Problem Transformed CSR 04 OvConsOS nokinds C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS nokinds C

stdout:

MAYBE

Problem:
active(zeros()) -> mark(cons(0(),zeros()))
active(U11(tt(),L)) -> mark(s(length(L)))
active(U21(tt())) -> mark(nil())
active(U31(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
active(and(tt(),X)) -> mark(X)
active(isNat(0())) -> mark(tt())
active(isNat(length(V1))) -> mark(isNatList(V1))
active(isNat(s(V1))) -> mark(isNat(V1))
active(isNatIList(V)) -> mark(isNatList(V))
active(isNatIList(zeros())) -> mark(tt())
active(isNatIList(cons(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2)))
active(isNatList(nil())) -> mark(tt())
active(isNatList(cons(V1,V2))) -> mark(and(isNat(V1),isNatList(V2)))
active(isNatList(take(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2)))
active(length(nil())) -> mark(0())
active(length(cons(N,L))) -> mark(U11(and(isNatList(L),isNat(N)),L))
active(take(0(),IL)) -> mark(U21(isNatIList(IL)))
active(take(s(M),cons(N,IL))) -> mark(U31(and(isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(U11(X1,X2)) -> U11(active(X1),X2)
active(s(X)) -> s(active(X))
active(length(X)) -> length(active(X))
active(U21(X)) -> U21(active(X))
active(U31(X1,X2,X3,X4)) -> U31(active(X1),X2,X3,X4)
active(take(X1,X2)) -> take(active(X1),X2)
active(take(X1,X2)) -> take(X1,active(X2))
active(and(X1,X2)) -> and(active(X1),X2)
cons(mark(X1),X2) -> mark(cons(X1,X2))
U11(mark(X1),X2) -> mark(U11(X1,X2))
s(mark(X)) -> mark(s(X))
length(mark(X)) -> mark(length(X))
U21(mark(X)) -> mark(U21(X))
U31(mark(X1),X2,X3,X4) -> mark(U31(X1,X2,X3,X4))
take(mark(X1),X2) -> mark(take(X1,X2))
take(X1,mark(X2)) -> mark(take(X1,X2))
and(mark(X1),X2) -> mark(and(X1,X2))
proper(zeros()) -> ok(zeros())
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(0()) -> ok(0())
proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
proper(tt()) -> ok(tt())
proper(s(X)) -> s(proper(X))
proper(length(X)) -> length(proper(X))
proper(U21(X)) -> U21(proper(X))
proper(nil()) -> ok(nil())
proper(U31(X1,X2,X3,X4)) -> U31(proper(X1),proper(X2),proper(X3),proper(X4))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
proper(and(X1,X2)) -> and(proper(X1),proper(X2))
proper(isNat(X)) -> isNat(proper(X))
proper(isNatList(X)) -> isNatList(proper(X))
proper(isNatIList(X)) -> isNatIList(proper(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
s(ok(X)) -> ok(s(X))
length(ok(X)) -> ok(length(X))
U21(ok(X)) -> ok(U21(X))
U31(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U31(X1,X2,X3,X4))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
and(ok(X1),ok(X2)) -> ok(and(X1,X2))
isNat(ok(X)) -> ok(isNat(X))
isNatList(ok(X)) -> ok(isNatList(X))
isNatIList(ok(X)) -> ok(isNatIList(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS nokinds C

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 OvConsOS nokinds C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  active(zeros()) -> mark(cons(0(), zeros()))
     , active(U11(tt(), L)) -> mark(s(length(L)))
     , active(U21(tt())) -> mark(nil())
     , active(U31(tt(), IL, M, N)) -> mark(cons(N, take(M, IL)))
     , active(and(tt(), X)) -> mark(X)
     , active(isNat(0())) -> mark(tt())
     , active(isNat(length(V1))) -> mark(isNatList(V1))
     , active(isNat(s(V1))) -> mark(isNat(V1))
     , active(isNatIList(V)) -> mark(isNatList(V))
     , active(isNatIList(zeros())) -> mark(tt())
     , active(isNatIList(cons(V1, V2))) ->
       mark(and(isNat(V1), isNatIList(V2)))
     , active(isNatList(nil())) -> mark(tt())
     , active(isNatList(cons(V1, V2))) ->
       mark(and(isNat(V1), isNatList(V2)))
     , active(isNatList(take(V1, V2))) ->
       mark(and(isNat(V1), isNatIList(V2)))
     , active(length(nil())) -> mark(0())
     , active(length(cons(N, L))) ->
       mark(U11(and(isNatList(L), isNat(N)), L))
     , active(take(0(), IL)) -> mark(U21(isNatIList(IL)))
     , active(take(s(M), cons(N, IL))) ->
       mark(U31(and(isNatIList(IL), and(isNat(M), isNat(N))), IL, M, N))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(U11(X1, X2)) -> U11(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(length(X)) -> length(active(X))
     , active(U21(X)) -> U21(active(X))
     , active(U31(X1, X2, X3, X4)) -> U31(active(X1), X2, X3, X4)
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(and(X1, X2)) -> and(active(X1), X2)
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , U11(mark(X1), X2) -> mark(U11(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , length(mark(X)) -> mark(length(X))
     , U21(mark(X)) -> mark(U21(X))
     , U31(mark(X1), X2, X3, X4) -> mark(U31(X1, X2, X3, X4))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(X1, mark(X2)) -> mark(take(X1, X2))
     , and(mark(X1), X2) -> mark(and(X1, X2))
     , proper(zeros()) -> ok(zeros())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
     , proper(tt()) -> ok(tt())
     , proper(s(X)) -> s(proper(X))
     , proper(length(X)) -> length(proper(X))
     , proper(U21(X)) -> U21(proper(X))
     , proper(nil()) -> ok(nil())
     , proper(U31(X1, X2, X3, X4)) ->
       U31(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , proper(and(X1, X2)) -> and(proper(X1), proper(X2))
     , proper(isNat(X)) -> isNat(proper(X))
     , proper(isNatList(X)) -> isNatList(proper(X))
     , proper(isNatIList(X)) -> isNatIList(proper(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
     , s(ok(X)) -> ok(s(X))
     , length(ok(X)) -> ok(length(X))
     , U21(ok(X)) -> ok(U21(X))
     , U31(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U31(X1, X2, X3, X4))
     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
     , and(ok(X1), ok(X2)) -> ok(and(X1, X2))
     , isNat(ok(X)) -> ok(isNat(X))
     , isNatList(ok(X)) -> ok(isNatList(X))
     , isNatIList(ok(X)) -> ok(isNatIList(X))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS nokinds C

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 OvConsOS nokinds C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  active(zeros()) -> mark(cons(0(), zeros()))
     , active(U11(tt(), L)) -> mark(s(length(L)))
     , active(U21(tt())) -> mark(nil())
     , active(U31(tt(), IL, M, N)) -> mark(cons(N, take(M, IL)))
     , active(and(tt(), X)) -> mark(X)
     , active(isNat(0())) -> mark(tt())
     , active(isNat(length(V1))) -> mark(isNatList(V1))
     , active(isNat(s(V1))) -> mark(isNat(V1))
     , active(isNatIList(V)) -> mark(isNatList(V))
     , active(isNatIList(zeros())) -> mark(tt())
     , active(isNatIList(cons(V1, V2))) ->
       mark(and(isNat(V1), isNatIList(V2)))
     , active(isNatList(nil())) -> mark(tt())
     , active(isNatList(cons(V1, V2))) ->
       mark(and(isNat(V1), isNatList(V2)))
     , active(isNatList(take(V1, V2))) ->
       mark(and(isNat(V1), isNatIList(V2)))
     , active(length(nil())) -> mark(0())
     , active(length(cons(N, L))) ->
       mark(U11(and(isNatList(L), isNat(N)), L))
     , active(take(0(), IL)) -> mark(U21(isNatIList(IL)))
     , active(take(s(M), cons(N, IL))) ->
       mark(U31(and(isNatIList(IL), and(isNat(M), isNat(N))), IL, M, N))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(U11(X1, X2)) -> U11(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(length(X)) -> length(active(X))
     , active(U21(X)) -> U21(active(X))
     , active(U31(X1, X2, X3, X4)) -> U31(active(X1), X2, X3, X4)
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(X1, X2)) -> take(X1, active(X2))
     , active(and(X1, X2)) -> and(active(X1), X2)
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , U11(mark(X1), X2) -> mark(U11(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , length(mark(X)) -> mark(length(X))
     , U21(mark(X)) -> mark(U21(X))
     , U31(mark(X1), X2, X3, X4) -> mark(U31(X1, X2, X3, X4))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(X1, mark(X2)) -> mark(take(X1, X2))
     , and(mark(X1), X2) -> mark(and(X1, X2))
     , proper(zeros()) -> ok(zeros())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(0()) -> ok(0())
     , proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
     , proper(tt()) -> ok(tt())
     , proper(s(X)) -> s(proper(X))
     , proper(length(X)) -> length(proper(X))
     , proper(U21(X)) -> U21(proper(X))
     , proper(nil()) -> ok(nil())
     , proper(U31(X1, X2, X3, X4)) ->
       U31(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , proper(and(X1, X2)) -> and(proper(X1), proper(X2))
     , proper(isNat(X)) -> isNat(proper(X))
     , proper(isNatList(X)) -> isNatList(proper(X))
     , proper(isNatIList(X)) -> isNatIList(proper(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
     , s(ok(X)) -> ok(s(X))
     , length(ok(X)) -> ok(length(X))
     , U21(ok(X)) -> ok(U21(X))
     , U31(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U31(X1, X2, X3, X4))
     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
     , and(ok(X1), ok(X2)) -> ok(and(X1, X2))
     , isNat(ok(X)) -> ok(isNat(X))
     , isNatList(ok(X)) -> ok(isNatList(X))
     , isNatIList(ok(X)) -> ok(isNatIList(X))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds