YES
Problem:
a(b(c(x1))) -> c(b(a(x1)))
C(B(A(x1))) -> A(B(C(x1)))
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> x1
Proof:
DP Processor:
DPs:
a#(b(c(x1))) -> a#(x1)
a#(b(c(x1))) -> b#(a(x1))
a#(b(c(x1))) -> c#(b(a(x1)))
C#(B(A(x1))) -> C#(x1)
C#(B(A(x1))) -> B#(C(x1))
C#(B(A(x1))) -> A#(B(C(x1)))
b#(a(C(x1))) -> b#(x1)
b#(a(C(x1))) -> a#(b(x1))
b#(a(C(x1))) -> C#(a(b(x1)))
c#(A(B(x1))) -> c#(x1)
c#(A(B(x1))) -> A#(c(x1))
c#(A(B(x1))) -> B#(A(c(x1)))
A#(c(b(x1))) -> A#(x1)
A#(c(b(x1))) -> c#(A(x1))
A#(c(b(x1))) -> b#(c(A(x1)))
B#(C(a(x1))) -> B#(x1)
B#(C(a(x1))) -> C#(B(x1))
B#(C(a(x1))) -> a#(C(B(x1)))
TRS:
a(b(c(x1))) -> c(b(a(x1)))
C(B(A(x1))) -> A(B(C(x1)))
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> x1
TDG Processor:
DPs:
a#(b(c(x1))) -> a#(x1)
a#(b(c(x1))) -> b#(a(x1))
a#(b(c(x1))) -> c#(b(a(x1)))
C#(B(A(x1))) -> C#(x1)
C#(B(A(x1))) -> B#(C(x1))
C#(B(A(x1))) -> A#(B(C(x1)))
b#(a(C(x1))) -> b#(x1)
b#(a(C(x1))) -> a#(b(x1))
b#(a(C(x1))) -> C#(a(b(x1)))
c#(A(B(x1))) -> c#(x1)
c#(A(B(x1))) -> A#(c(x1))
c#(A(B(x1))) -> B#(A(c(x1)))
A#(c(b(x1))) -> A#(x1)
A#(c(b(x1))) -> c#(A(x1))
A#(c(b(x1))) -> b#(c(A(x1)))
B#(C(a(x1))) -> B#(x1)
B#(C(a(x1))) -> C#(B(x1))
B#(C(a(x1))) -> a#(C(B(x1)))
TRS:
a(b(c(x1))) -> c(b(a(x1)))
C(B(A(x1))) -> A(B(C(x1)))
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> x1
graph:
A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> b#(c(A(x1)))
A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> c#(A(x1))
A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> A#(x1)
A#(c(b(x1))) -> c#(A(x1)) -> c#(A(B(x1))) -> B#(A(c(x1)))
A#(c(b(x1))) -> c#(A(x1)) -> c#(A(B(x1))) -> A#(c(x1))
A#(c(b(x1))) -> c#(A(x1)) -> c#(A(B(x1))) -> c#(x1)
A#(c(b(x1))) -> b#(c(A(x1))) -> b#(a(C(x1))) -> C#(a(b(x1)))
A#(c(b(x1))) -> b#(c(A(x1))) -> b#(a(C(x1))) -> a#(b(x1))
A#(c(b(x1))) -> b#(c(A(x1))) -> b#(a(C(x1))) -> b#(x1)
B#(C(a(x1))) -> B#(x1) -> B#(C(a(x1))) -> a#(C(B(x1)))
B#(C(a(x1))) -> B#(x1) -> B#(C(a(x1))) -> C#(B(x1))
B#(C(a(x1))) -> B#(x1) -> B#(C(a(x1))) -> B#(x1)
B#(C(a(x1))) -> C#(B(x1)) -> C#(B(A(x1))) -> A#(B(C(x1)))
B#(C(a(x1))) -> C#(B(x1)) -> C#(B(A(x1))) -> B#(C(x1))
B#(C(a(x1))) -> C#(B(x1)) -> C#(B(A(x1))) -> C#(x1)
B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> c#(b(a(x1)))
B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> b#(a(x1))
B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> a#(x1)
C#(B(A(x1))) -> A#(B(C(x1))) -> A#(c(b(x1))) -> b#(c(A(x1)))
C#(B(A(x1))) -> A#(B(C(x1))) -> A#(c(b(x1))) -> c#(A(x1))
C#(B(A(x1))) -> A#(B(C(x1))) -> A#(c(b(x1))) -> A#(x1)
C#(B(A(x1))) -> B#(C(x1)) -> B#(C(a(x1))) -> a#(C(B(x1)))
C#(B(A(x1))) -> B#(C(x1)) -> B#(C(a(x1))) -> C#(B(x1))
C#(B(A(x1))) -> B#(C(x1)) -> B#(C(a(x1))) -> B#(x1)
C#(B(A(x1))) -> C#(x1) -> C#(B(A(x1))) -> A#(B(C(x1)))
C#(B(A(x1))) -> C#(x1) -> C#(B(A(x1))) -> B#(C(x1))
C#(B(A(x1))) -> C#(x1) -> C#(B(A(x1))) -> C#(x1)
c#(A(B(x1))) -> A#(c(x1)) -> A#(c(b(x1))) -> b#(c(A(x1)))
c#(A(B(x1))) -> A#(c(x1)) -> A#(c(b(x1))) -> c#(A(x1))
c#(A(B(x1))) -> A#(c(x1)) -> A#(c(b(x1))) -> A#(x1)
c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> a#(C(B(x1)))
c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> C#(B(x1))
c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> B#(x1)
c#(A(B(x1))) -> c#(x1) -> c#(A(B(x1))) -> B#(A(c(x1)))
c#(A(B(x1))) -> c#(x1) -> c#(A(B(x1))) -> A#(c(x1))
c#(A(B(x1))) -> c#(x1) -> c#(A(B(x1))) -> c#(x1)
b#(a(C(x1))) -> C#(a(b(x1))) -> C#(B(A(x1))) -> A#(B(C(x1)))
b#(a(C(x1))) -> C#(a(b(x1))) -> C#(B(A(x1))) -> B#(C(x1))
b#(a(C(x1))) -> C#(a(b(x1))) -> C#(B(A(x1))) -> C#(x1)
b#(a(C(x1))) -> b#(x1) -> b#(a(C(x1))) -> C#(a(b(x1)))
b#(a(C(x1))) -> b#(x1) -> b#(a(C(x1))) -> a#(b(x1))
b#(a(C(x1))) -> b#(x1) -> b#(a(C(x1))) -> b#(x1)
b#(a(C(x1))) -> a#(b(x1)) -> a#(b(c(x1))) -> c#(b(a(x1)))
b#(a(C(x1))) -> a#(b(x1)) -> a#(b(c(x1))) -> b#(a(x1))
b#(a(C(x1))) -> a#(b(x1)) -> a#(b(c(x1))) -> a#(x1)
a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> B#(A(c(x1)))
a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> A#(c(x1))
a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> c#(x1)
a#(b(c(x1))) -> b#(a(x1)) -> b#(a(C(x1))) -> C#(a(b(x1)))
a#(b(c(x1))) -> b#(a(x1)) -> b#(a(C(x1))) -> a#(b(x1))
a#(b(c(x1))) -> b#(a(x1)) -> b#(a(C(x1))) -> b#(x1)
a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(b(a(x1)))
a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> b#(a(x1))
a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1)
Arctic Interpretation Processor:
dimension: 1
interpretation:
[A#](x0) = 4x0 + 1,
[B#](x0) = 3x0 + 4,
[C#](x0) = x0 + 0,
