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 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))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 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.86
↳8 BOUNDS(O(1), O(1))0.00/0.86
w(r(x)) → r(w(x)) 0.00/0.86
b(r(x)) → r(b(x)) 0.00/0.86
b(w(x)) → w(b(x))
Tuples:
w(r(z0)) → r(w(z0)) 0.00/0.86
b(r(z0)) → r(b(z0)) 0.00/0.86
b(w(z0)) → w(b(z0))
S tuples:
W(r(z0)) → c(W(z0)) 0.00/0.86
B(r(z0)) → c1(B(z0)) 0.00/0.86
B(w(z0)) → c2(W(b(z0)), B(z0))
K tuples:none
W(r(z0)) → c(W(z0)) 0.00/0.86
B(r(z0)) → c1(B(z0)) 0.00/0.86
B(w(z0)) → c2(W(b(z0)), B(z0))
w, b
W, B
c, c1, c2
We considered the (Usable) Rules:
B(r(z0)) → c1(B(z0)) 0.00/0.86
B(w(z0)) → c2(W(b(z0)), B(z0))
And the Tuples:
b(w(z0)) → w(b(z0)) 0.00/0.86
w(r(z0)) → r(w(z0))
The order we found is given by the following interpretation:
W(r(z0)) → c(W(z0)) 0.00/0.86
B(r(z0)) → c1(B(z0)) 0.00/0.86
B(w(z0)) → c2(W(b(z0)), B(z0))
POL(B(x1)) = [3]x1 0.00/0.86
POL(W(x1)) = [1] 0.00/0.86
POL(b(x1)) = [4]x1 0.00/0.86
POL(c(x1)) = x1 0.00/0.86
POL(c1(x1)) = x1 0.00/0.86
POL(c2(x1, x2)) = x1 + x2 0.00/0.86
POL(r(x1)) = [4] + x1 0.00/0.86
POL(w(x1)) = [4] + [4]x1
Tuples:
w(r(z0)) → r(w(z0)) 0.00/0.86
b(r(z0)) → r(b(z0)) 0.00/0.86
b(w(z0)) → w(b(z0))
S tuples:
W(r(z0)) → c(W(z0)) 0.00/0.86
B(r(z0)) → c1(B(z0)) 0.00/0.86
B(w(z0)) → c2(W(b(z0)), B(z0))
K tuples:
W(r(z0)) → c(W(z0))
Defined Rule Symbols:
B(r(z0)) → c1(B(z0)) 0.00/0.86
B(w(z0)) → c2(W(b(z0)), B(z0))
w, b
W, B
c, c1, c2
We considered the (Usable) Rules:
W(r(z0)) → c(W(z0))
And the Tuples:
b(w(z0)) → w(b(z0)) 0.00/0.86
w(r(z0)) → r(w(z0))
The order we found is given by the following interpretation:
W(r(z0)) → c(W(z0)) 0.00/0.86
B(r(z0)) → c1(B(z0)) 0.00/0.86
B(w(z0)) → c2(W(b(z0)), B(z0))
POL(B(x1)) = [2]x1 0.00/0.86
POL(W(x1)) = [4]x1 0.00/0.86
POL(b(x1)) = 0 0.00/0.86
POL(c(x1)) = x1 0.00/0.86
POL(c1(x1)) = x1 0.00/0.86
POL(c2(x1, x2)) = x1 + x2 0.00/0.86
POL(r(x1)) = [2] + x1 0.00/0.86
POL(w(x1)) = [2]x1
Tuples:
w(r(z0)) → r(w(z0)) 0.00/0.86
b(r(z0)) → r(b(z0)) 0.00/0.86
b(w(z0)) → w(b(z0))
S tuples:none
W(r(z0)) → c(W(z0)) 0.00/0.86
B(r(z0)) → c1(B(z0)) 0.00/0.86
B(w(z0)) → c2(W(b(z0)), B(z0))
Defined Rule Symbols:
B(r(z0)) → c1(B(z0)) 0.00/0.86
B(w(z0)) → c2(W(b(z0)), B(z0)) 0.00/0.86
W(r(z0)) → c(W(z0))
w, b
W, B
c, c1, c2