YES(?,O(n^3))
Problem:
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
top(mark(x)) -> top(check(x))
check(f(x)) -> f(check(x))
check(x) -> start(match(f(X()),x))
match(f(x),f(y)) -> f(match(x,y))
match(X(),x) -> proper(x)
proper(c()) -> ok(c())
proper(f(x)) -> f(proper(x))
f(ok(x)) -> ok(f(x))
start(ok(x)) -> found(x)
f(found(x)) -> found(f(x))
top(found(x)) -> top(active(x))
active(f(x)) -> f(active(x))
f(mark(x)) -> mark(f(x))
Proof:
Complexity Transformation Processor:
strict:
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
top(mark(x)) -> top(check(x))
check(f(x)) -> f(check(x))
check(x) -> start(match(f(X()),x))
match(f(x),f(y)) -> f(match(x,y))
match(X(),x) -> proper(x)
proper(c()) -> ok(c())
proper(f(x)) -> f(proper(x))
f(ok(x)) -> ok(f(x))
start(ok(x)) -> found(x)
f(found(x)) -> found(f(x))
top(found(x)) -> top(active(x))
active(f(x)) -> f(active(x))
f(mark(x)) -> mark(f(x))
weak:
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[found](x0) = x0 + 1,
[ok](x0) = x0,
[proper](x0) = x0,
[start](x0) = x0 + 1,
[match](x0, x1) = x0 + x1,
[X] = 0,
[check](x0) = x0,
[top](x0) = x0,
[c] = 0,
[mark](x0) = x0 + 1,
[active](x0) = x0,
[f](x0) = x0
orientation:
active(f(x)) = x >= x + 1 = mark(x)
top(active(c())) = 0 >= 1 = top(mark(c()))
top(mark(x)) = x + 1 >= x = top(check(x))
check(f(x)) = x >= x = f(check(x))
check(x) = x >= x + 1 = start(match(f(X()),x))
match(f(x),f(y)) = x + y >= x + y = f(match(x,y))
match(X(),x) = x >= x = proper(x)
proper(c()) = 0 >= 0 = ok(c())
proper(f(x)) = x >= x = f(proper(x))
f(ok(x)) = x >= x = ok(f(x))
start(ok(x)) = x + 1 >= x + 1 = found(x)
f(found(x)) = x + 1 >= x + 1 = found(f(x))
top(found(x)) = x + 1 >= x = top(active(x))
active(f(x)) = x >= x = f(active(x))
f(mark(x)) = x + 1 >= x + 1 = mark(f(x))
problem:
strict:
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
check(f(x)) -> f(check(x))
check(x) -> start(match(f(X()),x))
match(f(x),f(y)) -> f(match(x,y))
match(X(),x) -> proper(x)
proper(c()) -> ok(c())
proper(f(x)) -> f(proper(x))
f(ok(x)) -> ok(f(x))
start(ok(x)) -> found(x)
f(found(x)) -> found(f(x))
active(f(x)) -> f(active(x))
f(mark(x)) -> mark(f(x))
weak:
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[found](x0) = x0,
[ok](x0) = x0 + 1,
[proper](x0) = x0,
[start](x0) = x0 + 1,
[match](x0, x1) = x0 + x1,
[X] = 0,
[check](x0) = x0,
[top](x0) = x0,
[c] = 1,
[mark](x0) = x0,
[active](x0) = x0,
[f](x0) = x0
orientation:
active(f(x)) = x >= x = mark(x)
top(active(c())) = 1 >= 1 = top(mark(c()))
check(f(x)) = x >= x = f(check(x))
check(x) = x >= x + 1 = start(match(f(X()),x))
match(f(x),f(y)) = x + y >= x + y = f(match(x,y))
match(X(),x) = x >= x = proper(x)
proper(c()) = 1 >= 2 = ok(c())
proper(f(x)) = x >= x = f(proper(x))
f(ok(x)) = x + 1 >= x + 1 = ok(f(x))
start(ok(x)) = x + 2 >= x = found(x)
f(found(x)) = x >= x = found(f(x))
