app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(times, 0), y) → 0
app(app(times, app(s, x)), y) → app(app(plus, app(app(times, x), y)), y)
app(app(app(curry, g), x), y) → app(app(g, x), y)
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
inc → app(map, app(app(curry, plus), app(s, 0)))
double → app(map, app(app(curry, times), app(s, app(s, 0))))
↳ QTRS
↳ DependencyPairsProof
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(times, 0), y) → 0
app(app(times, app(s, x)), y) → app(app(plus, app(app(times, x), y)), y)
app(app(app(curry, g), x), y) → app(app(g, x), y)
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
inc → app(map, app(app(curry, plus), app(s, 0)))
double → app(map, app(app(curry, times), app(s, app(s, 0))))
DOUBLE → APP(s, 0)
INC → APP(map, app(app(curry, plus), app(s, 0)))
APP(app(plus, app(s, x)), y) → APP(app(plus, x), y)
APP(app(times, app(s, x)), y) → APP(times, x)
APP(app(times, app(s, x)), y) → APP(app(times, x), y)
DOUBLE → APP(app(curry, times), app(s, app(s, 0)))
APP(app(times, app(s, x)), y) → APP(plus, app(app(times, x), y))
INC → APP(curry, plus)
APP(app(plus, app(s, x)), y) → APP(plus, x)
INC → APP(app(curry, plus), app(s, 0))
APP(app(map, f), app(app(cons, x), xs)) → APP(f, x)
APP(app(map, f), app(app(cons, x), xs)) → APP(app(map, f), xs)
APP(app(times, app(s, x)), y) → APP(app(plus, app(app(times, x), y)), y)
DOUBLE → APP(map, app(app(curry, times), app(s, app(s, 0))))
APP(app(app(curry, g), x), y) → APP(g, x)
INC → APP(s, 0)
APP(app(app(curry, g), x), y) → APP(app(g, x), y)
APP(app(plus, app(s, x)), y) → APP(s, app(app(plus, x), y))
APP(app(map, f), app(app(cons, x), xs)) → APP(cons, app(f, x))
DOUBLE → APP(curry, times)
DOUBLE → APP(s, app(s, 0))
APP(app(map, f), app(app(cons, x), xs)) → APP(app(cons, app(f, x)), app(app(map, f), xs))
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(times, 0), y) → 0
app(app(times, app(s, x)), y) → app(app(plus, app(app(times, x), y)), y)
app(app(app(curry, g), x), y) → app(app(g, x), y)
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
inc → app(map, app(app(curry, plus), app(s, 0)))
double → app(map, app(app(curry, times), app(s, app(s, 0))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
DOUBLE → APP(s, 0)
INC → APP(map, app(app(curry, plus), app(s, 0)))
APP(app(plus, app(s, x)), y) → APP(app(plus, x), y)
APP(app(times, app(s, x)), y) → APP(times, x)
APP(app(times, app(s, x)), y) → APP(app(times, x), y)
DOUBLE → APP(app(curry, times), app(s, app(s, 0)))
APP(app(times, app(s, x)), y) → APP(plus, app(app(times, x), y))
INC → APP(curry, plus)
APP(app(plus, app(s, x)), y) → APP(plus, x)
INC → APP(app(curry, plus), app(s, 0))
APP(app(map, f), app(app(cons, x), xs)) → APP(f, x)
APP(app(map, f), app(app(cons, x), xs)) → APP(app(map, f), xs)
APP(app(times, app(s, x)), y) → APP(app(plus, app(app(times, x), y)), y)
DOUBLE → APP(map, app(app(curry, times), app(s, app(s, 0))))
APP(app(app(curry, g), x), y) → APP(g, x)
INC → APP(s, 0)
APP(app(app(curry, g), x), y) → APP(app(g, x), y)
APP(app(plus, app(s, x)), y) → APP(s, app(app(plus, x), y))
APP(app(map, f), app(app(cons, x), xs)) → APP(cons, app(f, x))
DOUBLE → APP(curry, times)
DOUBLE → APP(s, app(s, 0))
APP(app(map, f), app(app(cons, x), xs)) → APP(app(cons, app(f, x)), app(app(map, f), xs))
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(times, 0), y) → 0
app(app(times, app(s, x)), y) → app(app(plus, app(app(times, x), y)), y)
app(app(app(curry, g), x), y) → app(app(g, x), y)
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
inc → app(map, app(app(curry, plus), app(s, 0)))
double → app(map, app(app(curry, times), app(s, app(s, 0))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
APP(app(plus, app(s, x)), y) → APP(app(plus, x), y)
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(times, 0), y) → 0
app(app(times, app(s, x)), y) → app(app(plus, app(app(times, x), y)), y)
app(app(app(curry, g), x), y) → app(app(g, x), y)
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
inc → app(map, app(app(curry, plus), app(s, 0)))
double → app(map, app(app(curry, times), app(s, app(s, 0))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP(app(plus, app(s, x)), y) → APP(app(plus, x), y)
The value of delta used in the strict ordering is 1/4.
POL(APP(x1, x2)) = (1/4)x_1
POL(plus) = 0
POL(app(x1, x2)) = 1 + x_2
POL(s) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(times, 0), y) → 0
app(app(times, app(s, x)), y) → app(app(plus, app(app(times, x), y)), y)
app(app(app(curry, g), x), y) → app(app(g, x), y)
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
inc → app(map, app(app(curry, plus), app(s, 0)))
double → app(map, app(app(curry, times), app(s, app(s, 0))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
APP(app(times, app(s, x)), y) → APP(app(times, x), y)
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(times, 0), y) → 0
app(app(times, app(s, x)), y) → app(app(plus, app(app(times, x), y)), y)
app(app(app(curry, g), x), y) → app(app(g, x), y)
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
inc → app(map, app(app(curry, plus), app(s, 0)))
double → app(map, app(app(curry, times), app(s, app(s, 0))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP(app(times, app(s, x)), y) → APP(app(times, x), y)
The value of delta used in the strict ordering is 1/4.
POL(APP(x1, x2)) = (1/4)x_1
POL(times) = 0
POL(app(x1, x2)) = 1 + x_2
POL(s) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(times, 0), y) → 0
app(app(times, app(s, x)), y) → app(app(plus, app(app(times, x), y)), y)
app(app(app(curry, g), x), y) → app(app(g, x), y)
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
inc → app(map, app(app(curry, plus), app(s, 0)))
double → app(map, app(app(curry, times), app(s, app(s, 0))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
APP(app(app(curry, g), x), y) → APP(g, x)
APP(app(app(curry, g), x), y) → APP(app(g, x), y)
APP(app(map, f), app(app(cons, x), xs)) → APP(f, x)
APP(app(map, f), app(app(cons, x), xs)) → APP(app(map, f), xs)
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(times, 0), y) → 0
app(app(times, app(s, x)), y) → app(app(plus, app(app(times, x), y)), y)
app(app(app(curry, g), x), y) → app(app(g, x), y)
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
inc → app(map, app(app(curry, plus), app(s, 0)))
double → app(map, app(app(curry, times), app(s, app(s, 0))))