YES(O(1), O(n^1)) 0.00/0.84 YES(O(1), O(n^1)) 0.00/0.86 0.00/0.86 0.00/0.86
0.00/0.86 0.00/0.860 CpxTRS0.00/0.86
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.86
↳2 CdtProblem0.00/0.86
↳3 CdtLeafRemovalProof (ComplexityIfPolyImplication)0.00/0.86
↳4 CdtProblem0.00/0.86
↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.86
↳6 CdtProblem0.00/0.86
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.86
↳8 CdtProblem0.00/0.86
↳9 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.86
↳10 BOUNDS(O(1), O(1))0.00/0.86
addlist(Cons(x, xs'), Cons(S(0), xs)) → Cons(S(x), addlist(xs', xs)) 0.00/0.86
addlist(Cons(S(0), xs'), Cons(x, xs)) → Cons(S(x), addlist(xs', xs)) 0.00/0.86
addlist(Nil, ys) → Nil 0.00/0.86
notEmpty(Cons(x, xs)) → True 0.00/0.86
notEmpty(Nil) → False 0.00/0.86
goal(xs, ys) → addlist(xs, ys)
Tuples:
addlist(Cons(z0, z1), Cons(S(0), z2)) → Cons(S(z0), addlist(z1, z2)) 0.00/0.86
addlist(Cons(S(0), z0), Cons(z1, z2)) → Cons(S(z1), addlist(z0, z2)) 0.00/0.86
addlist(Nil, z0) → Nil 0.00/0.86
notEmpty(Cons(z0, z1)) → True 0.00/0.86
notEmpty(Nil) → False 0.00/0.86
goal(z0, z1) → addlist(z0, z1)
S tuples:
ADDLIST(Cons(z0, z1), Cons(S(0), z2)) → c(ADDLIST(z1, z2)) 0.00/0.86
ADDLIST(Cons(S(0), z0), Cons(z1, z2)) → c1(ADDLIST(z0, z2)) 0.00/0.86
GOAL(z0, z1) → c5(ADDLIST(z0, z1))
K tuples:none
ADDLIST(Cons(z0, z1), Cons(S(0), z2)) → c(ADDLIST(z1, z2)) 0.00/0.86
ADDLIST(Cons(S(0), z0), Cons(z1, z2)) → c1(ADDLIST(z0, z2)) 0.00/0.86
GOAL(z0, z1) → c5(ADDLIST(z0, z1))
addlist, notEmpty, goal
ADDLIST, GOAL
c, c1, c5
GOAL(z0, z1) → c5(ADDLIST(z0, z1))
Tuples:
addlist(Cons(z0, z1), Cons(S(0), z2)) → Cons(S(z0), addlist(z1, z2)) 0.00/0.86
addlist(Cons(S(0), z0), Cons(z1, z2)) → Cons(S(z1), addlist(z0, z2)) 0.00/0.86
addlist(Nil, z0) → Nil 0.00/0.86
notEmpty(Cons(z0, z1)) → True 0.00/0.86
notEmpty(Nil) → False 0.00/0.86
goal(z0, z1) → addlist(z0, z1)
S tuples:
ADDLIST(Cons(z0, z1), Cons(S(0), z2)) → c(ADDLIST(z1, z2)) 0.00/0.86
ADDLIST(Cons(S(0), z0), Cons(z1, z2)) → c1(ADDLIST(z0, z2))
K tuples:none
ADDLIST(Cons(z0, z1), Cons(S(0), z2)) → c(ADDLIST(z1, z2)) 0.00/0.86
ADDLIST(Cons(S(0), z0), Cons(z1, z2)) → c1(ADDLIST(z0, z2))
addlist, notEmpty, goal
ADDLIST
c, c1
We considered the (Usable) Rules:none
ADDLIST(Cons(z0, z1), Cons(S(0), z2)) → c(ADDLIST(z1, z2))
The order we found is given by the following interpretation:
ADDLIST(Cons(z0, z1), Cons(S(0), z2)) → c(ADDLIST(z1, z2)) 0.00/0.86
ADDLIST(Cons(S(0), z0), Cons(z1, z2)) → c1(ADDLIST(z0, z2))
POL(0) = 0 0.00/0.86
POL(ADDLIST(x1, x2)) = x2 0.00/0.86
POL(Cons(x1, x2)) = x1 + x2 0.00/0.86
POL(S(x1)) = [2] 0.00/0.86
POL(c(x1)) = x1 0.00/0.86
POL(c1(x1)) = x1
Tuples:
addlist(Cons(z0, z1), Cons(S(0), z2)) → Cons(S(z0), addlist(z1, z2)) 0.00/0.86
addlist(Cons(S(0), z0), Cons(z1, z2)) → Cons(S(z1), addlist(z0, z2)) 0.00/0.86
addlist(Nil, z0) → Nil 0.00/0.86
notEmpty(Cons(z0, z1)) → True 0.00/0.86
notEmpty(Nil) → False 0.00/0.86
goal(z0, z1) → addlist(z0, z1)
S tuples:
ADDLIST(Cons(z0, z1), Cons(S(0), z2)) → c(ADDLIST(z1, z2)) 0.00/0.86
ADDLIST(Cons(S(0), z0), Cons(z1, z2)) → c1(ADDLIST(z0, z2))
K tuples:
ADDLIST(Cons(S(0), z0), Cons(z1, z2)) → c1(ADDLIST(z0, z2))
Defined Rule Symbols:
ADDLIST(Cons(z0, z1), Cons(S(0), z2)) → c(ADDLIST(z1, z2))
addlist, notEmpty, goal
ADDLIST
c, c1
We considered the (Usable) Rules:none
ADDLIST(Cons(S(0), z0), Cons(z1, z2)) → c1(ADDLIST(z0, z2))
The order we found is given by the following interpretation:
ADDLIST(Cons(z0, z1), Cons(S(0), z2)) → c(ADDLIST(z1, z2)) 0.00/0.86
ADDLIST(Cons(S(0), z0), Cons(z1, z2)) → c1(ADDLIST(z0, z2))
POL(0) = [1] 0.00/0.86
POL(ADDLIST(x1, x2)) = [2]x1 0.00/0.86
POL(Cons(x1, x2)) = [1] + x2 0.00/0.86
POL(S(x1)) = [1] + x1 0.00/0.86
POL(c(x1)) = x1 0.00/0.86
POL(c1(x1)) = x1
Tuples:
addlist(Cons(z0, z1), Cons(S(0), z2)) → Cons(S(z0), addlist(z1, z2)) 0.00/0.86
addlist(Cons(S(0), z0), Cons(z1, z2)) → Cons(S(z1), addlist(z0, z2)) 0.00/0.86
addlist(Nil, z0) → Nil 0.00/0.86
notEmpty(Cons(z0, z1)) → True 0.00/0.86
notEmpty(Nil) → False 0.00/0.86
goal(z0, z1) → addlist(z0, z1)
S tuples:none
ADDLIST(Cons(z0, z1), Cons(S(0), z2)) → c(ADDLIST(z1, z2)) 0.00/0.86
ADDLIST(Cons(S(0), z0), Cons(z1, z2)) → c1(ADDLIST(z0, z2))
Defined Rule Symbols:
ADDLIST(Cons(z0, z1), Cons(S(0), z2)) → c(ADDLIST(z1, z2)) 0.00/0.86
ADDLIST(Cons(S(0), z0), Cons(z1, z2)) → c1(ADDLIST(z0, z2))
addlist, notEmpty, goal
ADDLIST
c, c1