active(f(x)) = x >= x = f(active(x))
f(mark(x)) = x >= x = mark(f(x))
top(mark(x)) = x >= x = top(check(x))
top(found(x)) = x >= x = top(active(x))
problem:
strict:
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
check(f(x)) -> f(check(x))
check(x) -> start(match(f(X()),x))
match(f(x),f(y)) -> f(match(x,y))
match(X(),x) -> proper(x)
proper(c()) -> ok(c())
proper(f(x)) -> f(proper(x))
f(ok(x)) -> ok(f(x))
f(found(x)) -> found(f(x))
active(f(x)) -> f(active(x))
f(mark(x)) -> mark(f(x))
weak:
start(ok(x)) -> found(x)
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[found](x0) = x0,
[ok](x0) = x0,
[proper](x0) = x0,
[start](x0) = x0 + 1,
[match](x0, x1) = x0 + x1,
[X] = 1,
[check](x0) = x0,
[top](x0) = x0,
[c] = 0,
[mark](x0) = x0,
[active](x0) = x0,
[f](x0) = x0
orientation:
active(f(x)) = x >= x = mark(x)
top(active(c())) = 0 >= 0 = top(mark(c()))
check(f(x)) = x >= x = f(check(x))
check(x) = x >= x + 2 = start(match(f(X()),x))
match(f(x),f(y)) = x + y >= x + y = f(match(x,y))
match(X(),x) = x + 1 >= x = proper(x)
proper(c()) = 0 >= 0 = ok(c())
proper(f(x)) = x >= x = f(proper(x))
f(ok(x)) = x >= x = ok(f(x))
f(found(x)) = x >= x = found(f(x))
active(f(x)) = x >= x = f(active(x))
f(mark(x)) = x >= x = mark(f(x))
start(ok(x)) = x + 1 >= x = found(x)
top(mark(x)) = x >= x = top(check(x))
top(found(x)) = x >= x = top(active(x))
problem:
strict:
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
check(f(x)) -> f(check(x))
check(x) -> start(match(f(X()),x))
match(f(x),f(y)) -> f(match(x,y))
proper(c()) -> ok(c())
proper(f(x)) -> f(proper(x))
f(ok(x)) -> ok(f(x))
f(found(x)) -> found(f(x))
active(f(x)) -> f(active(x))
f(mark(x)) -> mark(f(x))
weak:
match(X(),x) -> proper(x)
start(ok(x)) -> found(x)
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[found](x0) = x0 + 1,
[ok](x0) = x0,
[proper](x0) = x0 + 1,
[start](x0) = x0 + 1,
[match](x0, x1) = x0 + x1 + 1,
[X] = 0,
[check](x0) = x0,
[top](x0) = x0,
[c] = 0,
[mark](x0) = x0,
[active](x0) = x0,
[f](x0) = x0
orientation:
active(f(x)) = x >= x = mark(x)
top(active(c())) = 0 >= 0 = top(mark(c()))
check(f(x)) = x >= x = f(check(x))
check(x) = x >= x + 2 = start(match(f(X()),x))
match(f(x),f(y)) = x + y + 1 >= x + y + 1 = f(match(x,y))
proper(c()) = 1 >= 0 = ok(c())
proper(f(x)) = x + 1 >= x + 1 = f(proper(x))
f(ok(x)) = x >= x = ok(f(x))
f(found(x)) = x + 1 >= x + 1 = found(f(x))
active(f(x)) = x >= x = f(active(x))
f(mark(x)) = x >= x = mark(f(x))
match(X(),x) = x + 1 >= x + 1 = proper(x)
start(ok(x)) = x + 1 >= x + 1 = found(x)
top(mark(x)) = x >= x = top(check(x))
top(found(x)) = x + 1 >= x = top(active(x))
problem:
strict:
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
check(f(x)) -> f(check(x))
check(x) -> start(match(f(X()),x))
match(f(x),f(y)) -> f(match(x,y))
proper(f(x)) -> f(proper(x))
f(ok(x)) -> ok(f(x))
f(found(x)) -> found(f(x))
