MAYBE

Problem:
 op(i(x),op(y,z)) -> op(x,op(i(i(y)),z))
 op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w)))
 i(x) -> x

Proof:
 DP Processor:
  DPs:
   op#(i(x),op(y,z)) -> i#(y)
   op#(i(x),op(y,z)) -> i#(i(y))
   op#(i(x),op(y,z)) -> op#(i(i(y)),z)
   op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
   op#(i(x),op(y,op(z,w))) -> op#(y,w)
   op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
   op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
  TRS:
   op(i(x),op(y,z)) -> op(x,op(i(i(y)),z))
   op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w)))
   i(x) -> x
  CDG Processor:
   DPs:
    op#(i(x),op(y,z)) -> i#(y)
    op#(i(x),op(y,z)) -> i#(i(y))
    op#(i(x),op(y,z)) -> op#(i(i(y)),z)
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
    op#(i(x),op(y,op(z,w))) -> op#(y,w)
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
   TRS:
    op(i(x),op(y,z)) -> op(x,op(i(i(y)),z))
    op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w)))
    i(x) -> x
   graph:
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    op#(i(x),op(y,z)) -> i#(y)
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    op#(i(x),op(y,z)) -> i#(i(y))
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    op#(i(x),op(y,z)) -> op#(i(i(y)),z)
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    op#(i(x),op(y,op(z,w))) -> op#(y,w)
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
    op#(i(x),op(y,op(z,w))) -> op#(y,w) ->
    op#(i(x),op(y,z)) -> i#(y)
    op#(i(x),op(y,op(z,w))) -> op#(y,w) ->
    op#(i(x),op(y,z)) -> i#(i(y))
    op#(i(x),op(y,op(z,w))) -> op#(y,w) ->
    op#(i(x),op(y,z)) -> op#(i(i(y)),z)
    op#(i(x),op(y,op(z,w))) -> op#(y,w) ->
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
    op#(i(x),op(y,op(z,w))) -> op#(y,w) ->
    op#(i(x),op(y,op(z,w))) -> op#(y,w)
    op#(i(x),op(y,op(z,w))) -> op#(y,w) ->
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
    op#(i(x),op(y,op(z,w))) -> op#(y,w) ->
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,z)) -> i#(y)
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,z)) -> i#(i(y))
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,z)) -> op#(i(i(y)),z)
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,op(z,w))) -> op#(y,w)
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    op#(i(x),op(y,z)) -> i#(y)
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    op#(i(x),op(y,z)) -> i#(i(y))
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    op#(i(x),op(y,z)) -> op#(i(i(y)),z)
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    op#(i(x),op(y,op(z,w))) -> op#(y,w)
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) ->
    op#(i(x),op(y,z)) -> i#(y)
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) ->
    op#(i(x),op(y,z)) -> i#(i(y))
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) ->
    op#(i(x),op(y,z)) -> op#(i(i(y)),z)
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) ->
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) ->
    op#(i(x),op(y,op(z,w))) -> op#(y,w)
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) ->
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) -> op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
   Restore Modifier:
    DPs:
     op#(i(x),op(y,z)) -> i#(y)
     op#(i(x),op(y,z)) -> i#(i(y))
     op#(i(x),op(y,z)) -> op#(i(i(y)),z)
     op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
     op#(i(x),op(y,op(z,w))) -> op#(y,w)
     op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
     op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
    TRS:
     op(i(x),op(y,z)) -> op(x,op(i(i(y)),z))
     op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w)))
     i(x) -> x
    SCC Processor:
     #sccs: 1
     #rules: 5
     #arcs: 35/49
     DPs:
      op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
      op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
      op#(i(x),op(y,op(z,w))) -> op#(y,w)
      op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
      op#(i(x),op(y,z)) -> op#(i(i(y)),z)
     TRS:
      op(i(x),op(y,z)) -> op(x,op(i(i(y)),z))
      op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w)))
      i(x) -> x
     Open