R
↳Dependency Pair Analysis
ACTIVE(add(s(X), Y)) -> S(add(X, Y))
ACTIVE(add(s(X), Y)) -> ADD(X, Y)
ACTIVE(first(s(X), cons(Y, Z))) -> CONS(Y, first(X, Z))
ACTIVE(first(s(X), cons(Y, Z))) -> FIRST(X, Z)
ACTIVE(from(X)) -> CONS(X, from(s(X)))
ACTIVE(from(X)) -> FROM(s(X))
ACTIVE(from(X)) -> S(X)
ACTIVE(and(X1, X2)) -> AND(active(X1), X2)
ACTIVE(and(X1, X2)) -> ACTIVE(X1)
ACTIVE(if(X1, X2, X3)) -> IF(active(X1), X2, X3)
ACTIVE(if(X1, X2, X3)) -> ACTIVE(X1)
ACTIVE(add(X1, X2)) -> ADD(active(X1), X2)
ACTIVE(add(X1, X2)) -> ACTIVE(X1)
ACTIVE(first(X1, X2)) -> FIRST(active(X1), X2)
ACTIVE(first(X1, X2)) -> ACTIVE(X1)
ACTIVE(first(X1, X2)) -> FIRST(X1, active(X2))
ACTIVE(first(X1, X2)) -> ACTIVE(X2)
AND(mark(X1), X2) -> AND(X1, X2)
AND(ok(X1), ok(X2)) -> AND(X1, X2)
IF(mark(X1), X2, X3) -> IF(X1, X2, X3)
IF(ok(X1), ok(X2), ok(X3)) -> IF(X1, X2, X3)
ADD(mark(X1), X2) -> ADD(X1, X2)
ADD(ok(X1), ok(X2)) -> ADD(X1, X2)
FIRST(mark(X1), X2) -> FIRST(X1, X2)
FIRST(X1, mark(X2)) -> FIRST(X1, X2)
FIRST(ok(X1), ok(X2)) -> FIRST(X1, X2)
PROPER(and(X1, X2)) -> AND(proper(X1), proper(X2))
PROPER(and(X1, X2)) -> PROPER(X1)
PROPER(and(X1, X2)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> IF(proper(X1), proper(X2), proper(X3))
PROPER(if(X1, X2, X3)) -> PROPER(X1)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(add(X1, X2)) -> ADD(proper(X1), proper(X2))
PROPER(add(X1, X2)) -> PROPER(X1)
PROPER(add(X1, X2)) -> PROPER(X2)
PROPER(s(X)) -> S(proper(X))
PROPER(s(X)) -> PROPER(X)
PROPER(first(X1, X2)) -> FIRST(proper(X1), proper(X2))
PROPER(first(X1, X2)) -> PROPER(X1)
PROPER(first(X1, X2)) -> PROPER(X2)
PROPER(cons(X1, X2)) -> CONS(proper(X1), proper(X2))
PROPER(cons(X1, X2)) -> PROPER(X1)
PROPER(cons(X1, X2)) -> PROPER(X2)
PROPER(from(X)) -> FROM(proper(X))
PROPER(from(X)) -> PROPER(X)
S(ok(X)) -> S(X)
CONS(ok(X1), ok(X2)) -> CONS(X1, X2)
FROM(ok(X)) -> FROM(X)
TOP(mark(X)) -> TOP(proper(X))
TOP(mark(X)) -> PROPER(X)
TOP(ok(X)) -> TOP(active(X))
TOP(ok(X)) -> ACTIVE(X)
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
S(ok(X)) -> S(X)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
S(ok(X)) -> S(X)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = x1 POL(proper(x1)) = 1 POL(and(x1, x2)) = x2 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 1 + x1 POL(add(x1, x2)) = x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x2 POL(0) = 0 POL(first(x1, x2)) = x1 POL(cons(x1, x2)) = x1 POL(nil) = 0 POL(s(x1)) = x1 POL(S(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 11
↳Dependency Graph
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polynomial Ordering
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
ADD(ok(X1), ok(X2)) -> ADD(X1, X2)
ADD(mark(X1), X2) -> ADD(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ADD(ok(X1), ok(X2)) -> ADD(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = x1 POL(proper(x1)) = 1 POL(and(x1, x2)) = x2 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 1 + x1 POL(ADD(x1, x2)) = x2 POL(add(x1, x2)) = x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x2 POL(first(x1, x2)) = x1 POL(0) = 0 POL(cons(x1, x2)) = x1 POL(nil) = 0 POL(s(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 12
↳Polynomial Ordering
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
ADD(mark(X1), X2) -> ADD(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ADD(mark(X1), X2) -> ADD(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 1 POL(proper(x1)) = x1 POL(and(x1, x2)) = 1 + x1 + x2 POL(false) = 1 POL(true) = 1 POL(mark(x1)) = 1 + x1 POL(ok(x1)) = 0 POL(ADD(x1, x2)) = x1 + x2 POL(add(x1, x2)) = 1 + x1 + x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(first(x1, x2)) = x1 + x2 POL(0) = 1 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = 1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 12
↳Polo
...