active(f(x)) -> f(active(x))
f(mark(x)) -> mark(f(x))
weak:
proper(c()) -> ok(c())
match(X(),x) -> proper(x)
start(ok(x)) -> found(x)
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[found](x0) = x0 + 1,
[ok](x0) = x0,
[proper](x0) = x0 + 1,
[start](x0) = x0 + 1,
[match](x0, x1) = x0 + x1 + 1,
[X] = 0,
[check](x0) = x0,
[top](x0) = x0 + 1,
[c] = 1,
[mark](x0) = x0,
[active](x0) = x0 + 1,
[f](x0) = x0
orientation:
active(f(x)) = x + 1 >= x = mark(x)
top(active(c())) = 3 >= 2 = top(mark(c()))
check(f(x)) = x >= x = f(check(x))
check(x) = x >= x + 2 = start(match(f(X()),x))
match(f(x),f(y)) = x + y + 1 >= x + y + 1 = f(match(x,y))
proper(f(x)) = x + 1 >= x + 1 = f(proper(x))
f(ok(x)) = x >= x = ok(f(x))
f(found(x)) = x + 1 >= x + 1 = found(f(x))
active(f(x)) = x + 1 >= x + 1 = f(active(x))
f(mark(x)) = x >= x = mark(f(x))
proper(c()) = 2 >= 1 = ok(c())
match(X(),x) = x + 1 >= x + 1 = proper(x)
start(ok(x)) = x + 1 >= x + 1 = found(x)
top(mark(x)) = x + 1 >= x + 1 = top(check(x))
top(found(x)) = x + 2 >= x + 2 = top(active(x))
problem:
strict:
check(f(x)) -> f(check(x))
check(x) -> start(match(f(X()),x))
match(f(x),f(y)) -> f(match(x,y))
proper(f(x)) -> f(proper(x))
f(ok(x)) -> ok(f(x))
f(found(x)) -> found(f(x))
active(f(x)) -> f(active(x))
f(mark(x)) -> mark(f(x))
weak:
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
proper(c()) -> ok(c())
match(X(),x) -> proper(x)
start(ok(x)) -> found(x)
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[found](x0) = x0,
[ok](x0) = x0,
[proper](x0) = x0,
[start](x0) = x0,
[match](x0, x1) = x0 + x1 + 1,
[X] = 1,
[check](x0) = x0,
[top](x0) = x0 + 1,
[c] = 1,
[mark](x0) = x0,
[active](x0) = x0,
[f](x0) = x0 + 1
orientation:
check(f(x)) = x + 1 >= x + 1 = f(check(x))
check(x) = x >= x + 3 = start(match(f(X()),x))
match(f(x),f(y)) = x + y + 3 >= x + y + 2 = f(match(x,y))
proper(f(x)) = x + 1 >= x + 1 = f(proper(x))
f(ok(x)) = x + 1 >= x + 1 = ok(f(x))
f(found(x)) = x + 1 >= x + 1 = found(f(x))
active(f(x)) = x + 1 >= x + 1 = f(active(x))
f(mark(x)) = x + 1 >= x + 1 = mark(f(x))
active(f(x)) = x + 1 >= x = mark(x)
top(active(c())) = 2 >= 2 = top(mark(c()))
proper(c()) = 1 >= 1 = ok(c())
match(X(),x) = x + 2 >= x = proper(x)
start(ok(x)) = x >= x = found(x)
top(mark(x)) = x + 1 >= x + 1 = top(check(x))
top(found(x)) = x + 1 >= x + 1 = top(active(x))
problem:
strict:
check(f(x)) -> f(check(x))
check(x) -> start(match(f(X()),x))
proper(f(x)) -> f(proper(x))
f(ok(x)) -> ok(f(x))
f(found(x)) -> found(f(x))
active(f(x)) -> f(active(x))
f(mark(x)) -> mark(f(x))
weak:
match(f(x),f(y)) -> f(match(x,y))
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
proper(c()) -> ok(c())
match(X(),x) -> proper(x)
start(ok(x)) -> found(x)
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Matrix Interpretation Processor:
dimension: 2
max_matrix:
[1 1]
[0 1]
interpretation:
[found](x0) = x0,
[ok](x0) = x0,
[proper](x0) = x0,
[start](x0) = x0,
[1 0]
[match](x0, x1) = [0 0]x0 + x1,
[0]
[X] = [0],
[check](x0) = x0,
[1 0]
[top](x0) = [0 0]x0,
[0]
[c] = [0],
[0]
[mark](x0) = x0 + [1],
[active](x0) = x0,
[1 1] [0]
[f](x0) = [0 1]x0 + [1]
orientation:
[1 1] [0] [1 1] [0]
check(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(check(x))
check(x) = x >= x = start(match(f(X()),x))
[1 1] [0] [1 1] [0]
proper(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(proper(x))
[1 1] [0] [1 1] [0]
f(ok(x)) = [0 1]x + [1] >= [0 1]x + [1] = ok(f(x))
[1 1] [0] [1 1] [0]
f(found(x)) = [0 1]x + [1] >= [0 1]x + [1] = found(f(x))
[1 1] [0] [1 1] [0]
active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(active(x))
[1 1] [1] [1 1] [0]
f(mark(x)) = [0 1]x + [2] >= [0 1]x + [2] = mark(f(x))
[1 1] [1 1] [0] [1 0] [1 1] [0]
match(f(x),f(y)) = [0 0]x + [0 1]y + [1] >= [0 0]x + [0 1]y + [1] = f(match(x,y))
[1 1] [0] [0]
active(f(x)) = [0 1]x + [1] >= x + [1] = mark(x)
[0] [0]
top(active(c())) = [0] >= [0] = top(mark(c()))
[0] [0]
proper(c()) = [0] >= [0] = ok(c())
match(X(),x) = x >= x = proper(x)
start(ok(x)) = x >= x = found(x)
[1 0] [1 0]
top(mark(x)) = [0 0]x >= [0 0]x = top(check(x))
[1 0] [1 0]
top(found(x)) = [0 0]x >= [0 0]x = top(active(x))
problem:
strict:
check(f(x)) -> f(check(x))
check(x) -> start(match(f(X()),x))
proper(f(x)) -> f(proper(x))
f(ok(x)) -> ok(f(x))
f(found(x)) -> found(f(x))
active(f(x)) -> f(active(x))
weak:
f(mark(x)) -> mark(f(x))
match(f(x),f(y)) -> f(match(x,y))
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
proper(c()) -> ok(c())
match(X(),x) -> proper(x)
start(ok(x)) -> found(x)
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Matrix Interpretation Processor:
dimension: 2
max_matrix:
[1 1]
[0 1]
interpretation:
[0]
[found](x0) = x0 + [1],
[ok](x0) = x0,
[proper](x0) = x0,
[0]
[start](x0) = x0 + [1],
[1 0]
[match](x0, x1) = [0 0]x0 + x1,
[0]
[X] = [0],
[1 1] [0]
[check](x0) = [0 1]x0 + [1],
[1 0]
[top](x0) = [0 0]x0,
[0]
[c] = [0],
[1 1] [0]
[mark](x0) = [0 1]x0 + [1],
[active](x0) = x0,
[1 1] [0]
[f](x0) = [0 1]x0 + [1]
orientation:
[1 2] [1] [1 2] [1]
check(f(x)) = [0 1]x + [2] >= [0 1]x + [2] = f(check(x))
[1 1] [0] [0]
check(x) = [0 1]x + [1] >= x + [1] = start(match(f(X()),x))
[1 1] [0] [1 1] [0]
proper(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(proper(x))
[1 1] [0] [1 1] [0]
f(ok(x)) = [0 1]x + [1] >= [0 1]x + [1] = ok(f(x))
[1 1] [1] [1 1] [0]
f(found(x)) = [0 1]x + [2] >= [0 1]x + [2] = found(f(x))
[1 1] [0] [1 1] [0]
active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(active(x))
[1 2] [1] [1 2] [1]
f(mark(x)) = [0 1]x + [2] >= [0 1]x + [2] = mark(f(x))
[1 1] [1 1] [0] [1 0] [1 1] [0]
match(f(x),f(y)) = [0 0]x + [0 1]y + [1] >= [0 0]x + [0 1]y + [1] = f(match(x,y))
[1 1] [0] [1 1] [0]
active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = mark(x)
