YES(O(1), O(n^2)) 0.00/0.73 YES(O(1), O(n^2)) 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^2))))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
*(x, +(y, z)) → +(*(x, y), *(x, z)) 0.00/0.74
*(+(x, y), z) → +(*(x, z), *(y, z)) 0.00/0.74
*(x, 1) → x 0.00/0.74
*(1, y) → y
Tuples:
*(z0, +(z1, z2)) → +(*(z0, z1), *(z0, z2)) 0.00/0.74
*(+(z0, z1), z2) → +(*(z0, z2), *(z1, z2)) 0.00/0.74
*(z0, 1) → z0 0.00/0.74
*(1, z0) → z0
S tuples:
*'(z0, +(z1, z2)) → c(*'(z0, z1), *'(z0, z2)) 0.00/0.74
*'(+(z0, z1), z2) → c1(*'(z0, z2), *'(z1, z2))
K tuples:none
*'(z0, +(z1, z2)) → c(*'(z0, z1), *'(z0, z2)) 0.00/0.74
*'(+(z0, z1), z2) → c1(*'(z0, z2), *'(z1, z2))
*
*'
c, c1
We considered the (Usable) Rules:none
*'(z0, +(z1, z2)) → c(*'(z0, z1), *'(z0, z2)) 0.00/0.74
*'(+(z0, z1), z2) → c1(*'(z0, z2), *'(z1, z2))
The order we found is given by the following interpretation:
*'(z0, +(z1, z2)) → c(*'(z0, z1), *'(z0, z2)) 0.00/0.74
*'(+(z0, z1), z2) → c1(*'(z0, z2), *'(z1, z2))
POL(*'(x1, x2)) = [2]x1 + [2]x2 + [2]x1·x2 0.00/0.74
POL(+(x1, x2)) = [1] + x1 + x2 0.00/0.74
POL(c(x1, x2)) = x1 + x2 0.00/0.74
POL(c1(x1, x2)) = x1 + x2
Tuples:
*(z0, +(z1, z2)) → +(*(z0, z1), *(z0, z2)) 0.00/0.74
*(+(z0, z1), z2) → +(*(z0, z2), *(z1, z2)) 0.00/0.74
*(z0, 1) → z0 0.00/0.74
*(1, z0) → z0
S tuples:none
*'(z0, +(z1, z2)) → c(*'(z0, z1), *'(z0, z2)) 0.00/0.74
*'(+(z0, z1), z2) → c1(*'(z0, z2), *'(z1, z2))
Defined Rule Symbols:
*'(z0, +(z1, z2)) → c(*'(z0, z1), *'(z0, z2)) 0.00/0.74
*'(+(z0, z1), z2) → c1(*'(z0, z2), *'(z1, z2))
*
*'
c, c1