Problem Transformed CSR 04 Ex5 7 Luc97 C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex5 7 Luc97 C

stdout:

MAYBE

Problem:
active(dbl(0())) -> mark(0())
active(dbl(s(X))) -> mark(s(s(dbl(X))))
active(dbls(nil())) -> mark(nil())
active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
active(sel(0(),cons(X,Y))) -> mark(X)
active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
active(indx(nil(),X)) -> mark(nil())
active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
active(from(X)) -> mark(cons(X,from(s(X))))
active(dbl1(0())) -> mark(01())
active(dbl1(s(X))) -> mark(s1(s1(dbl1(X))))
active(sel1(0(),cons(X,Y))) -> mark(X)
active(sel1(s(X),cons(Y,Z))) -> mark(sel1(X,Z))
active(quote(0())) -> mark(01())
active(quote(s(X))) -> mark(s1(quote(X)))
active(quote(dbl(X))) -> mark(dbl1(X))
active(quote(sel(X,Y))) -> mark(sel1(X,Y))
active(dbl(X)) -> dbl(active(X))
active(dbls(X)) -> dbls(active(X))
active(sel(X1,X2)) -> sel(active(X1),X2)
active(sel(X1,X2)) -> sel(X1,active(X2))
active(indx(X1,X2)) -> indx(active(X1),X2)
active(dbl1(X)) -> dbl1(active(X))
active(s1(X)) -> s1(active(X))
active(sel1(X1,X2)) -> sel1(active(X1),X2)
active(sel1(X1,X2)) -> sel1(X1,active(X2))
active(quote(X)) -> quote(active(X))
dbl(mark(X)) -> mark(dbl(X))
dbls(mark(X)) -> mark(dbls(X))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
indx(mark(X1),X2) -> mark(indx(X1,X2))
dbl1(mark(X)) -> mark(dbl1(X))
s1(mark(X)) -> mark(s1(X))
sel1(mark(X1),X2) -> mark(sel1(X1,X2))
sel1(X1,mark(X2)) -> mark(sel1(X1,X2))
quote(mark(X)) -> mark(quote(X))
proper(dbl(X)) -> dbl(proper(X))
proper(0()) -> ok(0())
proper(s(X)) -> s(proper(X))
proper(dbls(X)) -> dbls(proper(X))
proper(nil()) -> ok(nil())
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
proper(from(X)) -> from(proper(X))
proper(dbl1(X)) -> dbl1(proper(X))
proper(01()) -> ok(01())
proper(s1(X)) -> s1(proper(X))
proper(sel1(X1,X2)) -> sel1(proper(X1),proper(X2))
proper(quote(X)) -> quote(proper(X))
dbl(ok(X)) -> ok(dbl(X))
s(ok(X)) -> ok(s(X))
dbls(ok(X)) -> ok(dbls(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
from(ok(X)) -> ok(from(X))
dbl1(ok(X)) -> ok(dbl1(X))
s1(ok(X)) -> ok(s1(X))
sel1(ok(X1),ok(X2)) -> ok(sel1(X1,X2))
quote(ok(X)) -> ok(quote(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 Ex5 7 Luc97 C

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex5 7 Luc97 C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  active(dbl(0())) -> mark(0())
     , active(dbl(s(X))) -> mark(s(s(dbl(X))))
     , active(dbls(nil())) -> mark(nil())
     , active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y)))
     , active(sel(0(), cons(X, Y))) -> mark(X)
     , active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
     , active(indx(nil(), X)) -> mark(nil())
     , active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z)))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(dbl1(0())) -> mark(01())
     , active(dbl1(s(X))) -> mark(s1(s1(dbl1(X))))
     , active(sel1(0(), cons(X, Y))) -> mark(X)
     , active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
     , active(quote(0())) -> mark(01())
     , active(quote(s(X))) -> mark(s1(quote(X)))
     , active(quote(dbl(X))) -> mark(dbl1(X))
     , active(quote(sel(X, Y))) -> mark(sel1(X, Y))
     , active(dbl(X)) -> dbl(active(X))
     , active(dbls(X)) -> dbls(active(X))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(indx(X1, X2)) -> indx(active(X1), X2)
     , active(dbl1(X)) -> dbl1(active(X))
     , active(s1(X)) -> s1(active(X))
     , active(sel1(X1, X2)) -> sel1(active(X1), X2)
     , active(sel1(X1, X2)) -> sel1(X1, active(X2))
     , active(quote(X)) -> quote(active(X))
     , dbl(mark(X)) -> mark(dbl(X))
     , dbls(mark(X)) -> mark(dbls(X))
     , sel(mark(X1), X2) -> mark(sel(X1, X2))
     , sel(X1, mark(X2)) -> mark(sel(X1, X2))
     , indx(mark(X1), X2) -> mark(indx(X1, X2))
     , dbl1(mark(X)) -> mark(dbl1(X))
     , s1(mark(X)) -> mark(s1(X))
     , sel1(mark(X1), X2) -> mark(sel1(X1, X2))
     , sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
     , quote(mark(X)) -> mark(quote(X))
     , proper(dbl(X)) -> dbl(proper(X))
     , proper(0()) -> ok(0())
     , proper(s(X)) -> s(proper(X))
     , proper(dbls(X)) -> dbls(proper(X))
     , proper(nil()) -> ok(nil())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(indx(X1, X2)) -> indx(proper(X1), proper(X2))
     , proper(from(X)) -> from(proper(X))
     , proper(dbl1(X)) -> dbl1(proper(X))
     , proper(01()) -> ok(01())
     , proper(s1(X)) -> s1(proper(X))
     , proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
     , proper(quote(X)) -> quote(proper(X))
     , dbl(ok(X)) -> ok(dbl(X))
     , s(ok(X)) -> ok(s(X))
     , dbls(ok(X)) -> ok(dbls(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
     , indx(ok(X1), ok(X2)) -> ok(indx(X1, X2))
     , from(ok(X)) -> ok(from(X))
     , dbl1(ok(X)) -> ok(dbl1(X))
     , s1(ok(X)) -> ok(s1(X))
     , sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
     , quote(ok(X)) -> ok(quote(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 Ex5 7 Luc97 C

