YES(O(1), O(n^1)) 0.00/0.73 YES(O(1), O(n^1)) 0.00/0.74 0.00/0.74 0.00/0.74
0.00/0.74 0.00/0.740 CpxTRS0.00/0.74
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.74
↳2 CdtProblem0.00/0.74
↳3 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.74
↳4 CdtProblem0.00/0.74
↳5 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.74
↳6 BOUNDS(O(1), O(1))0.00/0.74
is_empty(nil) → true 0.00/0.74
is_empty(cons(x, l)) → false 0.00/0.74
hd(cons(x, l)) → x 0.00/0.74
tl(cons(x, l)) → l 0.00/0.74
append(l1, l2) → ifappend(l1, l2, l1) 0.00/0.74
ifappend(l1, l2, nil) → l2 0.00/0.74
ifappend(l1, l2, cons(x, l)) → cons(x, append(l, l2))
Tuples:
is_empty(nil) → true 0.00/0.74
is_empty(cons(z0, z1)) → false 0.00/0.74
hd(cons(z0, z1)) → z0 0.00/0.74
tl(cons(z0, z1)) → z1 0.00/0.74
append(z0, z1) → ifappend(z0, z1, z0) 0.00/0.74
ifappend(z0, z1, nil) → z1 0.00/0.74
ifappend(z0, z1, cons(z2, z3)) → cons(z2, append(z3, z1))
S tuples:
APPEND(z0, z1) → c4(IFAPPEND(z0, z1, z0)) 0.00/0.74
IFAPPEND(z0, z1, cons(z2, z3)) → c6(APPEND(z3, z1))
K tuples:none
APPEND(z0, z1) → c4(IFAPPEND(z0, z1, z0)) 0.00/0.74
IFAPPEND(z0, z1, cons(z2, z3)) → c6(APPEND(z3, z1))
is_empty, hd, tl, append, ifappend
APPEND, IFAPPEND
c4, c6
We considered the (Usable) Rules:none
APPEND(z0, z1) → c4(IFAPPEND(z0, z1, z0)) 0.00/0.74
IFAPPEND(z0, z1, cons(z2, z3)) → c6(APPEND(z3, z1))
The order we found is given by the following interpretation:
APPEND(z0, z1) → c4(IFAPPEND(z0, z1, z0)) 0.00/0.74
IFAPPEND(z0, z1, cons(z2, z3)) → c6(APPEND(z3, z1))
POL(APPEND(x1, x2)) = [4] + [2]x1 0.00/0.74
POL(IFAPPEND(x1, x2, x3)) = [2]x3 0.00/0.74
POL(c4(x1)) = x1 0.00/0.74
POL(c6(x1)) = x1 0.00/0.74
POL(cons(x1, x2)) = [4] + x2
Tuples:
is_empty(nil) → true 0.00/0.74
is_empty(cons(z0, z1)) → false 0.00/0.74
hd(cons(z0, z1)) → z0 0.00/0.74
tl(cons(z0, z1)) → z1 0.00/0.74
append(z0, z1) → ifappend(z0, z1, z0) 0.00/0.74
ifappend(z0, z1, nil) → z1 0.00/0.74
ifappend(z0, z1, cons(z2, z3)) → cons(z2, append(z3, z1))
S tuples:none
APPEND(z0, z1) → c4(IFAPPEND(z0, z1, z0)) 0.00/0.74
IFAPPEND(z0, z1, cons(z2, z3)) → c6(APPEND(z3, z1))
Defined Rule Symbols:
APPEND(z0, z1) → c4(IFAPPEND(z0, z1, z0)) 0.00/0.74
IFAPPEND(z0, z1, cons(z2, z3)) → c6(APPEND(z3, z1))
is_empty, hd, tl, append, ifappend
APPEND, IFAPPEND
c4, c6