YES(O(1), O(n^1)) 0.00/0.70 YES(O(1), O(n^1)) 0.00/0.72 0.00/0.72 0.00/0.72
0.00/0.72 0.00/0.720 CpxTRS0.00/0.72
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.72
↳2 CdtProblem0.00/0.72
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))0.00/0.72
↳4 CdtProblem0.00/0.72
↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.72
↳6 CdtProblem0.00/0.72
↳7 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.72
↳8 BOUNDS(O(1), O(1))0.00/0.72
dbl(S(0), S(0)) → S(S(S(S(0)))) 0.00/0.72
save(S(x)) → dbl(0, save(x)) 0.00/0.72
save(0) → 0 0.00/0.72
dbl(0, y) → y
Tuples:
dbl(S(0), S(0)) → S(S(S(S(0)))) 0.00/0.72
dbl(0, z0) → z0 0.00/0.72
save(S(z0)) → dbl(0, save(z0)) 0.00/0.72
save(0) → 0
S tuples:
SAVE(S(z0)) → c2(DBL(0, save(z0)), SAVE(z0))
K tuples:none
SAVE(S(z0)) → c2(DBL(0, save(z0)), SAVE(z0))
dbl, save
SAVE
c2
Tuples:
dbl(S(0), S(0)) → S(S(S(S(0)))) 0.00/0.72
dbl(0, z0) → z0 0.00/0.72
save(S(z0)) → dbl(0, save(z0)) 0.00/0.72
save(0) → 0
S tuples:
SAVE(S(z0)) → c2(SAVE(z0))
K tuples:none
SAVE(S(z0)) → c2(SAVE(z0))
dbl, save
SAVE
c2
We considered the (Usable) Rules:none
SAVE(S(z0)) → c2(SAVE(z0))
The order we found is given by the following interpretation:
SAVE(S(z0)) → c2(SAVE(z0))
POL(S(x1)) = [1] + x1 0.00/0.72
POL(SAVE(x1)) = [3]x1 0.00/0.72
POL(c2(x1)) = x1
Tuples:
dbl(S(0), S(0)) → S(S(S(S(0)))) 0.00/0.72
dbl(0, z0) → z0 0.00/0.72
save(S(z0)) → dbl(0, save(z0)) 0.00/0.72
save(0) → 0
S tuples:none
SAVE(S(z0)) → c2(SAVE(z0))
Defined Rule Symbols:
SAVE(S(z0)) → c2(SAVE(z0))
dbl, save
SAVE
c2