YES(O(1), O(n^1)) 0.00/0.76 YES(O(1), O(n^1)) 0.00/0.77 0.00/0.77 0.00/0.77
0.00/0.77 0.00/0.770 CpxTRS0.00/0.77
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.77
↳2 CdtProblem0.00/0.77
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))0.00/0.77
↳4 CdtProblem0.00/0.77
↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.77
↳6 CdtProblem0.00/0.77
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.77
↳8 CdtProblem0.00/0.77
↳9 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.77
↳10 BOUNDS(O(1), O(1))0.00/0.77
a__f(X) → g(h(f(X))) 0.00/0.77
mark(f(X)) → a__f(mark(X)) 0.00/0.77
mark(g(X)) → g(X) 0.00/0.77
mark(h(X)) → h(mark(X)) 0.00/0.77
a__f(X) → f(X)
Tuples:
a__f(z0) → g(h(f(z0))) 0.00/0.77
a__f(z0) → f(z0) 0.00/0.77
mark(f(z0)) → a__f(mark(z0)) 0.00/0.77
mark(g(z0)) → g(z0) 0.00/0.77
mark(h(z0)) → h(mark(z0))
S tuples:
MARK(f(z0)) → c2(A__F(mark(z0)), MARK(z0)) 0.00/0.77
MARK(h(z0)) → c4(MARK(z0))
K tuples:none
MARK(f(z0)) → c2(A__F(mark(z0)), MARK(z0)) 0.00/0.77
MARK(h(z0)) → c4(MARK(z0))
a__f, mark
MARK
c2, c4
Tuples:
a__f(z0) → g(h(f(z0))) 0.00/0.77
a__f(z0) → f(z0) 0.00/0.77
mark(f(z0)) → a__f(mark(z0)) 0.00/0.77
mark(g(z0)) → g(z0) 0.00/0.77
mark(h(z0)) → h(mark(z0))
S tuples:
MARK(h(z0)) → c4(MARK(z0)) 0.00/0.77
MARK(f(z0)) → c2(MARK(z0))
K tuples:none
MARK(h(z0)) → c4(MARK(z0)) 0.00/0.77
MARK(f(z0)) → c2(MARK(z0))
a__f, mark
MARK
c4, c2
We considered the (Usable) Rules:none
MARK(h(z0)) → c4(MARK(z0))
The order we found is given by the following interpretation:
MARK(h(z0)) → c4(MARK(z0)) 0.00/0.77
MARK(f(z0)) → c2(MARK(z0))
POL(MARK(x1)) = [2]x1 0.00/0.77
POL(c2(x1)) = x1 0.00/0.77
POL(c4(x1)) = x1 0.00/0.77
POL(f(x1)) = x1 0.00/0.77
POL(h(x1)) = [1] + x1
Tuples:
a__f(z0) → g(h(f(z0))) 0.00/0.77
a__f(z0) → f(z0) 0.00/0.77
mark(f(z0)) → a__f(mark(z0)) 0.00/0.77
mark(g(z0)) → g(z0) 0.00/0.77
mark(h(z0)) → h(mark(z0))
S tuples:
MARK(h(z0)) → c4(MARK(z0)) 0.00/0.77
MARK(f(z0)) → c2(MARK(z0))
K tuples:
MARK(f(z0)) → c2(MARK(z0))
Defined Rule Symbols:
MARK(h(z0)) → c4(MARK(z0))
a__f, mark
MARK
c4, c2
We considered the (Usable) Rules:none
MARK(f(z0)) → c2(MARK(z0))
The order we found is given by the following interpretation:
MARK(h(z0)) → c4(MARK(z0)) 0.00/0.77
MARK(f(z0)) → c2(MARK(z0))
POL(MARK(x1)) = [3]x1 0.00/0.77
POL(c2(x1)) = x1 0.00/0.77
POL(c4(x1)) = x1 0.00/0.77
POL(f(x1)) = [1] + x1 0.00/0.77
POL(h(x1)) = x1
Tuples:
a__f(z0) → g(h(f(z0))) 0.00/0.77
a__f(z0) → f(z0) 0.00/0.77
mark(f(z0)) → a__f(mark(z0)) 0.00/0.77
mark(g(z0)) → g(z0) 0.00/0.77
mark(h(z0)) → h(mark(z0))
S tuples:none
MARK(h(z0)) → c4(MARK(z0)) 0.00/0.77
MARK(f(z0)) → c2(MARK(z0))
Defined Rule Symbols:
MARK(h(z0)) → c4(MARK(z0)) 0.00/0.77
MARK(f(z0)) → c2(MARK(z0))
a__f, mark
MARK
c4, c2