(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(x, a(b(c(y)))) → f(b(c(a(b(x)))), y)
f(a(x), y) → f(x, a(y))
f(b(x), y) → f(x, b(y))
f(c(x), y) → f(x, c(y))
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(a(z0), z1) → c2(F(z0, a(z1)))
F(b(z0), z1) → c3(F(z0, b(z1)))
F(c(z0), z1) → c4(F(z0, c(z1)))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(a(z0), z1) → c2(F(z0, a(z1)))
F(b(z0), z1) → c3(F(z0, b(z1)))
F(c(z0), z1) → c4(F(z0, c(z1)))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c2, c3, c4
(3) CdtInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use instantiation to replace
F(
a(
z0),
z1) →
c2(
F(
z0,
a(
z1))) by
F(a(z0), a(x1)) → c2(F(z0, a(a(x1))))
F(a(z0), b(x1)) → c2(F(z0, a(b(x1))))
F(a(z0), c(x1)) → c2(F(z0, a(c(x1))))
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(b(z0), z1) → c3(F(z0, b(z1)))
F(c(z0), z1) → c4(F(z0, c(z1)))
F(a(z0), a(x1)) → c2(F(z0, a(a(x1))))
F(a(z0), b(x1)) → c2(F(z0, a(b(x1))))
F(a(z0), c(x1)) → c2(F(z0, a(c(x1))))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(b(z0), z1) → c3(F(z0, b(z1)))
F(c(z0), z1) → c4(F(z0, c(z1)))
F(a(z0), a(x1)) → c2(F(z0, a(a(x1))))
F(a(z0), b(x1)) → c2(F(z0, a(b(x1))))
F(a(z0), c(x1)) → c2(F(z0, a(c(x1))))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c3, c4, c2
(5) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use forward instantiation to replace
F(
b(
z0),
z1) →
c3(
F(
z0,
b(
z1))) by
F(b(b(y0)), z1) → c3(F(b(y0), b(z1)))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(c(z0), z1) → c4(F(z0, c(z1)))
F(a(z0), a(x1)) → c2(F(z0, a(a(x1))))
F(a(z0), b(x1)) → c2(F(z0, a(b(x1))))
F(a(z0), c(x1)) → c2(F(z0, a(c(x1))))
F(b(b(y0)), z1) → c3(F(b(y0), b(z1)))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(c(z0), z1) → c4(F(z0, c(z1)))
F(a(z0), a(x1)) → c2(F(z0, a(a(x1))))
F(a(z0), b(x1)) → c2(F(z0, a(b(x1))))
F(a(z0), c(x1)) → c2(F(z0, a(c(x1))))
F(b(b(y0)), z1) → c3(F(b(y0), b(z1)))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c4, c2, c3
(7) CdtInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use instantiation to replace
F(
c(
z0),
z1) →
c4(
F(
z0,
c(
z1))) by
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
(8) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(a(z0), a(x1)) → c2(F(z0, a(a(x1))))
F(a(z0), b(x1)) → c2(F(z0, a(b(x1))))
F(a(z0), c(x1)) → c2(F(z0, a(c(x1))))
F(b(b(y0)), z1) → c3(F(b(y0), b(z1)))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(a(z0), a(x1)) → c2(F(z0, a(a(x1))))
F(a(z0), b(x1)) → c2(F(z0, a(b(x1))))
F(a(z0), c(x1)) → c2(F(z0, a(c(x1))))
F(b(b(y0)), z1) → c3(F(b(y0), b(z1)))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c2, c3, c4
(9) CdtInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use instantiation to replace
F(
a(
z0),
a(
x1)) →
c2(
F(
z0,
a(
a(
x1)))) by
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
(10) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(a(z0), b(x1)) → c2(F(z0, a(b(x1))))
F(a(z0), c(x1)) → c2(F(z0, a(c(x1))))
F(b(b(y0)), z1) → c3(F(b(y0), b(z1)))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(a(z0), b(x1)) → c2(F(z0, a(b(x1))))
F(a(z0), c(x1)) → c2(F(z0, a(c(x1))))
F(b(b(y0)), z1) → c3(F(b(y0), b(z1)))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c2, c3, c4
(11) CdtInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use instantiation to replace
F(
a(
z0),
c(
x1)) →
c2(
F(
z0,
a(
c(
x1)))) by
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
(12) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(a(z0), b(x1)) → c2(F(z0, a(b(x1))))
F(b(b(y0)), z1) → c3(F(b(y0), b(z1)))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(a(z0), b(x1)) → c2(F(z0, a(b(x1))))
F(b(b(y0)), z1) → c3(F(b(y0), b(z1)))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c2, c3, c4
(13) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use forward instantiation to replace
F(
a(
z0),
b(
x1)) →
c2(
F(
z0,
a(
b(
x1)))) by
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
(14) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(b(b(y0)), z1) → c3(F(b(y0), b(z1)))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(b(b(y0)), z1) → c3(F(b(y0), b(z1)))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c3, c4, c2
(15) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use forward instantiation to replace
F(
b(
b(
y0)),
z1) →
c3(
F(
b(
y0),
b(
z1))) by
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
(16) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(b(a(y0)), z1) → c3(F(a(y0), b(z1)))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c3, c4, c2
(17) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use forward instantiation to replace
F(
b(
a(
y0)),
z1) →
c3(
F(
a(
y0),
b(
z1))) by
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
(18) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(b(c(y0)), z1) → c3(F(c(y0), b(z1)))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c3, c4, c2
(19) CdtInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use instantiation to replace
F(
b(
c(
y0)),
z1) →
c3(
F(
c(
y0),
b(
z1))) by
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
(20) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(c(z0), c(x1)) → c4(F(z0, c(c(x1))))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c4, c2, c3
(21) CdtInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use instantiation to replace
F(
c(
z0),
c(
x1)) →
c4(
F(
z0,
c(
c(
x1)))) by
F(c(z0), c(c(x1))) → c4(F(z0, c(c(c(x1)))))
F(c(z0), c(a(a(x1)))) → c4(F(z0, c(c(a(a(x1))))))
F(c(z0), c(a(b(x1)))) → c4(F(z0, c(c(a(b(x1))))))
F(c(z0), c(a(c(x1)))) → c4(F(z0, c(c(a(c(x1))))))
F(c(z0), c(b(x1))) → c4(F(z0, c(c(b(x1)))))
(22) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
F(c(z0), c(c(x1))) → c4(F(z0, c(c(c(x1)))))
F(c(z0), c(a(a(x1)))) → c4(F(z0, c(c(a(a(x1))))))
