Problem Transformed CSR 04 OvConsOS nosorts noand C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 OvConsOS nosorts noand C

stdout:

MAYBE

Problem:
active(zeros()) -> mark(cons(0(),zeros()))
active(U11(tt(),L)) -> mark(U12(tt(),L))
active(U12(tt(),L)) -> mark(s(length(L)))
active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N))
active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N))
active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
active(length(nil())) -> mark(0())
active(length(cons(N,L))) -> mark(U11(tt(),L))
active(take(0(),IL)) -> mark(nil())
active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(U11(X1,X2)) -> U11(active(X1),X2)
active(U12(X1,X2)) -> U12(active(X1),X2)
active(s(X)) -> s(active(X))
active(length(X)) -> length(active(X))
active(U21(X1,X2,X3,X4)) -> U21(active(X1),X2,X3,X4)
active(U22(X1,X2,X3,X4)) -> U22(active(X1),X2,X3,X4)
active(U23(X1,X2,X3,X4)) -> U23(active(X1),X2,X3,X4)
active(take(X1,X2)) -> take(active(X1),X2)
active(take(X1,X2)) -> take(X1,active(X2))
cons(mark(X1),X2) -> mark(cons(X1,X2))
U11(mark(X1),X2) -> mark(U11(X1,X2))
U12(mark(X1),X2) -> mark(U12(X1,X2))
s(mark(X)) -> mark(s(X))
length(mark(X)) -> mark(length(X))
U21(mark(X1),X2,X3,X4) -> mark(U21(X1,X2,X3,X4))
U22(mark(X1),X2,X3,X4) -> mark(U22(X1,X2,X3,X4))
U23(mark(X1),X2,X3,X4) -> mark(U23(X1,X2,X3,X4))
take(mark(X1),X2) -> mark(take(X1,X2))
take(X1,mark(X2)) -> mark(take(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(U12(X1,X2)) -> U12(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(length(X)) -> length(proper(X))
proper(U21(X1,X2,X3,X4)) -> U21(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U22(X1,X2,X3,X4)) -> U22(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U23(X1,X2,X3,X4)) -> U23(proper(X1),proper(X2),proper(X3),proper(X4))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
proper(nil()) -> ok(nil())
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
s(ok(X)) -> ok(s(X))
length(ok(X)) -> ok(length(X))
U21(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U21(X1,X2,X3,X4))
U22(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U22(X1,X2,X3,X4))
U23(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U23(X1,X2,X3,X4))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 OvConsOS nosorts noand C

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 OvConsOS nosorts noand 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(U12(tt(), L))
     , active(U12(tt(), L)) -> mark(s(length(L)))
     , active(U21(tt(), IL, M, N)) -> mark(U22(tt(), IL, M, N))
     , active(U22(tt(), IL, M, N)) -> mark(U23(tt(), IL, M, N))
     , active(U23(tt(), IL, M, N)) -> mark(cons(N, take(M, IL)))
     , active(length(nil())) -> mark(0())
     , active(length(cons(N, L))) -> mark(U11(tt(), L))
     , active(take(0(), IL)) -> mark(nil())
     , active(take(s(M), cons(N, IL))) -> mark(U21(tt(), IL, M, N))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(U11(X1, X2)) -> U11(active(X1), X2)
     , active(U12(X1, X2)) -> U12(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(length(X)) -> length(active(X))
     , active(U21(X1, X2, X3, X4)) -> U21(active(X1), X2, X3, X4)
     , active(U22(X1, X2, X3, X4)) -> U22(active(X1), X2, X3, X4)
     , active(U23(X1, X2, X3, X4)) -> U23(active(X1), X2, X3, X4)
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(X1, X2)) -> take(X1, active(X2))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , U11(mark(X1), X2) -> mark(U11(X1, X2))
     , U12(mark(X1), X2) -> mark(U12(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , length(mark(X)) -> mark(length(X))
     , U21(mark(X1), X2, X3, X4) -> mark(U21(X1, X2, X3, X4))
     , U22(mark(X1), X2, X3, X4) -> mark(U22(X1, X2, X3, X4))
     , U23(mark(X1), X2, X3, X4) -> mark(U23(X1, X2, X3, X4))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(X1, mark(X2)) -> mark(take(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(U12(X1, X2)) -> U12(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(length(X)) -> length(proper(X))
     , proper(U21(X1, X2, X3, X4)) ->
       U21(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U22(X1, X2, X3, X4)) ->
       U22(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U23(X1, X2, X3, X4)) ->
       U23(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , proper(nil()) -> ok(nil())
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
     , U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
     , s(ok(X)) -> ok(s(X))
     , length(ok(X)) -> ok(length(X))
     , U21(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U21(X1, X2, X3, X4))
     , U22(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U22(X1, X2, X3, X4))
     , U23(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U23(X1, X2, X3, X4))
     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
     , 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	YES(?,O(n^1))
Input	Transformed CSR 04 OvConsOS nosorts noand C

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 OvConsOS nosorts noand 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(U12(tt(), L))
     , active(U12(tt(), L)) -> mark(s(length(L)))
     , active(U21(tt(), IL, M, N)) -> mark(U22(tt(), IL, M, N))
     , active(U22(tt(), IL, M, N)) -> mark(U23(tt(), IL, M, N))
     , active(U23(tt(), IL, M, N)) -> mark(cons(N, take(M, IL)))
     , active(length(nil())) -> mark(0())
     , active(length(cons(N, L))) -> mark(U11(tt(), L))
     , active(take(0(), IL)) -> mark(nil())
     , active(take(s(M), cons(N, IL))) -> mark(U21(tt(), IL, M, N))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(U11(X1, X2)) -> U11(active(X1), X2)
     , active(U12(X1, X2)) -> U12(active(X1), X2)
     , active(s(X)) -> s(active(X))
     , active(length(X)) -> length(active(X))
     , active(U21(X1, X2, X3, X4)) -> U21(active(X1), X2, X3, X4)
     , active(U22(X1, X2, X3, X4)) -> U22(active(X1), X2, X3, X4)
     , active(U23(X1, X2, X3, X4)) -> U23(active(X1), X2, X3, X4)
     , active(take(X1, X2)) -> take(active(X1), X2)
     , active(take(X1, X2)) -> take(X1, active(X2))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , U11(mark(X1), X2) -> mark(U11(X1, X2))
     , U12(mark(X1), X2) -> mark(U12(X1, X2))
     , s(mark(X)) -> mark(s(X))
     , length(mark(X)) -> mark(length(X))
     , U21(mark(X1), X2, X3, X4) -> mark(U21(X1, X2, X3, X4))
     , U22(mark(X1), X2, X3, X4) -> mark(U22(X1, X2, X3, X4))
     , U23(mark(X1), X2, X3, X4) -> mark(U23(X1, X2, X3, X4))
     , take(mark(X1), X2) -> mark(take(X1, X2))
     , take(X1, mark(X2)) -> mark(take(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(U12(X1, X2)) -> U12(proper(X1), proper(X2))
     , proper(s(X)) -> s(proper(X))
     , proper(length(X)) -> length(proper(X))
     , proper(U21(X1, X2, X3, X4)) ->
       U21(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U22(X1, X2, X3, X4)) ->
       U22(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(U23(X1, X2, X3, X4)) ->
       U23(proper(X1), proper(X2), proper(X3), proper(X4))
     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
     , proper(nil()) -> ok(nil())
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
     , U12(ok(X1), ok(X2)) -> ok(U12(X1, X2))
     , s(ok(X)) -> ok(s(X))
     , length(ok(X)) -> ok(length(X))
     , U21(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U21(X1, X2, X3, X4))
     , U22(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U22(X1, X2, X3, X4))
     , U23(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U23(X1, X2, X3, X4))
     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds