YES
Input TRS:
      1: a__U11(tt(),V1,V2) -> a__U12(a__isNat(V1),V2)
      2: a__U12(tt(),V2) -> a__U13(a__isNat(V2))
      3: a__U13(tt()) -> tt()
      4: a__U21(tt(),V1) -> a__U22(a__isNat(V1))
      5: a__U22(tt()) -> tt()
      6: a__U31(tt(),V1,V2) -> a__U32(a__isNat(V1),V2)
      7: a__U32(tt(),V2) -> a__U33(a__isNat(V2))
      8: a__U33(tt()) -> tt()
      9: a__U41(tt(),N) -> mark(N)
      10: a__U51(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
      11: a__U61(tt()) -> 0()
      12: a__U71(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N))
      13: a__and(tt(),X) -> mark(X)
      14: a__isNat(0()) -> tt()
      15: a__isNat(plus(V1,V2)) -> a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
      16: a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
      17: a__isNat(x(V1,V2)) -> a__U31(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
      18: a__isNatKind(0()) -> tt()
      19: a__isNatKind(plus(V1,V2)) -> a__and(a__isNatKind(V1),isNatKind(V2))
      20: a__isNatKind(s(V1)) -> a__isNatKind(V1)
      21: a__isNatKind(x(V1,V2)) -> a__and(a__isNatKind(V1),isNatKind(V2))
      22: a__plus(N,0()) -> a__U41(a__and(a__isNat(N),isNatKind(N)),N)
      23: a__plus(N,s(M)) -> a__U51(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
      24: a__x(N,0()) -> a__U61(a__and(a__isNat(N),isNatKind(N)))
      25: a__x(N,s(M)) -> a__U71(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
      26: mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
      27: mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
      28: mark(isNat(X)) -> a__isNat(X)
      29: mark(U13(X)) -> a__U13(mark(X))
      30: mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
      31: mark(U22(X)) -> a__U22(mark(X))
      32: mark(U31(X1,X2,X3)) -> a__U31(mark(X1),X2,X3)
      33: mark(U32(X1,X2)) -> a__U32(mark(X1),X2)
      34: mark(U33(X)) -> a__U33(mark(X))
      35: mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
      36: mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
      37: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
      38: mark(U61(X)) -> a__U61(mark(X))
      39: mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3)
      40: mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
      41: mark(and(X1,X2)) -> a__and(mark(X1),X2)
      42: mark(isNatKind(X)) -> a__isNatKind(X)
      43: mark(tt()) -> tt()
      44: mark(s(X)) -> s(mark(X))
      45: mark(0()) -> 0()
      46: a__U11(X1,X2,X3) -> U11(X1,X2,X3)
      47: a__U12(X1,X2) -> U12(X1,X2)
      48: a__isNat(X) -> isNat(X)
      49: a__U13(X) -> U13(X)
      50: a__U21(X1,X2) -> U21(X1,X2)
      51: a__U22(X) -> U22(X)
      52: a__U31(X1,X2,X3) -> U31(X1,X2,X3)
      53: a__U32(X1,X2) -> U32(X1,X2)
      54: a__U33(X) -> U33(X)
      55: a__U41(X1,X2) -> U41(X1,X2)
      56: a__U51(X1,X2,X3) -> U51(X1,X2,X3)
      57: a__plus(X1,X2) -> plus(X1,X2)
      58: a__U61(X) -> U61(X)
      59: a__U71(X1,X2,X3) -> U71(X1,X2,X3)
      60: a__x(X1,X2) -> x(X1,X2)
      61: a__and(X1,X2) -> and(X1,X2)
      62: a__isNatKind(X) -> isNatKind(X)
Number of strict rules: 62