F(c(z0), c(a(b(x1)))) → c4(F(z0, c(c(a(b(x1))))))
F(c(z0), c(a(c(x1)))) → c4(F(z0, c(c(a(c(x1))))))
F(c(z0), c(b(x1))) → c4(F(z0, c(c(b(x1)))))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(c(z0), a(a(x1))) → c4(F(z0, c(a(a(x1)))))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
F(c(z0), c(c(x1))) → c4(F(z0, c(c(c(x1)))))
F(c(z0), c(a(a(x1)))) → c4(F(z0, c(c(a(a(x1))))))
F(c(z0), c(a(b(x1)))) → c4(F(z0, c(c(a(b(x1))))))
F(c(z0), c(a(c(x1)))) → c4(F(z0, c(c(a(c(x1))))))
F(c(z0), c(b(x1))) → c4(F(z0, c(c(b(x1)))))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c4, c2, c3
(23) CdtInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use instantiation to replace
F(
c(
z0),
a(
a(
x1))) →
c4(
F(
z0,
c(
a(
a(
x1))))) by
F(c(z0), a(a(a(x1)))) → c4(F(z0, c(a(a(a(x1))))))
F(c(z0), a(a(b(x1)))) → c4(F(z0, c(a(a(b(x1))))))
F(c(z0), a(a(c(x1)))) → c4(F(z0, c(a(a(c(x1))))))
(24) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
F(c(z0), c(c(x1))) → c4(F(z0, c(c(c(x1)))))
F(c(z0), c(a(a(x1)))) → c4(F(z0, c(c(a(a(x1))))))
F(c(z0), c(a(b(x1)))) → c4(F(z0, c(c(a(b(x1))))))
F(c(z0), c(a(c(x1)))) → c4(F(z0, c(c(a(c(x1))))))
F(c(z0), c(b(x1))) → c4(F(z0, c(c(b(x1)))))
F(c(z0), a(a(a(x1)))) → c4(F(z0, c(a(a(a(x1))))))
F(c(z0), a(a(b(x1)))) → c4(F(z0, c(a(a(b(x1))))))
F(c(z0), a(a(c(x1)))) → c4(F(z0, c(a(a(c(x1))))))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(z0), a(c(x1))) → c4(F(z0, c(a(c(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
F(c(z0), c(c(x1))) → c4(F(z0, c(c(c(x1)))))
F(c(z0), c(a(a(x1)))) → c4(F(z0, c(c(a(a(x1))))))
F(c(z0), c(a(b(x1)))) → c4(F(z0, c(c(a(b(x1))))))
F(c(z0), c(a(c(x1)))) → c4(F(z0, c(c(a(c(x1))))))
F(c(z0), c(b(x1))) → c4(F(z0, c(c(b(x1)))))
F(c(z0), a(a(a(x1)))) → c4(F(z0, c(a(a(a(x1))))))
F(c(z0), a(a(b(x1)))) → c4(F(z0, c(a(a(b(x1))))))
F(c(z0), a(a(c(x1)))) → c4(F(z0, c(a(a(c(x1))))))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c4, c2, c3
(25) CdtInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use instantiation to replace
F(
c(
z0),
a(
c(
x1))) →
c4(
F(
z0,
c(
a(
c(
x1))))) by
F(c(z0), a(c(c(x1)))) → c4(F(z0, c(a(c(c(x1))))))
F(c(z0), a(c(a(a(x1))))) → c4(F(z0, c(a(c(a(a(x1)))))))
F(c(z0), a(c(a(b(x1))))) → c4(F(z0, c(a(c(a(b(x1)))))))
F(c(z0), a(c(a(c(x1))))) → c4(F(z0, c(a(c(a(c(x1)))))))
F(c(z0), a(c(b(x1)))) → c4(F(z0, c(a(c(b(x1))))))
(26) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
F(c(z0), c(c(x1))) → c4(F(z0, c(c(c(x1)))))
F(c(z0), c(a(a(x1)))) → c4(F(z0, c(c(a(a(x1))))))
F(c(z0), c(a(b(x1)))) → c4(F(z0, c(c(a(b(x1))))))
F(c(z0), c(a(c(x1)))) → c4(F(z0, c(c(a(c(x1))))))
F(c(z0), c(b(x1))) → c4(F(z0, c(c(b(x1)))))
F(c(z0), a(a(a(x1)))) → c4(F(z0, c(a(a(a(x1))))))
F(c(z0), a(a(b(x1)))) → c4(F(z0, c(a(a(b(x1))))))
F(c(z0), a(a(c(x1)))) → c4(F(z0, c(a(a(c(x1))))))
F(c(z0), a(c(c(x1)))) → c4(F(z0, c(a(c(c(x1))))))
