YES(O(1), O(n^1)) 96.12/33.42 YES(O(1), O(n^1)) 96.12/33.45 96.12/33.45 96.12/33.45
96.12/33.45 96.12/33.450 CpxTRS96.12/33.45
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳2 CdtProblem96.12/33.45
↳3 CdtNarrowingProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳4 CdtProblem96.12/33.45
↳5 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳6 CdtProblem96.12/33.45
↳7 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳8 CdtProblem96.12/33.45
↳9 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))96.12/33.45
↳10 CdtProblem96.12/33.45
↳11 CdtNarrowingProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳12 CdtProblem96.12/33.45
↳13 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳14 CdtProblem96.12/33.45
↳15 CdtNarrowingProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳16 CdtProblem96.12/33.45
↳17 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳18 CdtProblem96.12/33.45
↳19 CdtNarrowingProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳20 CdtProblem96.12/33.45
↳21 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳22 CdtProblem96.12/33.45
↳23 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))96.12/33.45
↳24 CdtProblem96.12/33.45
↳25 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))96.12/33.45
↳26 CdtProblem96.12/33.45
↳27 CdtNarrowingProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳28 CdtProblem96.12/33.45
↳29 CdtUnreachableProof (⇔)96.12/33.45
↳30 CdtProblem96.12/33.45
↳31 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳32 CdtProblem96.12/33.45
↳33 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳34 CdtProblem96.12/33.45
↳35 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))96.12/33.45
↳36 CdtProblem96.12/33.45
↳37 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))96.12/33.45
↳38 CdtProblem96.12/33.45
↳39 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))96.12/33.45
↳40 CdtProblem96.12/33.45
↳41 SIsEmptyProof (BOTH BOUNDS(ID, ID))96.12/33.45
↳42 BOUNDS(O(1), O(1))96.12/33.45
active(f(X, g(X), Y)) → mark(f(Y, Y, Y)) 96.12/33.45
active(g(b)) → mark(c) 96.12/33.45
active(b) → mark(c) 96.12/33.45
active(g(X)) → g(active(X)) 96.12/33.45
g(mark(X)) → mark(g(X)) 96.12/33.45
proper(f(X1, X2, X3)) → f(proper(X1), proper(X2), proper(X3)) 96.12/33.45
proper(g(X)) → g(proper(X)) 96.12/33.45
proper(b) → ok(b) 96.12/33.45
proper(c) → ok(c) 96.12/33.45
f(ok(X1), ok(X2), ok(X3)) → ok(f(X1, X2, X3)) 96.47/33.50
g(ok(X)) → ok(g(X)) 96.47/33.50
top(mark(X)) → top(proper(X)) 96.47/33.50
top(ok(X)) → top(active(X))
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.50
active(g(b)) → mark(c) 96.47/33.50
active(b) → mark(c) 96.47/33.50
active(g(z0)) → g(active(z0)) 96.47/33.50
g(mark(z0)) → mark(g(z0)) 96.47/33.50
g(ok(z0)) → ok(g(z0)) 96.47/33.50
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.50
proper(g(z0)) → g(proper(z0)) 96.47/33.50
proper(b) → ok(b) 96.47/33.50
proper(c) → ok(c) 96.47/33.50
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.50
top(mark(z0)) → top(proper(z0)) 96.47/33.50
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.50
ACTIVE(g(z0)) → c4(G(active(z0)), ACTIVE(z0)) 96.47/33.50
G(mark(z0)) → c5(G(z0)) 96.47/33.50
G(ok(z0)) → c6(G(z0)) 96.47/33.50
PROPER(f(z0, z1, z2)) → c7(F(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 96.47/33.50
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.50
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.50
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.50
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0))
K tuples:none
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.50
ACTIVE(g(z0)) → c4(G(active(z0)), ACTIVE(z0)) 96.47/33.50
G(mark(z0)) → c5(G(z0)) 96.47/33.50
G(ok(z0)) → c6(G(z0)) 96.47/33.50
PROPER(f(z0, z1, z2)) → c7(F(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 96.47/33.50
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.50
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.50
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.50
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0))
active, g, proper, f, top
ACTIVE, G, PROPER, F, TOP
c1, c4, c5, c6, c7, c8, c11, c12, c13
ACTIVE(g(f(z0, g(z0), z1))) → c4(G(mark(f(z1, z1, z1))), ACTIVE(f(z0, g(z0), z1))) 96.47/33.50
ACTIVE(g(g(b))) → c4(G(mark(c)), ACTIVE(g(b))) 96.47/33.50
ACTIVE(g(b)) → c4(G(mark(c)), ACTIVE(b)) 96.47/33.50
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0)))
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.50
active(g(b)) → mark(c) 96.47/33.50
active(b) → mark(c) 96.47/33.50
active(g(z0)) → g(active(z0)) 96.47/33.50
g(mark(z0)) → mark(g(z0)) 96.47/33.50
g(ok(z0)) → ok(g(z0)) 96.47/33.50
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.50
proper(g(z0)) → g(proper(z0)) 96.47/33.50
proper(b) → ok(b) 96.47/33.50
proper(c) → ok(c) 96.47/33.50
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.50
top(mark(z0)) → top(proper(z0)) 96.47/33.50
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.50
G(mark(z0)) → c5(G(z0)) 96.47/33.50
G(ok(z0)) → c6(G(z0)) 96.47/33.50
PROPER(f(z0, z1, z2)) → c7(F(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 96.47/33.50
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.50
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.50
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.50
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.50
ACTIVE(g(f(z0, g(z0), z1))) → c4(G(mark(f(z1, z1, z1))), ACTIVE(f(z0, g(z0), z1))) 96.47/33.50
ACTIVE(g(g(b))) → c4(G(mark(c)), ACTIVE(g(b))) 96.47/33.50
ACTIVE(g(b)) → c4(G(mark(c)), ACTIVE(b)) 96.47/33.50
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0)))
K tuples:none
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.50
G(mark(z0)) → c5(G(z0)) 96.47/33.50
G(ok(z0)) → c6(G(z0)) 96.47/33.50
PROPER(f(z0, z1, z2)) → c7(F(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 96.47/33.50
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.50
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.50
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.50
