MAYBE
Time: 1.998

Problem:
 Equations:
  
 TRS:
  1() -> s_(0())
  2() -> s_(s_(0()))
  3() -> s_(s_(s_(0())))
  4() -> s_(s_(s_(s_(0()))))
  5() -> s_(s_(s_(s_(s_(0())))))
  6() -> s_(s_(s_(s_(s_(s_(0()))))))
  7() -> s_(s_(s_(s_(s_(s_(s_(0())))))))
  U101(tt(),M,N) -> U102(isNat(N),M,N)
  U102(tt(),M,N) -> dC(N,M)
  U11(tt()) -> 0()
  U111(tt()) -> 0()
  U121(tt(),M',N') -> U122(isNzNat(N'),M',N')
  U122(tt(),M',N') -> U123(equal(_>_(N',M'),true()),M',N')
  U123(tt(),M',N') -> gcdC(dC(N',M'),M')
  U131(tt(),N') -> N'
  U141(tt(),V2) -> U142(isNat(V2))
  U142(tt()) -> tt()
  U151(tt(),V2) -> U152(isNat(V2))
  U152(tt()) -> tt()
  U161(tt()) -> tt()
  U171(tt(),V2) -> U172(isNat(V2))
  U172(tt()) -> tt()
  U181(tt(),V2) -> U182(isNat(V2))
  U182(tt()) -> tt()
  U191(tt(),V2) -> U192(isNat(V2))
  U192(tt()) -> tt()
  U201(tt(),V2) -> U202(isNat(V2))
  U202(tt()) -> tt()
  U21(tt(),M,N) -> U22(isNat(N),M,N)
  U211(tt()) -> tt()
  U22(tt(),M,N) -> s_(_+_C(N,_+_C(M,_*_C(N,M))))
  U221(tt(),V2) -> U222(isNzNat(V2))
  U222(tt()) -> tt()
  U231(tt(),V2) -> U232(isNzNat(V2))
  U232(tt()) -> tt()
  U241(tt(),V2) -> U242(isNzNat(V2))
  U242(tt()) -> tt()
  U251(tt()) -> tt()
  U261(tt(),N) -> N
  U271(tt()) -> s_(0())
  U281(tt(),M',N) -> U282(isNat(N),M',N)
  U282(tt(),M',N) -> U283(equal(_>_(M',N),true()))
  U283(tt()) -> 0()
  U291(tt(),M',N) -> U292(isNat(N),M',N)
  U292(tt(),M',N) -> U293(equal(_>_(N,M'),true()),M',N)
  U293(tt(),M',N) -> s_(quot(dC(N,M'),M'))
  U31(tt(),N) -> N
  U41(tt(),M,N) -> U42(isNat(N),M,N)
  U42(tt(),M,N) -> s_(s_(_+_C(N,M)))
  U51(tt(),M,N) -> U52(isNat(N),M,N)
  U52(tt(),M,N) -> _>_(M,N)
  U61(tt()) -> false()
  U71(tt()) -> true()
  U81(tt(),M,N) -> U82(isNat(N),M,N)
  U82(tt(),M,N) -> _>_(N,M)
  U91(tt(),N) -> N
  _*_C(N,0()) -> U11(isNat(N))
  _*_C(s_(N),s_(M)) -> U21(isNat(M),M,N)
  _+_C(N,0()) -> U31(isNat(N),N)
  _+_C(s_(N),s_(M)) -> U41(isNat(M),M,N)
  _<_(N,M) -> U51(isNat(M),M,N)
  _>_(0(),M) -> U61(isNat(M))
  _>_(N',0()) -> U71(isNzNat(N'))
  _>_(s_(N),s_(M)) -> U81(isNat(M),M,N)
  dC(0(),N) -> U91(isNat(N),N)
  dC(s_(N),s_(M)) -> U101(isNat(M),M,N)
  equal(X,X) -> tt()
  gcdC(0(),N) -> U111(isNat(N))
  gcdC(N',M') -> U121(isNzNat(M'),M',N')
  gcdC(N',N') -> U131(isNzNat(N'),N')
  isBoolean(false()) -> tt()
  isBoolean(true()) -> tt()
  isBoolean(_<_(V1,V2)) -> U141(isNat(V1),V2)
  isBoolean(_>_(V1,V2)) -> U151(isNat(V1),V2)
  isNat(0()) -> tt()
  isNat(V) -> U161(isNzNat(V))
  isNat(_*_C(V1,V2)) -> U171(isNat(V1),V2)
  isNat(_+_C(V1,V2)) -> U181(isNat(V1),V2)
  isNat(dC(V1,V2)) -> U191(isNat(V1),V2)
  isNat(gcdC(V1,V2)) -> U201(isNat(V1),V2)
  isNat(p_(V1)) -> U211(isNzNat(V1))
  isNat(quot(V1,V2)) -> U221(isNat(V1),V2)
  isNzNat(1()) -> tt()
  isNzNat(2()) -> tt()
  isNzNat(3()) -> tt()
  isNzNat(4()) -> tt()
  isNzNat(5()) -> tt()
  isNzNat(6()) -> tt()
  isNzNat(7()) -> tt()
  isNzNat(_*_C(V1,V2)) -> U231(isNzNat(V1),V2)
  isNzNat(gcdC(V1,V2)) -> U241(isNzNat(V1),V2)
  isNzNat(s_(V1)) -> U251(isNat(V1))
  p_(s_(N)) -> U261(isNat(N),N)
  quot(M',M') -> U271(isNzNat(M'))
  quot(N,M') -> U281(isNzNat(M'),M',N)
  quot(N,M') -> U291(isNzNat(M'),M',N)

Proof:
 Open