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a__U12(tt(),V2) -> #a__U13(a__isNat(V2))
     #2: #a__U12(tt(),V2) -> #a__isNat(V2)
     #3: #mark(U13(X)) -> #a__U13(mark(X))
     #4: #mark(U13(X)) -> #mark(X)
     #5: #mark(U41(X1,X2)) -> #a__U41(mark(X1),X2)
     #6: #mark(U41(X1,X2)) -> #mark(X1)
     #7: #mark(isNatKind(X)) -> #a__isNatKind(X)
     #8: #mark(and(X1,X2)) -> #a__and(mark(X1),X2)
     #9: #mark(and(X1,X2)) -> #mark(X1)
     #10: #mark(plus(X1,X2)) -> #a__plus(mark(X1),mark(X2))
     #11: #mark(plus(X1,X2)) -> #mark(X1)
     #12: #mark(plus(X1,X2)) -> #mark(X2)
     #13: #mark(U61(X)) -> #a__U61(mark(X))
     #14: #mark(U61(X)) -> #mark(X)
     #15: #a__U31(tt(),V1,V2) -> #a__U32(a__isNat(V1),V2)
     #16: #a__U31(tt(),V1,V2) -> #a__isNat(V1)
     #17: #mark(x(X1,X2)) -> #a__x(mark(X1),mark(X2))
     #18: #mark(x(X1,X2)) -> #mark(X1)
     #19: #mark(x(X1,X2)) -> #mark(X2)
     #20: #a__and(tt(),X) -> #mark(X)
     #21: #a__U41(tt(),N) -> #mark(N)
     #22: #a__x(N,0()) -> #a__U61(a__and(a__isNat(N),isNatKind(N)))
     #23: #a__x(N,0()) -> #a__and(a__isNat(N),isNatKind(N))
     #24: #a__x(N,0()) -> #a__isNat(N)
     #25: #a__plus(N,s(M)) -> #a__U51(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
     #26: #a__plus(N,s(M)) -> #a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))
     #27: #a__plus(N,s(M)) -> #a__and(a__isNat(M),isNatKind(M))
     #28: #a__plus(N,s(M)) -> #a__isNat(M)
     #29: #a__U71(tt(),M,N) -> #a__plus(a__x(mark(N),mark(M)),mark(N))
     #30: #a__U71(tt(),M,N) -> #a__x(mark(N),mark(M))
     #31: #a__U71(tt(),M,N) -> #mark(N)
     #32: #a__U71(tt(),M,N) -> #mark(M)
     #33: #a__U71(tt(),M,N) -> #mark(N)
     #34: #mark(U22(X)) -> #a__U22(mark(X))
     #35: #mark(U22(X)) -> #mark(X)
     #36: #mark(U21(X1,X2)) -> #a__U21(mark(X1),X2)
     #37: #mark(U21(X1,X2)) -> #mark(X1)
     #38: #a__x(N,s(M)) -> #a__U71(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
     #39: #a__x(N,s(M)) -> #a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))
     #40: #a__x(N,s(M)) -> #a__and(a__isNat(M),isNatKind(M))
     #41: #a__x(N,s(M)) -> #a__isNat(M)
     #42: #a__isNatKind(s(V1)) -> #a__isNatKind(V1)
     #43: #a__U32(tt(),V2) -> #a__U33(a__isNat(V2))
     #44: #a__U32(tt(),V2) -> #a__isNat(V2)
     #45: #mark(U71(X1,X2,X3)) -> #a__U71(mark(X1),X2,X3)
     #46: #mark(U71(X1,X2,X3)) -> #mark(X1)
     #47: #a__U51(tt(),M,N) -> #a__plus(mark(N),mark(M))
     #48: #a__U51(tt(),M,N) -> #mark(N)
     #49: #a__U51(tt(),M,N) -> #mark(M)
     #50: #mark(U32(X1,X2)) -> #a__U32(mark(X1),X2)
     #51: #mark(U32(X1,X2)) -> #mark(X1)
     #52: #mark(s(X)) -> #mark(X)
     #53: #mark(isNat(X)) -> #a__isNat(X)
     #54: #a__plus(N,0()) -> #a__U41(a__and(a__isNat(N),isNatKind(N)),N)
     #55: #a__plus(N,0()) -> #a__and(a__isNat(N),isNatKind(N))
     #56: #a__plus(N,0()) -> #a__isNat(N)
     #57: #mark(U33(X)) -> #a__U33(mark(X))
     #58: #mark(U33(X)) -> #mark(X)
     #59: #mark(U12(X1,X2)) -> #a__U12(mark(X1),X2)
     #60: #mark(U12(X1,X2)) -> #mark(X1)
     #61: #a__isNat(x(V1,V2)) -> #a__U31(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
     #62: #a__isNat(x(V1,V2)) -> #a__and(a__isNatKind(V1),isNatKind(V2))
