/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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MAYBE

Problem:
 zeros() -> cons(0(),n__zeros())
 U11(tt(),V1) -> U12(isNatList(activate(V1)))
 U12(tt()) -> tt()
 U21(tt(),V1) -> U22(isNat(activate(V1)))
 U22(tt()) -> tt()
 U31(tt(),V) -> U32(isNatList(activate(V)))
 U32(tt()) -> tt()
 U41(tt(),V1,V2) -> U42(isNat(activate(V1)),activate(V2))
 U42(tt(),V2) -> U43(isNatIList(activate(V2)))
 U43(tt()) -> tt()
 U51(tt(),V1,V2) -> U52(isNat(activate(V1)),activate(V2))
 U52(tt(),V2) -> U53(isNatList(activate(V2)))
 U53(tt()) -> tt()
 U61(tt(),V1,V2) -> U62(isNat(activate(V1)),activate(V2))
 U62(tt(),V2) -> U63(isNatIList(activate(V2)))
 U63(tt()) -> tt()
 U71(tt(),L) -> s(length(activate(L)))
 U81(tt()) -> nil()
 U91(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL)))
 and(tt(),X) -> activate(X)
 isNat(n__0()) -> tt()
 isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1))
 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
 isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V))
 isNatIList(n__zeros()) -> tt()
 isNatIList(n__cons(V1,V2)) ->
 U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
 isNatIListKind(n__nil()) -> tt()
 isNatIListKind(n__zeros()) -> tt()
 isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
 isNatIListKind(n__take(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
 isNatKind(n__0()) -> tt()
 isNatKind(n__length(V1)) -> isNatIListKind(activate(V1))
 isNatKind(n__s(V1)) -> isNatKind(activate(V1))
 isNatList(n__nil()) -> tt()
 isNatList(n__cons(V1,V2)) ->
 U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
 isNatList(n__take(V1,V2)) ->
 U61(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
 length(nil()) -> 0()
 length(cons(N,L)) ->
 U71(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and
                                                                    (
                                                                    n__isNat(N),n__isNatKind(N))),
     activate(L))
 take(0(),IL) -> U81(and(isNatIList(IL),n__isNatIListKind(IL)))
 take(s(M),cons(N,IL)) ->
 U91(and(and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL))),
         n__and(n__and(n__isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N)))),
     activate(IL),M,N)
 zeros() -> n__zeros()
 take(X1,X2) -> n__take(X1,X2)
 0() -> n__0()
 length(X) -> n__length(X)
 s(X) -> n__s(X)
 cons(X1,X2) -> n__cons(X1,X2)
 isNatIListKind(X) -> n__isNatIListKind(X)
 nil() -> n__nil()
 and(X1,X2) -> n__and(X1,X2)
 isNat(X) -> n__isNat(X)
 isNatKind(X) -> n__isNatKind(X)
 activate(n__zeros()) -> zeros()
 activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
 activate(n__0()) -> 0()
 activate(n__length(X)) -> length(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
 activate(n__isNatIListKind(X)) -> isNatIListKind(X)
 activate(n__nil()) -> nil()
 activate(n__and(X1,X2)) -> and(activate(X1),X2)
 activate(n__isNat(X)) -> isNat(X)
 activate(n__isNatKind(X)) -> isNatKind(X)
 activate(X) -> X

Proof:
 Open