YES(O(1), O(n^2)) 0.00/0.99 YES(O(1), O(n^2)) 2.52/1.01 2.52/1.01 2.52/1.01
2.52/1.01 2.52/1.010 CpxTRS2.52/1.01
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))2.52/1.01
↳2 CdtProblem2.52/1.01
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))2.52/1.01
↳4 CdtProblem2.52/1.01
↳5 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))2.52/1.01
↳6 CdtProblem2.52/1.01
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))2.52/1.01
↳8 CdtProblem2.52/1.01
↳9 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))2.52/1.01
↳10 CdtProblem2.52/1.01
↳11 SIsEmptyProof (BOTH BOUNDS(ID, ID))2.52/1.01
↳12 BOUNDS(O(1), O(1))2.52/1.01
and(tt, X) → activate(X) 2.52/1.01
plus(N, 0) → N 2.52/1.01
plus(N, s(M)) → s(plus(N, M)) 2.52/1.01
x(N, 0) → 0 2.52/1.01
x(N, s(M)) → plus(x(N, M), N) 2.52/1.01
activate(X) → X
Tuples:
and(tt, z0) → activate(z0) 2.52/1.01
plus(z0, 0) → z0 2.52/1.01
plus(z0, s(z1)) → s(plus(z0, z1)) 2.52/1.01
x(z0, 0) → 0 2.52/1.01
x(z0, s(z1)) → plus(x(z0, z1), z0) 2.52/1.01
activate(z0) → z0
S tuples:
AND(tt, z0) → c(ACTIVATE(z0)) 2.52/1.01
PLUS(z0, s(z1)) → c2(PLUS(z0, z1)) 2.52/1.01
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1))
K tuples:none
AND(tt, z0) → c(ACTIVATE(z0)) 2.52/1.01
PLUS(z0, s(z1)) → c2(PLUS(z0, z1)) 2.52/1.01
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1))
and, plus, x, activate
AND, PLUS, X
c, c2, c4
Tuples:
and(tt, z0) → activate(z0) 2.52/1.02
plus(z0, 0) → z0 2.52/1.02
plus(z0, s(z1)) → s(plus(z0, z1)) 2.52/1.02
x(z0, 0) → 0 2.52/1.02
x(z0, s(z1)) → plus(x(z0, z1), z0) 2.52/1.02
activate(z0) → z0
S tuples:
PLUS(z0, s(z1)) → c2(PLUS(z0, z1)) 2.52/1.02
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1)) 2.52/1.02
AND(tt, z0) → c
K tuples:none
PLUS(z0, s(z1)) → c2(PLUS(z0, z1)) 2.52/1.02
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1)) 2.52/1.02
AND(tt, z0) → c
and, plus, x, activate
PLUS, X, AND
c2, c4, c
AND(tt, z0) → c
Tuples:
and(tt, z0) → activate(z0) 2.52/1.02
plus(z0, 0) → z0 2.52/1.02
plus(z0, s(z1)) → s(plus(z0, z1)) 2.52/1.02
x(z0, 0) → 0 2.52/1.02
x(z0, s(z1)) → plus(x(z0, z1), z0) 2.52/1.02
activate(z0) → z0
S tuples:
PLUS(z0, s(z1)) → c2(PLUS(z0, z1)) 2.52/1.02
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1))
K tuples:none
PLUS(z0, s(z1)) → c2(PLUS(z0, z1)) 2.52/1.02
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1))
and, plus, x, activate
PLUS, X
c2, c4
We considered the (Usable) Rules:
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1))
And the Tuples:
x(z0, 0) → 0 2.52/1.02
x(z0, s(z1)) → plus(x(z0, z1), z0) 2.52/1.02
plus(z0, 0) → z0 2.52/1.02
plus(z0, s(z1)) → s(plus(z0, z1))
The order we found is given by the following interpretation:
PLUS(z0, s(z1)) → c2(PLUS(z0, z1)) 2.52/1.02
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1))
POL(0) = [3] 2.52/1.02
POL(PLUS(x1, x2)) = [1] 2.52/1.02
POL(X(x1, x2)) = [4]x2 2.52/1.02
POL(c2(x1)) = x1 2.52/1.02
POL(c4(x1, x2)) = x1 + x2 2.52/1.02
POL(plus(x1, x2)) = [3] + [5]x1 2.52/1.02
POL(s(x1)) = [4] + x1 2.52/1.02
POL(x(x1, x2)) = 0
Tuples:
and(tt, z0) → activate(z0) 2.52/1.02
plus(z0, 0) → z0 2.52/1.02
plus(z0, s(z1)) → s(plus(z0, z1)) 2.52/1.02
x(z0, 0) → 0 2.52/1.02
x(z0, s(z1)) → plus(x(z0, z1), z0) 2.52/1.02
activate(z0) → z0
S tuples:
PLUS(z0, s(z1)) → c2(PLUS(z0, z1)) 2.52/1.02
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1))
K tuples:
PLUS(z0, s(z1)) → c2(PLUS(z0, z1))
Defined Rule Symbols:
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1))
and, plus, x, activate
PLUS, X
c2, c4
We considered the (Usable) Rules:
PLUS(z0, s(z1)) → c2(PLUS(z0, z1))
And the Tuples:
x(z0, 0) → 0 2.52/1.02
x(z0, s(z1)) → plus(x(z0, z1), z0) 2.52/1.02
plus(z0, 0) → z0 2.52/1.02
plus(z0, s(z1)) → s(plus(z0, z1))
The order we found is given by the following interpretation:
PLUS(z0, s(z1)) → c2(PLUS(z0, z1)) 2.52/1.02
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1))
POL(0) = 0 2.52/1.02
POL(PLUS(x1, x2)) = x2 2.52/1.02
POL(X(x1, x2)) = [2]x1·x2 2.52/1.02
POL(c2(x1)) = x1 2.52/1.02
POL(c4(x1, x2)) = x1 + x2 2.52/1.02
POL(plus(x1, x2)) = [3] + [3]x2 + [3]x12 2.52/1.02
POL(s(x1)) = [1] + x1 2.52/1.02
POL(x(x1, x2)) = [3]x12
Tuples:
and(tt, z0) → activate(z0) 2.52/1.02
plus(z0, 0) → z0 2.52/1.02
plus(z0, s(z1)) → s(plus(z0, z1)) 2.52/1.02
x(z0, 0) → 0 2.52/1.02
x(z0, s(z1)) → plus(x(z0, z1), z0) 2.52/1.02
activate(z0) → z0
S tuples:none
PLUS(z0, s(z1)) → c2(PLUS(z0, z1)) 2.52/1.02
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1))
Defined Rule Symbols:
X(z0, s(z1)) → c4(PLUS(x(z0, z1), z0), X(z0, z1)) 2.52/1.02
PLUS(z0, s(z1)) → c2(PLUS(z0, z1))
and, plus, x, activate
PLUS, X
c2, c4