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.50
ACTIVE(g(f(z0, g(z0), z1))) → c4(G(mark(f(z1, z1, z1))), ACTIVE(f(z0, g(z0), z1))) 96.47/33.51
ACTIVE(g(g(b))) → c4(G(mark(c)), ACTIVE(g(b))) 96.47/33.51
ACTIVE(g(b)) → c4(G(mark(c)), ACTIVE(b)) 96.47/33.51
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0)))
active, g, proper, f, top
ACTIVE, G, PROPER, F, TOP
c1, c5, c6, c7, c8, c11, c12, c13, c4
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.51
active(g(b)) → mark(c) 96.47/33.51
active(b) → mark(c) 96.47/33.51
active(g(z0)) → g(active(z0)) 96.47/33.51
g(mark(z0)) → mark(g(z0)) 96.47/33.51
g(ok(z0)) → ok(g(z0)) 96.47/33.51
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.51
proper(g(z0)) → g(proper(z0)) 96.47/33.51
proper(b) → ok(b) 96.47/33.51
proper(c) → ok(c) 96.47/33.51
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.51
top(mark(z0)) → top(proper(z0)) 96.47/33.51
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.51
G(mark(z0)) → c5(G(z0)) 96.47/33.51
G(ok(z0)) → c6(G(z0)) 96.47/33.51
PROPER(f(z0, z1, z2)) → c7(F(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 96.47/33.51
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.51
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.51
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.51
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c4(G(mark(f(z1, z1, z1))), ACTIVE(f(z0, g(z0), z1))) 96.47/33.51
ACTIVE(g(g(b))) → c4(G(mark(c)), ACTIVE(g(b))) 96.47/33.51
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.51
ACTIVE(g(b)) → c4(G(mark(c)))
K tuples:none
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.51
G(mark(z0)) → c5(G(z0)) 96.47/33.51
G(ok(z0)) → c6(G(z0)) 96.47/33.51
PROPER(f(z0, z1, z2)) → c7(F(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 96.47/33.51
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.51
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.51
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.51
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c4(G(mark(f(z1, z1, z1))), ACTIVE(f(z0, g(z0), z1))) 96.47/33.51
ACTIVE(g(g(b))) → c4(G(mark(c)), ACTIVE(g(b))) 96.47/33.51
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.51
ACTIVE(g(b)) → c4(G(mark(c)))
active, g, proper, f, top
ACTIVE, G, PROPER, F, TOP
c1, c5, c6, c7, c8, c11, c12, c13, c4, c4
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.51
active(g(b)) → mark(c) 96.47/33.51
active(b) → mark(c) 96.47/33.51
active(g(z0)) → g(active(z0)) 96.47/33.51
g(mark(z0)) → mark(g(z0)) 96.47/33.51
g(ok(z0)) → ok(g(z0)) 96.47/33.51
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.51
proper(g(z0)) → g(proper(z0)) 96.47/33.51
proper(b) → ok(b) 96.47/33.51
proper(c) → ok(c) 96.47/33.51
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.51
top(mark(z0)) → top(proper(z0)) 96.47/33.51
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.51
G(mark(z0)) → c5(G(z0)) 96.47/33.51
G(ok(z0)) → c6(G(z0)) 96.47/33.51
PROPER(f(z0, z1, z2)) → c7(F(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 96.47/33.51
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.51
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.51
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.51
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.51
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.51
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.51
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.51
ACTIVE(g(g(b))) → c2(ACTIVE(g(b)))
K tuples:none
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.51
G(mark(z0)) → c5(G(z0)) 96.47/33.51
G(ok(z0)) → c6(G(z0)) 96.47/33.51
PROPER(f(z0, z1, z2)) → c7(F(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 96.47/33.51
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.51
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.51
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.51
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.51
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.51
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.51
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.51
ACTIVE(g(g(b))) → c2(ACTIVE(g(b)))
active, g, proper, f, top
ACTIVE, G, PROPER, F, TOP
c1, c5, c6, c7, c8, c11, c12, c13, c4, c4, c2
We considered the (Usable) Rules:
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.51
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.51
ACTIVE(g(g(b))) → c2(ACTIVE(g(b)))
And the Tuples:
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.51
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.51
active(g(b)) → mark(c) 96.47/33.51
active(b) → mark(c) 96.47/33.51
active(g(z0)) → g(active(z0)) 96.47/33.51
g(mark(z0)) → mark(g(z0)) 96.47/33.51
g(ok(z0)) → ok(g(z0)) 96.47/33.51
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.51
proper(g(z0)) → g(proper(z0)) 96.47/33.51
proper(b) → ok(b) 96.47/33.51
proper(c) → ok(c)
The order we found is given by the following interpretation:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.51
G(mark(z0)) → c5(G(z0)) 96.47/33.51
G(ok(z0)) → c6(G(z0)) 96.47/33.51
PROPER(f(z0, z1, z2)) → c7(F(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 96.47/33.51
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.51
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.51
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.51
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.51
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.51
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.51
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.51
ACTIVE(g(g(b))) → c2(ACTIVE(g(b)))
POL(ACTIVE(x1)) = x1 96.47/33.51
POL(F(x1, x2, x3)) = 0 96.47/33.51
POL(G(x1)) = 0 96.47/33.51
POL(PROPER(x1)) = 0 96.47/33.51
POL(TOP(x1)) = [4]x1 96.47/33.51
POL(active(x1)) = 0 96.47/33.51
POL(b) = [1] 96.47/33.51
POL(c) = 0 96.47/33.51
POL(c1(x1)) = x1 96.47/33.51
POL(c11(x1)) = x1 96.47/33.51
POL(c12(x1, x2)) = x1 + x2 96.47/33.51
POL(c13(x1, x2)) = x1 + x2 96.47/33.51
POL(c2(x1)) = x1 96.47/33.51
POL(c4(x1)) = x1 96.47/33.51
POL(c4(x1, x2)) = x1 + x2 96.47/33.51
POL(c5(x1)) = x1 96.47/33.51
POL(c6(x1)) = x1 96.47/33.51
POL(c7(x1, x2, x3, x4)) = x1 + x2 + x3 + x4 96.47/33.51
POL(c8(x1, x2)) = x1 + x2 96.47/33.51
POL(f(x1, x2, x3)) = 0 96.47/33.51
POL(g(x1)) = [2]x1 96.47/33.51
POL(mark(x1)) = x1 96.47/33.51
POL(ok(x1)) = x1 96.47/33.51
POL(proper(x1)) = x1
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.51
active(g(b)) → mark(c) 96.47/33.51
active(b) → mark(c) 96.47/33.51
active(g(z0)) → g(active(z0)) 96.47/33.51
g(mark(z0)) → mark(g(z0)) 96.47/33.51
g(ok(z0)) → ok(g(z0)) 96.47/33.51
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.51
proper(g(z0)) → g(proper(z0)) 96.47/33.51
proper(b) → ok(b) 96.47/33.51
proper(c) → ok(c) 96.47/33.51
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.51
top(mark(z0)) → top(proper(z0)) 96.47/33.51
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.51
G(mark(z0)) → c5(G(z0)) 96.47/33.51
G(ok(z0)) → c6(G(z0)) 96.47/33.51
PROPER(f(z0, z1, z2)) → c7(F(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 96.47/33.51
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.51
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.51
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.51
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.51
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.51
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.51
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.51
ACTIVE(g(g(b))) → c2(ACTIVE(g(b)))
K tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.51
G(mark(z0)) → c5(G(z0)) 96.47/33.51
G(ok(z0)) → c6(G(z0)) 96.47/33.51
PROPER(f(z0, z1, z2)) → c7(F(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 96.47/33.51
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.51
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.51
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.51
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.51
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1)))
Defined Rule Symbols:
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.51
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.51
ACTIVE(g(g(b))) → c2(ACTIVE(g(b)))
active, g, proper, f, top
ACTIVE, G, PROPER, F, TOP
c1, c5, c6, c7, c8, c11, c12, c13, c4, c4, c2
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.51
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.51
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1), PROPER(b)) 96.47/33.51
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1), PROPER(c)) 96.47/33.51
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.51
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.51
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(b), PROPER(x2)) 96.47/33.51
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(c), PROPER(x2)) 96.47/33.51
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.51
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.51
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(b), PROPER(x1), PROPER(x2)) 96.47/33.51
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(c), PROPER(x1), PROPER(x2))
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.51
active(g(b)) → mark(c) 96.47/33.51
active(b) → mark(c) 96.47/33.51
active(g(z0)) → g(active(z0)) 96.47/33.51
g(mark(z0)) → mark(g(z0)) 96.47/33.51
g(ok(z0)) → ok(g(z0)) 96.47/33.51
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.51
proper(g(z0)) → g(proper(z0)) 96.47/33.51
proper(b) → ok(b) 96.47/33.51
proper(c) → ok(c) 96.47/33.51
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.51
top(mark(z0)) → top(proper(z0)) 96.47/33.51
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.51
G(mark(z0)) → c5(G(z0)) 96.47/33.51
G(ok(z0)) → c6(G(z0)) 96.47/33.51
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.51
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.51
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.51
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.51
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.51
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.51
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.51
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.51
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.51
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.51
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.51
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1), PROPER(b)) 96.47/33.51
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1), PROPER(c)) 96.47/33.51
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.51
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.51
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(b), PROPER(x2)) 96.47/33.51
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(c), PROPER(x2)) 96.47/33.51
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.51
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.51
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(b), PROPER(x1), PROPER(x2)) 96.47/33.52
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(c), PROPER(x1), PROPER(x2))
K tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.52
G(mark(z0)) → c5(G(z0)) 96.47/33.52
G(ok(z0)) → c6(G(z0)) 96.47/33.52
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.52
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.52
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.52
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.52
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.52
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.52
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.52
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.52
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.52
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1), PROPER(b)) 96.47/33.52
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1), PROPER(c)) 96.47/33.52
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.52
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.52
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(b), PROPER(x2)) 96.47/33.52
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(c), PROPER(x2)) 96.47/33.52
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.52
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.52
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(b), PROPER(x1), PROPER(x2)) 96.47/33.52
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(c), PROPER(x1), PROPER(x2))
Defined Rule Symbols:
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.52
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.52
ACTIVE(g(g(b))) → c2(ACTIVE(g(b)))
active, g, proper, f, top
ACTIVE, G, PROPER, F, TOP
c1, c5, c6, c8, c11, c12, c13, c4, c4, c2, c7
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.52
active(g(b)) → mark(c) 96.47/33.52
active(b) → mark(c) 96.47/33.52
active(g(z0)) → g(active(z0)) 96.47/33.52
g(mark(z0)) → mark(g(z0)) 96.47/33.52
g(ok(z0)) → ok(g(z0)) 96.47/33.52
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.52
proper(g(z0)) → g(proper(z0)) 96.47/33.52
proper(b) → ok(b) 96.47/33.52
proper(c) → ok(c) 96.47/33.52
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.52
top(mark(z0)) → top(proper(z0)) 96.47/33.52
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.52
G(mark(z0)) → c5(G(z0)) 96.47/33.52
G(ok(z0)) → c6(G(z0)) 96.47/33.52
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.52
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.52
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.52
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.52
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.52
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.52
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.52
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.52
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.52
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.52
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.52
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.52
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.52
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.52
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.52
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.52
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.52
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.52
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.52
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.52
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.52
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.52
G(mark(z0)) → c5(G(z0)) 96.47/33.52
G(ok(z0)) → c6(G(z0)) 96.47/33.54
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
Defined Rule Symbols:
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b)))
active, g, proper, f, top
ACTIVE, G, PROPER, F, TOP
c1, c5, c6, c8, c11, c12, c13, c4, c4, c2, c7, c7
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b)), PROPER(b)) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c)), PROPER(c))
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.54
active(g(b)) → mark(c) 96.47/33.54
active(b) → mark(c) 96.47/33.54
active(g(z0)) → g(active(z0)) 96.47/33.54
g(mark(z0)) → mark(g(z0)) 96.47/33.54
g(ok(z0)) → ok(g(z0)) 96.47/33.54
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.54
proper(g(z0)) → g(proper(z0)) 96.47/33.54
proper(b) → ok(b) 96.47/33.54
proper(c) → ok(c) 96.47/33.54
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.54
top(mark(z0)) → top(proper(z0)) 96.47/33.54
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.54
G(mark(z0)) → c5(G(z0)) 96.47/33.54
G(ok(z0)) → c6(G(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b)), PROPER(b)) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c)), PROPER(c))
K tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.54
G(mark(z0)) → c5(G(z0)) 96.47/33.54
G(ok(z0)) → c6(G(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b)), PROPER(b)) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c)), PROPER(c))
Defined Rule Symbols:
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b)))
active, g, proper, f, top
ACTIVE, G, F, TOP, PROPER
c1, c5, c6, c11, c12, c13, c4, c4, c2, c7, c7, c8
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.54
active(g(b)) → mark(c) 96.47/33.54
active(b) → mark(c) 96.47/33.54
active(g(z0)) → g(active(z0)) 96.47/33.54
g(mark(z0)) → mark(g(z0)) 96.47/33.54
g(ok(z0)) → ok(g(z0)) 96.47/33.54
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.54
proper(g(z0)) → g(proper(z0)) 96.47/33.54
proper(b) → ok(b) 96.47/33.54
proper(c) → ok(c) 96.47/33.54
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.54
top(mark(z0)) → top(proper(z0)) 96.47/33.54
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.54
G(mark(z0)) → c5(G(z0)) 96.47/33.54
G(ok(z0)) → c6(G(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c)))
K tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.54
G(mark(z0)) → c5(G(z0)) 96.47/33.54
G(ok(z0)) → c6(G(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(mark(z0)) → c12(TOP(proper(z0)), PROPER(z0)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c)))
Defined Rule Symbols:
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b)))
active, g, proper, f, top
ACTIVE, G, F, TOP, PROPER
c1, c5, c6, c11, c12, c13, c4, c4, c2, c7, c7, c8, c8
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
TOP(mark(b)) → c12(TOP(ok(b)), PROPER(b)) 96.47/33.54
TOP(mark(c)) → c12(TOP(ok(c)), PROPER(c))
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.54
active(g(b)) → mark(c) 96.47/33.54
active(b) → mark(c) 96.47/33.54
active(g(z0)) → g(active(z0)) 96.47/33.54
g(mark(z0)) → mark(g(z0)) 96.47/33.54
g(ok(z0)) → ok(g(z0)) 96.47/33.54
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.54
proper(g(z0)) → g(proper(z0)) 96.47/33.54
proper(b) → ok(b) 96.47/33.54
proper(c) → ok(c) 96.47/33.54
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.54
top(mark(z0)) → top(proper(z0)) 96.47/33.54
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.54
G(mark(z0)) → c5(G(z0)) 96.47/33.54
G(ok(z0)) → c6(G(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.54
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
TOP(mark(b)) → c12(TOP(ok(b)), PROPER(b)) 96.47/33.54
TOP(mark(c)) → c12(TOP(ok(c)), PROPER(c))
K tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.54
G(mark(z0)) → c5(G(z0)) 96.47/33.54
G(ok(z0)) → c6(G(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.54
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
TOP(mark(b)) → c12(TOP(ok(b)), PROPER(b)) 96.47/33.54
TOP(mark(c)) → c12(TOP(ok(c)), PROPER(c))
Defined Rule Symbols:
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b)))
active, g, proper, f, top
ACTIVE, G, F, TOP, PROPER
c1, c5, c6, c11, c13, c4, c4, c2, c7, c7, c8, c8, c12
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.54
active(g(b)) → mark(c) 96.47/33.54
active(b) → mark(c) 96.47/33.54
active(g(z0)) → g(active(z0)) 96.47/33.54
g(mark(z0)) → mark(g(z0)) 96.47/33.54
g(ok(z0)) → ok(g(z0)) 96.47/33.54
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.54
proper(g(z0)) → g(proper(z0)) 96.47/33.54
proper(b) → ok(b) 96.47/33.54
proper(c) → ok(c) 96.47/33.54
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.54
top(mark(z0)) → top(proper(z0)) 96.47/33.54
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.54
G(mark(z0)) → c5(G(z0)) 96.47/33.54
G(ok(z0)) → c6(G(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.54
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
TOP(mark(b)) → c12(TOP(ok(b))) 96.47/33.54
TOP(mark(c)) → c12(TOP(ok(c)))
K tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.54
G(mark(z0)) → c5(G(z0)) 96.47/33.54
G(ok(z0)) → c6(G(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.54
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
TOP(mark(b)) → c12(TOP(ok(b))) 96.47/33.54
TOP(mark(c)) → c12(TOP(ok(c)))
Defined Rule Symbols:
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b)))
active, g, proper, f, top
ACTIVE, G, F, TOP, PROPER
c1, c5, c6, c11, c13, c4, c4, c2, c7, c7, c8, c8, c12, c12
We considered the (Usable) Rules:
TOP(mark(c)) → c12(TOP(ok(c)))
And the Tuples:
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.54
proper(g(z0)) → g(proper(z0)) 96.47/33.54
proper(b) → ok(b) 96.47/33.54
proper(c) → ok(c) 96.47/33.54
g(mark(z0)) → mark(g(z0)) 96.47/33.54
g(ok(z0)) → ok(g(z0)) 96.47/33.54
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.54
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.54
active(g(b)) → mark(c) 96.47/33.54
active(b) → mark(c) 96.47/33.54
active(g(z0)) → g(active(z0))
The order we found is given by the following interpretation:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.54
G(mark(z0)) → c5(G(z0)) 96.47/33.54
G(ok(z0)) → c6(G(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.54
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
TOP(mark(b)) → c12(TOP(ok(b))) 96.47/33.54
TOP(mark(c)) → c12(TOP(ok(c)))
POL(ACTIVE(x1)) = 0 96.47/33.54
POL(F(x1, x2, x3)) = 0 96.47/33.54
POL(G(x1)) = 0 96.47/33.54
POL(PROPER(x1)) = 0 96.47/33.54
POL(TOP(x1)) = x1 96.47/33.54
POL(active(x1)) = x1 96.47/33.54
POL(b) = [1] 96.47/33.54
POL(c) = 0 96.47/33.54
POL(c1(x1)) = x1 96.47/33.54
POL(c11(x1)) = x1 96.47/33.54
POL(c12(x1)) = x1 96.47/33.54
POL(c12(x1, x2)) = x1 + x2 96.47/33.54
POL(c13(x1, x2)) = x1 + x2 96.47/33.54
POL(c2(x1)) = x1 96.47/33.54
POL(c4(x1)) = x1 96.47/33.54
POL(c4(x1, x2)) = x1 + x2 96.47/33.54
POL(c5(x1)) = x1 96.47/33.54
POL(c6(x1)) = x1 96.47/33.54
POL(c7(x1, x2, x3)) = x1 + x2 + x3 96.47/33.54
POL(c7(x1, x2, x3, x4)) = x1 + x2 + x3 + x4 96.47/33.54
POL(c8(x1)) = x1 96.47/33.54
POL(c8(x1, x2)) = x1 + x2 96.47/33.54
POL(f(x1, x2, x3)) = [1] 96.47/33.54
POL(g(x1)) = [1] 96.47/33.54
POL(mark(x1)) = [1] 96.47/33.54
POL(ok(x1)) = x1 96.47/33.54
POL(proper(x1)) = 0
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.54
active(g(b)) → mark(c) 96.47/33.54
active(b) → mark(c) 96.47/33.54
active(g(z0)) → g(active(z0)) 96.47/33.54
g(mark(z0)) → mark(g(z0)) 96.47/33.54
g(ok(z0)) → ok(g(z0)) 96.47/33.54
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.54
proper(g(z0)) → g(proper(z0)) 96.47/33.54
proper(b) → ok(b) 96.47/33.54
proper(c) → ok(c) 96.47/33.54
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.54
top(mark(z0)) → top(proper(z0)) 96.47/33.54
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.54
G(mark(z0)) → c5(G(z0)) 96.47/33.54
G(ok(z0)) → c6(G(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.54
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
TOP(mark(b)) → c12(TOP(ok(b))) 96.47/33.54
TOP(mark(c)) → c12(TOP(ok(c)))
K tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.54
G(mark(z0)) → c5(G(z0)) 96.47/33.54
G(ok(z0)) → c6(G(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.54
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
TOP(mark(b)) → c12(TOP(ok(b)))
Defined Rule Symbols:
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.54
TOP(mark(c)) → c12(TOP(ok(c)))
active, g, proper, f, top
ACTIVE, G, F, TOP, PROPER
c1, c5, c6, c11, c13, c4, c4, c2, c7, c7, c8, c8, c12, c12
We considered the (Usable) Rules:
TOP(mark(b)) → c12(TOP(ok(b)))
And the Tuples:
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.54
proper(g(z0)) → g(proper(z0)) 96.47/33.54
proper(b) → ok(b) 96.47/33.54
proper(c) → ok(c) 96.47/33.54
g(mark(z0)) → mark(g(z0)) 96.47/33.54
g(ok(z0)) → ok(g(z0)) 96.47/33.54
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.54
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.54
active(g(b)) → mark(c) 96.47/33.54
active(b) → mark(c) 96.47/33.54
active(g(z0)) → g(active(z0))
The order we found is given by the following interpretation:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.54
G(mark(z0)) → c5(G(z0)) 96.47/33.54
G(ok(z0)) → c6(G(z0)) 96.47/33.54
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.54
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.54
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.54
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.54
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.54
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.54
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.54
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.54
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.54
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.54
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.54
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.54
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.54
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.54
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.54
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.54
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.54
TOP(mark(b)) → c12(TOP(ok(b))) 96.47/33.54
TOP(mark(c)) → c12(TOP(ok(c)))
POL(ACTIVE(x1)) = 0 96.47/33.54
POL(F(x1, x2, x3)) = 0 96.47/33.54
POL(G(x1)) = 0 96.47/33.54
POL(PROPER(x1)) = 0 96.47/33.54
POL(TOP(x1)) = x1 96.47/33.54
POL(active(x1)) = 0 96.47/33.54
POL(b) = [1] 96.47/33.54
POL(c) = 0 96.47/33.54
POL(c1(x1)) = x1 96.47/33.54
POL(c11(x1)) = x1 96.47/33.54
POL(c12(x1)) = x1 96.47/33.54
POL(c12(x1, x2)) = x1 + x2 96.47/33.54
POL(c13(x1, x2)) = x1 + x2 96.47/33.54
POL(c2(x1)) = x1 96.47/33.54
POL(c4(x1)) = x1 96.47/33.54
POL(c4(x1, x2)) = x1 + x2 96.47/33.54
POL(c5(x1)) = x1 96.47/33.54
POL(c6(x1)) = x1 96.47/33.54
POL(c7(x1, x2, x3)) = x1 + x2 + x3 96.47/33.54
POL(c7(x1, x2, x3, x4)) = x1 + x2 + x3 + x4 96.47/33.54
POL(c8(x1)) = x1 96.47/33.54
POL(c8(x1, x2)) = x1 + x2 96.47/33.54
POL(f(x1, x2, x3)) = 0 96.47/33.54
POL(g(x1)) = 0 96.47/33.54
POL(mark(x1)) = x1 96.47/33.54
POL(ok(x1)) = 0 96.47/33.54
POL(proper(x1)) = 0
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.55
active(g(b)) → mark(c) 96.47/33.55
active(b) → mark(c) 96.47/33.55
active(g(z0)) → g(active(z0)) 96.47/33.55
g(mark(z0)) → mark(g(z0)) 96.47/33.55
g(ok(z0)) → ok(g(z0)) 96.47/33.55
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.55
proper(g(z0)) → g(proper(z0)) 96.47/33.55
proper(b) → ok(b) 96.47/33.55
proper(c) → ok(c) 96.47/33.55
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.55
top(mark(z0)) → top(proper(z0)) 96.47/33.55
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.55
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.55
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.55
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.55
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.55
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.55
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.55
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.55
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.55
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.55
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.55
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.55
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.55
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.55
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.55
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.55
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.55
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.55
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.55
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.55
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.55
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.55
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.55
TOP(mark(b)) → c12(TOP(ok(b))) 96.47/33.55
TOP(mark(c)) → c12(TOP(ok(c)))
K tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.55
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.55
TOP(ok(z0)) → c13(TOP(active(z0)), ACTIVE(z0)) 96.47/33.55
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.55
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.55
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.55
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.55
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.55
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.55
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.55
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.55
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.55
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.55
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.55
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.55
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.55
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.55
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.55
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.55
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0)))
Defined Rule Symbols:
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.55
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.55
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.55
TOP(mark(c)) → c12(TOP(ok(c))) 96.47/33.55
TOP(mark(b)) → c12(TOP(ok(b)))
active, g, proper, f, top
ACTIVE, G, F, TOP, PROPER
c1, c5, c6, c11, c13, c4, c4, c2, c7, c7, c8, c8, c12, c12
TOP(ok(f(z0, g(z0), z1))) → c13(TOP(mark(f(z1, z1, z1))), ACTIVE(f(z0, g(z0), z1))) 96.47/33.55
TOP(ok(g(b))) → c13(TOP(mark(c)), ACTIVE(g(b))) 96.47/33.55
TOP(ok(b)) → c13(TOP(mark(c)), ACTIVE(b)) 96.47/33.55
TOP(ok(g(z0))) → c13(TOP(g(active(z0))), ACTIVE(g(z0)))
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.55
active(g(b)) → mark(c) 96.47/33.55
active(b) → mark(c) 96.47/33.55
active(g(z0)) → g(active(z0)) 96.47/33.55
g(mark(z0)) → mark(g(z0)) 96.47/33.55
g(ok(z0)) → ok(g(z0)) 96.47/33.55
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.55
proper(g(z0)) → g(proper(z0)) 96.47/33.55
proper(b) → ok(b) 96.47/33.55
proper(c) → ok(c) 96.47/33.55
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.55
top(mark(z0)) → top(proper(z0)) 96.47/33.55
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.55
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.55
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.55
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.55
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.55
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.55
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.55
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.55
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.55
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.55
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.55
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.55
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.55
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.55
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.55
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.55
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.55
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.55
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.55
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.55
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.55
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.55
TOP(mark(b)) → c12(TOP(ok(b))) 96.47/33.55
TOP(mark(c)) → c12(TOP(ok(c))) 96.47/33.55
TOP(ok(f(z0, g(z0), z1))) → c13(TOP(mark(f(z1, z1, z1))), ACTIVE(f(z0, g(z0), z1))) 96.47/33.55
TOP(ok(g(b))) → c13(TOP(mark(c)), ACTIVE(g(b))) 96.47/33.55
TOP(ok(b)) → c13(TOP(mark(c)), ACTIVE(b)) 96.47/33.55
TOP(ok(g(z0))) → c13(TOP(g(active(z0))), ACTIVE(g(z0)))
K tuples:
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.55
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.55
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.55
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.55
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.55
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.55
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.55
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.55
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.55
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.55
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.55
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.55
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.55
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.55
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.55
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.55
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.55
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.55
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.55
TOP(ok(f(z0, g(z0), z1))) → c13(TOP(mark(f(z1, z1, z1))), ACTIVE(f(z0, g(z0), z1))) 96.47/33.55
TOP(ok(g(b))) → c13(TOP(mark(c)), ACTIVE(g(b))) 96.47/33.55
TOP(ok(b)) → c13(TOP(mark(c)), ACTIVE(b)) 96.47/33.55
TOP(ok(g(z0))) → c13(TOP(g(active(z0))), ACTIVE(g(z0)))
Defined Rule Symbols:
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.55
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.55
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.55
TOP(mark(c)) → c12(TOP(ok(c))) 96.47/33.55
TOP(mark(b)) → c12(TOP(ok(b)))
active, g, proper, f, top
ACTIVE, G, F, PROPER, TOP
c1, c5, c6, c11, c4, c4, c2, c7, c7, c8, c8, c12, c12, c13
ACTIVE(f(z0, g(z0), z1)) → c1(F(z1, z1, z1)) 96.47/33.55
ACTIVE(g(g(z0))) → c4(G(g(active(z0))), ACTIVE(g(z0))) 96.47/33.55
ACTIVE(g(b)) → c4(G(mark(c))) 96.47/33.55
ACTIVE(g(f(z0, g(z0), z1))) → c2(G(mark(f(z1, z1, z1)))) 96.47/33.55
ACTIVE(g(f(z0, g(z0), z1))) → c2(ACTIVE(f(z0, g(z0), z1))) 96.47/33.55
ACTIVE(g(g(b))) → c2(G(mark(c))) 96.47/33.55
ACTIVE(g(g(b))) → c2(ACTIVE(g(b))) 96.47/33.55
PROPER(f(x0, x1, f(z0, z1, z2))) → c7(F(proper(x0), proper(x1), f(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(f(z0, z1, z2))) 96.47/33.55
PROPER(f(x0, x1, g(z0))) → c7(F(proper(x0), proper(x1), g(proper(z0))), PROPER(x0), PROPER(x1), PROPER(g(z0))) 96.47/33.55
PROPER(f(x0, f(z0, z1, z2), x2)) → c7(F(proper(x0), f(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(f(z0, z1, z2)), PROPER(x2)) 96.47/33.55
PROPER(f(x0, g(z0), x2)) → c7(F(proper(x0), g(proper(z0)), proper(x2)), PROPER(x0), PROPER(g(z0)), PROPER(x2)) 96.47/33.55
PROPER(f(f(z0, z1, z2), x1, x2)) → c7(F(f(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(f(z0, z1, z2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(g(z0), x1, x2)) → c7(F(g(proper(z0)), proper(x1), proper(x2)), PROPER(g(z0)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(x0, x1, b)) → c7(F(proper(x0), proper(x1), ok(b)), PROPER(x0), PROPER(x1)) 96.47/33.55
PROPER(f(x0, x1, c)) → c7(F(proper(x0), proper(x1), ok(c)), PROPER(x0), PROPER(x1)) 96.47/33.55
PROPER(f(x0, b, x2)) → c7(F(proper(x0), ok(b), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.55
PROPER(f(x0, c, x2)) → c7(F(proper(x0), ok(c), proper(x2)), PROPER(x0), PROPER(x2)) 96.47/33.55
PROPER(f(b, x1, x2)) → c7(F(ok(b), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(f(c, x1, x2)) → c7(F(ok(c), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 96.47/33.55
PROPER(g(f(z0, z1, z2))) → c8(G(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.55
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 96.47/33.55
PROPER(g(b)) → c8(G(ok(b))) 96.47/33.55
PROPER(g(c)) → c8(G(ok(c))) 96.47/33.55
TOP(mark(f(z0, z1, z2))) → c12(TOP(f(proper(z0), proper(z1), proper(z2))), PROPER(f(z0, z1, z2))) 96.47/33.55
TOP(mark(g(z0))) → c12(TOP(g(proper(z0))), PROPER(g(z0))) 96.47/33.55
TOP(ok(f(z0, g(z0), z1))) → c13(TOP(mark(f(z1, z1, z1))), ACTIVE(f(z0, g(z0), z1))) 96.47/33.55
TOP(ok(g(b))) → c13(TOP(mark(c)), ACTIVE(g(b))) 96.47/33.55
TOP(ok(g(z0))) → c13(TOP(g(active(z0))), ACTIVE(g(z0)))
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.55
active(g(b)) → mark(c) 96.47/33.55
active(b) → mark(c) 96.47/33.55
active(g(z0)) → g(active(z0)) 96.47/33.55
g(mark(z0)) → mark(g(z0)) 96.47/33.55
g(ok(z0)) → ok(g(z0)) 96.47/33.55
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.55
proper(g(z0)) → g(proper(z0)) 96.47/33.55
proper(b) → ok(b) 96.47/33.55
proper(c) → ok(c) 96.47/33.55
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.55
top(mark(z0)) → top(proper(z0)) 96.47/33.55
top(ok(z0)) → top(active(z0))
S tuples:
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.55
TOP(mark(b)) → c12(TOP(ok(b))) 96.47/33.55
TOP(mark(c)) → c12(TOP(ok(c))) 96.47/33.55
TOP(ok(b)) → c13(TOP(mark(c)), ACTIVE(b))
K tuples:
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.55
TOP(ok(b)) → c13(TOP(mark(c)), ACTIVE(b))
Defined Rule Symbols:
TOP(mark(c)) → c12(TOP(ok(c))) 96.47/33.55
TOP(mark(b)) → c12(TOP(ok(b)))
active, g, proper, f, top
G, F, TOP
c5, c6, c11, c12, c13
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.55
active(g(b)) → mark(c) 96.47/33.55
active(b) → mark(c) 96.47/33.55
active(g(z0)) → g(active(z0)) 96.47/33.55
g(mark(z0)) → mark(g(z0)) 96.47/33.55
g(ok(z0)) → ok(g(z0)) 96.47/33.55
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.55
proper(g(z0)) → g(proper(z0)) 96.47/33.55
proper(b) → ok(b) 96.47/33.55
proper(c) → ok(c) 96.47/33.55
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.55
top(mark(z0)) → top(proper(z0)) 96.47/33.55
top(ok(z0)) → top(active(z0))
S tuples:
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.55
TOP(mark(b)) → c12(TOP(ok(b))) 96.47/33.55
TOP(mark(c)) → c12 96.47/33.55
TOP(ok(b)) → c13(TOP(mark(c)))
K tuples:
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2)) 96.47/33.55
TOP(ok(b)) → c13(TOP(mark(c)))
Defined Rule Symbols:
TOP(mark(b)) → c12(TOP(ok(b))) 96.47/33.55
TOP(mark(c)) → c12
active, g, proper, f, top
G, F, TOP
c5, c6, c11, c12, c12, c13
TOP(mark(b)) → c12(TOP(ok(b))) 96.47/33.55
TOP(mark(c)) → c12 96.47/33.55
TOP(ok(b)) → c13(TOP(mark(c)))
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.55
active(g(b)) → mark(c) 96.47/33.55
active(b) → mark(c) 96.47/33.55
active(g(z0)) → g(active(z0)) 96.47/33.55
g(mark(z0)) → mark(g(z0)) 96.47/33.55
g(ok(z0)) → ok(g(z0)) 96.47/33.55
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.55
proper(g(z0)) → g(proper(z0)) 96.47/33.55
proper(b) → ok(b) 96.47/33.55
proper(c) → ok(c) 96.47/33.55
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.55
top(mark(z0)) → top(proper(z0)) 96.47/33.55
top(ok(z0)) → top(active(z0))
S tuples:
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2))
K tuples:none
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2))
active, g, proper, f, top
G, F
c5, c6, c11
We considered the (Usable) Rules:none
G(mark(z0)) → c5(G(z0))
The order we found is given by the following interpretation:
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2))
POL(F(x1, x2, x3)) = x1 + x2 96.47/33.55
POL(G(x1)) = [2]x1 96.47/33.55
POL(c11(x1)) = x1 96.47/33.55
POL(c5(x1)) = x1 96.47/33.55
POL(c6(x1)) = x1 96.47/33.55
POL(mark(x1)) = [3] + x1 96.47/33.55
POL(ok(x1)) = x1
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.55
active(g(b)) → mark(c) 96.47/33.55
active(b) → mark(c) 96.47/33.55
active(g(z0)) → g(active(z0)) 96.47/33.55
g(mark(z0)) → mark(g(z0)) 96.47/33.55
g(ok(z0)) → ok(g(z0)) 96.47/33.55
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.55
proper(g(z0)) → g(proper(z0)) 96.47/33.55
proper(b) → ok(b) 96.47/33.55
proper(c) → ok(c) 96.47/33.55
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.55
top(mark(z0)) → top(proper(z0)) 96.47/33.55
top(ok(z0)) → top(active(z0))
S tuples:
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2))
K tuples:
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2))
Defined Rule Symbols:
G(mark(z0)) → c5(G(z0))
active, g, proper, f, top
G, F
c5, c6, c11
We considered the (Usable) Rules:none
G(ok(z0)) → c6(G(z0))
The order we found is given by the following interpretation:
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2))
POL(F(x1, x2, x3)) = 0 96.47/33.55
POL(G(x1)) = [2]x1 96.47/33.55
POL(c11(x1)) = x1 96.47/33.55
POL(c5(x1)) = x1 96.47/33.55
POL(c6(x1)) = x1 96.47/33.55
POL(mark(x1)) = x1 96.47/33.55
POL(ok(x1)) = [1] + x1
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.55
active(g(b)) → mark(c) 96.47/33.55
active(b) → mark(c) 96.47/33.55
active(g(z0)) → g(active(z0)) 96.47/33.55
g(mark(z0)) → mark(g(z0)) 96.47/33.55
g(ok(z0)) → ok(g(z0)) 96.47/33.55
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.55
proper(g(z0)) → g(proper(z0)) 96.47/33.55
proper(b) → ok(b) 96.47/33.55
proper(c) → ok(c) 96.47/33.55
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.55
top(mark(z0)) → top(proper(z0)) 96.47/33.55
top(ok(z0)) → top(active(z0))
S tuples:
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2))
K tuples:
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2))
Defined Rule Symbols:
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0))
active, g, proper, f, top
G, F
c5, c6, c11
We considered the (Usable) Rules:none
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2))
The order we found is given by the following interpretation:
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2))
POL(F(x1, x2, x3)) = x3 96.47/33.55
POL(G(x1)) = [3]x1 96.47/33.55
POL(c11(x1)) = x1 96.47/33.55
POL(c5(x1)) = x1 96.47/33.55
POL(c6(x1)) = x1 96.47/33.55
POL(mark(x1)) = x1 96.47/33.55
POL(ok(x1)) = [2] + x1
Tuples:
active(f(z0, g(z0), z1)) → mark(f(z1, z1, z1)) 96.47/33.55
active(g(b)) → mark(c) 96.47/33.55
active(b) → mark(c) 96.47/33.55
active(g(z0)) → g(active(z0)) 96.47/33.55
g(mark(z0)) → mark(g(z0)) 96.47/33.55
g(ok(z0)) → ok(g(z0)) 96.47/33.55
proper(f(z0, z1, z2)) → f(proper(z0), proper(z1), proper(z2)) 96.47/33.55
proper(g(z0)) → g(proper(z0)) 96.47/33.55
proper(b) → ok(b) 96.47/33.55
proper(c) → ok(c) 96.47/33.55
f(ok(z0), ok(z1), ok(z2)) → ok(f(z0, z1, z2)) 96.47/33.55
top(mark(z0)) → top(proper(z0)) 96.47/33.55
top(ok(z0)) → top(active(z0))
S tuples:none
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2))
Defined Rule Symbols:
G(mark(z0)) → c5(G(z0)) 96.47/33.55
G(ok(z0)) → c6(G(z0)) 96.47/33.55
F(ok(z0), ok(z1), ok(z2)) → c11(F(z0, z1, z2))
active, g, proper, f, top
G, F
c5, c6, c11