(0) Obligation:
The Runtime Complexity (innermost) of the given
CpxTRS could be proven to be
BOUNDS(1, 1).
The TRS R consists of the following rules:
f(s(X), Y) → h(s(f(h(Y), X)))
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted Cpx (relative) TRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(s(z0), z1) → h(s(f(h(z1), z0)))
Tuples:
F(s(z0), z1) → c(F(h(z1), z0))
S tuples:
F(s(z0), z1) → c(F(h(z1), z0))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c
(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing nodes:
F(s(z0), z1) → c(F(h(z1), z0))
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(s(z0), z1) → h(s(f(h(z1), z0)))
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:none
Compound Symbols:none
(5) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)
The set S is empty
(6) BOUNDS(1, 1)