YES
Input TRS:
      1: foo(0(x1)) -> 0(s(p(p(p(s(s(s(p(s(x1))))))))))
      2: foo(s(x1)) -> p(s(p(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x1))))))))))))))))))))))))))
      3: bar(0(x1)) -> 0(p(s(s(s(x1)))))
      4: bar(s(x1)) -> p(s(p(p(s(s(foo(s(p(p(s(s(x1))))))))))))
      5: p(p(s(x1))) -> p(x1)
      6: p(s(x1)) -> x1
      7: p(0(x1)) -> 0(s(s(s(s(x1)))))
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Uncurrying foo p
      1: foo^1_0(x1) -> 0(s(p(p(p^1_s(s(s(p^1_s(x1))))))))
      2: foo^1_s(x1) -> p^1_s(p(p(p^1_s(s(p^1_s(s(p^1_s(foo(p(p^1_s(s(p^1_s(bar(p(p^1_s(s(p^1_s(x1))))))))))))))))))
      3: bar(0(x1)) -> 0(p^1_s(s(s(x1))))
      4: bar(s(x1)) -> p^1_s(p(p^1_s(s(foo^1_s(p(p^1_s(s(x1))))))))
      5: p(p^1_s(x1)) -> p(x1)
      6: p^1_s(x1) -> x1
      7: p^1_0(x1) -> 0(s(s(s(s(x1)))))
      8: p(0(_1)) ->= p^1_0(_1)
      9: p(s(_1)) ->= p^1_s(_1)
      10: foo(0(_1)) ->= foo^1_0(_1)
      11: foo(s(_1)) ->= foo^1_s(_1)
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #foo^1_s(x1) -> #p^1_s(p(p(p^1_s(s(p^1_s(s(p^1_s(foo(p(p^1_s(s(p^1_s(bar(p(p^1_s(s(p^1_s(x1))))))))))))))))))
     #2: #foo^1_s(x1) -> #p(p(p^1_s(s(p^1_s(s(p^1_s(foo(p(p^1_s(s(p^1_s(bar(p(p^1_s(s(p^1_s(x1)))))))))))))))))
     #3: #foo^1_s(x1) -> #p(p^1_s(s(p^1_s(s(p^1_s(foo(p(p^1_s(s(p^1_s(bar(p(p^1_s(s(p^1_s(x1))))))))))))))))
     #4: #foo^1_s(x1) -> #p^1_s(s(p^1_s(s(p^1_s(foo(p(p^1_s(s(p^1_s(bar(p(p^1_s(s(p^1_s(x1)))))))))))))))
     #5: #foo^1_s(x1) -> #p^1_s(s(p^1_s(foo(p(p^1_s(s(p^1_s(bar(p(p^1_s(s(p^1_s(x1)))))))))))))
     #6: #foo^1_s(x1) -> #p^1_s(foo(p(p^1_s(s(p^1_s(bar(p(p^1_s(s(p^1_s(x1)))))))))))
     #7: #foo^1_s(x1) -> #foo(p(p^1_s(s(p^1_s(bar(p(p^1_s(s(p^1_s(x1))))))))))
     #8: #foo^1_s(x1) -> #p(p^1_s(s(p^1_s(bar(p(p^1_s(s(p^1_s(x1)))))))))
     #9: #foo^1_s(x1) -> #p^1_s(s(p^1_s(bar(p(p^1_s(s(p^1_s(x1))))))))
     #10: #foo^1_s(x1) -> #p^1_s(bar(p(p^1_s(s(p^1_s(x1))))))
     #11: #foo^1_s(x1) -> #bar(p(p^1_s(s(p^1_s(x1)))))
     #12: #foo^1_s(x1) -> #p(p^1_s(s(p^1_s(x1))))
     #13: #foo^1_s(x1) -> #p^1_s(s(p^1_s(x1)))
     #14: #foo^1_s(x1) -> #p^1_s(x1)
     #15: #p(s(_1)) ->? #p^1_s(_1)
     #16: #foo(s(_1)) ->? #foo^1_s(_1)
     #17: #foo(0(_1)) ->? #foo^1_0(_1)
     #18: #p(p^1_s(x1)) -> #p(x1)
     #19: #bar(0(x1)) -> #p^1_s(s(s(x1)))
     #20: #foo^1_0(x1) -> #p(p(p^1_s(s(s(p^1_s(x1))))))
     #21: #foo^1_0(x1) -> #p(p^1_s(s(s(p^1_s(x1)))))
     #22: #foo^1_0(x1) -> #p^1_s(s(s(p^1_s(x1))))
     #23: #foo^1_0(x1) -> #p^1_s(x1)
     #24: #p(0(_1)) ->? #p^1_0(_1)
     #25: #bar(s(x1)) -> #p^1_s(p(p^1_s(s(foo^1_s(p(p^1_s(s(x1))))))))
     #26: #bar(s(x1)) -> #p(p^1_s(s(foo^1_s(p(p^1_s(s(x1)))))))
     #27: #bar(s(x1)) -> #p^1_s(s(foo^1_s(p(p^1_s(s(x1))))))
     #28: #bar(s(x1)) -> #foo^1_s(p(p^1_s(s(x1))))
     #29: #bar(s(x1)) -> #p(p^1_s(s(x1)))
     #30: #bar(s(x1)) -> #p^1_s(s(x1))
Number of SCCs: 2, DPs: 5
  SCC { #18 }
POLO(Sum)... succeeded.
      s 	w: 0
      #p^1_0	w: 0
      #p^1_s	w: 0
      p^1_0	w: 0
      #bar	w: 0
      p^1_s	w: x1 + 1
      #p 	w: x1
      foo^1_s	w: 0
      p 	w: 0
      foo^1_0	w: 0
      0 	w: 0
      #foo	w: 0
      bar	w: 0
      foo	w: 0
      #foo^1_0	w: 0
      #foo^1_s	w: 0
    USABLE RULES: { }
    Removed DPs: #18
Number of SCCs: 1, DPs: 4
  SCC { #7 #11 #16 #28 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      s 	w: max(x1 + 854095, 0)
      #p^1_0	w: 0
      #p^1_s	w: max(x1 - 1, 0)
      p^1_0	w: 0
      #bar	w: max(x1 - 106763, 0)
      p^1_s	w: max(x1 + 25786, 0)
      #p 	w: max(x1 - 1, 0)
      foo^1_s	w: 213524
      p 	w: max(x1 - 798905, 0)
      foo^1_0	w: 0
      0 	w: 0
      #foo	w: max(x1 - 427049, 0)
      bar	w: 320286
      foo	w: max(x1 - 640571, 0)
      #foo^1_0	w: 0
      #foo^1_s	w: max(x1 + 1, 0)
    USABLE RULES: { 1..11 }
    Removed DPs: #7 #11 #16 #28
Number of SCCs: 0, DPs: 0