(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(app(curry, f), x), y) → app(app(f, x), y)
add → app(curry, plus)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(0) = 1
POL(add) = 2
POL(app(x1, x2)) = 2·x1 + x2
POL(curry) = 0
POL(plus) = 2
POL(s) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
app(app(app(curry, f), x), y) → app(app(f, x), y)
add → app(curry, plus)
Q is empty.
(3) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Knuth-Bendix order [KBO] with precedence:
plus > add > curry > app2
and weight map:
curry=1
add=2
plus=1
app_2=0
The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
app(app(app(curry, f), x), y) → app(app(f, x), y)
add → app(curry, plus)
(4) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(5) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(6) YES