minus1(minus1(x)) -> x
minus1(+2(x, y)) -> *2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
minus1(*2(x, y)) -> +2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
f1(minus1(x)) -> minus1(minus1(minus1(f1(x))))
↳ QTRS
↳ DependencyPairsProof
minus1(minus1(x)) -> x
minus1(+2(x, y)) -> *2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
minus1(*2(x, y)) -> +2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
f1(minus1(x)) -> minus1(minus1(minus1(f1(x))))
F1(minus1(x)) -> MINUS1(f1(x))
MINUS1(+2(x, y)) -> MINUS1(minus1(x))
MINUS1(+2(x, y)) -> MINUS1(minus1(minus1(y)))
MINUS1(+2(x, y)) -> MINUS1(y)
MINUS1(+2(x, y)) -> MINUS1(x)
MINUS1(*2(x, y)) -> MINUS1(minus1(minus1(y)))
F1(minus1(x)) -> F1(x)
MINUS1(*2(x, y)) -> MINUS1(x)
MINUS1(*2(x, y)) -> MINUS1(minus1(y))
MINUS1(*2(x, y)) -> MINUS1(y)
F1(minus1(x)) -> MINUS1(minus1(f1(x)))
F1(minus1(x)) -> MINUS1(minus1(minus1(f1(x))))
MINUS1(*2(x, y)) -> MINUS1(minus1(minus1(x)))
MINUS1(+2(x, y)) -> MINUS1(minus1(minus1(x)))
MINUS1(*2(x, y)) -> MINUS1(minus1(x))
MINUS1(+2(x, y)) -> MINUS1(minus1(y))
minus1(minus1(x)) -> x
minus1(+2(x, y)) -> *2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
minus1(*2(x, y)) -> +2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
f1(minus1(x)) -> minus1(minus1(minus1(f1(x))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
F1(minus1(x)) -> MINUS1(f1(x))
MINUS1(+2(x, y)) -> MINUS1(minus1(x))
MINUS1(+2(x, y)) -> MINUS1(minus1(minus1(y)))
MINUS1(+2(x, y)) -> MINUS1(y)
MINUS1(+2(x, y)) -> MINUS1(x)
MINUS1(*2(x, y)) -> MINUS1(minus1(minus1(y)))
F1(minus1(x)) -> F1(x)
MINUS1(*2(x, y)) -> MINUS1(x)
MINUS1(*2(x, y)) -> MINUS1(minus1(y))
MINUS1(*2(x, y)) -> MINUS1(y)
F1(minus1(x)) -> MINUS1(minus1(f1(x)))
F1(minus1(x)) -> MINUS1(minus1(minus1(f1(x))))
MINUS1(*2(x, y)) -> MINUS1(minus1(minus1(x)))
MINUS1(+2(x, y)) -> MINUS1(minus1(minus1(x)))
MINUS1(*2(x, y)) -> MINUS1(minus1(x))
MINUS1(+2(x, y)) -> MINUS1(minus1(y))
minus1(minus1(x)) -> x
minus1(+2(x, y)) -> *2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
minus1(*2(x, y)) -> +2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
f1(minus1(x)) -> minus1(minus1(minus1(f1(x))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
MINUS1(+2(x, y)) -> MINUS1(minus1(x))
MINUS1(+2(x, y)) -> MINUS1(y)
MINUS1(+2(x, y)) -> MINUS1(minus1(minus1(y)))
MINUS1(+2(x, y)) -> MINUS1(x)
MINUS1(*2(x, y)) -> MINUS1(minus1(minus1(y)))
MINUS1(*2(x, y)) -> MINUS1(x)
MINUS1(*2(x, y)) -> MINUS1(minus1(minus1(x)))
MINUS1(+2(x, y)) -> MINUS1(minus1(minus1(x)))
MINUS1(*2(x, y)) -> MINUS1(minus1(x))
MINUS1(*2(x, y)) -> MINUS1(y)
MINUS1(*2(x, y)) -> MINUS1(minus1(y))
MINUS1(+2(x, y)) -> MINUS1(minus1(y))
minus1(minus1(x)) -> x
minus1(+2(x, y)) -> *2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
minus1(*2(x, y)) -> +2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
f1(minus1(x)) -> minus1(minus1(minus1(f1(x))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MINUS1(+2(x, y)) -> MINUS1(minus1(x))
MINUS1(+2(x, y)) -> MINUS1(y)
MINUS1(+2(x, y)) -> MINUS1(minus1(minus1(y)))
MINUS1(+2(x, y)) -> MINUS1(x)
MINUS1(*2(x, y)) -> MINUS1(minus1(minus1(y)))
MINUS1(*2(x, y)) -> MINUS1(x)
MINUS1(*2(x, y)) -> MINUS1(minus1(minus1(x)))
MINUS1(+2(x, y)) -> MINUS1(minus1(minus1(x)))
MINUS1(*2(x, y)) -> MINUS1(minus1(x))
MINUS1(*2(x, y)) -> MINUS1(y)
MINUS1(*2(x, y)) -> MINUS1(minus1(y))
MINUS1(+2(x, y)) -> MINUS1(minus1(y))
POL(*2(x1, x2)) = 2 + 2·x1 + 2·x2
POL(+2(x1, x2)) = 2 + 2·x1 + 2·x2
POL(MINUS1(x1)) = 2·x1
POL(minus1(x1)) = x1
minus1(minus1(x)) -> x
minus1(*2(x, y)) -> +2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
minus1(+2(x, y)) -> *2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
minus1(minus1(x)) -> x
minus1(+2(x, y)) -> *2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
minus1(*2(x, y)) -> +2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
f1(minus1(x)) -> minus1(minus1(minus1(f1(x))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
F1(minus1(x)) -> F1(x)
minus1(minus1(x)) -> x
minus1(+2(x, y)) -> *2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
minus1(*2(x, y)) -> +2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
f1(minus1(x)) -> minus1(minus1(minus1(f1(x))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F1(minus1(x)) -> F1(x)
POL(F1(x1)) = 2·x1
POL(minus1(x1)) = 1 + 2·x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
minus1(minus1(x)) -> x
minus1(+2(x, y)) -> *2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
minus1(*2(x, y)) -> +2(minus1(minus1(minus1(x))), minus1(minus1(minus1(y))))
f1(minus1(x)) -> minus1(minus1(minus1(f1(x))))