MAYBE
Time: 6.689

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) -> dC(N,M)
  U11(tt()) -> 0()
  U111(tt()) -> 0()
  U121(tt(),M',N') -> U122(equal(_>_(N',M'),true()),M',N')
  U122(tt(),M',N') -> gcdC(dC(N',M'),M')
  U131(tt(),N') -> N'
  U141(tt(),N) -> N
  U151(tt()) -> s_(0())
  U161(tt(),M',N) -> U162(equal(_>_(M',N),true()))
  U162(tt()) -> 0()
  U171(tt(),M',N) -> U172(equal(_>_(N,M'),true()),M',N)
  U172(tt(),M',N) -> s_(quot(dC(N,M'),M'))
  U21(tt(),M,N) -> s_(_+_C(N,_+_C(M,_*_C(N,M))))
  U31(tt(),N) -> N
  U41(tt(),M,N) -> s_(s_(_+_C(N,M)))
  U51(tt(),M,N) -> _>_(M,N)
  U61(tt()) -> false()
  U71(tt()) -> true()
  U81(tt(),M,N) -> _>_(N,M)
  U91(tt(),N) -> N
  _*_C(N,0()) -> U11(isNat(N))
  _*_C(s_(N),s_(M)) -> U21(and(isNat(M),isNat(N)),M,N)
  _+_C(N,0()) -> U31(isNat(N),N)
  _+_C(s_(N),s_(M)) -> U41(and(isNat(M),isNat(N)),M,N)
  _<_(N,M) -> U51(and(isNat(M),isNat(N)),M,N)
  _>_(0(),M) -> U61(isNat(M))
  _>_(N',0()) -> U71(isNzNat(N'))
  _>_(s_(N),s_(M)) -> U81(and(isNat(M),isNat(N)),M,N)
  and(tt(),X) -> X
  dC(0(),N) -> U91(isNat(N),N)
  dC(s_(N),s_(M)) -> U101(and(isNat(M),isNat(N)),M,N)
  equal(X,X) -> tt()
  gcdC(0(),N) -> U111(isNat(N))
  gcdC(N',M') -> U121(and(isNzNat(M'),isNzNat(N')),M',N')
  gcdC(N',N') -> U131(isNzNat(N'),N')
  isBoolean(false()) -> tt()
  isBoolean(true()) -> tt()
  isBoolean(_<_(V1,V2)) -> and(isNat(V1),isNat(V2))
  isBoolean(_>_(V1,V2)) -> and(isNat(V1),isNat(V2))
  isNat(0()) -> tt()
  isNat(V) -> isNzNat(V)
  isNat(_*_C(V1,V2)) -> and(isNat(V1),isNat(V2))
  isNat(_+_C(V1,V2)) -> and(isNat(V1),isNat(V2))
  isNat(dC(V1,V2)) -> and(isNat(V1),isNat(V2))
  isNat(gcdC(V1,V2)) -> and(isNat(V1),isNat(V2))
  isNat(p_(V1)) -> isNzNat(V1)
  isNat(quot(V1,V2)) -> and(isNat(V1),isNzNat(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)) -> and(isNzNat(V1),isNzNat(V2))
  isNzNat(gcdC(V1,V2)) -> and(isNzNat(V1),isNzNat(V2))
  isNzNat(s_(V1)) -> isNat(V1)
  p_(s_(N)) -> U141(isNat(N),N)
  quot(M',M') -> U151(isNzNat(M'))
  quot(N,M') -> U161(and(isNzNat(M'),isNat(N)),M',N)
  quot(N,M') -> U171(and(isNzNat(M'),isNat(N)),M',N)

Proof:
 DP Processor:
  Equations#:
   
  DPs:
   U101#(tt(),M,N) -> d{C,#}(N,M)
   U121#(tt(),M',N') -> _>_#(N',M')
   U121#(tt(),M',N') -> equal#(_>_(N',M'),true())
   U121#(tt(),M',N') -> U122#(equal(_>_(N',M'),true()),M',N')
   U122#(tt(),M',N') -> d{C,#}(N',M')
   U122#(tt(),M',N') -> gcd{C,#}(dC(N',M'),M')
   U161#(tt(),M',N) -> _>_#(M',N)
   U161#(tt(),M',N) -> equal#(_>_(M',N),true())
   U161#(tt(),M',N) -> U162#(equal(_>_(M',N),true()))
   U171#(tt(),M',N) -> _>_#(N,M')
   U171#(tt(),M',N) -> equal#(_>_(N,M'),true())
   U171#(tt(),M',N) -> U172#(equal(_>_(N,M'),true()),M',N)
   U172#(tt(),M',N) -> d{C,#}(N,M')
   U172#(tt(),M',N) -> quot#(dC(N,M'),M')
   U21#(tt(),M,N) -> _*_{C,#}(N,M)
   U21#(tt(),M,N) -> _+_{C,#}(M,_*_C(N,M))
   U21#(tt(),M,N) -> _+_{C,#}(N,_+_C(M,_*_C(N,M)))
   U41#(tt(),M,N) -> _+_{C,#}(N,M)
   U51#(tt(),M,N) -> _>_#(M,N)
   U81#(tt(),M,N) -> _>_#(N,M)
   _*_{C,#}(N,0()) -> isNat#(N)
   _*_{C,#}(N,0()) -> U11#(isNat(N))
   _*_{C,#}(s_(N),s_(M)) -> isNat#(N)
   _*_{C,#}(s_(N),s_(M)) -> isNat#(M)
   _*_{C,#}(s_(N),s_(M)) -> and#(isNat(M),isNat(N))
   _*_{C,#}(s_(N),s_(M)) -> U21#(and(isNat(M),isNat(N)),M,N)
   _+_{C,#}(N,0()) -> isNat#(N)
   _+_{C,#}(N,0()) -> U31#(isNat(N),N)
   _+_{C,#}(s_(N),s_(M)) -> isNat#(N)
   _+_{C,#}(s_(N),s_(M)) -> isNat#(M)
   _+_{C,#}(s_(N),s_(M)) -> and#(isNat(M),isNat(N))
   _+_{C,#}(s_(N),s_(M)) -> U41#(and(isNat(M),isNat(N)),M,N)
   _<_#(N,M) -> isNat#(N)
   _<_#(N,M) -> isNat#(M)
   _<_#(N,M) -> and#(isNat(M),isNat(N))
   _<_#(N,M) -> U51#(and(isNat(M),isNat(N)),M,N)
   _>_#(0(),M) -> isNat#(M)
   _>_#(0(),M) -> U61#(isNat(M))
   _>_#(N',0()) -> isNzNat#(N')
   _>_#(N',0()) -> U71#(isNzNat(N'))
   _>_#(s_(N),s_(M)) -> isNat#(N)
   _>_#(s_(N),s_(M)) -> isNat#(M)
   _>_#(s_(N),s_(M)) -> and#(isNat(M),isNat(N))
   _>_#(s_(N),s_(M)) -> U81#(and(isNat(M),isNat(N)),M,N)
   d{C,#}(0(),N) -> isNat#(N)
   d{C,#}(0(),N) -> U91#(isNat(N),N)
   d{C,#}(s_(N),s_(M)) -> isNat#(N)
   d{C,#}(s_(N),s_(M)) -> isNat#(M)
   d{C,#}(s_(N),s_(M)) -> and#(isNat(M),isNat(N))
   d{C,#}(s_(N),s_(M)) -> U101#(and(isNat(M),isNat(N)),M,N)
   gcd{C,#}(0(),N) -> isNat#(N)
   gcd{C,#}(0(),N) -> U111#(isNat(N))
   gcd{C,#}(N',M') -> isNzNat#(N')
   gcd{C,#}(N',M') -> isNzNat#(M')
   gcd{C,#}(N',M') -> and#(isNzNat(M'),isNzNat(N'))
   gcd{C,#}(N',M') -> U121#(and(isNzNat(M'),isNzNat(N')),M',N')
   gcd{C,#}(N',N') -> isNzNat#(N')
   gcd{C,#}(N',N') -> U131#(isNzNat(N'),N')
   isBoolean#(_<_(V1,V2)) -> isNat#(V2)
   isBoolean#(_<_(V1,V2)) -> isNat#(V1)
   isBoolean#(_<_(V1,V2)) -> and#(isNat(V1),isNat(V2))
   isBoolean#(_>_(V1,V2)) -> isNat#(V2)
   isBoolean#(_>_(V1,V2)) -> isNat#(V1)
   isBoolean#(_>_(V1,V2)) -> and#(isNat(V1),isNat(V2))
   isNat#(V) -> isNzNat#(V)
   isNat#(_*_C(V1,V2)) -> isNat#(V2)
   isNat#(_*_C(V1,V2)) -> isNat#(V1)
   isNat#(_*_C(V1,V2)) -> and#(isNat(V1),isNat(V2))
   isNat#(_+_C(V1,V2)) -> isNat#(V2)
   isNat#(_+_C(V1,V2)) -> isNat#(V1)
   isNat#(_+_C(V1,V2)) -> and#(isNat(V1),isNat(V2))
   isNat#(dC(V1,V2)) -> isNat#(V2)
   isNat#(dC(V1,V2)) -> isNat#(V1)
   isNat#(dC(V1,V2)) -> and#(isNat(V1),isNat(V2))
   isNat#(gcdC(V1,V2)) -> isNat#(V2)
   isNat#(gcdC(V1,V2)) -> isNat#(V1)
   isNat#(gcdC(V1,V2)) -> and#(isNat(V1),isNat(V2))
   isNat#(p_(V1)) -> isNzNat#(V1)
   isNat#(quot(V1,V2)) -> isNzNat#(V2)
   isNat#(quot(V1,V2)) -> isNat#(V1)
   isNat#(quot(V1,V2)) -> and#(isNat(V1),isNzNat(V2))
   isNzNat#(_*_C(V1,V2)) -> isNzNat#(V2)
   isNzNat#(_*_C(V1,V2)) -> isNzNat#(V1)
   isNzNat#(_*_C(V1,V2)) -> and#(isNzNat(V1),isNzNat(V2))
   isNzNat#(gcdC(V1,V2)) -> isNzNat#(V2)
   isNzNat#(gcdC(V1,V2)) -> isNzNat#(V1)
   isNzNat#(gcdC(V1,V2)) -> and#(isNzNat(V1),isNzNat(V2))
   isNzNat#(s_(V1)) -> isNat#(V1)
   p_#(s_(N)) -> isNat#(N)
   p_#(s_(N)) -> U141#(isNat(N),N)
   quot#(M',M') -> isNzNat#(M')
   quot#(M',M') -> U151#(isNzNat(M'))
   quot#(N,M') -> isNat#(N)
   quot#(N,M') -> isNzNat#(M')
   quot#(N,M') -> and#(isNzNat(M'),isNat(N))
   quot#(N,M') -> U161#(and(isNzNat(M'),isNat(N)),M',N)
   quot#(N,M') -> U171#(and(isNzNat(M'),isNat(N)),M',N)
  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) -> dC(N,M)
   U11(tt()) -> 0()
   U111(tt()) -> 0()
   U121(tt(),M',N') -> U122(equal(_>_(N',M'),true()),M',N')
   U122(tt(),M',N') -> gcdC(dC(N',M'),M')
   U131(tt(),N') -> N'
   U141(tt(),N) -> N
   U151(tt()) -> s_(0())
   U161(tt(),M',N) -> U162(equal(_>_(M',N),true()))
   U162(tt()) -> 0()
   U171(tt(),M',N) -> U172(equal(_>_(N,M'),true()),M',N)
   U172(tt(),M',N) -> s_(quot(dC(N,M'),M'))
   U21(tt(),M,N) -> s_(_+_C(N,_+_C(M,_*_C(N,M))))
   U31(tt(),N) -> N
   U41(tt(),M,N) -> s_(s_(_+_C(N,M)))
   U51(tt(),M,N) -> _>_(M,N)
   U61(tt()) -> false()
   U71(tt()) -> true()
   U81(tt(),M,N) -> _>_(N,M)
   U91(tt(),N) -> N
   _*_C(N,0()) -> U11(isNat(N))
   _*_C(s_(N),s_(M)) -> U21(and(isNat(M),isNat(N)),M,N)
   _+_C(N,0()) -> U31(isNat(N),N)
   _+_C(s_(N),s_(M)) -> U41(and(isNat(M),isNat(N)),M,N)
   _<_(N,M) -> U51(and(isNat(M),isNat(N)),M,N)
   _>_(0(),M) -> U61(isNat(M))
   _>_(N',0()) -> U71(isNzNat(N'))
   _>_(s_(N),s_(M)) -> U81(and(isNat(M),isNat(N)),M,N)
   and(tt(),X) -> X
   dC(0(),N) -> U91(isNat(N),N)
   dC(s_(N),s_(M)) -> U101(and(isNat(M),isNat(N)),M,N)
   equal(X,X) -> tt()
   gcdC(0(),N) -> U111(isNat(N))
   gcdC(N',M') -> U121(and(isNzNat(M'),isNzNat(N')),M',N')
   gcdC(N',N') -> U131(isNzNat(N'),N')
   isBoolean(false()) -> tt()
   isBoolean(true()) -> tt()
   isBoolean(_<_(V1,V2)) -> and(isNat(V1),isNat(V2))
   isBoolean(_>_(V1,V2)) -> and(isNat(V1),isNat(V2))
   isNat(0()) -> tt()
   isNat(V) -> isNzNat(V)
   isNat(_*_C(V1,V2)) -> and(isNat(V1),isNat(V2))
   isNat(_+_C(V1,V2)) -> and(isNat(V1),isNat(V2))
   isNat(dC(V1,V2)) -> and(isNat(V1),isNat(V2))
   isNat(gcdC(V1,V2)) -> and(isNat(V1),isNat(V2))
   isNat(p_(V1)) -> isNzNat(V1)
   isNat(quot(V1,V2)) -> and(isNat(V1),isNzNat(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)) -> and(isNzNat(V1),isNzNat(V2))
   isNzNat(gcdC(V1,V2)) -> and(isNzNat(V1),isNzNat(V2))
   isNzNat(s_(V1)) -> isNat(V1)
   p_(s_(N)) -> U141(isNat(N),N)
   quot(M',M') -> U151(isNzNat(M'))
   quot(N,M') -> U161(and(isNzNat(M'),isNat(N)),M',N)
   quot(N,M') -> U171(and(isNzNat(M'),isNat(N)),M',N)
  S:
   
  AC-EDG Processor:
   Equations#:
    
   DPs:
    U101#(tt(),M,N) -> d{C,#}(N,M)
    U121#(tt(),M',N') -> _>_#(N',M')
    U121#(tt(),M',N') -> equal#(_>_(N',M'),true())
    U121#(tt(),M',N') -> U122#(equal(_>_(N',M'),true()),M',N')
    U122#(tt(),M',N') -> d{C,#}(N',M')
    U122#(tt(),M',N') -> gcd{C,#}(dC(N',M'),M')
    U161#(tt(),M',N) -> _>_#(M',N)
    U161#(tt(),M',N) -> equal#(_>_(M',N),true())
    U161#(tt(),M',N) -> U162#(equal(_>_(M',N),true()))
    U171#(tt(),M',N) -> _>_#(N,M')
    U171#(tt(),M',N) -> equal#(_>_(N,M'),true())
    U171#(tt(),M',N) -> U172#(equal(_>_(N,M'),true()),M',N)
    U172#(tt(),M',N) -> d{C,#}(N,M')
    U172#(tt(),M',N) -> quot#(dC(N,M'),M')
    U21#(tt(),M,N) -> _*_{C,#}(N,M)
    U21#(tt(),M,N) -> _+_{C,#}(M,_*_C(N,M))
    U21#(tt(),M,N) -> _+_{C,#}(N,_+_C(M,_*_C(N,M)))
    U41#(tt(),M,N) -> _+_{C,#}(N,M)
    U51#(tt(),M,N) -> _>_#(M,N)
    U81#(tt(),M,N) -> _>_#(N,M)
    _*_{C,#}(N,0()) -> isNat#(N)
    _*_{C,#}(N,0()) -> U11#(isNat(N))
    _*_{C,#}(s_(N),s_(M)) -> isNat#(N)
    _*_{C,#}(s_(N),s_(M)) -> isNat#(M)
    _*_{C,#}(s_(N),s_(M)) -> and#(isNat(M),isNat(N))
    _*_{C,#}(s_(N),s_(M)) -> U21#(and(isNat(M),isNat(N)),M,N)
    _+_{C,#}(N,0()) -> isNat#(N)
    _+_{C,#}(N,0()) -> U31#(isNat(N),N)
    _+_{C,#}(s_(N),s_(M)) -> isNat#(N)
    _+_{C,#}(s_(N),s_(M)) -> isNat#(M)
    _+_{C,#}(s_(N),s_(M)) -> and#(isNat(M),isNat(N))
    _+_{C,#}(s_(N),s_(M)) -> U41#(and(isNat(M),isNat(N)),M,N)
    _<_#(N,M) -> isNat#(N)
    _<_#(N,M) -> isNat#(M)
    _<_#(N,M) -> and#(isNat(M),isNat(N))
    _<_#(N,M) -> U51#(and(isNat(M),isNat(N)),M,N)
    _>_#(0(),M) -> isNat#(M)
    _>_#(0(),M) -> U61#(isNat(M))
    _>_#(N',0()) -> isNzNat#(N')
    _>_#(N',0()) -> U71#(isNzNat(N'))
    _>_#(s_(N),s_(M)) -> isNat#(N)
    _>_#(s_(N),s_(M)) -> isNat#(M)
    _>_#(s_(N),s_(M)) -> and#(isNat(M),isNat(N))
    _>_#(s_(N),s_(M)) -> U81#(and(isNat(M),isNat(N)),M,N)
    d{C,#}(0(),N) -> isNat#(N)
    d{C,#}(0(),N) -> U91#(isNat(N),N)
    d{C,#}(s_(N),s_(M)) -> isNat#(N)
    d{C,#}(s_(N),s_(M)) -> isNat#(M)
    d{C,#}(s_(N),s_(M)) -> and#(isNat(M),isNat(N))
    d{C,#}(s_(N),s_(M)) -> U101#(and(isNat(M),isNat(N)),M,N)
    gcd{C,#}(0(),N) -> isNat#(N)
    gcd{C,#}(0(),N) -> U111#(isNat(N))
    gcd{C,#}(N',M') -> isNzNat#(N')
    gcd{C,#}(N',M') -> isNzNat#(M')
    gcd{C,#}(N',M') -> and#(isNzNat(M'),isNzNat(N'))
    gcd{C,#}(N',M') -> U121#(and(isNzNat(M'),isNzNat(N')),M',N')
    gcd{C,#}(N',N') -> isNzNat#(N')
    gcd{C,#}(N',N') -> U131#(isNzNat(N'),N')
    isBoolean#(_<_(V1,V2)) -> isNat#(V2)
    isBoolean#(_<_(V1,V2)) -> isNat#(V1)
    isBoolean#(_<_(V1,V2)) -> and#(isNat(V1),isNat(V2))
    isBoolean#(_>_(V1,V2)) -> isNat#(V2)
    isBoolean#(_>_(V1,V2)) -> isNat#(V1)
    isBoolean#(_>_(V1,V2)) -> and#(isNat(V1),isNat(V2))
    isNat#(V) -> isNzNat#(V)
    isNat#(_*_C(V1,V2)) -> isNat#(V2)
    isNat#(_*_C(V1,V2)) -> isNat#(V1)
    isNat#(_*_C(V1,V2)) -> and#(isNat(V1),isNat(V2))
    isNat#(_+_C(V1,V2)) -> isNat#(V2)
    isNat#(_+_C(V1,V2)) -> isNat#(V1)
    isNat#(_+_C(V1,V2)) -> and#(isNat(V1),isNat(V2))
    isNat#(dC(V1,V2)) -> isNat#(V2)
    isNat#(dC(V1,V2)) -> isNat#(V1)
    isNat#(dC(V1,V2)) -> and#(isNat(V1),isNat(V2))
    isNat#(gcdC(V1,V2)) -> isNat#(V2)
    isNat#(gcdC(V1,V2)) -> isNat#(V1)
    isNat#(gcdC(V1,V2)) -> and#(isNat(V1),isNat(V2))
    isNat#(p_(V1)) -> isNzNat#(V1)
    isNat#(quot(V1,V2)) -> isNzNat#(V2)
    isNat#(quot(V1,V2)) -> isNat#(V1)
    isNat#(quot(V1,V2)) -> and#(isNat(V1),isNzNat(V2))
    isNzNat#(_*_C(V1,V2)) -> isNzNat#(V2)
    isNzNat#(_*_C(V1,V2)) -> isNzNat#(V1)
    isNzNat#(_*_C(V1,V2)) -> and#(isNzNat(V1),isNzNat(V2))
    isNzNat#(gcdC(V1,V2)) -> isNzNat#(V2)
    isNzNat#(gcdC(V1,V2)) -> isNzNat#(V1)
    isNzNat#(gcdC(V1,V2)) -> and#(isNzNat(V1),isNzNat(V2))
    isNzNat#(s_(V1)) -> isNat#(V1)
    p_#(s_(N)) -> isNat#(N)
    p_#(s_(N)) -> U141#(isNat(N),N)
    quot#(M',M') -> isNzNat#(M')
    quot#(M',M') -> U151#(isNzNat(M'))
    quot#(N,M') -> isNat#(N)
    quot#(N,M') -> isNzNat#(M')
    quot#(N,M') -> and#(isNzNat(M'),isNat(N))
    quot#(N,M') -> U161#(and(isNzNat(M'),isNat(N)),M',N)
    quot#(N,M') -> U171#(and(isNzNat(M'),isNat(N)),M',N)
   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) -> dC(N,M)
    U11(tt()) -> 0()
    U111(tt()) -> 0()
    U121(tt(),M',N') -> U122(equal(_>_(N',M'),true()),M',N')
    U122(tt(),M',N') -> gcdC(dC(N',M'),M')
    U131(tt(),N') -> N'
    U141(tt(),N) -> N
    U151(tt()) -> s_(0())
    U161(tt(),M',N) -> U162(equal(_>_(M',N),true()))
    U162(tt()) -> 0()
    U171(tt(),M',N) -> U172(equal(_>_(N,M'),true()),M',N)
    U172(tt(),M',N) -> s_(quot(dC(N,M'),M'))
    U21(tt(),M,N) -> s_(_+_C(N,_+_C(M,_*_C(N,M))))
    U31(tt(),N) -> N
    U41(tt(),M,N) -> s_(s_(_+_C(N,M)))
    U51(tt(),M,N) -> _>_(M,N)
    U61(tt()) -> false()
    U71(tt()) -> true()
    U81(tt(),M,N) -> _>_(N,M)
    U91(tt(),N) -> N
    _*_C(N,0()) -> U11(isNat(N))
    _*_C(s_(N),s_(M)) -> U21(and(isNat(M),isNat(N)),M,N)
    _+_C(N,0()) -> U31(isNat(N),N)
    _+_C(s_(N),s_(M)) -> U41(and(isNat(M),isNat(N)),M,N)
    _<_(N,M) -> U51(and(isNat(M),isNat(N)),M,N)
    _>_(0(),M) -> U61(isNat(M))
    _>_(N',0()) -> U71(isNzNat(N'))
    _>_(s_(N),s_(M)) -> U81(and(isNat(M),isNat(N)),M,N)
    and(tt(),X) -> X
    dC(0(),N) -> U91(isNat(N),N)
    dC(s_(N),s_(M)) -> U101(and(isNat(M),isNat(N)),M,N)
    equal(X,X) -> tt()
    gcdC(0(),N) -> U111(isNat(N))
    gcdC(N',M') -> U121(and(isNzNat(M'),isNzNat(N')),M',N')
    gcdC(N',N') -> U131(isNzNat(N'),N')
    isBoolean(false()) -> tt()
    isBoolean(true()) -> tt()
    isBoolean(_<_(V1,V2)) -> and(isNat(V1),isNat(V2))
    isBoolean(_>_(V1,V2)) -> and(isNat(V1),isNat(V2))
    isNat(0()) -> tt()
    isNat(V) -> isNzNat(V)
    isNat(_*_C(V1,V2)) -> and(isNat(V1),isNat(V2))
    isNat(_+_C(V1,V2)) -> and(isNat(V1),isNat(V2))
    isNat(dC(V1,V2)) -> and(isNat(V1),isNat(V2))
    isNat(gcdC(V1,V2)) -> and(isNat(V1),isNat(V2))
    isNat(p_(V1)) -> isNzNat(V1)
    isNat(quot(V1,V2)) -> and(isNat(V1),isNzNat(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)) -> and(isNzNat(V1),isNzNat(V2))
    isNzNat(gcdC(V1,V2)) -> and(isNzNat(V1),isNzNat(V2))
    isNzNat(s_(V1)) -> isNat(V1)
    p_(s_(N)) -> U141(isNat(N),N)
    quot(M',M') -> U151(isNzNat(M'))
    quot(N,M') -> U161(and(isNzNat(M'),isNat(N)),M',N)
    quot(N,M') -> U171(and(isNzNat(M'),isNat(N)),M',N)
   S:
    
   Open