TRS Equational pair #487092871

details

property	value
status	complete
benchmark	PEANO-NAT_complete.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Mixed_C

run statistics

property	value
solver	NaTT v.1.6c
configuration	Default
runtime (wallclock)	1.85339 seconds
cpu usage	2.05
user time	1.88
system time	0.17
max virtual memory	369308.0
max residence set size	9336.0

stage attributes

key	value
starexec-result	MAYBE

output

MAYBE
Input TRS:
C symbols: d _+_ _*_ gcd
      1: 1() -> s_(0())
      2: 2() -> s_(s_(0()))
      3: 3() -> s_(s_(s_(0())))
      4: 4() -> s_(s_(s_(s_(0()))))
      5: 5() -> s_(s_(s_(s_(s_(0())))))
      6: 6() -> s_(s_(s_(s_(s_(s_(0()))))))
      7: 7() -> s_(s_(s_(s_(s_(s_(s_(0())))))))
      8: U101(tt(),M,N) -> d(N,M)
      9: U11(tt()) -> 0()
      10: U111(tt()) -> 0()
      11: U121(tt(),M',N') -> U122(equal(_>_(N',M'),true()),M',N')
      12: U122(tt(),M',N') -> gcd(d(N',M'),M')
      13: U131(tt(),N') -> N'
      14: U141(tt(),V1,V2) -> U142(isNat(V1),V2)
      15: U142(tt(),V2) -> U143(isNat(V2))
      16: U143(tt()) -> tt()
      17: U151(tt(),V1,V2) -> U152(isNat(V1),V2)
      18: U152(tt(),V2) -> U153(isNat(V2))
      19: U153(tt()) -> tt()
      20: U161(tt(),V) -> U162(isNzNat(V))
      21: U162(tt()) -> tt()
      22: U171(tt(),V1,V2) -> U172(isNat(V1),V2)
      23: U172(tt(),V2) -> U173(isNat(V2))
      24: U173(tt()) -> tt()
      25: U181(tt(),V1,V2) -> U182(isNat(V1),V2)
      26: U182(tt(),V2) -> U183(isNat(V2))
      27: U183(tt()) -> tt()
      28: U191(tt(),V1,V2) -> U192(isNat(V1),V2)
      29: U192(tt(),V2) -> U193(isNat(V2))
      30: U193(tt()) -> tt()
      31: U201(tt(),V1,V2) -> U202(isNat(V1),V2)
      32: U202(tt(),V2) -> U203(isNat(V2))
      33: U203(tt()) -> tt()
      34: U21(tt(),M,N) -> s_(_+_(N,_+_(M,_*_(N,M))))
      35: U211(tt(),V1) -> U212(isNzNat(V1))
      36: U212(tt()) -> tt()
      37: U221(tt(),V1,V2) -> U222(isNat(V1),V2)
      38: U222(tt(),V2) -> U223(isNzNat(V2))
      39: U223(tt()) -> tt()
      40: U231(tt(),V1,V2) -> U232(isNzNat(V1),V2)
      41: U232(tt(),V2) -> U233(isNzNat(V2))
      42: U233(tt()) -> tt()
      43: U241(tt(),V1,V2) -> U242(isNzNat(V1),V2)
      44: U242(tt(),V2) -> U243(isNzNat(V2))
      45: U243(tt()) -> tt()
      46: U251(tt(),V1) -> U252(isNat(V1))
      47: U252(tt()) -> tt()
      48: U261(tt(),N) -> N
      49: U271(tt()) -> s_(0())
      50: U281(tt(),M',N) -> U282(equal(_>_(M',N),true()))
      51: U282(tt()) -> 0()
      52: U291(tt(),M',N) -> U292(equal(_>_(N,M'),true()),M',N)
      53: U292(tt(),M',N) -> s_(quot(d(N,M'),M'))
      54: U31(tt(),N) -> N
      55: U41(tt(),M,N) -> s_(s_(_+_(N,M)))
      56: U51(tt(),M,N) -> _>_(M,N)
      57: U61(tt()) -> false()
      58: U71(tt()) -> true()
      59: U81(tt(),M,N) -> _>_(N,M)
      60: U91(tt(),N) -> N
      61: _*_(N,0()) -> U11(and(isNat(N),isNatKind(N)))
      62: _*_(s_(N),s_(M)) -> U21(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
      63: _+_(N,0()) -> U31(and(isNat(N),isNatKind(N)),N)
      64: _+_(s_(N),s_(M)) -> U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
      65: _<_(N,M) -> U51(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
      66: _>_(0(),M) -> U61(and(isNat(M),isNatKind(M)))
      67: _>_(N',0()) -> U71(and(isNzNat(N'),isNatKind(N')))
      68: _>_(s_(N),s_(M)) -> U81(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
      69: and(tt(),X) -> X
      70: d(0(),N) -> U91(and(isNat(N),isNatKind(N)),N)
      71: d(s_(N),s_(M)) -> U101(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
      72: equal(X,X) -> tt()
      73: gcd(0(),N) -> U111(and(isNat(N),isNatKind(N)))
      74: gcd(N',M') -> U121(and(and(isNzNat(M'),isNatKind(M')),and(isNzNat(N'),isNatKind(N'))),M',N')
      75: gcd(N',N') -> U131(and(isNzNat(N'),isNatKind(N')),N')
      76: isBoolean(false()) -> tt()
      77: isBoolean(true()) -> tt()
      78: isBoolean(_<_(V1,V2)) -> U141(and(isNatKind(V1),isNatKind(V2)),V1,V2)
      79: isBoolean(_>_(V1,V2)) -> U151(and(isNatKind(V1),isNatKind(V2)),V1,V2)
      80: isBooleanKind(false()) -> tt()
      81: isBooleanKind(true()) -> tt()
      82: isBooleanKind(_<_(V1,V2)) -> and(isNatKind(V1),isNatKind(V2))
      83: isBooleanKind(_>_(V1,V2)) -> and(isNatKind(V1),isNatKind(V2))
      84: isNat(0()) -> tt()
      85: isNat(V) -> U161(isNatKind(V),V)
      86: isNat(_*_(V1,V2)) -> U171(and(isNatKind(V1),isNatKind(V2)),V1,V2)
      87: isNat(_+_(V1,V2)) -> U181(and(isNatKind(V1),isNatKind(V2)),V1,V2)
      88: isNat(d(V1,V2)) -> U191(and(isNatKind(V1),isNatKind(V2)),V1,V2)
      89: isNat(gcd(V1,V2)) -> U201(and(isNatKind(V1),isNatKind(V2)),V1,V2)
      90: isNat(p_(V1)) -> U211(isNatKind(V1),V1)
      91: isNat(quot(V1,V2)) -> U221(and(isNatKind(V1),isNatKind(V2)),V1,V2)
      92: isNatKind(0()) -> tt()
      93: isNatKind(1()) -> tt()
      94: isNatKind(2()) -> tt()
      95: isNatKind(3()) -> tt()
      96: isNatKind(4()) -> tt()
      97: isNatKind(5()) -> tt()

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job log

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actions all output return to TRS Equational