F(c(z0), a(c(a(a(x1))))) → c4(F(z0, c(a(c(a(a(x1)))))))
F(c(z0), a(c(a(b(x1))))) → c4(F(z0, c(a(c(a(b(x1)))))))
F(c(z0), a(c(a(c(x1))))) → c4(F(z0, c(a(c(a(c(x1)))))))
F(c(z0), a(c(b(x1)))) → c4(F(z0, c(a(c(b(x1))))))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(c(z0), a(b(x1))) → c4(F(z0, c(a(b(x1)))))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
F(c(z0), c(c(x1))) → c4(F(z0, c(c(c(x1)))))
F(c(z0), c(a(a(x1)))) → c4(F(z0, c(c(a(a(x1))))))
F(c(z0), c(a(b(x1)))) → c4(F(z0, c(c(a(b(x1))))))
F(c(z0), c(a(c(x1)))) → c4(F(z0, c(c(a(c(x1))))))
F(c(z0), c(b(x1))) → c4(F(z0, c(c(b(x1)))))
F(c(z0), a(a(a(x1)))) → c4(F(z0, c(a(a(a(x1))))))
F(c(z0), a(a(b(x1)))) → c4(F(z0, c(a(a(b(x1))))))
F(c(z0), a(a(c(x1)))) → c4(F(z0, c(a(a(c(x1))))))
F(c(z0), a(c(c(x1)))) → c4(F(z0, c(a(c(c(x1))))))
F(c(z0), a(c(a(a(x1))))) → c4(F(z0, c(a(c(a(a(x1)))))))
F(c(z0), a(c(a(b(x1))))) → c4(F(z0, c(a(c(a(b(x1)))))))
F(c(z0), a(c(a(c(x1))))) → c4(F(z0, c(a(c(a(c(x1)))))))
F(c(z0), a(c(b(x1)))) → c4(F(z0, c(a(c(b(x1))))))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c4, c2, c3
(27) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use forward instantiation to replace
F(
c(
z0),
a(
b(
x1))) →
c4(
F(
z0,
c(
a(
b(
x1))))) by
F(c(a(y0)), a(b(z1))) → c4(F(a(y0), c(a(b(z1)))))
F(c(b(b(b(y0)))), a(b(z1))) → c4(F(b(b(b(y0))), c(a(b(z1)))))
F(c(b(b(c(y0)))), a(b(z1))) → c4(F(b(b(c(y0))), c(a(b(z1)))))
F(c(b(b(a(y0)))), a(b(z1))) → c4(F(b(b(a(y0))), c(a(b(z1)))))
F(c(b(a(y0))), a(b(z1))) → c4(F(b(a(y0)), c(a(b(z1)))))
F(c(b(a(b(b(y0))))), a(b(z1))) → c4(F(b(a(b(b(y0)))), c(a(b(z1)))))
F(c(b(a(b(c(y0))))), a(b(z1))) → c4(F(b(a(b(c(y0)))), c(a(b(z1)))))
F(c(b(a(b(a(y0))))), a(b(z1))) → c4(F(b(a(b(a(y0)))), c(a(b(z1)))))
F(c(b(a(c(y0)))), a(b(z1))) → c4(F(b(a(c(y0))), c(a(b(z1)))))
F(c(b(a(a(y0)))), a(b(z1))) → c4(F(b(a(a(y0))), c(a(b(z1)))))
F(c(b(c(a(b(y0))))), a(b(z1))) → c4(F(b(c(a(b(y0)))), c(a(b(z1)))))
F(c(b(c(y0))), a(b(z1))) → c4(F(b(c(y0)), c(a(b(z1)))))
F(c(c(y0)), a(b(z1))) → c4(F(c(y0), c(a(b(z1)))))
(28) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
F(c(z0), c(c(x1))) → c4(F(z0, c(c(c(x1)))))
F(c(z0), c(a(a(x1)))) → c4(F(z0, c(c(a(a(x1))))))
F(c(z0), c(a(b(x1)))) → c4(F(z0, c(c(a(b(x1))))))
F(c(z0), c(a(c(x1)))) → c4(F(z0, c(c(a(c(x1))))))
F(c(z0), c(b(x1))) → c4(F(z0, c(c(b(x1)))))
F(c(z0), a(a(a(x1)))) → c4(F(z0, c(a(a(a(x1))))))
F(c(z0), a(a(b(x1)))) → c4(F(z0, c(a(a(b(x1))))))
F(c(z0), a(a(c(x1)))) → c4(F(z0, c(a(a(c(x1))))))
F(c(z0), a(c(c(x1)))) → c4(F(z0, c(a(c(c(x1))))))
F(c(z0), a(c(a(a(x1))))) → c4(F(z0, c(a(c(a(a(x1)))))))
F(c(z0), a(c(a(b(x1))))) → c4(F(z0, c(a(c(a(b(x1)))))))
F(c(z0), a(c(a(c(x1))))) → c4(F(z0, c(a(c(a(c(x1)))))))
F(c(z0), a(c(b(x1)))) → c4(F(z0, c(a(c(b(x1))))))
F(c(a(y0)), a(b(z1))) → c4(F(a(y0), c(a(b(z1)))))
F(c(b(b(b(y0)))), a(b(z1))) → c4(F(b(b(b(y0))), c(a(b(z1)))))
F(c(b(b(c(y0)))), a(b(z1))) → c4(F(b(b(c(y0))), c(a(b(z1)))))
