(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
terms(N) → cons(recip(sqr(N)))
sqr(0) → 0
sqr(s) → s
dbl(0) → 0
dbl(s) → s
add(0, X) → X
add(s, Y) → s
first(0, X) → nil
first(s, cons(Y)) → cons(Y)
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
terms(z0) → cons(recip(sqr(z0)))
sqr(0) → 0
sqr(s) → s
dbl(0) → 0
dbl(s) → s
add(0, z0) → z0
add(s, z0) → s
first(0, z0) → nil
first(s, cons(z0)) → cons(z0)
Tuples:
TERMS(z0) → c(SQR(z0))
S tuples:
TERMS(z0) → c(SQR(z0))
K tuples:none
Defined Rule Symbols:
terms, sqr, dbl, add, first
Defined Pair Symbols:
TERMS
Compound Symbols:
c
(3) CdtGraphRemoveDanglingProof (ComplexityIfPolyImplication transformation)
Removed 1 of 1 dangling nodes:
TERMS(z0) → c(SQR(z0))
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
terms(z0) → cons(recip(sqr(z0)))
sqr(0) → 0
sqr(s) → s
dbl(0) → 0
dbl(s) → s
add(0, z0) → z0
add(s, z0) → s
first(0, z0) → nil
first(s, cons(z0)) → cons(z0)
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
terms, sqr, dbl, add, first
Defined Pair Symbols:none
Compound Symbols:none
(5) SIsEmptyProof (EQUIVALENT transformation)
The set S is empty
(6) BOUNDS(O(1), O(1))