YES(O(1), O(n^2)) 15.82/4.51 YES(O(1), O(n^2)) 16.48/4.69 16.48/4.69 16.48/4.69
16.48/4.69 16.48/4.690 CpxTRS16.48/4.69
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))16.48/4.69
↳2 CdtProblem16.48/4.69
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))16.48/4.69
↳4 CdtProblem16.48/4.69
↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))16.48/4.69
↳6 CdtProblem16.48/4.69
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))16.48/4.69
↳8 CdtProblem16.48/4.69
↳9 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))16.48/4.69
↳10 CdtProblem16.48/4.69
↳11 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))16.48/4.69
↳12 CdtProblem16.48/4.69
↳13 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))16.48/4.69
↳14 CdtProblem16.48/4.69
↳15 SIsEmptyProof (BOTH BOUNDS(ID, ID))16.48/4.69
↳16 BOUNDS(O(1), O(1))16.48/4.69
minus(x, 0) → x 16.48/4.69
minus(s(x), s(y)) → minus(x, y) 16.48/4.69
quot(0, s(y)) → 0 16.48/4.69
quot(s(x), s(y)) → s(quot(minus(x, y), s(y))) 16.48/4.69
plus(0, y) → y 16.48/4.69
plus(s(x), y) → s(plus(x, y)) 16.48/4.69
plus(minus(x, s(0)), minus(y, s(s(z)))) → plus(minus(y, s(s(z))), minus(x, s(0))) 16.48/4.69
plus(plus(x, s(0)), plus(y, s(s(z)))) → plus(plus(y, s(s(z))), plus(x, s(0)))
Tuples:
minus(z0, 0) → z0 16.48/4.69
minus(s(z0), s(z1)) → minus(z0, z1) 16.48/4.69
quot(0, s(z0)) → 0 16.48/4.69
quot(s(z0), s(z1)) → s(quot(minus(z0, z1), s(z1))) 16.48/4.69
plus(0, z0) → z0 16.48/4.69
plus(s(z0), z1) → s(plus(z0, z1)) 16.48/4.69
plus(minus(z0, s(0)), minus(z1, s(s(z2)))) → plus(minus(z1, s(s(z2))), minus(z0, s(0))) 16.48/4.69
plus(plus(z0, s(0)), plus(z1, s(s(z2)))) → plus(plus(z1, s(s(z2))), plus(z0, s(0)))
S tuples:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.48/4.69
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.48/4.69
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.48/4.69
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c6(PLUS(minus(z1, s(s(z2))), minus(z0, s(0))), MINUS(z1, s(s(z2))), MINUS(z0, s(0))) 16.48/4.69
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(plus(z1, s(s(z2))), plus(z0, s(0))), PLUS(z1, s(s(z2))), PLUS(z0, s(0)))
K tuples:none
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.48/4.69
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.48/4.69
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.48/4.69
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c6(PLUS(minus(z1, s(s(z2))), minus(z0, s(0))), MINUS(z1, s(s(z2))), MINUS(z0, s(0))) 16.48/4.69
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(plus(z1, s(s(z2))), plus(z0, s(0))), PLUS(z1, s(s(z2))), PLUS(z0, s(0)))
minus, quot, plus
MINUS, QUOT, PLUS
c1, c3, c5, c6, c7
Tuples:
minus(z0, 0) → z0 16.83/4.71
minus(s(z0), s(z1)) → minus(z0, z1) 16.83/4.71
quot(0, s(z0)) → 0 16.83/4.71
quot(s(z0), s(z1)) → s(quot(minus(z0, z1), s(z1))) 16.83/4.71
plus(0, z0) → z0 16.83/4.71
plus(s(z0), z1) → s(plus(z0, z1)) 16.83/4.71
plus(minus(z0, s(0)), minus(z1, s(s(z2)))) → plus(minus(z1, s(s(z2))), minus(z0, s(0))) 16.83/4.71
plus(plus(z0, s(0)), plus(z1, s(s(z2)))) → plus(plus(z1, s(s(z2))), plus(z0, s(0)))
S tuples:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c6(MINUS(z1, s(s(z2))), MINUS(z0, s(0))) 16.83/4.71
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0)))
K tuples:none
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c6(MINUS(z1, s(s(z2))), MINUS(z0, s(0))) 16.83/4.71
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0)))
minus, quot, plus
MINUS, QUOT, PLUS
c1, c3, c5, c6, c7
Tuples:
minus(z0, 0) → z0 16.83/4.71
minus(s(z0), s(z1)) → minus(z0, z1) 16.83/4.71
quot(0, s(z0)) → 0 16.83/4.71
quot(s(z0), s(z1)) → s(quot(minus(z0, z1), s(z1))) 16.83/4.71
plus(0, z0) → z0 16.83/4.71
plus(s(z0), z1) → s(plus(z0, z1)) 16.83/4.71
plus(minus(z0, s(0)), minus(z1, s(s(z2)))) → plus(minus(z1, s(s(z2))), minus(z0, s(0))) 16.83/4.71
plus(plus(z0, s(0)), plus(z1, s(s(z2)))) → plus(plus(z1, s(s(z2))), plus(z0, s(0)))
S tuples:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0)))
K tuples:none
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0)))
minus, quot, plus
MINUS, QUOT, PLUS
c1, c3, c5, c7, c
We considered the (Usable) Rules:
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0)))
And the Tuples:
minus(z0, 0) → z0 16.83/4.71
minus(s(z0), s(z1)) → minus(z0, z1)
The order we found is given by the following interpretation:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0)))
POL(0) = 0 16.83/4.71
POL(MINUS(x1, x2)) = 0 16.83/4.71
POL(PLUS(x1, x2)) = [3]x2 16.83/4.71
POL(QUOT(x1, x2)) = 0 16.83/4.71
POL(c(x1)) = x1 16.83/4.71
POL(c1(x1)) = x1 16.83/4.71
POL(c3(x1, x2)) = x1 + x2 16.83/4.71
POL(c5(x1)) = x1 16.83/4.71
POL(c7(x1, x2)) = x1 + x2 16.83/4.71
POL(minus(x1, x2)) = [4] + [2]x1 16.83/4.71
POL(plus(x1, x2)) = [4]x2 16.83/4.71
POL(s(x1)) = [2]
Tuples:
minus(z0, 0) → z0 16.83/4.71
minus(s(z0), s(z1)) → minus(z0, z1) 16.83/4.71
quot(0, s(z0)) → 0 16.83/4.71
quot(s(z0), s(z1)) → s(quot(minus(z0, z1), s(z1))) 16.83/4.71
plus(0, z0) → z0 16.83/4.71
plus(s(z0), z1) → s(plus(z0, z1)) 16.83/4.71
plus(minus(z0, s(0)), minus(z1, s(s(z2)))) → plus(minus(z1, s(s(z2))), minus(z0, s(0))) 16.83/4.71
plus(plus(z0, s(0)), plus(z1, s(s(z2)))) → plus(plus(z1, s(s(z2))), plus(z0, s(0)))
S tuples:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0)))
K tuples:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1))
Defined Rule Symbols:
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0)))
minus, quot, plus
MINUS, QUOT, PLUS
c1, c3, c5, c7, c
We considered the (Usable) Rules:
PLUS(s(z0), z1) → c5(PLUS(z0, z1))
And the Tuples:
minus(z0, 0) → z0 16.83/4.71
minus(s(z0), s(z1)) → minus(z0, z1)
The order we found is given by the following interpretation:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0)))
POL(0) = [2] 16.83/4.71
POL(MINUS(x1, x2)) = 0 16.83/4.71
POL(PLUS(x1, x2)) = [2]x1 + x2 16.83/4.71
POL(QUOT(x1, x2)) = 0 16.83/4.71
POL(c(x1)) = x1 16.83/4.71
POL(c1(x1)) = x1 16.83/4.71
POL(c3(x1, x2)) = x1 + x2 16.83/4.71
POL(c5(x1)) = x1 16.83/4.71
POL(c7(x1, x2)) = x1 + x2 16.83/4.71
POL(minus(x1, x2)) = 0 16.83/4.71
POL(plus(x1, x2)) = [1] + [4]x1 + x2 16.83/4.71
POL(s(x1)) = [1] + x1
Tuples:
minus(z0, 0) → z0 16.83/4.71
minus(s(z0), s(z1)) → minus(z0, z1) 16.83/4.71
quot(0, s(z0)) → 0 16.83/4.71
quot(s(z0), s(z1)) → s(quot(minus(z0, z1), s(z1))) 16.83/4.71
plus(0, z0) → z0 16.83/4.71
plus(s(z0), z1) → s(plus(z0, z1)) 16.83/4.71
plus(minus(z0, s(0)), minus(z1, s(s(z2)))) → plus(minus(z1, s(s(z2))), minus(z0, s(0))) 16.83/4.71
plus(plus(z0, s(0)), plus(z1, s(s(z2)))) → plus(plus(z1, s(s(z2))), plus(z0, s(0)))
S tuples:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0)))
K tuples:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
Defined Rule Symbols:
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0))) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1))
minus, quot, plus
MINUS, QUOT, PLUS
c1, c3, c5, c7, c
We considered the (Usable) Rules:
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
And the Tuples:
minus(z0, 0) → z0 16.83/4.71
minus(s(z0), s(z1)) → minus(z0, z1)
The order we found is given by the following interpretation:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0)))
POL(0) = 0 16.83/4.71
POL(MINUS(x1, x2)) = 0 16.83/4.71
POL(PLUS(x1, x2)) = 0 16.83/4.71
POL(QUOT(x1, x2)) = [5]x1 16.83/4.71
POL(c(x1)) = x1 16.83/4.71
POL(c1(x1)) = x1 16.83/4.71
POL(c3(x1, x2)) = x1 + x2 16.83/4.71
POL(c5(x1)) = x1 16.83/4.71
POL(c7(x1, x2)) = x1 + x2 16.83/4.71
POL(minus(x1, x2)) = [3] + x1 16.83/4.71
POL(plus(x1, x2)) = 0 16.83/4.71
POL(s(x1)) = [4] + x1
Tuples:
minus(z0, 0) → z0 16.83/4.71
minus(s(z0), s(z1)) → minus(z0, z1) 16.83/4.71
quot(0, s(z0)) → 0 16.83/4.71
quot(s(z0), s(z1)) → s(quot(minus(z0, z1), s(z1))) 16.83/4.71
plus(0, z0) → z0 16.83/4.71
plus(s(z0), z1) → s(plus(z0, z1)) 16.83/4.71
plus(minus(z0, s(0)), minus(z1, s(s(z2)))) → plus(minus(z1, s(s(z2))), minus(z0, s(0))) 16.83/4.71
plus(plus(z0, s(0)), plus(z1, s(s(z2)))) → plus(plus(z1, s(s(z2))), plus(z0, s(0)))
S tuples:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0)))
K tuples:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1))
Defined Rule Symbols:
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0))) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1))
minus, quot, plus
MINUS, QUOT, PLUS
c1, c3, c5, c7, c
We considered the (Usable) Rules:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1))
And the Tuples:
minus(z0, 0) → z0 16.83/4.71
minus(s(z0), s(z1)) → minus(z0, z1)
The order we found is given by the following interpretation:
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0)))
POL(0) = 0 16.83/4.71
POL(MINUS(x1, x2)) = [2]x1 16.83/4.71
POL(PLUS(x1, x2)) = [2]x1 + [2]x2 16.83/4.71
POL(QUOT(x1, x2)) = [2]x12 16.83/4.71
POL(c(x1)) = x1 16.83/4.71
POL(c1(x1)) = x1 16.83/4.71
POL(c3(x1, x2)) = x1 + x2 16.83/4.71
POL(c5(x1)) = x1 16.83/4.71
POL(c7(x1, x2)) = x1 + x2 16.83/4.71
POL(minus(x1, x2)) = x1 16.83/4.71
POL(plus(x1, x2)) = x2 + [2]x1·x2 16.83/4.71
POL(s(x1)) = [2] + x1
Tuples:
minus(z0, 0) → z0 16.83/4.71
minus(s(z0), s(z1)) → minus(z0, z1) 16.83/4.71
quot(0, s(z0)) → 0 16.83/4.71
quot(s(z0), s(z1)) → s(quot(minus(z0, z1), s(z1))) 16.83/4.71
plus(0, z0) → z0 16.83/4.71
plus(s(z0), z1) → s(plus(z0, z1)) 16.83/4.71
plus(minus(z0, s(0)), minus(z1, s(s(z2)))) → plus(minus(z1, s(s(z2))), minus(z0, s(0))) 16.83/4.71
plus(plus(z0, s(0)), plus(z1, s(s(z2)))) → plus(plus(z1, s(s(z2))), plus(z0, s(0)))
S tuples:none
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0)))
Defined Rule Symbols:
PLUS(plus(z0, s(0)), plus(z1, s(s(z2)))) → c7(PLUS(z1, s(s(z2))), PLUS(z0, s(0))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z1, s(s(z2)))) 16.83/4.71
PLUS(minus(z0, s(0)), minus(z1, s(s(z2)))) → c(MINUS(z0, s(0))) 16.83/4.71
PLUS(s(z0), z1) → c5(PLUS(z0, z1)) 16.83/4.71
QUOT(s(z0), s(z1)) → c3(QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1)) 16.83/4.71
MINUS(s(z0), s(z1)) → c1(MINUS(z0, z1))
minus, quot, plus
MINUS, QUOT, PLUS
c1, c3, c5, c7, c