YES(O(1), O(n^1)) 19.63/6.75 YES(O(1), O(n^1)) 19.63/6.76 19.63/6.76 19.63/6.76
19.63/6.76 19.63/6.760 CpxTRS19.63/6.76
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))19.63/6.76
↳2 CdtProblem19.63/6.76
↳3 CdtNarrowingProof (BOTH BOUNDS(ID, ID))19.63/6.76
↳4 CdtProblem19.63/6.76
↳5 CdtUnreachableProof (⇔)19.63/6.76
↳6 CdtProblem19.63/6.76
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))19.63/6.76
↳8 CdtProblem19.63/6.76
↳9 SIsEmptyProof (BOTH BOUNDS(ID, ID))19.63/6.76
↳10 BOUNDS(O(1), O(1))19.63/6.76
h(z, e(x)) → h(c(z), d(z, x)) 19.63/6.76
d(z, g(0, 0)) → e(0) 19.63/6.76
d(z, g(x, y)) → g(e(x), d(z, y)) 19.63/6.76
d(c(z), g(g(x, y), 0)) → g(d(c(z), g(x, y)), d(z, g(x, y))) 19.63/6.76
g(e(x), e(y)) → e(g(x, y))
Tuples:
h(z0, e(z1)) → h(c(z0), d(z0, z1)) 19.63/6.76
d(z0, g(0, 0)) → e(0) 19.63/6.76
d(z0, g(z1, z2)) → g(e(z1), d(z0, z2)) 19.63/6.76
d(c(z0), g(g(z1, z2), 0)) → g(d(c(z0), g(z1, z2)), d(z0, g(z1, z2))) 19.63/6.76
g(e(z0), e(z1)) → e(g(z0, z1))
S tuples:
H(z0, e(z1)) → c1(H(c(z0), d(z0, z1)), D(z0, z1)) 19.63/6.76
D(z0, g(z1, z2)) → c3(G(e(z1), d(z0, z2)), D(z0, z2)) 19.63/6.76
D(c(z0), g(g(z1, z2), 0)) → c4(G(d(c(z0), g(z1, z2)), d(z0, g(z1, z2))), D(c(z0), g(z1, z2)), G(z1, z2), D(z0, g(z1, z2)), G(z1, z2)) 19.63/6.76
G(e(z0), e(z1)) → c5(G(z0, z1))
K tuples:none
H(z0, e(z1)) → c1(H(c(z0), d(z0, z1)), D(z0, z1)) 19.63/6.76
D(z0, g(z1, z2)) → c3(G(e(z1), d(z0, z2)), D(z0, z2)) 19.63/6.76
D(c(z0), g(g(z1, z2), 0)) → c4(G(d(c(z0), g(z1, z2)), d(z0, g(z1, z2))), D(c(z0), g(z1, z2)), G(z1, z2), D(z0, g(z1, z2)), G(z1, z2)) 19.63/6.76
G(e(z0), e(z1)) → c5(G(z0, z1))
h, d, g
H, D, G
c1, c3, c4, c5
H(z0, e(g(0, 0))) → c1(H(c(z0), e(0)), D(z0, g(0, 0))) 19.63/6.76
H(z0, e(g(z1, z2))) → c1(H(c(z0), g(e(z1), d(z0, z2))), D(z0, g(z1, z2))) 19.63/6.76
H(c(z0), e(g(g(z1, z2), 0))) → c1(H(c(c(z0)), g(d(c(z0), g(z1, z2)), d(z0, g(z1, z2)))), D(c(z0), g(g(z1, z2), 0)))
Tuples:
h(z0, e(z1)) → h(c(z0), d(z0, z1)) 19.63/6.76
d(z0, g(0, 0)) → e(0) 19.63/6.76
d(z0, g(z1, z2)) → g(e(z1), d(z0, z2)) 19.63/6.76
d(c(z0), g(g(z1, z2), 0)) → g(d(c(z0), g(z1, z2)), d(z0, g(z1, z2))) 19.63/6.76
g(e(z0), e(z1)) → e(g(z0, z1))
S tuples:
D(z0, g(z1, z2)) → c3(G(e(z1), d(z0, z2)), D(z0, z2)) 19.63/6.76
D(c(z0), g(g(z1, z2), 0)) → c4(G(d(c(z0), g(z1, z2)), d(z0, g(z1, z2))), D(c(z0), g(z1, z2)), G(z1, z2), D(z0, g(z1, z2)), G(z1, z2)) 19.63/6.76
