2.63/1.23	MAYBE
2.63/1.23	
2.63/1.23	Proof:
2.63/1.23	ConCon could not decide confluence of the system.
2.63/1.23	\cite{ALS94}, Theorem 4.1 does not apply.
2.63/1.23	This system is of type 3 or smaller.
2.63/1.23	This system is strongly deterministic.
2.63/1.23	This system is quasi-decreasing.
2.63/1.23	By \cite{A14}, Theorem 11.5.9.
2.63/1.23	This system is of type 3 or smaller.
2.63/1.23	This system is deterministic.
2.63/1.23	System R transformed to V(R) + Emb.
2.63/1.23	This system is terminating.
2.63/1.23	Call external tool:
2.63/1.23	./ttt2.sh
2.63/1.23	Input:
2.63/1.23	  a -> c
2.63/1.23	  a -> d
2.63/1.23	  b -> c
2.63/1.23	  b -> d
2.63/1.23	  c -> e
2.63/1.23	  c -> k
2.63/1.23	  d -> k
2.63/1.23	  f(x) -> x
2.63/1.23	  g(x, x) -> C
2.63/1.23	  g(x, x) -> A
2.63/1.23	  h(x) -> i(x, x)
2.63/1.23	  h(x) -> x
2.63/1.23	  g(x, y) -> x
2.63/1.23	  g(x, y) -> y
2.63/1.23	  f(x) -> x
2.63/1.23	  i(x, y) -> x
2.63/1.23	  i(x, y) -> y
2.63/1.23	
2.63/1.23	 Polynomial Interpretation Processor:
2.63/1.23	  dimension: 1
2.63/1.23	  interpretation:
2.63/1.23	   [i](x0, x1) = x0 + 6x1 + x0x0 + 1,
2.63/1.23	   
2.63/1.23	   [h](x0) = 7x0 + 2x0x0 + 2,
2.63/1.23	   
2.63/1.23	   [A] = 0,
2.63/1.23	   
2.63/1.23	   [C] = 0,
2.63/1.23	   
2.63/1.23	   [g](x0, x1) = x0 + 2x1 + 1,
2.63/1.23	   
2.63/1.23	   [f](x0) = x0 + 4,
2.63/1.23	   
2.63/1.23	   [k] = 0,
2.63/1.23	   
2.63/1.23	   [e] = 0,
2.63/1.23	   
2.63/1.23	   [b] = 7,
2.63/1.23	   
2.63/1.23	   [d] = 2,
2.63/1.23	   
2.63/1.23	   [c] = 4,
2.63/1.23	   
2.63/1.23	   [a] = 5
2.63/1.23	  orientation:
2.63/1.23	   a() = 5 >= 4 = c()
2.63/1.23	   
2.63/1.23	   a() = 5 >= 2 = d()
2.63/1.23	   
2.63/1.23	   b() = 7 >= 4 = c()
2.63/1.23	   
2.63/1.23	   b() = 7 >= 2 = d()
2.63/1.23	   
2.63/1.23	   c() = 4 >= 0 = e()
2.63/1.23	   
2.63/1.23	   c() = 4 >= 0 = k()
2.63/1.23	   
2.63/1.23	   d() = 2 >= 0 = k()
2.63/1.23	   
2.63/1.23	   f(x) = x + 4 >= x = x
2.63/1.23	   
2.63/1.23	   g(x,x) = 3x + 1 >= 0 = C()
2.63/1.23	   
2.63/1.23	   g(x,x) = 3x + 1 >= 0 = A()
2.63/1.23	   
2.63/1.23	   h(x) = 7x + 2x*x + 2 >= 7x + x*x + 1 = i(x,x)
2.63/1.23	   
2.63/1.23	   h(x) = 7x + 2x*x + 2 >= x = x
2.63/1.23	   
2.63/1.23	   g(x,y) = x + 2y + 1 >= x = x
2.63/1.23	   
2.63/1.23	   g(x,y) = x + 2y + 1 >= y = y
2.63/1.23	   
2.63/1.23	   i(x,y) = x + x*x + 6y + 1 >= x = x
2.63/1.23	   
2.63/1.23	   i(x,y) = x + x*x + 6y + 1 >= y = y
2.63/1.23	  problem:
2.63/1.23	   
2.63/1.24	  Qed
2.63/1.24	This critical pair is not trivial.
2.63/1.24	
2.63/1.26	EOF