
 a__c() -> b()
 mark(f(X1,X2,X3)) -> a__f(mark(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#(mark(X),X,mark(X))
   mark#(f(X1,X2,X3)) -> mark#(X3)
   mark#(f(X1,X2,X3)) -> mark#(X1)
   mark#(f(X1,X2,X3)) -> a__f#(mark(X1),X2,mark(X3))
   mark#(c()) -> a__c#()
  TRS:
   a__f(a(),b(),X) -> a__f(mark(X),X,mark(X))
   a__c() -> a()
   a__c() -> b()
   mark(f(X1,X2,X3)) -> a__f(mark(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#(mark(X),X,mark(X))
    mark#(f(X1,X2,X3)) -> mark#(X3)
    mark#(f(X1,X2,X3)) -> mark#(X1)
    mark#(f(X1,X2,X3)) -> a__f#(mark(X1),X2,mark(X3))
    mark#(c()) -> a__c#()
   TRS:
    a__f(a(),b(),X) -> a__f(mark(X),X,mark(X))
    a__c() -> a()
    a__c() -> b()
    mark(f(X1,X2,X3)) -> a__f(mark(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#(mark(X1),X2,mark(X3))
    mark#(f(X1,X2,X3)) -> mark#(X3) ->
    mark#(f(X1,X2,X3)) -> mark#(X1)
    mark#(f(X1,X2,X3)) -> mark#(X3) ->
    mark#(f(X1,X2,X3)) -> mark#(X3)
    mark#(f(X1,X2,X3)) -> mark#(X1) -> mark#(c()) -> a__c#()
    mark#(f(X1,X2,X3)) -> mark#(X1) ->
    mark#(f(X1,X2,X3)) -> a__f#(mark(X1),X2,mark(X3))
    mark#(f(X1,X2,X3)) -> mark#(X1) ->
    mark#(f(X1,X2,X3)) -> mark#(X1)
    mark#(f(X1,X2,X3)) -> mark#(X1) ->
    mark#(f(X1,X2,X3)) -> mark#(X3)
    mark#(f(X1,X2,X3)) -> a__f#(mark(X1),X2,mark(X3)) ->
    a__f#(a(),b(),X) -> a__f#(mark(X),X,mark(X))
    mark#(f(X1,X2,X3)) -> a__f#(mark(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#(mark(X1),X2,mark(X3))
    a__f#(a(),b(),X) -> mark#(X) -> mark#(f(X1,X2,X3)) -> mark#(X1)
    a__f#(a(),b(),X) -> mark#(X) ->
    mark#(f(X1,X2,X3)) -> mark#(X3)
    a__f#(a(),b(),X) -> a__f#(mark(X),X,mark(X)) ->
    a__f#(a(),b(),X) -> a__f#(mark(X),X,mark(X))
    a__f#(a(),b(),X) -> a__f#(mark(X),X,mark(X)) -> a__f#(a(),b(),X) -> mark#(X)
   SCC Processor:
    #sccs: 1
    #rules: 5
    #arcs: 16/36
    DPs:
     mark#(f(X1,X2,X3)) -> mark#(X3)
     mark#(f(X1,X2,X3)) -> mark#(X1)
     mark#(f(X1,X2,X3)) -> a__f#(mark(X1),X2,mark(X3))
     a__f#(a(),b(),X) -> mark#(X)
     a__f#(a(),b(),X) -> a__f#(mark(X),X,mark(X))
    TRS:
     a__f(a(),b(),X) -> a__f(mark(X),X,mark(X))
     a__c() -> a()
     a__c() -> b()
     mark(f(X1,X2,X3)) -> a__f(mark(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