(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(X) → if(X, c, f(true))
if(true, X, Y) → X
if(false, X, Y) → Y
Rewrite Strategy: FULL
(1) CpxTrsToCpxRelTrsProof (BOTH BOUNDS(ID, ID) transformation)
Transformed TRS to relative TRS where S is empty.
(2) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
f(X) → if(X, c, f(true))
if(true, X, Y) → X
if(false, X, Y) → Y
S is empty.
Rewrite Strategy: FULL
(3) InfiniteLowerBoundProof (EQUIVALENT transformation)
The loop following loop proves infinite runtime complexity:
The rewrite sequence
f(X) →+ if(X, c, f(true))
gives rise to a decreasing loop by considering the right hand sides subterm at position [2].
The pumping substitution is [ ].
The result substitution is [X / true].
(4) BOUNDS(INF, INF)