R
↳Dependency Pair Analysis
+'(0(x), 0(y)) -> 0'(+(x, y))
+'(0(x), 0(y)) -> +'(x, y)
+'(0(x), 1(y)) -> +'(x, y)
+'(1(x), 0(y)) -> +'(x, y)
+'(1(x), 1(y)) -> 0'(+(+(x, y), 1(#)))
+'(1(x), 1(y)) -> +'(+(x, y), 1(#))
+'(1(x), 1(y)) -> +'(x, y)
+'(x, +(y, z)) -> +'(+(x, y), z)
+'(x, +(y, z)) -> +'(x, y)
-'(0(x), 0(y)) -> 0'(-(x, y))
-'(0(x), 0(y)) -> -'(x, y)
-'(0(x), 1(y)) -> -'(-(x, y), 1(#))
-'(0(x), 1(y)) -> -'(x, y)
-'(1(x), 0(y)) -> -'(x, y)
-'(1(x), 1(y)) -> 0'(-(x, y))
-'(1(x), 1(y)) -> -'(x, y)
GE(0(x), 0(y)) -> GE(x, y)
GE(0(x), 1(y)) -> NOT(ge(y, x))
GE(0(x), 1(y)) -> GE(y, x)
GE(1(x), 0(y)) -> GE(x, y)
GE(1(x), 1(y)) -> GE(x, y)
GE(#, 0(x)) -> GE(#, x)
MIN(n(x, y, z)) -> MIN(y)
MAX(n(x, y, z)) -> MAX(z)
BS(n(x, y, z)) -> AND(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
BS(n(x, y, z)) -> AND(ge(x, max(y)), ge(min(z), x))
BS(n(x, y, z)) -> GE(x, max(y))
BS(n(x, y, z)) -> MAX(y)
BS(n(x, y, z)) -> GE(min(z), x)
BS(n(x, y, z)) -> MIN(z)
BS(n(x, y, z)) -> AND(bs(y), bs(z))
BS(n(x, y, z)) -> BS(y)
BS(n(x, y, z)) -> BS(z)
SIZE(n(x, y, z)) -> +'(+(size(x), size(y)), 1(#))
SIZE(n(x, y, z)) -> +'(size(x), size(y))
SIZE(n(x, y, z)) -> SIZE(x)
SIZE(n(x, y, z)) -> SIZE(y)
WB(n(x, y, z)) -> AND(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
WB(n(x, y, z)) -> IF(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y))))
WB(n(x, y, z)) -> GE(size(y), size(z))
WB(n(x, y, z)) -> SIZE(y)
WB(n(x, y, z)) -> SIZE(z)
WB(n(x, y, z)) -> GE(1(#), -(size(y), size(z)))
WB(n(x, y, z)) -> -'(size(y), size(z))
WB(n(x, y, z)) -> GE(1(#), -(size(z), size(y)))
WB(n(x, y, z)) -> -'(size(z), size(y))
WB(n(x, y, z)) -> AND(wb(y), wb(z))
WB(n(x, y, z)) -> WB(y)
WB(n(x, y, z)) -> WB(z)
R
↳DPs
→DP Problem 1
↳Narrowing Transformation
→DP Problem 2
↳Nar
→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
+'(x, +(y, z)) -> +'(x, y)
+'(x, +(y, z)) -> +'(+(x, y), z)
+'(1(x), 1(y)) -> +'(x, y)
+'(1(x), 1(y)) -> +'(+(x, y), 1(#))
+'(1(x), 0(y)) -> +'(x, y)
+'(0(x), 1(y)) -> +'(x, y)
+'(0(x), 0(y)) -> +'(x, y)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
seven new Dependency Pairs are created:
+'(1(x), 1(y)) -> +'(+(x, y), 1(#))
+'(1(x''), 1(#)) -> +'(x'', 1(#))
+'(1(#), 1(y')) -> +'(y', 1(#))
+'(1(0(x'')), 1(0(y''))) -> +'(0(+(x'', y'')), 1(#))
+'(1(0(x'')), 1(1(y''))) -> +'(1(+(x'', y'')), 1(#))
+'(1(1(x'')), 1(0(y''))) -> +'(1(+(x'', y'')), 1(#))
+'(1(1(x'')), 1(1(y''))) -> +'(0(+(+(x'', y''), 1(#))), 1(#))
+'(1(x''), 1(+(y'', z'))) -> +'(+(+(x'', y''), z'), 1(#))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 10
↳Narrowing Transformation
→DP Problem 2
↳Nar
→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
+'(1(x''), 1(+(y'', z'))) -> +'(+(+(x'', y''), z'), 1(#))
+'(1(1(x'')), 1(1(y''))) -> +'(0(+(+(x'', y''), 1(#))), 1(#))
+'(1(1(x'')), 1(0(y''))) -> +'(1(+(x'', y'')), 1(#))
+'(1(0(x'')), 1(1(y''))) -> +'(1(+(x'', y'')), 1(#))
+'(1(0(x'')), 1(0(y''))) -> +'(0(+(x'', y'')), 1(#))
+'(1(#), 1(y')) -> +'(y', 1(#))
+'(1(x''), 1(#)) -> +'(x'', 1(#))
+'(x, +(y, z)) -> +'(+(x, y), z)
+'(1(x), 1(y)) -> +'(x, y)
+'(1(x), 0(y)) -> +'(x, y)
+'(0(x), 1(y)) -> +'(x, y)
+'(0(x), 0(y)) -> +'(x, y)
+'(x, +(y, z)) -> +'(x, y)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
nine new Dependency Pairs are created:
+'(1(x''), 1(+(y'', z'))) -> +'(+(+(x'', y''), z'), 1(#))
+'(1(x'''), 1(+(y''', #))) -> +'(+(x''', y'''), 1(#))
+'(1(x'''), 1(+(y''', +(y', z'')))) -> +'(+(+(+(x''', y'''), y'), z''), 1(#))
+'(1(x'''), 1(+(#, z'))) -> +'(+(x''', z'), 1(#))
+'(1(#), 1(+(y''', z'))) -> +'(+(y''', z'), 1(#))
+'(1(0(x')), 1(+(0(y'), z'))) -> +'(+(0(+(x', y')), z'), 1(#))
+'(1(0(x')), 1(+(1(y'), z'))) -> +'(+(1(+(x', y')), z'), 1(#))
+'(1(1(x')), 1(+(0(y'), z'))) -> +'(+(1(+(x', y')), z'), 1(#))
+'(1(1(x')), 1(+(1(y'), z'))) -> +'(+(0(+(+(x', y'), 1(#))), z'), 1(#))
+'(1(x'''), 1(+(+(y', z''), z'))) -> +'(+(+(+(x''', y'), z''), z'), 1(#))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 10
↳Nar
...
→DP Problem 11
↳Polynomial Ordering
→DP Problem 2
↳Nar
→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
+'(1(x'''), 1(+(+(y', z''), z'))) -> +'(+(+(+(x''', y'), z''), z'), 1(#))
+'(1(1(x')), 1(+(1(y'), z'))) -> +'(+(0(+(+(x', y'), 1(#))), z'), 1(#))
+'(1(1(x')), 1(+(0(y'), z'))) -> +'(+(1(+(x', y')), z'), 1(#))
+'(1(0(x')), 1(+(1(y'), z'))) -> +'(+(1(+(x', y')), z'), 1(#))
+'(1(0(x')), 1(+(0(y'), z'))) -> +'(+(0(+(x', y')), z'), 1(#))
+'(1(#), 1(+(y''', z'))) -> +'(+(y''', z'), 1(#))
+'(1(x'''), 1(+(#, z'))) -> +'(+(x''', z'), 1(#))
+'(1(x'''), 1(+(y''', +(y', z'')))) -> +'(+(+(+(x''', y'''), y'), z''), 1(#))
+'(1(x'''), 1(+(y''', #))) -> +'(+(x''', y'''), 1(#))
+'(1(1(x'')), 1(0(y''))) -> +'(1(+(x'', y'')), 1(#))
+'(1(0(x'')), 1(1(y''))) -> +'(1(+(x'', y'')), 1(#))
+'(1(0(x'')), 1(0(y''))) -> +'(0(+(x'', y'')), 1(#))
+'(1(#), 1(y')) -> +'(y', 1(#))
+'(1(x''), 1(#)) -> +'(x'', 1(#))
+'(x, +(y, z)) -> +'(x, y)
+'(x, +(y, z)) -> +'(+(x, y), z)
+'(1(x), 1(y)) -> +'(x, y)
+'(1(x), 0(y)) -> +'(x, y)
+'(0(x), 0(y)) -> +'(x, y)
+'(0(x), 1(y)) -> +'(x, y)
+'(1(1(x'')), 1(1(y''))) -> +'(0(+(+(x'', y''), 1(#))), 1(#))
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
+'(1(1(x')), 1(+(0(y'), z'))) -> +'(+(1(+(x', y')), z'), 1(#))
+'(1(0(x')), 1(+(0(y'), z'))) -> +'(+(0(+(x', y')), z'), 1(#))
+'(1(1(x'')), 1(0(y''))) -> +'(1(+(x'', y'')), 1(#))
+'(1(0(x'')), 1(0(y''))) -> +'(0(+(x'', y'')), 1(#))
+'(1(x), 0(y)) -> +'(x, y)
+'(0(x), 0(y)) -> +'(x, y)
POL(#) = 0 POL(0(x1)) = 1 + x1 POL(1(x1)) = x1 POL(+(x1, x2)) = x1 + x2 POL(+'(x1, x2)) = 1 + x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 10
↳Nar
...
→DP Problem 12
↳Polynomial Ordering
→DP Problem 2
↳Nar
→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
+'(1(x'''), 1(+(+(y', z''), z'))) -> +'(+(+(+(x''', y'), z''), z'), 1(#))
+'(1(1(x')), 1(+(1(y'), z'))) -> +'(+(0(+(+(x', y'), 1(#))), z'), 1(#))
+'(1(0(x')), 1(+(1(y'), z'))) -> +'(+(1(+(x', y')), z'), 1(#))
+'(1(#), 1(+(y''', z'))) -> +'(+(y''', z'), 1(#))
+'(1(x'''), 1(+(#, z'))) -> +'(+(x''', z'), 1(#))
+'(1(x'''), 1(+(y''', +(y', z'')))) -> +'(+(+(+(x''', y'''), y'), z''), 1(#))
+'(1(x'''), 1(+(y''', #))) -> +'(+(x''', y'''), 1(#))
+'(1(0(x'')), 1(1(y''))) -> +'(1(+(x'', y'')), 1(#))
+'(1(#), 1(y')) -> +'(y', 1(#))
+'(1(x''), 1(#)) -> +'(x'', 1(#))
+'(x, +(y, z)) -> +'(x, y)
+'(x, +(y, z)) -> +'(+(x, y), z)
+'(1(x), 1(y)) -> +'(x, y)
+'(0(x), 1(y)) -> +'(x, y)
+'(1(1(x'')), 1(1(y''))) -> +'(0(+(+(x'', y''), 1(#))), 1(#))
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
+'(1(1(x')), 1(+(1(y'), z'))) -> +'(+(0(+(+(x', y'), 1(#))), z'), 1(#))
+'(1(0(x')), 1(+(1(y'), z'))) -> +'(+(1(+(x', y')), z'), 1(#))
+'(1(0(x'')), 1(1(y''))) -> +'(1(+(x'', y'')), 1(#))
+'(1(x), 1(y)) -> +'(x, y)
+'(0(x), 1(y)) -> +'(x, y)
+'(1(1(x'')), 1(1(y''))) -> +'(0(+(+(x'', y''), 1(#))), 1(#))
POL(#) = 0 POL(0(x1)) = 0 POL(1(x1)) = 1 + x1 POL(+(x1, x2)) = x1 + x2 POL(+'(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 10
↳Nar
...
→DP Problem 13
↳Dependency Graph
→DP Problem 2
↳Nar
→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
+'(1(x'''), 1(+(+(y', z''), z'))) -> +'(+(+(+(x''', y'), z''), z'), 1(#))
+'(1(#), 1(+(y''', z'))) -> +'(+(y''', z'), 1(#))
+'(1(x'''), 1(+(#, z'))) -> +'(+(x''', z'), 1(#))
+'(1(x'''), 1(+(y''', +(y', z'')))) -> +'(+(+(+(x''', y'''), y'), z''), 1(#))
+'(1(x'''), 1(+(y''', #))) -> +'(+(x''', y'''), 1(#))
+'(1(#), 1(y')) -> +'(y', 1(#))
+'(1(x''), 1(#)) -> +'(x'', 1(#))
+'(x, +(y, z)) -> +'(x, y)
+'(x, +(y, z)) -> +'(+(x, y), z)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 10
↳Nar
...
→DP Problem 14
↳Instantiation Transformation
→DP Problem 2
↳Nar
→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
+'(1(#), 1(y')) -> +'(y', 1(#))
+'(1(x''), 1(#)) -> +'(x'', 1(#))
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
one new Dependency Pair is created:
+'(1(#), 1(y')) -> +'(y', 1(#))
+'(1(#), 1(#)) -> +'(#, 1(#))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 10
↳Nar
...
→DP Problem 16
↳Polynomial Ordering
→DP Problem 2
↳Nar
→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
+'(1(x''), 1(#)) -> +'(x'', 1(#))
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
+'(1(x''), 1(#)) -> +'(x'', 1(#))
POL(#) = 0 POL(1(x1)) = 1 + x1 POL(+'(x1, x2)) = x1
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 10
↳Nar
...