     #63: #a__isNat(x(V1,V2)) -> #a__isNatKind(V1)
     #64: #mark(U31(X1,X2,X3)) -> #a__U31(mark(X1),X2,X3)
     #65: #mark(U31(X1,X2,X3)) -> #mark(X1)
     #66: #a__isNatKind(plus(V1,V2)) -> #a__and(a__isNatKind(V1),isNatKind(V2))
     #67: #a__isNatKind(plus(V1,V2)) -> #a__isNatKind(V1)
     #68: #mark(U11(X1,X2,X3)) -> #a__U11(mark(X1),X2,X3)
     #69: #mark(U11(X1,X2,X3)) -> #mark(X1)
     #70: #mark(U51(X1,X2,X3)) -> #a__U51(mark(X1),X2,X3)
     #71: #mark(U51(X1,X2,X3)) -> #mark(X1)
     #72: #a__isNatKind(x(V1,V2)) -> #a__and(a__isNatKind(V1),isNatKind(V2))
     #73: #a__isNatKind(x(V1,V2)) -> #a__isNatKind(V1)
     #74: #a__isNat(s(V1)) -> #a__U21(a__isNatKind(V1),V1)
     #75: #a__isNat(s(V1)) -> #a__isNatKind(V1)
     #76: #a__U11(tt(),V1,V2) -> #a__U12(a__isNat(V1),V2)
     #77: #a__U11(tt(),V1,V2) -> #a__isNat(V1)
     #78: #a__isNat(plus(V1,V2)) -> #a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
     #79: #a__isNat(plus(V1,V2)) -> #a__and(a__isNatKind(V1),isNatKind(V2))
     #80: #a__isNat(plus(V1,V2)) -> #a__isNatKind(V1)
     #81: #a__U21(tt(),V1) -> #a__U22(a__isNat(V1))
     #82: #a__U21(tt(),V1) -> #a__isNat(V1)
Number of SCCs: 1, DPs: 74
  SCC { #2 #4..12 #14..21 #23..33 #35..42 #44..56 #58..80 #82 }
POLO(Sum)... POLO(max)... succeeded.
      #a__isNatKind	w: 0
      isNatKind	w: 0
      a__plus	w: max(x1, x2 + 21654)
      U21	w: max(x1, x2)
      #a__U71	w: max(x2 + 22758, x3 + 22756)
      U11	w: max(x1, x2, x3 + 15452)
      s 	w: x1
      #a__U31	w: 0
      #a__U33	w: 0
      a__U33	w: x1 + 5600
      #a__isNat	w: 0
      U71	w: max(x1 + 21653, x2 + 22758, x3 + 22756)
      and	w: max(x1, x2)
      #a__U13	w: 0
      #a__U51	w: max(x1, x2, x3)
      #a__x	w: max(x1 + 22756, x2 + 22758)
      a__U22	w: x1
      #a__U11	w: 0
      a__U31	w: max(x1 + 22758, x2 + 22756, x3 + 22757)
      a__U51	w: max(x1, x2 + 21654, x3)
      a__x	w: max(x1 + 22756, x2 + 22758)
      U12	w: max(x1, x2 + 6132)
      a__U41	w: max(x1, x2)
      x 	w: max(x1 + 22756, x2 + 22758)
      #a__U12	w: 0
      #a__U21	w: 0
      #a__U61	w: 0
      #a__plus	w: max(x1, x2)
      #mark	w: x1
      0 	w: 14098
      #a__and	w: max(x1, x2)
      a__U21	w: max(x1, x2)
      a__U32	w: max(x1 + 1, x2 + 21174)
      mark	w: x1
      a__U11	w: max(x1, x2, x3 + 15452)
      U32	w: max(x1 + 1, x2 + 21174)
      U33	w: x1 + 5600
      a__U12	w: max(x1, x2 + 6132)
      isNat	w: x1
      plus	w: max(x1, x2 + 21654)
      U61	w: x1 + 14098
      #a__U22	w: 0
      a__U13	w: x1 + 6132
      U31	w: max(x1 + 22758, x2 + 22756, x3 + 22757)
      a__U71	w: max(x1 + 21653, x2 + 22758, x3 + 22756)
      a__U61	w: x1 + 14098
      #a__U41	w: max(x2)
      tt	w: 0
      a__isNat	w: x1
      U13	w: x1 + 6132
      a__isNatKind	w: 0
      U22	w: x1
      U51	w: max(x1, x2 + 21654, x3)
      a__and	w: max(x1, x2)
      U41	w: max(x1, x2)
      #a__U32	w: 0
    USABLE RULES: { 1..62 }
    Removed DPs: #4 #12 #14 #18 #19 #23 #24 #31..33 #39..41 #46 #50 #51 #56 #58 #59 #64 #65 #68
Number of SCCs: 1, DPs: 52
  SCC { #2 #5..11 #15..17 #20 #21 #25..30 #35..38 #42 #44 #45 #47..49 #52..55 #60..63 #66 #67 #69..80 #82 }
POLO(Sum)... POLO(max)... succeeded.
      #a__isNatKind	w: 0
      isNatKind	w: 0
      a__plus	w: max(x1, x2 + 1)
      U21	w: max(x1, x2)
      #a__U71	w: max(x2 + 4, x3 + 2)
      U11	w: max(x1, x2, x3 + 1)
      s 	w: x1
      #a__U31	w: 0
      #a__U33	w: 0
      a__U33	w: x1 + 2
      #a__isNat	w: 0
      U71	w: max(x2 + 4, x3 + 2)
      and	w: max(x1, x2)
      #a__U13	w: 0
      #a__U51	w: max(x2 + 1, x3)
      #a__x	w: max(x1 + 2, x2 + 4)
      a__U22	w: x1
      #a__U11	w: 0
      a__U31	w: max(x1 + 4, x2 + 2, x3 + 3)
      a__U51	w: max(x1, x2 + 1, x3)
      a__x	w: max(x1 + 2, x2 + 4)
      U12	w: max(x1, x2 + 1)
      a__U41	w: max(x1, x2)
      x 	w: max(x1 + 2, x2 + 4)
      #a__U12	w: 0
      #a__U21	w: 0
      #a__U61	w: 0
      #a__plus	w: max(x1, x2 + 1)
      #mark	w: x1
      0 	w: 2
      #a__and	w: max(x2)
      a__U21	w: max(x1, x2)
      a__U32	w: max(x1 + 1, x2 + 2)
      mark	w: x1
      a__U11	w: max(x1, x2, x3 + 1)
      U32	w: max(x1 + 1, x2 + 2)
      U33	w: x1 + 2
      a__U12	w: max(x1, x2 + 1)
      isNat	w: x1
      plus	w: max(x1, x2 + 1)
      U61	w: 2
      #a__U22	w: 0
      a__U13	w: x1 + 1
      U31	w: max(x1 + 4, x2 + 2, x3 + 3)
      a__U71	w: max(x2 + 4, x3 + 2)
      a__U61	w: 2
      #a__U41	w: max(x2)
      tt	w: 0
      a__isNat	w: x1
      U13	w: x1 + 1
      a__isNatKind	w: 0
      U22	w: x1
      U51	w: max(x1, x2 + 1, x3)
      a__and	w: max(x1, x2)
      U41	w: max(x1, x2)
      #a__U32	w: 0
    USABLE RULES: { 1..62 }
    Removed DPs: #27 #28 #49 #55
Number of SCCs: 1, DPs: 48
  SCC { #2 #5..11 #15..17 #20 #21 #25 #26 #29 #30 #35..38 #42 #44 #45 #47 #48 #52..54 #60..63 #66 #67 #69..80 #82 }
POLO(Sum)... POLO(max)... succeeded.
      #a__isNatKind	w: 1
      isNatKind	w: 0
      a__plus	w: max(x1, x2 + 2)
      U21	w: max(x1, x2)
      #a__U71	w: max(x2 + 6, x3 + 4)
      U11	w: max(x1, x2, x3 + 1)
      s 	w: x1
      #a__U31	w: max(x2 + 3, x3 + 3)
      #a__U33	w: 0
      a__U33	w: x1 + 3
      #a__isNat	w: x1 + 1
      U71	w: max(x2 + 5, x3 + 3)
      and	w: max(x1, x2)
      #a__U13	w: 0
      #a__U51	w: max(x2 + 3, x3 + 1)
      #a__x	w: max(x1 + 4, x2 + 6)
      a__U22	w: x1
      #a__U11	w: max(x2 + 1, x3 + 2)
      a__U31	w: max(x1 + 5, x2 + 3, x3 + 4)
      a__U51	w: max(x1, x2 + 2, x3)
      a__x	w: max(x1 + 3, x2 + 5)
      U12	w: max(x1, x2 + 1)
      a__U41	w: max(x1, x2)
      x 	w: max(x1 + 3, x2 + 5)
      #a__U12	w: max(x2 + 2)
      #a__U21	w: max(x2 + 1)
      #a__U61	w: 0
      #a__plus	w: max(x1 + 1, x2 + 3)
      #mark	w: x1 + 1
      0 	w: 1
      #a__and	w: max(x2 + 1)
      a__U21	w: max(x1, x2)
      a__U32	w: max(x1 + 2, x2 + 3)
      mark	w: x1
      a__U11	w: max(x1, x2, x3 + 1)
      U32	w: max(x1 + 2, x2 + 3)
      U33	w: x1 + 3
      a__U12	w: max(x1, x2 + 1)
      isNat	w: x1
      plus	w: max(x1, x2 + 2)
      U61	w: 3
      #a__U22	w: 0
      a__U13	w: x1 + 1
      U31	w: max(x1 + 5, x2 + 3, x3 + 4)
      a__U71	w: max(x2 + 5, x3 + 3)
      a__U61	w: 3
      #a__U41	w: max(x2 + 1)
      tt	w: 0
      a__isNat	w: x1
      U13	w: x1 + 1
      a__isNatKind	w: 0
      U22	w: x1
      U51	w: max(x1, x2 + 2, x3)
      a__and	w: max(x1, x2)
      U41	w: max(x1, x2)
      #a__U32	w: max(x2 + 2)
    USABLE RULES: { 1..62 }
    Removed DPs: #2 #15 #16 #44 #61..63 #79 #80
Number of SCCs: 1, DPs: 38
  SCC { #5..11 #17 #20 #21 #25 #26 #29 #30 #35..38 #42 #45 #47 #48 #52..54 #60 #66 #67 #69..75 #77 #78 #82 }
POLO(Sum)... POLO(max)... succeeded.
      #a__isNatKind	w: 32294
      isNatKind	w: 1
      a__plus	w: max(x1, x2 + 8)
      U21	w: max(x1 + 2)
      #a__U71	w: max(x1 + 32297, x3 + 51803)
      U11	w: max(x1 + 2)
      s 	w: x1
      #a__U31	w: 0
      #a__U33	w: 0
      a__U33	w: 1
      #a__isNat	w: 32295
      U71	w: max(x1 + 5, x3 + 19510)
      and	w: max(x1, x2)
      #a__U13	w: 0
      #a__U51	w: max(x1 + 32294, x2 + 32297, x3 + 32293)
      #a__x	w: max(x1 + 51803)
      a__U22	w: x1
      #a__U11	w: max(x1 + 32294)
      a__U31	w: max(x1 + 2)
      a__U51	w: max(x1 + 1, x2 + 8, x3)
      a__x	w: max(x1 + 19510)
      U12	w: max(x1)
      a__U41	w: max(x1 + 5108, x2)
      x 	w: max(x1 + 19510)
      #a__U12	w: 0
      #a__U21	w: max(x1 + 32294)
      #a__U61	w: 0
      #a__plus	w: max(x1 + 32293, x2 + 32297)
      #mark	w: x1 + 32293
      0 	w: 12579
      #a__and	w: max(x2 + 32293)
      a__U21	w: max(x1 + 2)
      a__U32	w: max(x1)
      mark	w: x1
      a__U11	w: max(x1 + 2)
      U32	w: max(x1)
      U33	w: 1
      a__U12	w: max(x1)
      isNat	w: 3
      plus	w: max(x1, x2 + 8)
      U61	w: 12579
      #a__U22	w: 0
      a__U13	w: 1
      U31	w: max(x1 + 2)
      a__U71	w: max(x1 + 5, x3 + 19510)
      a__U61	w: 12579
      #a__U41	w: max(x2 + 32293)
      tt	w: 1
      a__isNat	w: 3
      U13	w: 1
      a__isNatKind	w: 1
      U22	w: x1
      U51	w: max(x1 + 1, x2 + 8, x3)
      a__and	w: max(x1, x2)
      U41	w: max(x1 + 5108, x2)
      #a__U32	w: 0
    USABLE RULES: { 1..62 }
    Removed DPs: #6 #26 #36 #37 #53 #69 #71 #75
Number of SCCs: 2, DPs: 30
  SCC { #74 #77 #78 #82 }
POLO(Sum)... succeeded.
      #a__isNatKind	w: 0
      isNatKind	w: 4448
      a__plus	w: 4449
      U21	w: 4449
      #a__U71	w: 0
      U11	w: 4449
      s 	w: x1 + 2
      #a__U31	w: 0
      #a__U33	w: 0
      a__U33	w: 4450
      #a__isNat	w: x1
      U71	w: 4449
      and	w: 2
      #a__U13	w: 0
      #a__U51	w: 0
      #a__x	w: 0
      a__U22	w: 4449
      #a__U11	w: x2 + 1
      a__U31	w: 4448
      a__U51	w: 4450
      a__x	w: 4447
      U12	w: 4450
      a__U41	w: 4450
      x 	w: x1 + 4448
      #a__U12	w: 0
      #a__U21	w: x2 + 1
      #a__U61	w: 0
      #a__plus	w: 0
      #mark	w: 0
      0 	w: 4449
      #a__and	w: 0
      a__U21	w: x2 + 4448
      a__U32	w: x2 + 4449
      mark	w: 4446
      a__U11	w: x2 + x3 + 4448
      U32	w: x1 + 4450
      U33	w: x1 + 4451
      a__U12	w: 4449
      isNat	w: 4448
      plus	w: x1 + 4450
      U61	w: x1 + 4449
      #a__U22	w: 0
      a__U13	w: 4450
      U31	w: x1 + x2 + x3 + 4449
      a__U71	w: x2 + 4448
      a__U61	w: 4448
      #a__U41	w: 0
      tt	w: 4451
      a__isNat	w: 4447
      U13	w: x1 + 4451
      a__isNatKind	w: 4447
      U22	w: 4450
      U51	w: 4451
      a__and	w: 1
      U41	w: 4451
      #a__U32	w: 0
    USABLE RULES: { }
    Removed DPs: #74 #77 #78 #82
Number of SCCs: 1, DPs: 26
  SCC { #5 #7..11 #17 #20 #21 #25 #29 #30 #35 #38 #42 #45 #47 #48 #52 #54 #60 #66 #67 #70 #72 #73 }
POLO(Sum)... POLO(max)... succeeded.
      #a__isNatKind	w: x1 + 1
      isNatKind	w: x1 + 2
      a__plus	w: max(x1, x2 + 2)
      U21	w: max(x1 + 1, x2 + 4)
      #a__U71	w: max(x2 + 4, x3 + 2)
      U11	w: max(x1 + 1, x2 + 4, x3 + 3)
      s 	w: x1
      #a__U31	w: 0
      #a__U33	w: 0
      a__U33	w: x1 + 1
      #a__isNat	w: 32295
      U71	w: max(x2 + 4, x3 + 2)
      and	w: max(x1, x2 + 2)
      #a__U13	w: 0
      #a__U51	w: max(x3)
      #a__x	w: max(x1 + 2, x2 + 4)
      a__U22	w: x1
      #a__U11	w: 0
      a__U31	w: max(x1 + 4, x3 + 8)
      a__U51	w: max(x2 + 2, x3)
      a__x	w: max(x1 + 2, x2 + 4)
      U12	w: max(x1, x2 + 1)
      a__U41	w: max(x2)
      x 	w: max(x1 + 2, x2 + 4)
      #a__U12	w: 0
      #a__U21	w: 0
      #a__U61	w: 0
      #a__plus	w: max(x1)
      #mark	w: x1
      0 	w: 1
      #a__and	w: max(x2)
      a__U21	w: max(x1 + 1, x2 + 4)
      a__U32	w: max(x2 + 5)
      mark	w: x1
      a__U11	w: max(x1 + 1, x2 + 4, x3 + 3)
      U32	w: max(x2 + 5)
      U33	w: x1 + 1
      a__U12	w: max(x1, x2 + 1)
      isNat	w: x1 + 4
      plus	w: max(x1, x2 + 2)
      U61	w: 1
      #a__U22	w: 0
      a__U13	w: 2
      U31	w: max(x1 + 4, x3 + 8)
      a__U71	w: max(x2 + 4, x3 + 2)
      a__U61	w: 1
      #a__U41	w: max(x2)
      tt	w: 2
      a__isNat	w: x1 + 4
      U13	w: 2
      a__isNatKind	w: x1 + 2
      U22	w: x1
      U51	w: max(x2 + 2, x3)
      a__and	w: max(x1, x2 + 2)
      U41	w: max(x2)
      #a__U32	w: 0
    USABLE RULES: { 1..62 }
    Removed DPs: #7 #8 #66 #72 #73
Number of SCCs: 2, DPs: 20
  SCC { #42 #67 }
POLO(Sum)... succeeded.
      #a__isNatKind	w: x1 + 2
      isNatKind	w: 43587
      a__plus	w: 43588
      U21	w: 43588
      #a__U71	w: 2
      U11	w: 43588
      s 	w: x1 + 2
      #a__U31	w: 0
      #a__U33	w: 0
      a__U33	w: 43589
      #a__isNat	w: 0
      U71	w: 43588
      and	w: x1 + 43585
      #a__U13	w: 0
      #a__U51	w: 0
      #a__x	w: 0
      a__U22	w: 43588
      #a__U11	w: 1
      a__U31	w: x1 + 3
      a__U51	w: 43589
      a__x	w: 43586
      U12	w: 43589
      a__U41	w: x1 + 5
      x 	w: 43587
      #a__U12	w: 0
      #a__U21	w: 1
      #a__U61	w: 0
      #a__plus	w: 0
      #mark	w: 2
      0 	w: 43588
      #a__and	w: 2
      a__U21	w: 43587
      a__U32	w: x1 + 8
      mark	w: 43585
      a__U11	w: x2 + x3 + 43587
      U32	w: x2 + 9
      U33	w: x1 + 43590
      a__U12	w: x2 + 43588
      isNat	w: x1 + 43587
      plus	w: x1 + 43589
      U61	w: x1 + 43588
      #a__U22	w: 0
      a__U13	w: 43589
      U31	w: x3 + 4
      a__U71	w: 43587
      a__U61	w: 43587
      #a__U41	w: 0
      tt	w: 43590
      a__isNat	w: 43586
      U13	w: x1 + 43590
      a__isNatKind	w: 43586
      U22	w: 43589
      U51	w: 43590
      a__and	w: 43584
      U41	w: 6
      #a__U32	w: 0
    USABLE RULES: { }
    Removed DPs: #42 #67
Number of SCCs: 1, DPs: 18
  SCC { #5 #9..11 #17 #21 #25 #29 #30 #35 #38 #45 #47 #48 #52 #54 #60 #70 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      #a__isNatKind	s: 1
