/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

Problem:
 ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
 u21(ackout(X),Y) -> u22(ackin(Y,X))

Proof:
 DP Processor:
  DPs:
   ackin#(s(X),s(Y)) -> ackin#(s(X),Y)
   ackin#(s(X),s(Y)) -> u21#(ackin(s(X),Y),X)
   u21#(ackout(X),Y) -> ackin#(Y,X)
  TRS:
   ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
   u21(ackout(X),Y) -> u22(ackin(Y,X))
  TDG Processor:
   DPs:
    ackin#(s(X),s(Y)) -> ackin#(s(X),Y)
    ackin#(s(X),s(Y)) -> u21#(ackin(s(X),Y),X)
    u21#(ackout(X),Y) -> ackin#(Y,X)
   TRS:
    ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
    u21(ackout(X),Y) -> u22(ackin(Y,X))
   graph:
    u21#(ackout(X),Y) -> ackin#(Y,X) ->
    ackin#(s(X),s(Y)) -> u21#(ackin(s(X),Y),X)
    u21#(ackout(X),Y) -> ackin#(Y,X) ->
    ackin#(s(X),s(Y)) -> ackin#(s(X),Y)
    ackin#(s(X),s(Y)) -> u21#(ackin(s(X),Y),X) ->
    u21#(ackout(X),Y) -> ackin#(Y,X)
    ackin#(s(X),s(Y)) -> ackin#(s(X),Y) ->
    ackin#(s(X),s(Y)) -> u21#(ackin(s(X),Y),X)
    ackin#(s(X),s(Y)) -> ackin#(s(X),Y) -> ackin#(s(X),s(Y)) -> ackin#(s(X),Y)
   Subterm Criterion Processor:
    simple projection:
     pi(ackin#) = 0
     pi(u21#) = 1
    problem:
     DPs:
      ackin#(s(X),s(Y)) -> ackin#(s(X),Y)
      u21#(ackout(X),Y) -> ackin#(Y,X)
     TRS:
      ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
      u21(ackout(X),Y) -> u22(ackin(Y,X))
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 5/4
     DPs:
      ackin#(s(X),s(Y)) -> ackin#(s(X),Y)
     TRS:
      ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
      u21(ackout(X),Y) -> u22(ackin(Y,X))
     Subterm Criterion Processor:
      simple projection:
       pi(ackin#) = 1
      problem:
       DPs:
        
       TRS:
        ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
        u21(ackout(X),Y) -> u22(ackin(Y,X))
      Qed