→DP Problem 15
↳Polynomial Ordering
→DP Problem 2
↳Nar
→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
+'(x, +(y, z)) -> +'(+(x, y), z)
+'(x, +(y, z)) -> +'(x, y)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
+'(x, +(y, z)) -> +'(+(x, y), z)
+'(x, +(y, z)) -> +'(x, y)
POL(#) = 0 POL(0(x1)) = 0 POL(1(x1)) = 0 POL(+(x1, x2)) = 1 + x1 + x2 POL(+'(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 10
↳Nar
...
→DP Problem 17
↳Dependency Graph
→DP Problem 2
↳Nar
→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
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Narrowing Transformation
→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
-'(1(x), 1(y)) -> -'(x, y)
-'(1(x), 0(y)) -> -'(x, y)
-'(0(x), 1(y)) -> -'(x, y)
-'(0(x), 1(y)) -> -'(-(x, y), 1(#))
-'(0(x), 0(y)) -> -'(x, y)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
six new Dependency Pairs are created:
-'(0(x), 1(y)) -> -'(-(x, y), 1(#))
-'(0(x''), 1(#)) -> -'(x'', 1(#))
-'(0(#), 1(y')) -> -'(#, 1(#))
-'(0(0(x'')), 1(0(y''))) -> -'(0(-(x'', y'')), 1(#))
-'(0(0(x'')), 1(1(y''))) -> -'(1(-(-(x'', y''), 1(#))), 1(#))
-'(0(1(x'')), 1(0(y''))) -> -'(1(-(x'', y'')), 1(#))
-'(0(1(x'')), 1(1(y''))) -> -'(0(-(x'', y'')), 1(#))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→DP Problem 19
↳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
-'(0(1(x'')), 1(1(y''))) -> -'(0(-(x'', y'')), 1(#))
-'(0(1(x'')), 1(0(y''))) -> -'(1(-(x'', y'')), 1(#))
-'(0(0(x'')), 1(1(y''))) -> -'(1(-(-(x'', y''), 1(#))), 1(#))
-'(0(0(x'')), 1(0(y''))) -> -'(0(-(x'', y'')), 1(#))
-'(0(x''), 1(#)) -> -'(x'', 1(#))
-'(1(x), 0(y)) -> -'(x, y)
-'(0(x), 1(y)) -> -'(x, y)
-'(0(x), 0(y)) -> -'(x, y)
-'(1(x), 1(y)) -> -'(x, y)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
-'(0(1(x'')), 1(0(y''))) -> -'(1(-(x'', y'')), 1(#))
-'(0(0(x'')), 1(0(y''))) -> -'(0(-(x'', y'')), 1(#))
-'(1(x), 0(y)) -> -'(x, y)
-'(0(x), 0(y)) -> -'(x, y)
POL(#) = 0 POL(0(x1)) = 1 + x1 POL(-'(x1, x2)) = x2 POL(1(x1)) = x1 POL(-(x1, x2)) = 0
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→DP Problem 19
↳Polo
...
→DP Problem 20
↳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
-'(0(1(x'')), 1(1(y''))) -> -'(0(-(x'', y'')), 1(#))
-'(0(0(x'')), 1(1(y''))) -> -'(1(-(-(x'', y''), 1(#))), 1(#))
-'(0(x''), 1(#)) -> -'(x'', 1(#))
-'(0(x), 1(y)) -> -'(x, y)
-'(1(x), 1(y)) -> -'(x, y)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
-'(0(1(x'')), 1(1(y''))) -> -'(0(-(x'', y'')), 1(#))
-'(0(0(x'')), 1(1(y''))) -> -'(1(-(-(x'', y''), 1(#))), 1(#))
-'(0(x), 1(y)) -> -'(x, y)
-'(1(x), 1(y)) -> -'(x, y)
POL(#) = 0 POL(0(x1)) = 0 POL(-'(x1, x2)) = x2 POL(1(x1)) = 1 + x1 POL(-(x1, x2)) = 0
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→DP Problem 19
↳Polo
...
→DP Problem 21
↳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
-'(0(x''), 1(#)) -> -'(x'', 1(#))
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
-'(0(x''), 1(#)) -> -'(x'', 1(#))
POL(#) = 0 POL(-'(x1, x2)) = x1 POL(0(x1)) = 1 + x1 POL(1(x1)) = 0
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→DP Problem 19
↳Polo
...
→DP Problem 22
↳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
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→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
GE(#, 0(x)) -> GE(#, x)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
GE(#, 0(x)) -> GE(#, x)
POL(#) = 0 POL(0(x1)) = 1 + x1 POL(GE(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→DP Problem 3
↳Polo
→DP Problem 23
↳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
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→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
MIN(n(x, y, z)) -> MIN(y)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
MIN(n(x, y, z)) -> MIN(y)
POL(MIN(x1)) = x1 POL(n(x1, x2, x3)) = 1 + x2
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 24
↳Dependency Graph
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→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
MAX(n(x, y, z)) -> MAX(z)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
MAX(n(x, y, z)) -> MAX(z)
POL(MAX(x1)) = x1 POL(n(x1, x2, x3)) = 1 + x3
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 25
↳Dependency Graph
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→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
SIZE(n(x, y, z)) -> SIZE(y)
SIZE(n(x, y, z)) -> SIZE(x)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
SIZE(n(x, y, z)) -> SIZE(y)
SIZE(n(x, y, z)) -> SIZE(x)
POL(n(x1, x2, x3)) = 1 + x1 + x2 POL(SIZE(x1)) = x1
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 26
↳Dependency Graph
→DP Problem 7
↳Polo
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→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
GE(1(x), 1(y)) -> GE(x, y)
GE(1(x), 0(y)) -> GE(x, y)
GE(0(x), 1(y)) -> GE(y, x)
GE(0(x), 0(y)) -> GE(x, y)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
GE(1(x), 1(y)) -> GE(x, y)
GE(1(x), 0(y)) -> GE(x, y)
GE(0(x), 1(y)) -> GE(y, x)
POL(0(x1)) = x1 POL(GE(x1, x2)) = 1 + x1 + x2 POL(1(x1)) = 1 + x1
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 27
↳Polynomial Ordering
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
GE(0(x), 0(y)) -> GE(x, y)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
GE(0(x), 0(y)) -> GE(x, y)
POL(0(x1)) = 1 + x1 POL(GE(x1, x2)) = x1
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→DP Problem 3
↳Polo
→DP Problem 4
↳Polo
→DP Problem 5
↳Polo
→DP Problem 6
↳Polo
→DP Problem 7
↳Polo
→DP Problem 27
↳Polo
...
→DP Problem 28
↳Dependency Graph
→DP Problem 8
↳Polo
→DP Problem 9
↳Polo
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→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
WB(n(x, y, z)) -> WB(z)
WB(n(x, y, z)) -> WB(y)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
WB(n(x, y, z)) -> WB(z)
WB(n(x, y, z)) -> WB(y)
POL(n(x1, x2, x3)) = 1 + x2 + x3 POL(WB(x1)) = x1
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→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 29
↳Dependency Graph
→DP Problem 9
↳Polo
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→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
BS(n(x, y, z)) -> BS(z)
BS(n(x, y, z)) -> BS(y)
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))
BS(n(x, y, z)) -> BS(z)
BS(n(x, y, z)) -> BS(y)
POL(BS(x1)) = x1 POL(n(x1, x2, x3)) = 1 + x2 + x3
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
→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 30
↳Dependency Graph
0(#) -> #
+(x, #) -> x
+(#, x) -> x
+(0(x), 0(y)) -> 0(+(x, y))
+(0(x), 1(y)) -> 1(+(x, y))
+(1(x), 0(y)) -> 1(+(x, y))
+(1(x), 1(y)) -> 0(+(+(x, y), 1(#)))
+(x, +(y, z)) -> +(+(x, y), z)
-(x, #) -> x
-(#, x) -> #
-(0(x), 0(y)) -> 0(-(x, y))
-(0(x), 1(y)) -> 1(-(-(x, y), 1(#)))
-(1(x), 0(y)) -> 1(-(x, y))
-(1(x), 1(y)) -> 0(-(x, y))
not(false) -> true
not(true) -> false
and(x, true) -> x
and(x, false) -> false
if(true, x, y) -> x
if(false, x, y) -> y
ge(0(x), 0(y)) -> ge(x, y)
ge(0(x), 1(y)) -> not(ge(y, x))
ge(1(x), 0(y)) -> ge(x, y)
ge(1(x), 1(y)) -> ge(x, y)
ge(x, #) -> true
ge(#, 1(x)) -> false
ge(#, 0(x)) -> ge(#, x)
val(l(x)) -> x
val(n(x, y, z)) -> x
min(l(x)) -> x
min(n(x, y, z)) -> min(y)
max(l(x)) -> x
max(n(x, y, z)) -> max(z)
bs(l(x)) -> true
bs(n(x, y, z)) -> and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
size(l(x)) -> 1(#)
size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#))
wb(l(x)) -> true
wb(n(x, y, z)) -> and(if(ge(size(y), size(z)), ge(1(#), -(size(y), size(z))), ge(1(#), -(size(z), size(y)))), and(wb(y), wb(z)))