F(c(b(b(a(y0)))), a(b(z1))) → c4(F(b(b(a(y0))), c(a(b(z1)))))
F(c(b(a(y0))), a(b(z1))) → c4(F(b(a(y0)), c(a(b(z1)))))
F(c(b(a(b(b(y0))))), a(b(z1))) → c4(F(b(a(b(b(y0)))), c(a(b(z1)))))
F(c(b(a(b(c(y0))))), a(b(z1))) → c4(F(b(a(b(c(y0)))), c(a(b(z1)))))
F(c(b(a(b(a(y0))))), a(b(z1))) → c4(F(b(a(b(a(y0)))), c(a(b(z1)))))
F(c(b(a(c(y0)))), a(b(z1))) → c4(F(b(a(c(y0))), c(a(b(z1)))))
F(c(b(a(a(y0)))), a(b(z1))) → c4(F(b(a(a(y0))), c(a(b(z1)))))
F(c(b(c(a(b(y0))))), a(b(z1))) → c4(F(b(c(a(b(y0)))), c(a(b(z1)))))
F(c(b(c(y0))), a(b(z1))) → c4(F(b(c(y0)), c(a(b(z1)))))
F(c(c(y0)), a(b(z1))) → c4(F(c(y0), c(a(b(z1)))))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(c(x0), b(x1)) → c4(F(x0, c(b(x1))))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
F(c(z0), c(c(x1))) → c4(F(z0, c(c(c(x1)))))
F(c(z0), c(a(a(x1)))) → c4(F(z0, c(c(a(a(x1))))))
F(c(z0), c(a(b(x1)))) → c4(F(z0, c(c(a(b(x1))))))
F(c(z0), c(a(c(x1)))) → c4(F(z0, c(c(a(c(x1))))))
F(c(z0), c(b(x1))) → c4(F(z0, c(c(b(x1)))))
F(c(z0), a(a(a(x1)))) → c4(F(z0, c(a(a(a(x1))))))
F(c(z0), a(a(b(x1)))) → c4(F(z0, c(a(a(b(x1))))))
F(c(z0), a(a(c(x1)))) → c4(F(z0, c(a(a(c(x1))))))
F(c(z0), a(c(c(x1)))) → c4(F(z0, c(a(c(c(x1))))))
F(c(z0), a(c(a(a(x1))))) → c4(F(z0, c(a(c(a(a(x1)))))))
F(c(z0), a(c(a(b(x1))))) → c4(F(z0, c(a(c(a(b(x1)))))))
F(c(z0), a(c(a(c(x1))))) → c4(F(z0, c(a(c(a(c(x1)))))))
F(c(z0), a(c(b(x1)))) → c4(F(z0, c(a(c(b(x1))))))
F(c(a(y0)), a(b(z1))) → c4(F(a(y0), c(a(b(z1)))))
F(c(b(b(b(y0)))), a(b(z1))) → c4(F(b(b(b(y0))), c(a(b(z1)))))
F(c(b(b(c(y0)))), a(b(z1))) → c4(F(b(b(c(y0))), c(a(b(z1)))))
F(c(b(b(a(y0)))), a(b(z1))) → c4(F(b(b(a(y0))), c(a(b(z1)))))
F(c(b(a(y0))), a(b(z1))) → c4(F(b(a(y0)), c(a(b(z1)))))
F(c(b(a(b(b(y0))))), a(b(z1))) → c4(F(b(a(b(b(y0)))), c(a(b(z1)))))
F(c(b(a(b(c(y0))))), a(b(z1))) → c4(F(b(a(b(c(y0)))), c(a(b(z1)))))
F(c(b(a(b(a(y0))))), a(b(z1))) → c4(F(b(a(b(a(y0)))), c(a(b(z1)))))
F(c(b(a(c(y0)))), a(b(z1))) → c4(F(b(a(c(y0))), c(a(b(z1)))))
F(c(b(a(a(y0)))), a(b(z1))) → c4(F(b(a(a(y0))), c(a(b(z1)))))
F(c(b(c(a(b(y0))))), a(b(z1))) → c4(F(b(c(a(b(y0)))), c(a(b(z1)))))
F(c(b(c(y0))), a(b(z1))) → c4(F(b(c(y0)), c(a(b(z1)))))
F(c(c(y0)), a(b(z1))) → c4(F(c(y0), c(a(b(z1)))))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c4, c2, c3
(29) CdtInstantiationProof (BOTH BOUNDS(ID, ID) transformation)
Use instantiation to replace
F(
c(
x0),
b(
x1)) →
c4(
F(
x0,
c(
b(
x1)))) by
F(c(a(b(x0))), b(x1)) → c4(F(a(b(x0)), c(b(x1))))
F(c(x0), b(c(c(x1)))) → c4(F(x0, c(b(c(c(x1))))))
F(c(x0), b(c(a(a(x1))))) → c4(F(x0, c(b(c(a(a(x1)))))))
F(c(x0), b(c(a(b(x1))))) → c4(F(x0, c(b(c(a(b(x1)))))))
F(c(x0), b(c(a(c(x1))))) → c4(F(x0, c(b(c(a(c(x1)))))))
F(c(x0), b(c(b(x1)))) → c4(F(x0, c(b(c(b(x1))))))
F(c(x0), b(a(a(a(x1))))) → c4(F(x0, c(b(a(a(a(x1)))))))
F(c(x0), b(a(a(b(x1))))) → c4(F(x0, c(b(a(a(b(x1)))))))
F(c(x0), b(a(a(c(x1))))) → c4(F(x0, c(b(a(a(c(x1)))))))
F(c(x0), b(a(c(c(x1))))) → c4(F(x0, c(b(a(c(c(x1)))))))
F(c(x0), b(a(c(a(a(x1)))))) → c4(F(x0, c(b(a(c(a(a(x1))))))))
F(c(x0), b(a(c(a(b(x1)))))) → c4(F(x0, c(b(a(c(a(b(x1))))))))
F(c(x0), b(a(c(a(c(x1)))))) → c4(F(x0, c(b(a(c(a(c(x1))))))))
F(c(x0), b(a(c(b(x1))))) → c4(F(x0, c(b(a(c(b(x1)))))))
F(c(x0), b(a(b(c(x1))))) → c4(F(x0, c(b(a(b(c(x1)))))))
F(c(x0), b(a(b(x1)))) → c4(F(x0, c(b(a(b(x1))))))
F(c(x0), b(b(x1))) → c4(F(x0, c(b(b(x1)))))
(30) Obligation:
Complexity Dependency Tuples Problem
Rules:
f(z0, a(b(c(z1)))) → f(b(c(a(b(z0)))), z1)
f(a(z0), z1) → f(z0, a(z1))
f(b(z0), z1) → f(z0, b(z1))
f(c(z0), z1) → f(z0, c(z1))
Tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
F(c(z0), c(c(x1))) → c4(F(z0, c(c(c(x1)))))
F(c(z0), c(a(a(x1)))) → c4(F(z0, c(c(a(a(x1))))))
F(c(z0), c(a(b(x1)))) → c4(F(z0, c(c(a(b(x1))))))
F(c(z0), c(a(c(x1)))) → c4(F(z0, c(c(a(c(x1))))))
F(c(z0), c(b(x1))) → c4(F(z0, c(c(b(x1)))))
F(c(z0), a(a(a(x1)))) → c4(F(z0, c(a(a(a(x1))))))
F(c(z0), a(a(b(x1)))) → c4(F(z0, c(a(a(b(x1))))))
F(c(z0), a(a(c(x1)))) → c4(F(z0, c(a(a(c(x1))))))
F(c(z0), a(c(c(x1)))) → c4(F(z0, c(a(c(c(x1))))))
F(c(z0), a(c(a(a(x1))))) → c4(F(z0, c(a(c(a(a(x1)))))))
F(c(z0), a(c(a(b(x1))))) → c4(F(z0, c(a(c(a(b(x1)))))))
F(c(z0), a(c(a(c(x1))))) → c4(F(z0, c(a(c(a(c(x1)))))))
F(c(z0), a(c(b(x1)))) → c4(F(z0, c(a(c(b(x1))))))
F(c(a(y0)), a(b(z1))) → c4(F(a(y0), c(a(b(z1)))))
F(c(b(b(b(y0)))), a(b(z1))) → c4(F(b(b(b(y0))), c(a(b(z1)))))
F(c(b(b(c(y0)))), a(b(z1))) → c4(F(b(b(c(y0))), c(a(b(z1)))))
F(c(b(b(a(y0)))), a(b(z1))) → c4(F(b(b(a(y0))), c(a(b(z1)))))
F(c(b(a(y0))), a(b(z1))) → c4(F(b(a(y0)), c(a(b(z1)))))
F(c(b(a(b(b(y0))))), a(b(z1))) → c4(F(b(a(b(b(y0)))), c(a(b(z1)))))
F(c(b(a(b(c(y0))))), a(b(z1))) → c4(F(b(a(b(c(y0)))), c(a(b(z1)))))
F(c(b(a(b(a(y0))))), a(b(z1))) → c4(F(b(a(b(a(y0)))), c(a(b(z1)))))
F(c(b(a(c(y0)))), a(b(z1))) → c4(F(b(a(c(y0))), c(a(b(z1)))))
F(c(b(a(a(y0)))), a(b(z1))) → c4(F(b(a(a(y0))), c(a(b(z1)))))
F(c(b(c(a(b(y0))))), a(b(z1))) → c4(F(b(c(a(b(y0)))), c(a(b(z1)))))
F(c(b(c(y0))), a(b(z1))) → c4(F(b(c(y0)), c(a(b(z1)))))
F(c(c(y0)), a(b(z1))) → c4(F(c(y0), c(a(b(z1)))))
F(c(a(b(x0))), b(x1)) → c4(F(a(b(x0)), c(b(x1))))
F(c(x0), b(c(c(x1)))) → c4(F(x0, c(b(c(c(x1))))))
F(c(x0), b(c(a(a(x1))))) → c4(F(x0, c(b(c(a(a(x1)))))))
F(c(x0), b(c(a(b(x1))))) → c4(F(x0, c(b(c(a(b(x1)))))))
F(c(x0), b(c(a(c(x1))))) → c4(F(x0, c(b(c(a(c(x1)))))))
F(c(x0), b(c(b(x1)))) → c4(F(x0, c(b(c(b(x1))))))
F(c(x0), b(a(a(a(x1))))) → c4(F(x0, c(b(a(a(a(x1)))))))
F(c(x0), b(a(a(b(x1))))) → c4(F(x0, c(b(a(a(b(x1)))))))
F(c(x0), b(a(a(c(x1))))) → c4(F(x0, c(b(a(a(c(x1)))))))
F(c(x0), b(a(c(c(x1))))) → c4(F(x0, c(b(a(c(c(x1)))))))
F(c(x0), b(a(c(a(a(x1)))))) → c4(F(x0, c(b(a(c(a(a(x1))))))))
F(c(x0), b(a(c(a(b(x1)))))) → c4(F(x0, c(b(a(c(a(b(x1))))))))
F(c(x0), b(a(c(a(c(x1)))))) → c4(F(x0, c(b(a(c(a(c(x1))))))))
F(c(x0), b(a(c(b(x1))))) → c4(F(x0, c(b(a(c(b(x1)))))))
F(c(x0), b(a(b(c(x1))))) → c4(F(x0, c(b(a(b(c(x1)))))))
F(c(x0), b(a(b(x1)))) → c4(F(x0, c(b(a(b(x1))))))
F(c(x0), b(b(x1))) → c4(F(x0, c(b(b(x1)))))
S tuples:
F(z0, a(b(c(z1)))) → c1(F(b(c(a(b(z0)))), z1))
F(a(z0), a(a(x1))) → c2(F(z0, a(a(a(x1)))))
F(a(z0), a(b(x1))) → c2(F(z0, a(a(b(x1)))))
F(a(z0), a(c(x1))) → c2(F(z0, a(a(c(x1)))))
F(a(z0), c(c(x1))) → c2(F(z0, a(c(c(x1)))))
F(a(z0), c(a(a(x1)))) → c2(F(z0, a(c(a(a(x1))))))
F(a(z0), c(a(b(x1)))) → c2(F(z0, a(c(a(b(x1))))))
F(a(z0), c(a(c(x1)))) → c2(F(z0, a(c(a(c(x1))))))
F(a(z0), c(b(x1))) → c2(F(z0, a(c(b(x1)))))
F(a(z0), b(c(y1))) → c2(F(z0, a(b(c(y1)))))
F(a(b(b(y0))), b(z1)) → c2(F(b(b(y0)), a(b(z1))))
F(a(b(c(y0))), b(z1)) → c2(F(b(c(y0)), a(b(z1))))
F(a(b(a(y0))), b(z1)) → c2(F(b(a(y0)), a(b(z1))))
F(a(c(y0)), b(z1)) → c2(F(c(y0), a(b(z1))))
F(a(a(y0)), b(z1)) → c2(F(a(y0), a(b(z1))))
F(b(b(b(y0))), z1) → c3(F(b(b(y0)), b(z1)))
F(b(b(c(y0))), z1) → c3(F(b(c(y0)), b(z1)))
F(b(b(a(y0))), z1) → c3(F(b(a(y0)), b(z1)))
F(b(a(z0)), c(y1)) → c3(F(a(z0), b(c(y1))))
F(b(a(b(b(y0)))), z1) → c3(F(a(b(b(y0))), b(z1)))
F(b(a(b(c(y0)))), z1) → c3(F(a(b(c(y0))), b(z1)))
F(b(a(b(a(y0)))), z1) → c3(F(a(b(a(y0))), b(z1)))
F(b(a(c(y0))), z1) → c3(F(a(c(y0)), b(z1)))
F(b(a(a(y0))), z1) → c3(F(a(a(y0)), b(z1)))
F(b(c(a(b(x0)))), x1) → c3(F(c(a(b(x0))), b(x1)))
F(b(c(z0)), c(c(x1))) → c3(F(c(z0), b(c(c(x1)))))
F(b(c(z0)), c(a(a(x1)))) → c3(F(c(z0), b(c(a(a(x1))))))
F(b(c(z0)), c(a(b(x1)))) → c3(F(c(z0), b(c(a(b(x1))))))
F(b(c(z0)), c(a(c(x1)))) → c3(F(c(z0), b(c(a(c(x1))))))
F(b(c(z0)), c(b(x1))) → c3(F(c(z0), b(c(b(x1)))))
F(b(c(z0)), a(a(a(x1)))) → c3(F(c(z0), b(a(a(a(x1))))))
F(b(c(z0)), a(a(b(x1)))) → c3(F(c(z0), b(a(a(b(x1))))))
F(b(c(z0)), a(a(c(x1)))) → c3(F(c(z0), b(a(a(c(x1))))))
F(b(c(z0)), a(c(c(x1)))) → c3(F(c(z0), b(a(c(c(x1))))))
F(b(c(z0)), a(c(a(a(x1))))) → c3(F(c(z0), b(a(c(a(a(x1)))))))
F(b(c(z0)), a(c(a(b(x1))))) → c3(F(c(z0), b(a(c(a(b(x1)))))))
F(b(c(z0)), a(c(a(c(x1))))) → c3(F(c(z0), b(a(c(a(c(x1)))))))
F(b(c(z0)), a(c(b(x1)))) → c3(F(c(z0), b(a(c(b(x1))))))
F(b(c(z0)), a(b(c(x1)))) → c3(F(c(z0), b(a(b(c(x1))))))
F(b(c(x0)), a(b(x1))) → c3(F(c(x0), b(a(b(x1)))))
F(b(c(x0)), b(x1)) → c3(F(c(x0), b(b(x1))))
F(c(z0), c(c(x1))) → c4(F(z0, c(c(c(x1)))))
F(c(z0), c(a(a(x1)))) → c4(F(z0, c(c(a(a(x1))))))
F(c(z0), c(a(b(x1)))) → c4(F(z0, c(c(a(b(x1))))))
F(c(z0), c(a(c(x1)))) → c4(F(z0, c(c(a(c(x1))))))
F(c(z0), c(b(x1))) → c4(F(z0, c(c(b(x1)))))
F(c(z0), a(a(a(x1)))) → c4(F(z0, c(a(a(a(x1))))))
F(c(z0), a(a(b(x1)))) → c4(F(z0, c(a(a(b(x1))))))
F(c(z0), a(a(c(x1)))) → c4(F(z0, c(a(a(c(x1))))))
F(c(z0), a(c(c(x1)))) → c4(F(z0, c(a(c(c(x1))))))
F(c(z0), a(c(a(a(x1))))) → c4(F(z0, c(a(c(a(a(x1)))))))
F(c(z0), a(c(a(b(x1))))) → c4(F(z0, c(a(c(a(b(x1)))))))
F(c(z0), a(c(a(c(x1))))) → c4(F(z0, c(a(c(a(c(x1)))))))
F(c(z0), a(c(b(x1)))) → c4(F(z0, c(a(c(b(x1))))))
F(c(a(y0)), a(b(z1))) → c4(F(a(y0), c(a(b(z1)))))
F(c(b(b(b(y0)))), a(b(z1))) → c4(F(b(b(b(y0))), c(a(b(z1)))))
F(c(b(b(c(y0)))), a(b(z1))) → c4(F(b(b(c(y0))), c(a(b(z1)))))
F(c(b(b(a(y0)))), a(b(z1))) → c4(F(b(b(a(y0))), c(a(b(z1)))))
F(c(b(a(y0))), a(b(z1))) → c4(F(b(a(y0)), c(a(b(z1)))))
F(c(b(a(b(b(y0))))), a(b(z1))) → c4(F(b(a(b(b(y0)))), c(a(b(z1)))))
F(c(b(a(b(c(y0))))), a(b(z1))) → c4(F(b(a(b(c(y0)))), c(a(b(z1)))))
F(c(b(a(b(a(y0))))), a(b(z1))) → c4(F(b(a(b(a(y0)))), c(a(b(z1)))))
F(c(b(a(c(y0)))), a(b(z1))) → c4(F(b(a(c(y0))), c(a(b(z1)))))
F(c(b(a(a(y0)))), a(b(z1))) → c4(F(b(a(a(y0))), c(a(b(z1)))))
F(c(b(c(a(b(y0))))), a(b(z1))) → c4(F(b(c(a(b(y0)))), c(a(b(z1)))))
F(c(b(c(y0))), a(b(z1))) → c4(F(b(c(y0)), c(a(b(z1)))))
F(c(c(y0)), a(b(z1))) → c4(F(c(y0), c(a(b(z1)))))
F(c(a(b(x0))), b(x1)) → c4(F(a(b(x0)), c(b(x1))))
F(c(x0), b(c(c(x1)))) → c4(F(x0, c(b(c(c(x1))))))
F(c(x0), b(c(a(a(x1))))) → c4(F(x0, c(b(c(a(a(x1)))))))
F(c(x0), b(c(a(b(x1))))) → c4(F(x0, c(b(c(a(b(x1)))))))
F(c(x0), b(c(a(c(x1))))) → c4(F(x0, c(b(c(a(c(x1)))))))
F(c(x0), b(c(b(x1)))) → c4(F(x0, c(b(c(b(x1))))))
F(c(x0), b(a(a(a(x1))))) → c4(F(x0, c(b(a(a(a(x1)))))))
F(c(x0), b(a(a(b(x1))))) → c4(F(x0, c(b(a(a(b(x1)))))))
F(c(x0), b(a(a(c(x1))))) → c4(F(x0, c(b(a(a(c(x1)))))))
F(c(x0), b(a(c(c(x1))))) → c4(F(x0, c(b(a(c(c(x1)))))))
F(c(x0), b(a(c(a(a(x1)))))) → c4(F(x0, c(b(a(c(a(a(x1))))))))
F(c(x0), b(a(c(a(b(x1)))))) → c4(F(x0, c(b(a(c(a(b(x1))))))))
F(c(x0), b(a(c(a(c(x1)))))) → c4(F(x0, c(b(a(c(a(c(x1))))))))
F(c(x0), b(a(c(b(x1))))) → c4(F(x0, c(b(a(c(b(x1)))))))
F(c(x0), b(a(b(c(x1))))) → c4(F(x0, c(b(a(b(c(x1)))))))
F(c(x0), b(a(b(x1)))) → c4(F(x0, c(b(a(b(x1))))))
F(c(x0), b(b(x1))) → c4(F(x0, c(b(b(x1)))))
K tuples:none
Defined Rule Symbols:
f
Defined Pair Symbols:
F
Compound Symbols:
c1, c2, c3, c4
(31) CpxTrsMatchBoundsTAProof (EQUIVALENT transformation)
A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 3.
The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by:
final states : [1]
transitions:
a0(0) → 0
b0(0) → 0
c0(0) → 0
f0(0, 0) → 1
b1(0) → 5
a1(5) → 4
c1(4) → 3
b1(3) → 2
f1(2, 0) → 1
a1(0) → 6
f1(0, 6) → 1
b1(0) → 7
f1(0, 7) → 1
c1(0) → 8
f1(0, 8) → 1
b1(2) → 5
a1(6) → 6
a1(7) → 6
a1(8) → 6
b1(6) → 7
b1(7) → 7
b1(8) → 7
b2(0) → 9
f2(3, 9) → 1
c1(6) → 8
c1(7) → 8
c1(8) → 8
b2(0) → 13
a2(13) → 12
c2(12) → 11
b2(11) → 10
f2(10, 0) → 1
f2(10, 6) → 1
f2(10, 7) → 1
f2(10, 8) → 1
c2(9) → 14
f2(4, 14) → 1
b1(10) → 5
b2(10) → 13
a2(14) → 15
f2(5, 15) → 1
b3(0) → 16
f3(11, 16) → 1
b3(6) → 16
b3(7) → 16
b3(8) → 16
b2(15) → 9
f2(0, 9) → 1
f2(2, 9) → 1
f2(10, 9) → 1
c3(16) → 17
f3(12, 17) → 1
a1(9) → 6
b1(9) → 7
b2(9) → 9
b3(9) → 16
c1(9) → 8
a3(17) → 18
f3(13, 18) → 1
b3(18) → 16
f3(0, 16) → 1
f3(10, 16) → 1
a1(16) → 6
b1(16) → 7
b3(16) → 16
c1(16) → 8
f2(10, 16) → 1
(32) BOUNDS(O(1), O(n^1))