[c#](x0) = x0 + 0,
[b#](x0) = x0 + 0,
[a#](x0) = x0 + 0,
[C](x0) = x0,
[B](x0) = 3x0 + 0,
[A](x0) = 4x0 + 1,
[a](x0) = x0,
[b](x0) = x0,
[c](x0) = x0
orientation:
a#(b(c(x1))) = x1 + 0 >= x1 + 0 = a#(x1)
a#(b(c(x1))) = x1 + 0 >= x1 + 0 = b#(a(x1))
a#(b(c(x1))) = x1 + 0 >= x1 + 0 = c#(b(a(x1)))
C#(B(A(x1))) = 7x1 + 4 >= x1 + 0 = C#(x1)
C#(B(A(x1))) = 7x1 + 4 >= 3x1 + 4 = B#(C(x1))
C#(B(A(x1))) = 7x1 + 4 >= 7x1 + 4 = A#(B(C(x1)))
b#(a(C(x1))) = x1 + 0 >= x1 + 0 = b#(x1)
b#(a(C(x1))) = x1 + 0 >= x1 + 0 = a#(b(x1))
b#(a(C(x1))) = x1 + 0 >= x1 + 0 = C#(a(b(x1)))
c#(A(B(x1))) = 7x1 + 4 >= x1 + 0 = c#(x1)
c#(A(B(x1))) = 7x1 + 4 >= 4x1 + 1 = A#(c(x1))
c#(A(B(x1))) = 7x1 + 4 >= 7x1 + 4 = B#(A(c(x1)))
A#(c(b(x1))) = 4x1 + 1 >= 4x1 + 1 = A#(x1)
A#(c(b(x1))) = 4x1 + 1 >= 4x1 + 1 = c#(A(x1))
A#(c(b(x1))) = 4x1 + 1 >= 4x1 + 1 = b#(c(A(x1)))
B#(C(a(x1))) = 3x1 + 4 >= 3x1 + 4 = B#(x1)
B#(C(a(x1))) = 3x1 + 4 >= 3x1 + 0 = C#(B(x1))
B#(C(a(x1))) = 3x1 + 4 >= 3x1 + 0 = a#(C(B(x1)))
a(b(c(x1))) = x1 >= x1 = c(b(a(x1)))
C(B(A(x1))) = 7x1 + 4 >= 7x1 + 4 = A(B(C(x1)))
b(a(C(x1))) = x1 >= x1 = C(a(b(x1)))
c(A(B(x1))) = 7x1 + 4 >= 7x1 + 4 = B(A(c(x1)))
A(c(b(x1))) = 4x1 + 1 >= 4x1 + 1 = b(c(A(x1)))
B(C(a(x1))) = 3x1 + 0 >= 3x1 + 0 = a(C(B(x1)))
a(A(x1)) = 4x1 + 1 >= x1 = x1
A(a(x1)) = 4x1 + 1 >= x1 = x1
b(B(x1)) = 3x1 + 0 >= x1 = x1
B(b(x1)) = 3x1 + 0 >= x1 = x1
c(C(x1)) = x1 >= x1 = x1
C(c(x1)) = x1 >= x1 = x1
problem:
DPs:
a#(b(c(x1))) -> a#(x1)
a#(b(c(x1))) -> b#(a(x1))
a#(b(c(x1))) -> c#(b(a(x1)))
C#(B(A(x1))) -> B#(C(x1))
C#(B(A(x1))) -> A#(B(C(x1)))
b#(a(C(x1))) -> b#(x1)
b#(a(C(x1))) -> a#(b(x1))
b#(a(C(x1))) -> C#(a(b(x1)))
c#(A(B(x1))) -> B#(A(c(x1)))
A#(c(b(x1))) -> A#(x1)
A#(c(b(x1))) -> c#(A(x1))
A#(c(b(x1))) -> b#(c(A(x1)))
B#(C(a(x1))) -> B#(x1)
B#(C(a(x1))) -> C#(B(x1))
B#(C(a(x1))) -> a#(C(B(x1)))
TRS:
a(b(c(x1))) -> c(b(a(x1)))
C(B(A(x1))) -> A(B(C(x1)))
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> x1
EDG Processor:
DPs:
a#(b(c(x1))) -> a#(x1)
a#(b(c(x1))) -> b#(a(x1))
a#(b(c(x1))) -> c#(b(a(x1)))
C#(B(A(x1))) -> B#(C(x1))
C#(B(A(x1))) -> A#(B(C(x1)))
b#(a(C(x1))) -> b#(x1)
b#(a(C(x1))) -> a#(b(x1))
b#(a(C(x1))) -> C#(a(b(x1)))
c#(A(B(x1))) -> B#(A(c(x1)))
A#(c(b(x1))) -> A#(x1)
A#(c(b(x1))) -> c#(A(x1))
A#(c(b(x1))) -> b#(c(A(x1)))
B#(C(a(x1))) -> B#(x1)
B#(C(a(x1))) -> C#(B(x1))
B#(C(a(x1))) -> a#(C(B(x1)))
TRS:
a(b(c(x1))) -> c(b(a(x1)))
C(B(A(x1))) -> A(B(C(x1)))
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> x1
graph:
A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> A#(x1)
A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> c#(A(x1))
A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> b#(c(A(x1)))
A#(c(b(x1))) -> c#(A(x1)) -> c#(A(B(x1))) -> B#(A(c(x1)))
A#(c(b(x1))) -> b#(c(A(x1))) -> b#(a(C(x1))) -> b#(x1)
A#(c(b(x1))) -> b#(c(A(x1))) -> b#(a(C(x1))) -> a#(b(x1))
A#(c(b(x1))) -> b#(c(A(x1))) -> b#(a(C(x1))) -> C#(a(b(x1)))
B#(C(a(x1))) -> B#(x1) -> B#(C(a(x1))) -> B#(x1)
B#(C(a(x1))) -> B#(x1) -> B#(C(a(x1))) -> C#(B(x1))
B#(C(a(x1))) -> B#(x1) -> B#(C(a(x1))) -> a#(C(B(x1)))
B#(C(a(x1))) -> C#(B(x1)) -> C#(B(A(x1))) -> B#(C(x1))
B#(C(a(x1))) -> C#(B(x1)) -> C#(B(A(x1))) -> A#(B(C(x1)))
B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> a#(x1)
B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> b#(a(x1))
B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> c#(b(a(x1)))
C#(B(A(x1))) -> A#(B(C(x1))) -> A#(c(b(x1))) -> A#(x1)
C#(B(A(x1))) -> A#(B(C(x1))) -> A#(c(b(x1))) -> c#(A(x1))
C#(B(A(x1))) -> A#(B(C(x1))) -> A#(c(b(x1))) -> b#(c(A(x1)))
C#(B(A(x1))) -> B#(C(x1)) -> B#(C(a(x1))) -> B#(x1)
C#(B(A(x1))) -> B#(C(x1)) -> B#(C(a(x1))) -> C#(B(x1))
C#(B(A(x1))) -> B#(C(x1)) -> B#(C(a(x1))) -> a#(C(B(x1)))
c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> B#(x1)
c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> C#(B(x1))
c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> a#(C(B(x1)))
b#(a(C(x1))) -> C#(a(b(x1))) -> C#(B(A(x1))) -> B#(C(x1))
b#(a(C(x1))) -> C#(a(b(x1))) -> C#(B(A(x1))) -> A#(B(C(x1)))
b#(a(C(x1))) -> b#(x1) -> b#(a(C(x1))) -> b#(x1)
b#(a(C(x1))) -> b#(x1) -> b#(a(C(x1))) -> a#(b(x1))
b#(a(C(x1))) -> b#(x1) -> b#(a(C(x1))) -> C#(a(b(x1)))
b#(a(C(x1))) -> a#(b(x1)) -> a#(b(c(x1))) -> a#(x1)
b#(a(C(x1))) -> a#(b(x1)) -> a#(b(c(x1))) -> b#(a(x1))
b#(a(C(x1))) -> a#(b(x1)) -> a#(b(c(x1))) -> c#(b(a(x1)))
a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> B#(A(c(x1)))
a#(b(c(x1))) -> b#(a(x1)) -> b#(a(C(x1))) -> b#(x1)
a#(b(c(x1))) -> b#(a(x1)) -> b#(a(C(x1))) -> a#(b(x1))
a#(b(c(x1))) -> b#(a(x1)) -> b#(a(C(x1))) -> C#(a(b(x1)))
a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1)
a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> b#(a(x1))
a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(b(a(x1)))
KBO Processor:
argument filtering:
pi(c) = 0
pi(b) = 0
pi(a) = 0
pi(A) = [0]
pi(B) = 0
pi(C) = [0]
pi(a#) = 0
pi(b#) = 0
pi(c#) = 0
pi(C#) = [0]
pi(B#) = 0
pi(A#) = [0]
weight function:
w0 = 1
w(A#) = w(B#) = w(C#) = w(C) = w(A) = 1
w(c#) = w(b#) = w(a#) = w(B) = w(a) = w(b) = w(c) = 0
precedence:
C > C# > A# > B# ~ c# ~ b# ~ a# ~ B ~ A ~ a ~ b ~ c
problem:
DPs:
a#(b(c(x1))) -> a#(x1)
a#(b(c(x1))) -> b#(a(x1))
a#(b(c(x1))) -> c#(b(a(x1)))
c#(A(B(x1))) -> B#(A(c(x1)))
A#(c(b(x1))) -> A#(x1)
B#(C(a(x1))) -> a#(C(B(x1)))
TRS:
a(b(c(x1))) -> c(b(a(x1)))
C(B(A(x1))) -> A(B(C(x1)))
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> x1
EDG Processor:
DPs:
a#(b(c(x1))) -> a#(x1)
a#(b(c(x1))) -> b#(a(x1))
a#(b(c(x1))) -> c#(b(a(x1)))
c#(A(B(x1))) -> B#(A(c(x1)))
A#(c(b(x1))) -> A#(x1)
B#(C(a(x1))) -> a#(C(B(x1)))
TRS:
a(b(c(x1))) -> c(b(a(x1)))
C(B(A(x1))) -> A(B(C(x1)))
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> x1
graph:
A#(c(b(x1))) -> A#(x1) -> A#(c(b(x1))) -> A#(x1)
B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> c#(b(a(x1)))
B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> b#(a(x1))
B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> a#(x1)
c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> a#(C(B(x1)))
a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> B#(A(c(x1)))
a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(b(a(x1)))
a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> b#(a(x1))
a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1)
CDG Processor:
DPs:
a#(b(c(x1))) -> a#(x1)
a#(b(c(x1))) -> b#(a(x1))
a#(b(c(x1))) -> c#(b(a(x1)))
c#(A(B(x1))) -> B#(A(c(x1)))
A#(c(b(x1))) -> A#(x1)
B#(C(a(x1))) -> a#(C(B(x1)))
TRS:
a(b(c(x1))) -> c(b(a(x1)))
C(B(A(x1))) -> A(B(C(x1)))
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> x1
graph:
B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> a#(x1)
B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> b#(a(x1))
B#(C(a(x1))) -> a#(C(B(x1))) -> a#(b(c(x1))) -> c#(b(a(x1)))
c#(A(B(x1))) -> B#(A(c(x1))) -> B#(C(a(x1))) -> a#(C(B(x1)))
a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> B#(A(c(x1)))
a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1)
a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> b#(a(x1))
a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(b(a(x1)))
SCC Processor:
#sccs: 1
#rules: 4
#arcs: 8/36
DPs:
B#(C(a(x1))) -> a#(C(B(x1)))
a#(b(c(x1))) -> c#(b(a(x1)))
c#(A(B(x1))) -> B#(A(c(x1)))
a#(b(c(x1))) -> a#(x1)
TRS:
a(b(c(x1))) -> c(b(a(x1)))
C(B(A(x1))) -> A(B(C(x1)))
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> x1
Arctic Interpretation Processor:
dimension: 1
interpretation:
[B#](x0) = 4x0,
[c#](x0) = 13x0,
[a#](x0) = 6x0,
[C](x0) = 5x0,
[B](x0) = x0,
[A](x0) = 1x0,
[a](x0) = 2x0,
[b](x0) = x0,
[c](x0) = 9x0
orientation:
B#(C(a(x1))) = 11x1 >= 11x1 = a#(C(B(x1)))
a#(b(c(x1))) = 15x1 >= 15x1 = c#(b(a(x1)))
c#(A(B(x1))) = 14x1 >= 14x1 = B#(A(c(x1)))
a#(b(c(x1))) = 15x1 >= 6x1 = a#(x1)
a(b(c(x1))) = 11x1 >= 11x1 = c(b(a(x1)))
C(B(A(x1))) = 6x1 >= 6x1 = A(B(C(x1)))
b(a(C(x1))) = 7x1 >= 7x1 = C(a(b(x1)))
c(A(B(x1))) = 10x1 >= 10x1 = B(A(c(x1)))
A(c(b(x1))) = 10x1 >= 10x1 = b(c(A(x1)))
B(C(a(x1))) = 7x1 >= 7x1 = a(C(B(x1)))
a(A(x1)) = 3x1 >= x1 = x1
A(a(x1)) = 3x1 >= x1 = x1
b(B(x1)) = x1 >= x1 = x1
B(b(x1)) = x1 >= x1 = x1
c(C(x1)) = 14x1 >= x1 = x1
C(c(x1)) = 14x1 >= x1 = x1
problem:
DPs:
B#(C(a(x1))) -> a#(C(B(x1)))
a#(b(c(x1))) -> c#(b(a(x1)))
c#(A(B(x1))) -> B#(A(c(x1)))
TRS:
a(b(c(x1))) -> c(b(a(x1)))
C(B(A(x1))) -> A(B(C(x1)))
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> x1
EDG Processor:
DPs:
B#(C(a(x1))) -> a#(C(B(x1)))
a#(b(c(x1))) -> c#(b(a(x1)))
c#(A(B(x1))) -> B#(A(c(x1)))
TRS:
a(b(c(x1))) -> c(b(a(x1)))
C(B(A(x1))) -> A(B(C(x1)))
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> x1
graph:
B#(C(a(x1))) -> a#(C(B(x1))) ->
a#(b(c(x1))) -> c#(b(a(x1)))
c#(A(B(x1))) -> B#(A(c(x1))) ->
B#(C(a(x1))) -> a#(C(B(x1)))
a#(b(c(x1))) -> c#(b(a(x1))) -> c#(A(B(x1))) -> B#(A(c(x1)))
KBO Processor:
argument filtering:
pi(c) = [0]
pi(b) = 0
pi(a) = [0]
pi(A) = 0
pi(B) = 0
pi(C) = 0
pi(a#) = [0]
pi(c#) = [0]
pi(B#) = 0
weight function:
w0 = 1
w(B#) = w(c#) = w(a#) = w(a) = w(c) = 1
w(C) = w(B) = w(A) = w(b) = 0
precedence:
a > a# > c# > B# ~ C ~ B ~ A ~ b ~ c
problem:
DPs:
TRS:
a(b(c(x1))) -> c(b(a(x1)))
C(B(A(x1))) -> A(B(C(x1)))
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> x1
Qed