[0] [0]
top(active(c())) = [0] >= [0] = top(mark(c()))
[0] [0]
proper(c()) = [0] >= [0] = ok(c())
match(X(),x) = x >= x = proper(x)
[0] [0]
start(ok(x)) = x + [1] >= x + [1] = found(x)
[1 1] [1 1]
top(mark(x)) = [0 0]x >= [0 0]x = top(check(x))
[1 0] [1 0]
top(found(x)) = [0 0]x >= [0 0]x = top(active(x))
problem:
strict:
check(f(x)) -> f(check(x))
check(x) -> start(match(f(X()),x))
proper(f(x)) -> f(proper(x))
f(ok(x)) -> ok(f(x))
active(f(x)) -> f(active(x))
weak:
f(found(x)) -> found(f(x))
f(mark(x)) -> mark(f(x))
match(f(x),f(y)) -> f(match(x,y))
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
proper(c()) -> ok(c())
match(X(),x) -> proper(x)
start(ok(x)) -> found(x)
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Matrix Interpretation Processor:
dimension: 2
max_matrix:
[1 1]
[0 1]
interpretation:
[found](x0) = x0,
[ok](x0) = x0,
[proper](x0) = x0,
[start](x0) = x0,
[1 0]
[match](x0, x1) = [0 0]x0 + x1,
[0]
[X] = [0],
[1 1]
[check](x0) = [0 1]x0,
[1 0] [0]
[top](x0) = [0 0]x0 + [1],
[0]
[c] = [0],
[1 1] [0]
[mark](x0) = [0 1]x0 + [1],
[active](x0) = x0,
[1 1] [0]
[f](x0) = [0 1]x0 + [1]
orientation:
[1 2] [1] [1 2] [0]
check(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(check(x))
[1 1]
check(x) = [0 1]x >= x = start(match(f(X()),x))
[1 1] [0] [1 1] [0]
proper(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(proper(x))
[1 1] [0] [1 1] [0]
f(ok(x)) = [0 1]x + [1] >= [0 1]x + [1] = ok(f(x))
[1 1] [0] [1 1] [0]
active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(active(x))
[1 1] [0] [1 1] [0]
f(found(x)) = [0 1]x + [1] >= [0 1]x + [1] = found(f(x))
[1 2] [1] [1 2] [1]
f(mark(x)) = [0 1]x + [2] >= [0 1]x + [2] = mark(f(x))
[1 1] [1 1] [0] [1 0] [1 1] [0]
match(f(x),f(y)) = [0 0]x + [0 1]y + [1] >= [0 0]x + [0 1]y + [1] = f(match(x,y))
[1 1] [0] [1 1] [0]
active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = mark(x)
[0] [0]
top(active(c())) = [1] >= [1] = top(mark(c()))
[0] [0]
proper(c()) = [0] >= [0] = ok(c())
match(X(),x) = x >= x = proper(x)
start(ok(x)) = x >= x = found(x)
[1 1] [0] [1 1] [0]
top(mark(x)) = [0 0]x + [1] >= [0 0]x + [1] = top(check(x))
[1 0] [0] [1 0] [0]
top(found(x)) = [0 0]x + [1] >= [0 0]x + [1] = top(active(x))
problem:
strict:
check(x) -> start(match(f(X()),x))
proper(f(x)) -> f(proper(x))
f(ok(x)) -> ok(f(x))
active(f(x)) -> f(active(x))
weak:
check(f(x)) -> f(check(x))
f(found(x)) -> found(f(x))
f(mark(x)) -> mark(f(x))
match(f(x),f(y)) -> f(match(x,y))
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
proper(c()) -> ok(c())
match(X(),x) -> proper(x)
start(ok(x)) -> found(x)
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Matrix Interpretation Processor:
dimension: 2
max_matrix:
[1 1]
[0 1]
interpretation:
[found](x0) = x0,
[ok](x0) = x0,
[1 1]
[proper](x0) = [0 1]x0,
[0]
[start](x0) = x0 + [1],