G(e(z0), e(z1)) → c5(G(z0, z1)) 19.63/6.76
H(z0, e(g(0, 0))) → c1(H(c(z0), e(0)), D(z0, g(0, 0))) 19.63/6.76
H(z0, e(g(z1, z2))) → c1(H(c(z0), g(e(z1), d(z0, z2))), D(z0, g(z1, z2))) 19.63/6.76
H(c(z0), e(g(g(z1, z2), 0))) → c1(H(c(c(z0)), g(d(c(z0), g(z1, z2)), d(z0, g(z1, z2)))), D(c(z0), g(g(z1, z2), 0)))
K tuples:none
D(z0, g(z1, z2)) → c3(G(e(z1), d(z0, z2)), D(z0, z2)) 19.63/6.76
D(c(z0), g(g(z1, z2), 0)) → c4(G(d(c(z0), g(z1, z2)), d(z0, g(z1, z2))), D(c(z0), g(z1, z2)), G(z1, z2), D(z0, g(z1, z2)), G(z1, z2)) 19.63/6.76
G(e(z0), e(z1)) → c5(G(z0, z1)) 19.63/6.76
H(z0, e(g(0, 0))) → c1(H(c(z0), e(0)), D(z0, g(0, 0))) 19.63/6.77
H(z0, e(g(z1, z2))) → c1(H(c(z0), g(e(z1), d(z0, z2))), D(z0, g(z1, z2))) 19.63/6.77
H(c(z0), e(g(g(z1, z2), 0))) → c1(H(c(c(z0)), g(d(c(z0), g(z1, z2)), d(z0, g(z1, z2)))), D(c(z0), g(g(z1, z2), 0)))
h, d, g
D, G, H
c3, c4, c5, c1
D(z0, g(z1, z2)) → c3(G(e(z1), d(z0, z2)), D(z0, z2)) 19.63/6.77
D(c(z0), g(g(z1, z2), 0)) → c4(G(d(c(z0), g(z1, z2)), d(z0, g(z1, z2))), D(c(z0), g(z1, z2)), G(z1, z2), D(z0, g(z1, z2)), G(z1, z2)) 19.63/6.77
H(z0, e(g(0, 0))) → c1(H(c(z0), e(0)), D(z0, g(0, 0))) 19.63/6.77
H(z0, e(g(z1, z2))) → c1(H(c(z0), g(e(z1), d(z0, z2))), D(z0, g(z1, z2))) 19.63/6.77
H(c(z0), e(g(g(z1, z2), 0))) → c1(H(c(c(z0)), g(d(c(z0), g(z1, z2)), d(z0, g(z1, z2)))), D(c(z0), g(g(z1, z2), 0)))
Tuples:
h(z0, e(z1)) → h(c(z0), d(z0, z1)) 19.63/6.77
d(z0, g(0, 0)) → e(0) 19.63/6.77
d(z0, g(z1, z2)) → g(e(z1), d(z0, z2)) 19.63/6.77
d(c(z0), g(g(z1, z2), 0)) → g(d(c(z0), g(z1, z2)), d(z0, g(z1, z2))) 19.63/6.77
g(e(z0), e(z1)) → e(g(z0, z1))
S tuples:
G(e(z0), e(z1)) → c5(G(z0, z1))
K tuples:none
G(e(z0), e(z1)) → c5(G(z0, z1))
h, d, g
G
c5
We considered the (Usable) Rules:none
G(e(z0), e(z1)) → c5(G(z0, z1))
The order we found is given by the following interpretation:
G(e(z0), e(z1)) → c5(G(z0, z1))
POL(G(x1, x2)) = [2]x2 19.63/6.77
POL(c5(x1)) = x1 19.63/6.77
POL(e(x1)) = [1] + x1
Tuples:
h(z0, e(z1)) → h(c(z0), d(z0, z1)) 19.63/6.77
d(z0, g(0, 0)) → e(0) 19.63/6.77
d(z0, g(z1, z2)) → g(e(z1), d(z0, z2)) 19.63/6.77
d(c(z0), g(g(z1, z2), 0)) → g(d(c(z0), g(z1, z2)), d(z0, g(z1, z2))) 19.63/6.77
g(e(z0), e(z1)) → e(g(z0, z1))
S tuples:none
G(e(z0), e(z1)) → c5(G(z0, z1))
Defined Rule Symbols:
G(e(z0), e(z1)) → c5(G(z0, z1))
h, d, g
G
c5