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex5 7 Luc97 C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  active(dbl(0())) -> mark(0())
     , active(dbl(s(X))) -> mark(s(s(dbl(X))))
     , active(dbls(nil())) -> mark(nil())
     , active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y)))
     , active(sel(0(), cons(X, Y))) -> mark(X)
     , active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
     , active(indx(nil(), X)) -> mark(nil())
     , active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z)))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(dbl1(0())) -> mark(01())
     , active(dbl1(s(X))) -> mark(s1(s1(dbl1(X))))
     , active(sel1(0(), cons(X, Y))) -> mark(X)
     , active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z))
     , active(quote(0())) -> mark(01())
     , active(quote(s(X))) -> mark(s1(quote(X)))
     , active(quote(dbl(X))) -> mark(dbl1(X))
     , active(quote(sel(X, Y))) -> mark(sel1(X, Y))
     , active(dbl(X)) -> dbl(active(X))
     , active(dbls(X)) -> dbls(active(X))
     , active(sel(X1, X2)) -> sel(active(X1), X2)
     , active(sel(X1, X2)) -> sel(X1, active(X2))
     , active(indx(X1, X2)) -> indx(active(X1), X2)
     , active(dbl1(X)) -> dbl1(active(X))
     , active(s1(X)) -> s1(active(X))
     , active(sel1(X1, X2)) -> sel1(active(X1), X2)
     , active(sel1(X1, X2)) -> sel1(X1, active(X2))
     , active(quote(X)) -> quote(active(X))
     , dbl(mark(X)) -> mark(dbl(X))
     , dbls(mark(X)) -> mark(dbls(X))
     , sel(mark(X1), X2) -> mark(sel(X1, X2))
     , sel(X1, mark(X2)) -> mark(sel(X1, X2))
     , indx(mark(X1), X2) -> mark(indx(X1, X2))
     , dbl1(mark(X)) -> mark(dbl1(X))
     , s1(mark(X)) -> mark(s1(X))
     , sel1(mark(X1), X2) -> mark(sel1(X1, X2))
     , sel1(X1, mark(X2)) -> mark(sel1(X1, X2))
     , quote(mark(X)) -> mark(quote(X))
     , proper(dbl(X)) -> dbl(proper(X))
     , proper(0()) -> ok(0())
     , proper(s(X)) -> s(proper(X))
     , proper(dbls(X)) -> dbls(proper(X))
     , proper(nil()) -> ok(nil())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
     , proper(indx(X1, X2)) -> indx(proper(X1), proper(X2))
     , proper(from(X)) -> from(proper(X))
     , proper(dbl1(X)) -> dbl1(proper(X))
     , proper(01()) -> ok(01())
     , proper(s1(X)) -> s1(proper(X))
     , proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2))
     , proper(quote(X)) -> quote(proper(X))
     , dbl(ok(X)) -> ok(dbl(X))
     , s(ok(X)) -> ok(s(X))
     , dbls(ok(X)) -> ok(dbls(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
     , indx(ok(X1), ok(X2)) -> ok(indx(X1, X2))
     , from(ok(X)) -> ok(from(X))
     , dbl1(ok(X)) -> ok(dbl1(X))
     , s1(ok(X)) -> ok(s1(X))
     , sel1(ok(X1), ok(X2)) -> ok(sel1(X1, X2))
     , quote(ok(X)) -> ok(quote(X))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds