f(X) → if(X, c, n__f(true))
if(true, X, Y) → X
if(false, X, Y) → activate(Y)
f(X) → n__f(X)
activate(n__f(X)) → f(X)
activate(X) → X
Renamed function symbols to avoid clashes with predefined symbol.
Runtime Complexity TRS:
The TRS R consists of the following rules:
f'(X) → if'(X, c', n__f'(true'))
if'(true', X, Y) → X
if'(false', X, Y) → activate'(Y)
f'(X) → n__f'(X)
activate'(n__f'(X)) → f'(X)
activate'(X) → X
Infered types.
Rules:
f'(X) → if'(X, c', n__f'(true'))
if'(true', X, Y) → X
if'(false', X, Y) → activate'(Y)
f'(X) → n__f'(X)
activate'(n__f'(X)) → f'(X)
activate'(X) → X
Types:
f' :: true':false' → c':n__f'
if' :: true':false' → c':n__f' → c':n__f' → c':n__f'
c' :: c':n__f'
n__f' :: true':false' → c':n__f'
true' :: true':false'
false' :: true':false'
activate' :: c':n__f' → c':n__f'
_hole_c':n__f'1 :: c':n__f'
_hole_true':false'2 :: true':false'
Heuristically decided to analyse the following defined symbols:
f', activate'
They will be analysed ascendingly in the following order:
f' = activate'
Rules:
f'(X) → if'(X, c', n__f'(true'))
if'(true', X, Y) → X
if'(false', X, Y) → activate'(Y)
f'(X) → n__f'(X)
activate'(n__f'(X)) → f'(X)
activate'(X) → X
Types:
f' :: true':false' → c':n__f'
if' :: true':false' → c':n__f' → c':n__f' → c':n__f'
c' :: c':n__f'
n__f' :: true':false' → c':n__f'
true' :: true':false'
false' :: true':false'
activate' :: c':n__f' → c':n__f'
_hole_c':n__f'1 :: c':n__f'
_hole_true':false'2 :: true':false'
Generator Equations:
The following defined symbols remain to be analysed:
activate', f'
They will be analysed ascendingly in the following order:
f' = activate'
Could not prove a rewrite lemma for the defined symbol activate'.
Rules:
f'(X) → if'(X, c', n__f'(true'))
if'(true', X, Y) → X
if'(false', X, Y) → activate'(Y)
f'(X) → n__f'(X)
activate'(n__f'(X)) → f'(X)
activate'(X) → X
Types:
f' :: true':false' → c':n__f'
if' :: true':false' → c':n__f' → c':n__f' → c':n__f'
c' :: c':n__f'
n__f' :: true':false' → c':n__f'
true' :: true':false'
false' :: true':false'
activate' :: c':n__f' → c':n__f'
_hole_c':n__f'1 :: c':n__f'
_hole_true':false'2 :: true':false'
Generator Equations:
The following defined symbols remain to be analysed:
f'
They will be analysed ascendingly in the following order:
f' = activate'
Could not prove a rewrite lemma for the defined symbol f'.
Rules:
f'(X) → if'(X, c', n__f'(true'))
if'(true', X, Y) → X
if'(false', X, Y) → activate'(Y)
f'(X) → n__f'(X)
activate'(n__f'(X)) → f'(X)
activate'(X) → X
Types:
f' :: true':false' → c':n__f'
if' :: true':false' → c':n__f' → c':n__f' → c':n__f'
c' :: c':n__f'
n__f' :: true':false' → c':n__f'
true' :: true':false'
false' :: true':false'
activate' :: c':n__f' → c':n__f'
_hole_c':n__f'1 :: c':n__f'
_hole_true':false'2 :: true':false'
Generator Equations:
No more defined symbols left to analyse.