→DP Problem 13
↳Dependency Graph
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polynomial Ordering
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
CONS(ok(X1), ok(X2)) -> CONS(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
CONS(ok(X1), ok(X2)) -> CONS(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = x1 POL(proper(x1)) = 1 POL(and(x1, x2)) = x2 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 1 + x1 POL(CONS(x1, x2)) = x1 POL(add(x1, x2)) = x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x2 POL(first(x1, x2)) = x1 POL(0) = 0 POL(cons(x1, x2)) = x1 POL(nil) = 0 POL(s(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 14
↳Dependency Graph
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polynomial Ordering
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
FIRST(ok(X1), ok(X2)) -> FIRST(X1, X2)
FIRST(X1, mark(X2)) -> FIRST(X1, X2)
FIRST(mark(X1), X2) -> FIRST(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
FIRST(mark(X1), X2) -> FIRST(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 1 POL(proper(x1)) = x1 POL(and(x1, x2)) = 1 + x1 + x2 POL(false) = 1 POL(true) = 1 POL(mark(x1)) = 1 + x1 POL(ok(x1)) = x1 POL(add(x1, x2)) = 1 + x1 + x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(0) = 1 POL(first(x1, x2)) = x1 + x2 POL(cons(x1, x2)) = 0 POL(FIRST(x1, x2)) = x1 POL(nil) = 0 POL(s(x1)) = 1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 15
↳Polynomial Ordering
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
FIRST(ok(X1), ok(X2)) -> FIRST(X1, X2)
FIRST(X1, mark(X2)) -> FIRST(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
FIRST(ok(X1), ok(X2)) -> FIRST(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = x1 POL(proper(x1)) = 1 POL(and(x1, x2)) = x2 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 1 + x1 POL(add(x1, x2)) = x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x2 POL(0) = 0 POL(first(x1, x2)) = x1 POL(cons(x1, x2)) = x1 POL(FIRST(x1, x2)) = x1 POL(nil) = 0 POL(s(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 15
↳Polo
...
→DP Problem 16
↳Polynomial Ordering
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
FIRST(X1, mark(X2)) -> FIRST(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
FIRST(X1, mark(X2)) -> FIRST(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 1 POL(proper(x1)) = x1 POL(and(x1, x2)) = 1 + x1 + x2 POL(false) = 1 POL(true) = 1 POL(mark(x1)) = 1 + x1 POL(ok(x1)) = 0 POL(add(x1, x2)) = 1 + x1 + x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(0) = 1 POL(first(x1, x2)) = x1 + x2 POL(cons(x1, x2)) = 0 POL(FIRST(x1, x2)) = x1 + x2 POL(nil) = 0 POL(s(x1)) = 1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 15
↳Polo
...
→DP Problem 17
↳Dependency Graph
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polynomial Ordering
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
FROM(ok(X)) -> FROM(X)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
FROM(ok(X)) -> FROM(X)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(FROM(x1)) = x1 POL(from(x1)) = x1 POL(proper(x1)) = 1 POL(and(x1, x2)) = x2 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 1 + x1 POL(add(x1, x2)) = x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x2 POL(first(x1, x2)) = x1 POL(0) = 0 POL(cons(x1, x2)) = x1 POL(nil) = 0 POL(s(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 18
↳Dependency Graph
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polynomial Ordering
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
AND(ok(X1), ok(X2)) -> AND(X1, X2)
AND(mark(X1), X2) -> AND(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
AND(ok(X1), ok(X2)) -> AND(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = x1 POL(proper(x1)) = 1 POL(and(x1, x2)) = x2 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 1 + x1 POL(AND(x1, x2)) = x2 POL(add(x1, x2)) = x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x2 POL(first(x1, x2)) = x1 POL(0) = 0 POL(cons(x1, x2)) = x1 POL(nil) = 0 POL(s(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 19
↳Polynomial Ordering
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
AND(mark(X1), X2) -> AND(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
AND(mark(X1), X2) -> AND(X1, X2)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 1 POL(proper(x1)) = x1 POL(and(x1, x2)) = 1 + x1 + x2 POL(false) = 1 POL(true) = 1 POL(mark(x1)) = 1 + x1 POL(ok(x1)) = 0 POL(AND(x1, x2)) = x1 + x2 POL(add(x1, x2)) = 1 + x1 + x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(first(x1, x2)) = x1 + x2 POL(0) = 1 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = 1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 19
↳Polo
...
→DP Problem 20
↳Dependency Graph
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polynomial Ordering
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
IF(ok(X1), ok(X2), ok(X3)) -> IF(X1, X2, X3)
IF(mark(X1), X2, X3) -> IF(X1, X2, X3)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
IF(ok(X1), ok(X2), ok(X3)) -> IF(X1, X2, X3)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = x1 POL(proper(x1)) = 1 POL(and(x1, x2)) = x2 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 1 + x1 POL(IF(x1, x2, x3)) = x2 POL(add(x1, x2)) = x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x2 POL(first(x1, x2)) = x1 POL(0) = 0 POL(cons(x1, x2)) = x1 POL(nil) = 0 POL(s(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 21
↳Polynomial Ordering
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
IF(mark(X1), X2, X3) -> IF(X1, X2, X3)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
IF(mark(X1), X2, X3) -> IF(X1, X2, X3)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 1 POL(proper(x1)) = x1 POL(and(x1, x2)) = 1 + x1 + x2 POL(false) = 1 POL(true) = 1 POL(mark(x1)) = 1 + x1 POL(ok(x1)) = 0 POL(IF(x1, x2, x3)) = x1 + x2 + x3 POL(add(x1, x2)) = 1 + x1 + x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(first(x1, x2)) = x1 + x2 POL(0) = 1 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = 1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 21
↳Polo
...
→DP Problem 22
↳Dependency Graph
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polynomial Ordering
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
ACTIVE(first(X1, X2)) -> ACTIVE(X2)
ACTIVE(first(X1, X2)) -> ACTIVE(X1)
ACTIVE(add(X1, X2)) -> ACTIVE(X1)
ACTIVE(if(X1, X2, X3)) -> ACTIVE(X1)
ACTIVE(and(X1, X2)) -> ACTIVE(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ACTIVE(and(X1, X2)) -> ACTIVE(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 0 POL(proper(x1)) = x1 POL(and(x1, x2)) = 1 + x1 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 0 POL(add(x1, x2)) = x1 POL(top(x1)) = 0 POL(ACTIVE(x1)) = x1 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x1 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = 0
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 23
↳Polynomial Ordering
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
ACTIVE(first(X1, X2)) -> ACTIVE(X2)
ACTIVE(first(X1, X2)) -> ACTIVE(X1)
ACTIVE(add(X1, X2)) -> ACTIVE(X1)
ACTIVE(if(X1, X2, X3)) -> ACTIVE(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ACTIVE(if(X1, X2, X3)) -> ACTIVE(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 0 POL(proper(x1)) = x1 POL(and(x1, x2)) = 0 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 0 POL(add(x1, x2)) = x1 POL(top(x1)) = 0 POL(ACTIVE(x1)) = x1 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = 1 + x1 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = 0
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 23
↳Polo
...
→DP Problem 24
↳Polynomial Ordering
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
ACTIVE(first(X1, X2)) -> ACTIVE(X2)
ACTIVE(first(X1, X2)) -> ACTIVE(X1)
ACTIVE(add(X1, X2)) -> ACTIVE(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ACTIVE(add(X1, X2)) -> ACTIVE(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 0 POL(proper(x1)) = x1 POL(and(x1, x2)) = 0 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 0 POL(add(x1, x2)) = 1 + x1 POL(top(x1)) = 0 POL(ACTIVE(x1)) = x1 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = 0 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = 0
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 23
↳Polo
...
→DP Problem 25
↳Polynomial Ordering
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
ACTIVE(first(X1, X2)) -> ACTIVE(X2)
ACTIVE(first(X1, X2)) -> ACTIVE(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
ACTIVE(first(X1, X2)) -> ACTIVE(X2)
ACTIVE(first(X1, X2)) -> ACTIVE(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 0 POL(proper(x1)) = x1 POL(and(x1, x2)) = 0 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 0 POL(add(x1, x2)) = 0 POL(top(x1)) = 0 POL(ACTIVE(x1)) = 1 + x1 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = 0 POL(first(x1, x2)) = 1 + x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = 0
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 23
↳Polo
...
→DP Problem 26
↳Dependency Graph
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polynomial Ordering
→DP Problem 10
↳Polo
PROPER(from(X)) -> PROPER(X)
PROPER(cons(X1, X2)) -> PROPER(X2)
PROPER(cons(X1, X2)) -> PROPER(X1)
PROPER(first(X1, X2)) -> PROPER(X2)
PROPER(first(X1, X2)) -> PROPER(X1)
PROPER(s(X)) -> PROPER(X)
PROPER(add(X1, X2)) -> PROPER(X2)
PROPER(add(X1, X2)) -> PROPER(X1)
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
PROPER(and(X1, X2)) -> PROPER(X2)
PROPER(and(X1, X2)) -> PROPER(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(from(X)) -> PROPER(X)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 1 + x1 POL(proper(x1)) = x1 POL(and(x1, x2)) = x1 + x2 POL(PROPER(x1)) = x1 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 0 POL(add(x1, x2)) = x1 + x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = x1 + x2 POL(nil) = 0 POL(s(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 27
↳Polynomial Ordering
→DP Problem 10
↳Polo
PROPER(cons(X1, X2)) -> PROPER(X2)
PROPER(cons(X1, X2)) -> PROPER(X1)
PROPER(first(X1, X2)) -> PROPER(X2)
PROPER(first(X1, X2)) -> PROPER(X1)
PROPER(s(X)) -> PROPER(X)
PROPER(add(X1, X2)) -> PROPER(X2)
PROPER(add(X1, X2)) -> PROPER(X1)
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
PROPER(and(X1, X2)) -> PROPER(X2)
PROPER(and(X1, X2)) -> PROPER(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(cons(X1, X2)) -> PROPER(X2)
PROPER(cons(X1, X2)) -> PROPER(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 0 POL(proper(x1)) = x1 POL(and(x1, x2)) = x1 + x2 POL(PROPER(x1)) = x1 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 0 POL(add(x1, x2)) = x1 + x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 1 + x1 + x2 POL(nil) = 0 POL(s(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 28
↳Polynomial Ordering
→DP Problem 10
↳Polo
PROPER(first(X1, X2)) -> PROPER(X2)
PROPER(first(X1, X2)) -> PROPER(X1)
PROPER(s(X)) -> PROPER(X)
PROPER(add(X1, X2)) -> PROPER(X2)
PROPER(add(X1, X2)) -> PROPER(X1)
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
PROPER(and(X1, X2)) -> PROPER(X2)
PROPER(and(X1, X2)) -> PROPER(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(and(X1, X2)) -> PROPER(X2)
PROPER(and(X1, X2)) -> PROPER(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 0 POL(proper(x1)) = x1 POL(and(x1, x2)) = 1 + x1 + x2 POL(PROPER(x1)) = x1 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 0 POL(add(x1, x2)) = x1 + x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 29
↳Polynomial Ordering
→DP Problem 10
↳Polo
PROPER(first(X1, X2)) -> PROPER(X2)
PROPER(first(X1, X2)) -> PROPER(X1)
PROPER(s(X)) -> PROPER(X)
PROPER(add(X1, X2)) -> PROPER(X2)
PROPER(add(X1, X2)) -> PROPER(X1)
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(s(X)) -> PROPER(X)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 0 POL(proper(x1)) = x1 POL(and(x1, x2)) = 0 POL(PROPER(x1)) = x1 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 0 POL(add(x1, x2)) = x1 + x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 30
↳Polynomial Ordering
→DP Problem 10
↳Polo
PROPER(first(X1, X2)) -> PROPER(X2)
PROPER(first(X1, X2)) -> PROPER(X1)
PROPER(add(X1, X2)) -> PROPER(X2)
PROPER(add(X1, X2)) -> PROPER(X1)
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(if(X1, X2, X3)) -> PROPER(X3)
PROPER(if(X1, X2, X3)) -> PROPER(X2)
PROPER(if(X1, X2, X3)) -> PROPER(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 0 POL(proper(x1)) = x1 POL(and(x1, x2)) = 0 POL(PROPER(x1)) = x1 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 0 POL(add(x1, x2)) = x1 + x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = 1 + x1 + x2 + x3 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = 0
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 31
↳Polynomial Ordering
→DP Problem 10
↳Polo
PROPER(first(X1, X2)) -> PROPER(X2)
PROPER(first(X1, X2)) -> PROPER(X1)
PROPER(add(X1, X2)) -> PROPER(X2)
PROPER(add(X1, X2)) -> PROPER(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(add(X1, X2)) -> PROPER(X2)
