TRS Standard pair #487069292

details

property	value
status	complete
benchmark	prov.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.41349 seconds
cpu usage	0.606955
user time	0.472241
system time	0.134714
max virtual memory	96176.0
max residence set size	59452.0

stage attributes

key	value
starexec-result	YES

output

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

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