[1 0] [1 1]
[match](x0, x1) = [0 0]x0 + [0 1]x1,
[0]
[X] = [0],
[1 1] [0]
[check](x0) = [0 1]x0 + [1],
[1 0]
[top](x0) = [0 0]x0,
[0]
[c] = [0],
[1 1] [0]
[mark](x0) = [0 1]x0 + [1],
[active](x0) = x0,
[1 1] [0]
[f](x0) = [0 1]x0 + [1]
orientation:
[1 1] [0] [1 1] [0]
check(x) = [0 1]x + [1] >= [0 1]x + [1] = start(match(f(X()),x))
[1 2] [1] [1 2] [0]
proper(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(proper(x))
[1 1] [0] [1 1] [0]
f(ok(x)) = [0 1]x + [1] >= [0 1]x + [1] = ok(f(x))
[1 1] [0] [1 1] [0]
active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(active(x))
[1 2] [1] [1 2] [1]
check(f(x)) = [0 1]x + [2] >= [0 1]x + [2] = f(check(x))
[1 1] [0] [1 1] [0]
f(found(x)) = [0 1]x + [1] >= [0 1]x + [1] = found(f(x))
[1 2] [1] [1 2] [1]
f(mark(x)) = [0 1]x + [2] >= [0 1]x + [2] = mark(f(x))
[1 1] [1 2] [1] [1 0] [1 2] [0]
match(f(x),f(y)) = [0 0]x + [0 1]y + [1] >= [0 0]x + [0 1]y + [1] = f(match(x,y))
[1 1] [0] [1 1] [0]
active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = mark(x)
[0] [0]
top(active(c())) = [0] >= [0] = top(mark(c()))
[0] [0]
proper(c()) = [0] >= [0] = ok(c())
[1 1] [1 1]
match(X(),x) = [0 1]x >= [0 1]x = proper(x)
[0]
start(ok(x)) = x + [1] >= x = found(x)
[1 1] [1 1]
top(mark(x)) = [0 0]x >= [0 0]x = top(check(x))
[1 0] [1 0]
top(found(x)) = [0 0]x >= [0 0]x = top(active(x))
problem:
strict:
check(x) -> start(match(f(X()),x))
f(ok(x)) -> ok(f(x))
active(f(x)) -> f(active(x))
weak:
proper(f(x)) -> f(proper(x))
check(f(x)) -> f(check(x))
f(found(x)) -> found(f(x))
f(mark(x)) -> mark(f(x))
match(f(x),f(y)) -> f(match(x,y))
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
proper(c()) -> ok(c())
match(X(),x) -> proper(x)
start(ok(x)) -> found(x)
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Matrix Interpretation Processor:
dimension: 2
max_matrix:
[1 1]
[0 1]
interpretation:
[1 1] [0]
[found](x0) = [0 1]x0 + [1],
[ok](x0) = x0,
[proper](x0) = x0,
[1 1] [0]
[start](x0) = [0 1]x0 + [1],
[1 0]
[match](x0, x1) = [0 0]x0 + x1,
[0]
[X] = [0],
[1 1] [0]
[check](x0) = [0 1]x0 + [1],
[1 0]
[top](x0) = [0 0]x0,
[0]
[c] = [0],
[1 1] [0]
[mark](x0) = [0 1]x0 + [1],
[1 1]
[active](x0) = [0 1]x0,
[1 1] [0]
[f](x0) = [0 1]x0 + [1]
orientation:
[1 1] [0] [1 1] [0]
check(x) = [0 1]x + [1] >= [0 1]x + [1] = start(match(f(X()),x))
[1 1] [0] [1 1] [0]
f(ok(x)) = [0 1]x + [1] >= [0 1]x + [1] = ok(f(x))
[1 2] [1] [1 2] [0]
active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(active(x))
[1 1] [0] [1 1] [0]
proper(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(proper(x))
[1 2] [1] [1 2] [1]
check(f(x)) = [0 1]x + [2] >= [0 1]x + [2] = f(check(x))
[1 2] [1] [1 2] [1]
f(found(x)) = [0 1]x + [2] >= [0 1]x + [2] = found(f(x))
[1 2] [1] [1 2] [1]
f(mark(x)) = [0 1]x + [2] >= [0 1]x + [2] = mark(f(x))
[1 1] [1 1] [0] [1 0] [1 1] [0]
