YES(O(1), O(n^1)) 0.00/0.80 YES(O(1), O(n^1)) 0.00/0.81 0.00/0.81 0.00/0.81
0.00/0.81 0.00/0.810 CpxTRS0.00/0.81
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.81
↳2 CdtProblem0.00/0.81
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))0.00/0.81
↳4 CdtProblem0.00/0.81
↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.81
↳6 CdtProblem0.00/0.81
↳7 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.81
↳8 BOUNDS(O(1), O(1))0.00/0.81
+(0, y) → y 0.00/0.81
+(s(x), 0) → s(x) 0.00/0.81
+(s(x), s(y)) → s(+(s(x), +(y, 0)))
Tuples:
+(0, z0) → z0 0.00/0.81
+(s(z0), 0) → s(z0) 0.00/0.81
+(s(z0), s(z1)) → s(+(s(z0), +(z1, 0)))
S tuples:
+'(s(z0), s(z1)) → c2(+'(s(z0), +(z1, 0)), +'(z1, 0))
K tuples:none
+'(s(z0), s(z1)) → c2(+'(s(z0), +(z1, 0)), +'(z1, 0))
+
+'
c2
Tuples:
+(0, z0) → z0 0.00/0.81
+(s(z0), 0) → s(z0) 0.00/0.81
+(s(z0), s(z1)) → s(+(s(z0), +(z1, 0)))
S tuples:
+'(s(z0), s(z1)) → c2(+'(s(z0), +(z1, 0)))
K tuples:none
+'(s(z0), s(z1)) → c2(+'(s(z0), +(z1, 0)))
+
+'
c2
We considered the (Usable) Rules:
+'(s(z0), s(z1)) → c2(+'(s(z0), +(z1, 0)))
And the Tuples:
+(0, z0) → z0 0.00/0.81
+(s(z0), 0) → s(z0)
The order we found is given by the following interpretation:
+'(s(z0), s(z1)) → c2(+'(s(z0), +(z1, 0)))
POL(+(x1, x2)) = x1 + [4]x2 0.00/0.81
POL(+'(x1, x2)) = [4]x2 0.00/0.81
POL(0) = 0 0.00/0.81
POL(c2(x1)) = x1 0.00/0.81
POL(s(x1)) = [4] + x1
Tuples:
+(0, z0) → z0 0.00/0.81
+(s(z0), 0) → s(z0) 0.00/0.81
+(s(z0), s(z1)) → s(+(s(z0), +(z1, 0)))
S tuples:none
+'(s(z0), s(z1)) → c2(+'(s(z0), +(z1, 0)))
Defined Rule Symbols:
+'(s(z0), s(z1)) → c2(+'(s(z0), +(z1, 0)))
+
+'
c2