YES(O(1), O(n^1)) 0.00/0.75 YES(O(1), O(n^1)) 0.00/0.76 0.00/0.76 0.00/0.76
0.00/0.76 0.00/0.760 CpxTRS0.00/0.76
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.76
↳2 CdtProblem0.00/0.76
↳3 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.76
↳4 CdtProblem0.00/0.76
↳5 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.76
↳6 BOUNDS(O(1), O(1))0.00/0.76
double(0) → 0 0.00/0.76
double(s(x)) → s(s(double(x))) 0.00/0.76
+(x, 0) → x 0.00/0.76
+(x, s(y)) → s(+(x, y)) 0.00/0.76
+(s(x), y) → s(+(x, y)) 0.00/0.76
double(x) → +(x, x)
Tuples:
double(0) → 0 0.00/0.76
double(s(z0)) → s(s(double(z0))) 0.00/0.76
double(z0) → +(z0, z0) 0.00/0.76
+(z0, 0) → z0 0.00/0.76
+(z0, s(z1)) → s(+(z0, z1)) 0.00/0.76
+(s(z0), z1) → s(+(z0, z1))
S tuples:
DOUBLE(s(z0)) → c1(DOUBLE(z0)) 0.00/0.76
DOUBLE(z0) → c2(+'(z0, z0)) 0.00/0.76
+'(z0, s(z1)) → c4(+'(z0, z1)) 0.00/0.76
+'(s(z0), z1) → c5(+'(z0, z1))
K tuples:none
DOUBLE(s(z0)) → c1(DOUBLE(z0)) 0.00/0.76
DOUBLE(z0) → c2(+'(z0, z0)) 0.00/0.76
+'(z0, s(z1)) → c4(+'(z0, z1)) 0.00/0.76
+'(s(z0), z1) → c5(+'(z0, z1))
double, +
DOUBLE, +'
c1, c2, c4, c5
We considered the (Usable) Rules:none
DOUBLE(s(z0)) → c1(DOUBLE(z0)) 0.00/0.76
DOUBLE(z0) → c2(+'(z0, z0)) 0.00/0.76
+'(z0, s(z1)) → c4(+'(z0, z1)) 0.00/0.76
+'(s(z0), z1) → c5(+'(z0, z1))
The order we found is given by the following interpretation:
DOUBLE(s(z0)) → c1(DOUBLE(z0)) 0.00/0.76
DOUBLE(z0) → c2(+'(z0, z0)) 0.00/0.76
+'(z0, s(z1)) → c4(+'(z0, z1)) 0.00/0.76
+'(s(z0), z1) → c5(+'(z0, z1))
POL(+'(x1, x2)) = [1] + x1 + x2 0.00/0.76
POL(DOUBLE(x1)) = [2] + [5]x1 0.00/0.76
POL(c1(x1)) = x1 0.00/0.76
POL(c2(x1)) = x1 0.00/0.76
POL(c4(x1)) = x1 0.00/0.76
POL(c5(x1)) = x1 0.00/0.76
POL(s(x1)) = [3] + x1
Tuples:
double(0) → 0 0.00/0.76
double(s(z0)) → s(s(double(z0))) 0.00/0.76
double(z0) → +(z0, z0) 0.00/0.76
+(z0, 0) → z0 0.00/0.76
+(z0, s(z1)) → s(+(z0, z1)) 0.00/0.76
+(s(z0), z1) → s(+(z0, z1))
S tuples:none
DOUBLE(s(z0)) → c1(DOUBLE(z0)) 0.00/0.76
DOUBLE(z0) → c2(+'(z0, z0)) 0.00/0.76
+'(z0, s(z1)) → c4(+'(z0, z1)) 0.00/0.76
+'(s(z0), z1) → c5(+'(z0, z1))
Defined Rule Symbols:
DOUBLE(s(z0)) → c1(DOUBLE(z0)) 0.00/0.76
DOUBLE(z0) → c2(+'(z0, z0)) 0.00/0.76
+'(z0, s(z1)) → c4(+'(z0, z1)) 0.00/0.76
+'(s(z0), z1) → c5(+'(z0, z1))
double, +
DOUBLE, +'
c1, c2, c4, c5