PROPER(add(X1, X2)) -> PROPER(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 0 POL(proper(x1)) = x1 POL(and(x1, x2)) = 0 POL(PROPER(x1)) = x1 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 0 POL(add(x1, x2)) = 1 + x1 + x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = 0 POL(first(x1, x2)) = x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = 0
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 32
↳Polynomial Ordering
→DP Problem 10
↳Polo
PROPER(first(X1, X2)) -> PROPER(X2)
PROPER(first(X1, X2)) -> PROPER(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
PROPER(first(X1, X2)) -> PROPER(X2)
PROPER(first(X1, X2)) -> PROPER(X1)
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 0 POL(proper(x1)) = x1 POL(and(x1, x2)) = 0 POL(PROPER(x1)) = 1 + x1 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(ok(x1)) = 0 POL(add(x1, x2)) = 0 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = 0 POL(first(x1, x2)) = 1 + x1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = 0
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 33
↳Dependency Graph
→DP Problem 10
↳Polo
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polynomial Ordering
TOP(ok(X)) -> TOP(active(X))
TOP(mark(X)) -> TOP(proper(X))
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
TOP(mark(X)) -> TOP(proper(X))
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = 1 POL(proper(x1)) = x1 POL(and(x1, x2)) = 1 + x1 + x2 POL(false) = 1 POL(true) = 1 POL(mark(x1)) = 1 + x1 POL(TOP(x1)) = x1 POL(ok(x1)) = x1 POL(add(x1, x2)) = 1 + x1 + x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(first(x1, x2)) = x1 + x2 POL(0) = 1 POL(cons(x1, x2)) = 0 POL(nil) = 0 POL(s(x1)) = 1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
→DP Problem 34
↳Polynomial Ordering
TOP(ok(X)) -> TOP(active(X))
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
TOP(ok(X)) -> TOP(active(X))
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
s(ok(X)) -> ok(s(X))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
POL(from(x1)) = x1 POL(proper(x1)) = 1 POL(and(x1, x2)) = x2 POL(false) = 0 POL(true) = 0 POL(mark(x1)) = 0 POL(TOP(x1)) = x1 POL(ok(x1)) = 1 + x1 POL(add(x1, x2)) = x2 POL(top(x1)) = 0 POL(active(x1)) = x1 POL(if(x1, x2, x3)) = x2 POL(first(x1, x2)) = x1 POL(0) = 0 POL(cons(x1, x2)) = x1 POL(nil) = 0 POL(s(x1)) = x1
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Polo
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
→DP Problem 10
↳Polo
→DP Problem 34
↳Polo
...
→DP Problem 35
↳Dependency Graph
active(and(true, X)) -> mark(X)
active(and(false, Y)) -> mark(false)
active(if(true, X, Y)) -> mark(X)
active(if(false, X, Y)) -> mark(Y)
active(add(0, X)) -> mark(X)
active(add(s(X), Y)) -> mark(s(add(X, Y)))
active(first(0, X)) -> mark(nil)
active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
active(from(X)) -> mark(cons(X, from(s(X))))
active(and(X1, X2)) -> and(active(X1), X2)
active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
active(add(X1, X2)) -> add(active(X1), X2)
active(first(X1, X2)) -> first(active(X1), X2)
active(first(X1, X2)) -> first(X1, active(X2))
and(mark(X1), X2) -> mark(and(X1, X2))
and(ok(X1), ok(X2)) -> ok(and(X1, X2))
if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
add(mark(X1), X2) -> mark(add(X1, X2))
add(ok(X1), ok(X2)) -> ok(add(X1, X2))
first(mark(X1), X2) -> mark(first(X1, X2))
first(X1, mark(X2)) -> mark(first(X1, X2))
first(ok(X1), ok(X2)) -> ok(first(X1, X2))
proper(and(X1, X2)) -> and(proper(X1), proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
proper(add(X1, X2)) -> add(proper(X1), proper(X2))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(first(X1, X2)) -> first(proper(X1), proper(X2))
proper(nil) -> ok(nil)
proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
proper(from(X)) -> from(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
from(ok(X)) -> ok(from(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))