YES(O(1), O(n^1)) 0.00/0.96 YES(O(1), O(n^1)) 0.00/0.99 0.00/0.99 0.00/0.99
0.00/0.99 0.00/0.990 CpxTRS0.00/0.99
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.99
↳2 CdtProblem0.00/0.99
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))0.00/0.99
↳4 CdtProblem0.00/0.99
↳5 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))0.00/0.99
↳6 CdtProblem0.00/0.99
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.99
↳8 CdtProblem0.00/0.99
↳9 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.99
↳10 CdtProblem0.00/0.99
↳11 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.99
↳12 BOUNDS(O(1), O(1))0.00/0.99
a__f(b, X, c) → a__f(X, a__c, X) 0.00/0.99
a__c → b 0.00/0.99
mark(f(X1, X2, X3)) → a__f(X1, mark(X2), X3) 0.00/0.99
mark(c) → a__c 0.00/0.99
mark(b) → b 0.00/0.99
a__f(X1, X2, X3) → f(X1, X2, X3) 0.00/0.99
a__c → c
Tuples:
a__f(b, z0, c) → a__f(z0, a__c, z0) 0.00/0.99
a__f(z0, z1, z2) → f(z0, z1, z2) 0.00/0.99
a__c → b 0.00/0.99
a__c → c 0.00/0.99
mark(f(z0, z1, z2)) → a__f(z0, mark(z1), z2) 0.00/0.99
mark(c) → a__c 0.00/0.99
mark(b) → b
S tuples:
A__F(b, z0, c) → c1(A__F(z0, a__c, z0), A__C) 0.00/0.99
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
MARK(c) → c6(A__C)
K tuples:none
A__F(b, z0, c) → c1(A__F(z0, a__c, z0), A__C) 0.00/0.99
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
MARK(c) → c6(A__C)
a__f, a__c, mark
A__F, MARK
c1, c5, c6
Tuples:
a__f(b, z0, c) → a__f(z0, a__c, z0) 0.00/0.99
a__f(z0, z1, z2) → f(z0, z1, z2) 0.00/0.99
a__c → b 0.00/0.99
a__c → c 0.00/0.99
mark(f(z0, z1, z2)) → a__f(z0, mark(z1), z2) 0.00/0.99
mark(c) → a__c 0.00/0.99
mark(b) → b
S tuples:
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
A__F(b, z0, c) → c1 0.00/0.99
MARK(c) → c6
K tuples:none
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
A__F(b, z0, c) → c1 0.00/0.99
MARK(c) → c6
a__f, a__c, mark
MARK, A__F
c5, c1, c6
MARK(c) → c6 0.00/0.99
A__F(b, z0, c) → c1
Tuples:
a__f(b, z0, c) → a__f(z0, a__c, z0) 0.00/0.99
a__f(z0, z1, z2) → f(z0, z1, z2) 0.00/0.99
a__c → b 0.00/0.99
a__c → c 0.00/0.99
mark(f(z0, z1, z2)) → a__f(z0, mark(z1), z2) 0.00/0.99
mark(c) → a__c 0.00/0.99
mark(b) → b
S tuples:
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
A__F(b, z0, c) → c1 0.00/0.99
MARK(c) → c6
K tuples:none
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
A__F(b, z0, c) → c1 0.00/0.99
MARK(c) → c6
a__f, a__c, mark
MARK, A__F
c5, c1, c6
We considered the (Usable) Rules:
MARK(c) → c6
And the Tuples:
mark(f(z0, z1, z2)) → a__f(z0, mark(z1), z2) 0.00/0.99
mark(c) → a__c 0.00/0.99
mark(b) → b 0.00/0.99
a__c → b 0.00/0.99
a__c → c 0.00/0.99
a__f(b, z0, c) → a__f(z0, a__c, z0) 0.00/0.99
a__f(z0, z1, z2) → f(z0, z1, z2)
The order we found is given by the following interpretation:
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
A__F(b, z0, c) → c1 0.00/0.99
MARK(c) → c6
POL(A__F(x1, x2, x3)) = 0 0.00/0.99
POL(MARK(x1)) = [3] 0.00/0.99
POL(a__c) = 0 0.00/0.99
POL(a__f(x1, x2, x3)) = [3] + [3]x2 0.00/0.99
POL(b) = [3] 0.00/0.99
POL(c) = [3] 0.00/0.99
POL(c1) = 0 0.00/0.99
POL(c5(x1, x2)) = x1 + x2 0.00/0.99
POL(c6) = 0 0.00/0.99
POL(f(x1, x2, x3)) = x1 + x3 0.00/0.99
POL(mark(x1)) = 0
Tuples:
a__f(b, z0, c) → a__f(z0, a__c, z0) 0.00/0.99
a__f(z0, z1, z2) → f(z0, z1, z2) 0.00/0.99
a__c → b 0.00/0.99
a__c → c 0.00/0.99
mark(f(z0, z1, z2)) → a__f(z0, mark(z1), z2) 0.00/0.99
mark(c) → a__c 0.00/0.99
mark(b) → b
S tuples:
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
A__F(b, z0, c) → c1 0.00/0.99
MARK(c) → c6
K tuples:
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
A__F(b, z0, c) → c1
Defined Rule Symbols:
MARK(c) → c6
a__f, a__c, mark
MARK, A__F
c5, c1, c6
We considered the (Usable) Rules:
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
A__F(b, z0, c) → c1
And the Tuples:
mark(f(z0, z1, z2)) → a__f(z0, mark(z1), z2) 0.00/0.99
mark(c) → a__c 0.00/0.99
mark(b) → b 0.00/0.99
a__c → b 0.00/0.99
a__c → c 0.00/0.99
a__f(b, z0, c) → a__f(z0, a__c, z0) 0.00/0.99
a__f(z0, z1, z2) → f(z0, z1, z2)
The order we found is given by the following interpretation:
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
A__F(b, z0, c) → c1 0.00/0.99
MARK(c) → c6
POL(A__F(x1, x2, x3)) = [4] 0.00/0.99
POL(MARK(x1)) = [2]x1 0.00/0.99
POL(a__c) = 0 0.00/0.99
POL(a__f(x1, x2, x3)) = [3] + [3]x2 0.00/0.99
POL(b) = 0 0.00/0.99
POL(c) = 0 0.00/0.99
POL(c1) = 0 0.00/0.99
POL(c5(x1, x2)) = x1 + x2 0.00/0.99
POL(c6) = 0 0.00/0.99
POL(f(x1, x2, x3)) = [4] + x1 + x2 0.00/0.99
POL(mark(x1)) = 0
Tuples:
a__f(b, z0, c) → a__f(z0, a__c, z0) 0.00/0.99
a__f(z0, z1, z2) → f(z0, z1, z2) 0.00/0.99
a__c → b 0.00/0.99
a__c → c 0.00/0.99
mark(f(z0, z1, z2)) → a__f(z0, mark(z1), z2) 0.00/0.99
mark(c) → a__c 0.00/0.99
mark(b) → b
S tuples:none
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
A__F(b, z0, c) → c1 0.00/0.99
MARK(c) → c6
Defined Rule Symbols:
MARK(c) → c6 0.00/0.99
MARK(f(z0, z1, z2)) → c5(A__F(z0, mark(z1), z2), MARK(z1)) 0.00/0.99
A__F(b, z0, c) → c1
a__f, a__c, mark
MARK, A__F
c5, c1, c6