app(app(add, 0), y) → y
app(app(add, app(s, x)), y) → app(s, app(app(add, x), y))
app(app(mult, 0), y) → 0
app(app(mult, app(s, x)), y) → app(app(add, app(app(mult, x), y)), y)
app(app(app(rec, f), x), 0) → x
app(app(app(rec, f), x), app(s, y)) → app(app(f, app(s, y)), app(app(app(rec, f), x), y))
fact → app(app(rec, mult), app(s, 0))
↳ QTRS
↳ DependencyPairsProof
app(app(add, 0), y) → y
app(app(add, app(s, x)), y) → app(s, app(app(add, x), y))
app(app(mult, 0), y) → 0
app(app(mult, app(s, x)), y) → app(app(add, app(app(mult, x), y)), y)
app(app(app(rec, f), x), 0) → x
app(app(app(rec, f), x), app(s, y)) → app(app(f, app(s, y)), app(app(app(rec, f), x), y))
fact → app(app(rec, mult), app(s, 0))
APP(app(mult, app(s, x)), y) → APP(app(add, app(app(mult, x), y)), y)
FACT → APP(rec, mult)
FACT → APP(s, 0)
APP(app(add, app(s, x)), y) → APP(s, app(app(add, x), y))
APP(app(app(rec, f), x), app(s, y)) → APP(app(app(rec, f), x), y)
APP(app(app(rec, f), x), app(s, y)) → APP(app(f, app(s, y)), app(app(app(rec, f), x), y))
APP(app(mult, app(s, x)), y) → APP(app(mult, x), y)
APP(app(app(rec, f), x), app(s, y)) → APP(f, app(s, y))
APP(app(add, app(s, x)), y) → APP(app(add, x), y)
APP(app(mult, app(s, x)), y) → APP(mult, x)
APP(app(add, app(s, x)), y) → APP(add, x)
APP(app(mult, app(s, x)), y) → APP(add, app(app(mult, x), y))
FACT → APP(app(rec, mult), app(s, 0))
app(app(add, 0), y) → y
app(app(add, app(s, x)), y) → app(s, app(app(add, x), y))
app(app(mult, 0), y) → 0
app(app(mult, app(s, x)), y) → app(app(add, app(app(mult, x), y)), y)
app(app(app(rec, f), x), 0) → x
app(app(app(rec, f), x), app(s, y)) → app(app(f, app(s, y)), app(app(app(rec, f), x), y))
fact → app(app(rec, mult), app(s, 0))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
APP(app(mult, app(s, x)), y) → APP(app(add, app(app(mult, x), y)), y)
FACT → APP(rec, mult)
FACT → APP(s, 0)
APP(app(add, app(s, x)), y) → APP(s, app(app(add, x), y))
APP(app(app(rec, f), x), app(s, y)) → APP(app(app(rec, f), x), y)
APP(app(app(rec, f), x), app(s, y)) → APP(app(f, app(s, y)), app(app(app(rec, f), x), y))
APP(app(mult, app(s, x)), y) → APP(app(mult, x), y)
APP(app(app(rec, f), x), app(s, y)) → APP(f, app(s, y))
APP(app(add, app(s, x)), y) → APP(app(add, x), y)
APP(app(mult, app(s, x)), y) → APP(mult, x)
APP(app(add, app(s, x)), y) → APP(add, x)
APP(app(mult, app(s, x)), y) → APP(add, app(app(mult, x), y))
FACT → APP(app(rec, mult), app(s, 0))
app(app(add, 0), y) → y
app(app(add, app(s, x)), y) → app(s, app(app(add, x), y))
app(app(mult, 0), y) → 0
app(app(mult, app(s, x)), y) → app(app(add, app(app(mult, x), y)), y)
app(app(app(rec, f), x), 0) → x
app(app(app(rec, f), x), app(s, y)) → app(app(f, app(s, y)), app(app(app(rec, f), x), y))
fact → app(app(rec, mult), app(s, 0))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
APP(app(add, app(s, x)), y) → APP(app(add, x), y)
app(app(add, 0), y) → y
app(app(add, app(s, x)), y) → app(s, app(app(add, x), y))
app(app(mult, 0), y) → 0
app(app(mult, app(s, x)), y) → app(app(add, app(app(mult, x), y)), y)
app(app(app(rec, f), x), 0) → x
app(app(app(rec, f), x), app(s, y)) → app(app(f, app(s, y)), app(app(app(rec, f), x), y))
fact → app(app(rec, mult), app(s, 0))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP(app(add, app(s, x)), y) → APP(app(add, x), y)
The value of delta used in the strict ordering is 2.
POL(APP(x1, x2)) = (2)x_1
POL(add) = 0
POL(app(x1, x2)) = 1 + x_2
POL(s) = 3
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
app(app(add, 0), y) → y
app(app(add, app(s, x)), y) → app(s, app(app(add, x), y))
app(app(mult, 0), y) → 0
app(app(mult, app(s, x)), y) → app(app(add, app(app(mult, x), y)), y)
app(app(app(rec, f), x), 0) → x
app(app(app(rec, f), x), app(s, y)) → app(app(f, app(s, y)), app(app(app(rec, f), x), y))
fact → app(app(rec, mult), app(s, 0))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
APP(app(mult, app(s, x)), y) → APP(app(mult, x), y)
app(app(add, 0), y) → y
app(app(add, app(s, x)), y) → app(s, app(app(add, x), y))
app(app(mult, 0), y) → 0
app(app(mult, app(s, x)), y) → app(app(add, app(app(mult, x), y)), y)
app(app(app(rec, f), x), 0) → x
app(app(app(rec, f), x), app(s, y)) → app(app(f, app(s, y)), app(app(app(rec, f), x), y))
fact → app(app(rec, mult), app(s, 0))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP(app(mult, app(s, x)), y) → APP(app(mult, x), y)
The value of delta used in the strict ordering is 36.
POL(APP(x1, x2)) = (4)x_1
POL(app(x1, x2)) = 3 + (3)x_2
POL(mult) = 0
POL(s) = 4
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
app(app(add, 0), y) → y
app(app(add, app(s, x)), y) → app(s, app(app(add, x), y))
app(app(mult, 0), y) → 0
app(app(mult, app(s, x)), y) → app(app(add, app(app(mult, x), y)), y)
app(app(app(rec, f), x), 0) → x
app(app(app(rec, f), x), app(s, y)) → app(app(f, app(s, y)), app(app(app(rec, f), x), y))
fact → app(app(rec, mult), app(s, 0))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
APP(app(app(rec, f), x), app(s, y)) → APP(f, app(s, y))
APP(app(app(rec, f), x), app(s, y)) → APP(app(app(rec, f), x), y)
APP(app(app(rec, f), x), app(s, y)) → APP(app(f, app(s, y)), app(app(app(rec, f), x), y))
app(app(add, 0), y) → y
app(app(add, app(s, x)), y) → app(s, app(app(add, x), y))
app(app(mult, 0), y) → 0
app(app(mult, app(s, x)), y) → app(app(add, app(app(mult, x), y)), y)
app(app(app(rec, f), x), 0) → x
app(app(app(rec, f), x), app(s, y)) → app(app(f, app(s, y)), app(app(app(rec, f), x), y))
fact → app(app(rec, mult), app(s, 0))