      isNatKind	s: [1]	p: 5
      a__plus	s: [1,2]	p: 9
      U21	s: [2,1]	p: 3
      #a__U71	s: [3,2]	p: 10
      U11	s: [2]	p: 8
      s 	s: [1]	p: 5
      #a__U31	s: [1,3,2]	p: 0
      #a__U33	s: 1
      a__U33	s: []	p: 6
      #a__isNat	s: []	p: 0
      U71	s: [3,2,1]	p: 10
      and	s: [1,2]	p: 0
      #a__U13	s: []	p: 0
      #a__U51	s: 3
      #a__x	s: [1,2]	p: 10
      a__U22	s: [1]	p: 2
      #a__U11	s: [2,3,1]	p: 0
      a__U31	s: [2,3,1]	p: 0
      a__U51	s: [3,2,1]	p: 9
      a__x	s: [1,2]	p: 10
      U12	s: [1]	p: 7
      a__U41	s: [2,1]	p: 1
      x 	s: [1,2]	p: 10
      #a__U12	s: [2,1]	p: 0
      #a__U21	s: [2,1]	p: 0
      #a__U61	s: []	p: 0
      #a__plus	s: 1
      #mark	s: 1
      0 	s: []	p: 11
      #a__and	s: 2
      a__U21	s: [2,1]	p: 3
      a__U32	s: []	p: 6
      mark	s: 1
      a__U11	s: [2]	p: 8
      U32	s: []	p: 6
      U33	s: []	p: 6
      a__U12	s: [1]	p: 7
      isNat	s: [1]	p: 3
      plus	s: [1,2]	p: 9
      U61	s: []	p: 11
      #a__U22	s: []	p: 0
      a__U13	s: []	p: 6
      U31	s: [2,3,1]	p: 0
      a__U71	s: [3,2,1]	p: 10
      a__U61	s: []	p: 11
      #a__U41	s: 2
      tt	s: []	p: 6
      a__isNat	s: [1]	p: 3
      U13	s: []	p: 6
      a__isNatKind	s: [1]	p: 5
      U22	s: [1]	p: 2
      U51	s: [3,2,1]	p: 9
      a__and	s: [1,2]	p: 0
      U41	s: [2,1]	p: 1
      #a__U32	s: 1
    USABLE RULES: { 1..62 }
    Removed DPs: #5 #9..11 #35 #38 #45 #52 #60 #70
Number of SCCs: 1, DPs: 2
  SCC { #25 #47 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      #a__isNatKind	s: 1
      isNatKind	s: [1]	p: 4
      a__plus	s: [1,2]	p: 9
      U21	s: [2,1]	p: 3
      #a__U71	s: [3,2]	p: 10
      U11	s: [2]	p: 8
      s 	s: [1]	p: 4
      #a__U31	s: [1,3,2]	p: 0
      #a__U33	s: 1
      a__U33	s: []	p: 6
      #a__isNat	s: []	p: 0
      U71	s: [3,2,1]	p: 10
      and	s: [1,2]	p: 0
      #a__U13	s: []	p: 0
      #a__U51	s: 2
      #a__x	s: [1,2]	p: 10
      a__U22	s: [1]	p: 2
      #a__U11	s: [2,3,1]	p: 0
      a__U31	s: [2,3,1]	p: 0
      a__U51	s: [3,2,1]	p: 9
      a__x	s: [1,2]	p: 10
      U12	s: [1]	p: 7
      a__U41	s: [2,1]	p: 1
      x 	s: [1,2]	p: 10
      #a__U12	s: [2,1]	p: 0
      #a__U21	s: [2,1]	p: 0
      #a__U61	s: []	p: 0
      #a__plus	s: 2
      #mark	s: 1
      0 	s: []	p: 11
      #a__and	s: 2
      a__U21	s: [2,1]	p: 3
      a__U32	s: []	p: 6
      mark	s: 1
      a__U11	s: [2]	p: 8
      U32	s: []	p: 6
      U33	s: []	p: 6
      a__U12	s: [1]	p: 7
      isNat	s: [1]	p: 3
      plus	s: [1,2]	p: 9
      U61	s: []	p: 11
      #a__U22	s: []	p: 0
      a__U13	s: []	p: 6
      U31	s: [2,3,1]	p: 0
      a__U71	s: [3,2,1]	p: 10
      a__U61	s: []	p: 11
      #a__U41	s: 2
      tt	s: []	p: 6
      a__isNat	s: [1]	p: 3
      U13	s: []	p: 6
      a__isNatKind	s: [1]	p: 4
      U22	s: [1]	p: 2
      U51	s: [3,2,1]	p: 9
      a__and	s: [1,2]	p: 0
      U41	s: [2,1]	p: 1
      #a__U32	s: 1
    USABLE RULES: { 1..62 }
    Removed DPs: #25
Number of SCCs: 0, DPs: 0