YES(O(1), O(n^1)) 0.00/0.75 YES(O(1), O(n^1)) 0.00/0.77 0.00/0.77 0.00/0.77
0.00/0.77 0.00/0.770 CpxTRS0.00/0.77
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.77
↳2 CdtProblem0.00/0.77
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))0.00/0.77
↳4 CdtProblem0.00/0.77
↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.77
↳6 CdtProblem0.00/0.77
↳7 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.77
↳8 BOUNDS(O(1), O(1))0.00/0.77
admit(x, nil) → nil 0.00/0.77
admit(x, .(u, .(v, .(w, z)))) → cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z))))) 0.00/0.77
cond(true, y) → y
Tuples:
admit(z0, nil) → nil 0.00/0.77
admit(z0, .(z1, .(z2, .(w, z3)))) → cond(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))) 0.00/0.77
cond(true, z0) → z0
S tuples:
ADMIT(z0, .(z1, .(z2, .(w, z3)))) → c1(COND(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))), ADMIT(carry(z0, z1, z2), z3))
K tuples:none
ADMIT(z0, .(z1, .(z2, .(w, z3)))) → c1(COND(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))), ADMIT(carry(z0, z1, z2), z3))
admit, cond
ADMIT
c1
Tuples:
admit(z0, nil) → nil 0.00/0.77
admit(z0, .(z1, .(z2, .(w, z3)))) → cond(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))) 0.00/0.77
cond(true, z0) → z0
S tuples:
ADMIT(z0, .(z1, .(z2, .(w, z3)))) → c1(ADMIT(carry(z0, z1, z2), z3))
K tuples:none
ADMIT(z0, .(z1, .(z2, .(w, z3)))) → c1(ADMIT(carry(z0, z1, z2), z3))
admit, cond
ADMIT
c1
We considered the (Usable) Rules:none
ADMIT(z0, .(z1, .(z2, .(w, z3)))) → c1(ADMIT(carry(z0, z1, z2), z3))
The order we found is given by the following interpretation:
ADMIT(z0, .(z1, .(z2, .(w, z3)))) → c1(ADMIT(carry(z0, z1, z2), z3))
POL(.(x1, x2)) = x1 + x2 0.00/0.77
POL(ADMIT(x1, x2)) = x1 + x2 0.00/0.77
POL(c1(x1)) = x1 0.00/0.77
POL(carry(x1, x2, x3)) = x1 + x2 + x3 0.00/0.77
POL(w) = [1]
Tuples:
admit(z0, nil) → nil 0.00/0.77
admit(z0, .(z1, .(z2, .(w, z3)))) → cond(=(sum(z0, z1, z2), w), .(z1, .(z2, .(w, admit(carry(z0, z1, z2), z3))))) 0.00/0.77
cond(true, z0) → z0
S tuples:none
ADMIT(z0, .(z1, .(z2, .(w, z3)))) → c1(ADMIT(carry(z0, z1, z2), z3))
Defined Rule Symbols:
ADMIT(z0, .(z1, .(z2, .(w, z3)))) → c1(ADMIT(carry(z0, z1, z2), z3))
admit, cond
ADMIT
c1