match(f(x),f(y)) = [0 0]x + [0 1]y + [1] >= [0 0]x + [0 1]y + [1] = f(match(x,y))
[1 2] [1] [1 1] [0]
active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = mark(x)
[0] [0]
top(active(c())) = [0] >= [0] = top(mark(c()))
[0] [0]
proper(c()) = [0] >= [0] = ok(c())
match(X(),x) = x >= x = proper(x)
[1 1] [0] [1 1] [0]
start(ok(x)) = [0 1]x + [1] >= [0 1]x + [1] = found(x)
[1 1] [1 1]
top(mark(x)) = [0 0]x >= [0 0]x = top(check(x))
[1 1] [1 1]
top(found(x)) = [0 0]x >= [0 0]x = top(active(x))
problem:
strict:
check(x) -> start(match(f(X()),x))
f(ok(x)) -> ok(f(x))
weak:
active(f(x)) -> f(active(x))
proper(f(x)) -> f(proper(x))
check(f(x)) -> f(check(x))
f(found(x)) -> found(f(x))
f(mark(x)) -> mark(f(x))
match(f(x),f(y)) -> f(match(x,y))
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
proper(c()) -> ok(c())
match(X(),x) -> proper(x)
start(ok(x)) -> found(x)
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Matrix Interpretation Processor:
dimension: 2
max_matrix:
[1 1]
[0 1]
interpretation:
[found](x0) = x0,
[0]
[ok](x0) = x0 + [1],
[1 1] [0]
[proper](x0) = [0 1]x0 + [1],
[start](x0) = x0,
[1 0] [1 1] [0]
[match](x0, x1) = [0 0]x0 + [0 1]x1 + [1],
[0]
[X] = [0],
[1 1] [0]
[check](x0) = [0 1]x0 + [1],
[1 0]
[top](x0) = [0 0]x0,
[0]
[c] = [0],
[1 1] [0]
[mark](x0) = [0 1]x0 + [1],
[active](x0) = x0,
[1 1] [0]
[f](x0) = [0 1]x0 + [1]
orientation:
[1 1] [0] [1 1] [0]
check(x) = [0 1]x + [1] >= [0 1]x + [1] = start(match(f(X()),x))
[1 1] [1] [1 1] [0]
f(ok(x)) = [0 1]x + [2] >= [0 1]x + [2] = ok(f(x))
[1 1] [0] [1 1] [0]
active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(active(x))
[1 2] [1] [1 2] [1]
proper(f(x)) = [0 1]x + [2] >= [0 1]x + [2] = f(proper(x))
[1 2] [1] [1 2] [1]
check(f(x)) = [0 1]x + [2] >= [0 1]x + [2] = f(check(x))
[1 1] [0] [1 1] [0]
f(found(x)) = [0 1]x + [1] >= [0 1]x + [1] = found(f(x))
[1 2] [1] [1 2] [1]
f(mark(x)) = [0 1]x + [2] >= [0 1]x + [2] = mark(f(x))
[1 1] [1 2] [1] [1 0] [1 2] [1]
match(f(x),f(y)) = [0 0]x + [0 1]y + [2] >= [0 0]x + [0 1]y + [2] = f(match(x,y))
[1 1] [0] [1 1] [0]
active(f(x)) = [0 1]x + [1] >= [0 1]x + [1] = mark(x)
[0] [0]
top(active(c())) = [0] >= [0] = top(mark(c()))
[0] [0]
proper(c()) = [1] >= [1] = ok(c())
[1 1] [0] [1 1] [0]
match(X(),x) = [0 1]x + [1] >= [0 1]x + [1] = proper(x)
[0]
start(ok(x)) = x + [1] >= x = found(x)
[1 1] [1 1]
top(mark(x)) = [0 0]x >= [0 0]x = top(check(x))
[1 0] [1 0]
top(found(x)) = [0 0]x >= [0 0]x = top(active(x))
problem:
strict:
check(x) -> start(match(f(X()),x))
weak:
f(ok(x)) -> ok(f(x))
active(f(x)) -> f(active(x))
proper(f(x)) -> f(proper(x))
check(f(x)) -> f(check(x))
f(found(x)) -> found(f(x))
f(mark(x)) -> mark(f(x))
match(f(x),f(y)) -> f(match(x,y))
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
proper(c()) -> ok(c())
match(X(),x) -> proper(x)
start(ok(x)) -> found(x)
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Matrix Interpretation Processor:
dimension: 3
max_matrix:
[1 1 1]
[0 1 0]
[0 0 1]
interpretation:
[1 1 1] [0]
[found](x0) = [0 0 0]x0 + [0]
[0 0 0] [1],
[ok](x0) = x0
,
[1 0 0] [0]
[proper](x0) = [0 0 0]x0 + [1]
[0 0 1] [0],
[1 1 1] [0]
[start](x0) = [0 0 0]x0 + [0]
[0 0 0] [1],
[1 0 0] [1 0 0]
[match](x0, x1) = [0 1 0]x0 + [0 0 0]x1
[0 0 0] [0 0 1] ,
[0]
[X] = [1]
[0],
[1 0 1] [1]
[check](x0) = [0 0 0]x0 + [0]
[0 0 0] [1],
[1 1 0] [0]
[top](x0) = [0 0 0]x0 + [1]
[0 0 0] [0],
[1]
[c] = [1]
[0],
[1 0 1] [1]
[mark](x0) = [0 0 0]x0 + [0]
[0 0 0] [1],
[1 0 1] [0]
[active](x0) = [0 1 0]x0 + [0]
[0 0 0] [1],
[1 0 1] [0]
[f](x0) = [0 0 0]x0 + [0]
[0 0 0] [1]
orientation:
[1 0 1] [1] [1 0 1] [0]
check(x) = [0 0 0]x + [0] >= [0 0 0]x + [0] = start(match(f(X()),x))
[0 0 0] [1] [0 0 0] [1]
[1 0 1] [0] [1 0 1] [0]
f(ok(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = ok(f(x))
[0 0 0] [1] [0 0 0] [1]
[1 0 1] [1] [1 0 1] [1]
active(f(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = f(active(x))
[0 0 0] [1] [0 0 0] [1]
[1 0 1] [0] [1 0 1] [0]
proper(f(x)) = [0 0 0]x + [1] >= [0 0 0]x + [0] = f(proper(x))
[0 0 0] [1] [0 0 0] [1]
[1 0 1] [2] [1 0 1] [2]
check(f(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = f(check(x))
[0 0 0] [1] [0 0 0] [1]
[1 1 1] [1] [1 0 1] [1]
f(found(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = found(f(x))
[0 0 0] [1] [0 0 0] [1]
[1 0 1] [2] [1 0 1] [2]
f(mark(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = mark(f(x))
[0 0 0] [1] [0 0 0] [1]
[1 0 1] [1 0 1] [0] [1 0 0] [1 0 1] [0]
match(f(x),f(y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = f(match(x,y))
[0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1]
[1 0 1] [1] [1 0 1] [1]
active(f(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = mark(x)
[0 0 0] [1] [0 0 0] [1]
[2] [2]
top(active(c())) = [1] >= [1] = top(mark(c()))
[0] [0]
[1] [1]
proper(c()) = [1] >= [1] = ok(c())
[0] [0]
[1 0 0] [0] [1 0 0] [0]
match(X(),x) = [0 0 0]x + [1] >= [0 0 0]x + [1] = proper(x)
[0 0 1] [0] [0 0 1] [0]
[1 1 1] [0] [1 1 1] [0]
start(ok(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = found(x)
[0 0 0] [1] [0 0 0] [1]
[1 0 1] [1] [1 0 1] [1]
top(mark(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = top(check(x))
[0 0 0] [0] [0 0 0] [0]
[1 1 1] [0] [1 1 1] [0]
top(found(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = top(active(x))
[0 0 0] [0] [0 0 0] [0]
problem:
strict:
weak:
check(x) -> start(match(f(X()),x))
f(ok(x)) -> ok(f(x))
active(f(x)) -> f(active(x))
proper(f(x)) -> f(proper(x))
check(f(x)) -> f(check(x))
f(found(x)) -> found(f(x))
f(mark(x)) -> mark(f(x))
match(f(x),f(y)) -> f(match(x,y))
active(f(x)) -> mark(x)
top(active(c())) -> top(mark(c()))
proper(c()) -> ok(c())
match(X(),x) -> proper(x)
start(ok(x)) -> found(x)
top(mark(x)) -> top(check(x))
top(found(x)) -> top(active(x))
Qed