YES(O(1), O(n^1)) 0.00/0.69 YES(O(1), O(n^1)) 0.00/0.70 0.00/0.70 0.00/0.70
0.00/0.70 0.00/0.700 CpxTRS0.00/0.70
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.70
↳2 CdtProblem0.00/0.70
↳3 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.70
↳4 CdtProblem0.00/0.70
↳5 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.70
↳6 BOUNDS(O(1), O(1))0.00/0.70
a(b(x)) → b(a(x)) 0.00/0.70
a(c(x)) → x
Tuples:
a(b(z0)) → b(a(z0)) 0.00/0.70
a(c(z0)) → z0
S tuples:
A(b(z0)) → c1(A(z0))
K tuples:none
A(b(z0)) → c1(A(z0))
a
A
c1
We considered the (Usable) Rules:none
A(b(z0)) → c1(A(z0))
The order we found is given by the following interpretation:
A(b(z0)) → c1(A(z0))
POL(A(x1)) = [3]x1 0.00/0.70
POL(b(x1)) = [1] + x1 0.00/0.70
POL(c1(x1)) = x1
Tuples:
a(b(z0)) → b(a(z0)) 0.00/0.70
a(c(z0)) → z0
S tuples:none
A(b(z0)) → c1(A(z0))
Defined Rule Symbols:
A(b(z0)) → c1(A(z0))
a
A
c1