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)
↳ QTRS
↳ DependencyPairsProof
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)
APP(app(plus, app(s, x)), y) → APP(app(plus, x), y)
APP(app(app(curry, f), x), y) → APP(f, x)
APP(app(app(curry, f), x), y) → APP(app(f, x), y)
APP(app(plus, app(s, x)), y) → APP(s, app(app(plus, x), y))
ADD → APP(curry, plus)
APP(app(plus, app(s, x)), y) → APP(plus, x)
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)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
APP(app(plus, app(s, x)), y) → APP(app(plus, x), y)
APP(app(app(curry, f), x), y) → APP(f, x)
APP(app(app(curry, f), x), y) → APP(app(f, x), y)
APP(app(plus, app(s, x)), y) → APP(s, app(app(plus, x), y))
ADD → APP(curry, plus)
APP(app(plus, app(s, x)), y) → APP(plus, x)
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)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ 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(app(curry, f), x), y) → app(app(f, x), y)
add → app(curry, plus)
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 2.
POL(APP(x1, x2)) = (2)x_1
POL(plus) = 0
POL(app(x1, x2)) = 1 + x_2
POL(s) = 3
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ 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(app(curry, f), x), y) → app(app(f, x), y)
add → app(curry, plus)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
APP(app(app(curry, f), x), y) → APP(f, x)
APP(app(app(curry, f), x), y) → APP(app(f, x), y)
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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP(app(app(curry, f), x), y) → APP(f, x)
APP(app(app(curry, f), x), y) → APP(app(f, x), y)
The value of delta used in the strict ordering is 15.
POL(APP(x1, x2)) = (4)x_1 + (15/4)x_2
POL(curry) = 0
POL(plus) = 3/2
POL(app(x1, x2)) = 3/2 + (5/2)x_1 + x_2
POL(s) = 4
POL(0) = 0
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)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
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)