diff(x, y) → cond1(equal(x, y), x, y)
cond1(true, x, y) → 0
cond1(false, x, y) → cond2(gt(x, y), x, y)
cond2(true, x, y) → s(diff(x, s(y)))
cond2(false, x, y) → s(diff(s(x), y))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
equal(0, 0) → true
equal(s(x), 0) → false
equal(0, s(y)) → false
equal(s(x), s(y)) → equal(x, y)
↳ QTRS
↳ DependencyPairsProof
diff(x, y) → cond1(equal(x, y), x, y)
cond1(true, x, y) → 0
cond1(false, x, y) → cond2(gt(x, y), x, y)
cond2(true, x, y) → s(diff(x, s(y)))
cond2(false, x, y) → s(diff(s(x), y))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
equal(0, 0) → true
equal(s(x), 0) → false
equal(0, s(y)) → false
equal(s(x), s(y)) → equal(x, y)
EQUAL(s(x), s(y)) → EQUAL(x, y)
COND2(true, x, y) → DIFF(x, s(y))
DIFF(x, y) → COND1(equal(x, y), x, y)
GT(s(u), s(v)) → GT(u, v)
COND2(false, x, y) → DIFF(s(x), y)
COND1(false, x, y) → COND2(gt(x, y), x, y)
COND1(false, x, y) → GT(x, y)
DIFF(x, y) → EQUAL(x, y)
diff(x, y) → cond1(equal(x, y), x, y)
cond1(true, x, y) → 0
cond1(false, x, y) → cond2(gt(x, y), x, y)
cond2(true, x, y) → s(diff(x, s(y)))
cond2(false, x, y) → s(diff(s(x), y))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
equal(0, 0) → true
equal(s(x), 0) → false
equal(0, s(y)) → false
equal(s(x), s(y)) → equal(x, y)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
EQUAL(s(x), s(y)) → EQUAL(x, y)
COND2(true, x, y) → DIFF(x, s(y))
DIFF(x, y) → COND1(equal(x, y), x, y)
GT(s(u), s(v)) → GT(u, v)
COND2(false, x, y) → DIFF(s(x), y)
COND1(false, x, y) → COND2(gt(x, y), x, y)
COND1(false, x, y) → GT(x, y)
DIFF(x, y) → EQUAL(x, y)
diff(x, y) → cond1(equal(x, y), x, y)
cond1(true, x, y) → 0
cond1(false, x, y) → cond2(gt(x, y), x, y)
cond2(true, x, y) → s(diff(x, s(y)))
cond2(false, x, y) → s(diff(s(x), y))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
equal(0, 0) → true
equal(s(x), 0) → false
equal(0, s(y)) → false
equal(s(x), s(y)) → equal(x, y)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
EQUAL(s(x), s(y)) → EQUAL(x, y)
diff(x, y) → cond1(equal(x, y), x, y)
cond1(true, x, y) → 0
cond1(false, x, y) → cond2(gt(x, y), x, y)
cond2(true, x, y) → s(diff(x, s(y)))
cond2(false, x, y) → s(diff(s(x), y))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
equal(0, 0) → true
equal(s(x), 0) → false
equal(0, s(y)) → false
equal(s(x), s(y)) → equal(x, y)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
EQUAL(s(x), s(y)) → EQUAL(x, y)
The value of delta used in the strict ordering is 3.
POL(EQUAL(x1, x2)) = (3)x_2
POL(s(x1)) = 1 + (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
diff(x, y) → cond1(equal(x, y), x, y)
cond1(true, x, y) → 0
cond1(false, x, y) → cond2(gt(x, y), x, y)
cond2(true, x, y) → s(diff(x, s(y)))
cond2(false, x, y) → s(diff(s(x), y))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
equal(0, 0) → true
equal(s(x), 0) → false
equal(0, s(y)) → false
equal(s(x), s(y)) → equal(x, y)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
GT(s(u), s(v)) → GT(u, v)
diff(x, y) → cond1(equal(x, y), x, y)
cond1(true, x, y) → 0
cond1(false, x, y) → cond2(gt(x, y), x, y)
cond2(true, x, y) → s(diff(x, s(y)))
cond2(false, x, y) → s(diff(s(x), y))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
equal(0, 0) → true
equal(s(x), 0) → false
equal(0, s(y)) → false
equal(s(x), s(y)) → equal(x, y)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
GT(s(u), s(v)) → GT(u, v)
The value of delta used in the strict ordering is 3.
POL(s(x1)) = 1 + (4)x_1
POL(GT(x1, x2)) = (3)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
diff(x, y) → cond1(equal(x, y), x, y)
cond1(true, x, y) → 0
cond1(false, x, y) → cond2(gt(x, y), x, y)
cond2(true, x, y) → s(diff(x, s(y)))
cond2(false, x, y) → s(diff(s(x), y))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
equal(0, 0) → true
equal(s(x), 0) → false
equal(0, s(y)) → false
equal(s(x), s(y)) → equal(x, y)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
COND2(true, x, y) → DIFF(x, s(y))
DIFF(x, y) → COND1(equal(x, y), x, y)
COND2(false, x, y) → DIFF(s(x), y)
COND1(false, x, y) → COND2(gt(x, y), x, y)
diff(x, y) → cond1(equal(x, y), x, y)
cond1(true, x, y) → 0
cond1(false, x, y) → cond2(gt(x, y), x, y)
cond2(true, x, y) → s(diff(x, s(y)))
cond2(false, x, y) → s(diff(s(x), y))
gt(0, v) → false
gt(s(u), 0) → true
gt(s(u), s(v)) → gt(u, v)
equal(0, 0) → true
equal(s(x), 0) → false
equal(0, s(y)) → false
equal(s(x), s(y)) → equal(x, y)