3.41/1.40	MAYBE
3.41/1.40	
3.41/1.40	Proof:
3.41/1.40	ConCon could not decide confluence of the system.
3.41/1.40	\cite{ALS94}, Theorem 4.1 does not apply.
3.41/1.40	This system is of type 3 or smaller.
3.41/1.40	This system is strongly deterministic.
3.41/1.40	This system is quasi-decreasing.
3.41/1.40	By \cite{A14}, Theorem 11.5.9.
3.41/1.40	This system is of type 3 or smaller.
3.41/1.40	This system is deterministic.
3.41/1.40	System R transformed to V(R) + Emb.
3.41/1.40	This system is terminating.
3.41/1.40	Call external tool:
3.41/1.40	./ttt2.sh
3.41/1.40	Input:
3.41/1.40	  a -> c
3.41/1.40	  a -> d
3.41/1.40	  b -> c
3.41/1.40	  b -> d
3.41/1.40	  s(k) -> t(a)
3.41/1.40	  s(l) -> t(a)
3.41/1.40	  g(x, x) -> h(x, x)
3.41/1.40	  f(x, y) -> y
3.41/1.40	  f(x, y) -> s(x)
3.41/1.40	  h(x, y) -> x
3.41/1.40	  h(x, y) -> y
3.41/1.40	  s(x) -> x
3.41/1.40	  g(x, y) -> x
3.41/1.40	  g(x, y) -> y
3.41/1.40	  t(x) -> x
3.41/1.40	  f(x, y) -> x
3.41/1.40	  f(x, y) -> y
3.41/1.40	
3.41/1.41	 Polynomial Interpretation Processor:
3.41/1.41	  dimension: 1
3.41/1.41	  interpretation:
3.41/1.41	   [f](x0, x1) = 2x0 + x1 + 3x1x1 + 4,
3.41/1.41	   
3.41/1.41	   [h](x0, x1) = x0 + 4x1 + 4x0x0 + 4x1x1 + 1,
3.41/1.41	   
3.41/1.41	   [g](x0, x1) = 4x0 + 4x1 + x0x0 + 7x1x1 + 4,
3.41/1.41	   
3.41/1.41	   [l] = 2,
3.41/1.41	   
3.41/1.41	   [t](x0) = 2x0 + x0x0 + 1,
3.41/1.41	   
3.41/1.41	   [s](x0) = 2x0 + 1,
3.41/1.41	   
3.41/1.41	   [k] = 2,
3.41/1.41	   
3.41/1.41	   [b] = 1,
3.41/1.41	   
3.41/1.41	   [d] = 0,
3.41/1.41	   
3.41/1.41	   [c] = 0,
3.41/1.41	   
3.41/1.41	   [a] = 1
3.41/1.41	  orientation:
3.41/1.41	   a() = 1 >= 0 = c()
3.41/1.41	   
3.41/1.41	   a() = 1 >= 0 = d()
3.41/1.41	   
3.41/1.41	   b() = 1 >= 0 = c()
3.41/1.41	   
3.41/1.41	   b() = 1 >= 0 = d()
3.41/1.41	   
3.41/1.41	   s(k()) = 5 >= 4 = t(a())
3.41/1.41	   
3.41/1.41	   s(l()) = 5 >= 4 = t(a())
3.41/1.41	   
3.41/1.41	   g(x,x) = 8x + 8x*x + 4 >= 5x + 8x*x + 1 = h(x,x)
3.41/1.41	   
3.41/1.41	   f(x,y) = 2x + y + 3y*y + 4 >= y = y
3.41/1.41	   
3.41/1.41	   f(x,y) = 2x + y + 3y*y + 4 >= 2x + 1 = s(x)
3.41/1.41	   
3.41/1.41	   h(x,y) = x + 4x*x + 4y + 4y*y + 1 >= x = x
3.41/1.41	   
3.41/1.41	   h(x,y) = x + 4x*x + 4y + 4y*y + 1 >= y = y
3.41/1.41	   
3.41/1.41	   s(x) = 2x + 1 >= x = x
3.41/1.41	   
3.41/1.41	   g(x,y) = 4x + x*x + 4y + 7y*y + 4 >= x = x
3.41/1.41	   
3.41/1.41	   g(x,y) = 4x + x*x + 4y + 7y*y + 4 >= y = y
3.41/1.41	   
3.41/1.41	   t(x) = 2x + x*x + 1 >= x = x
3.41/1.41	   
3.41/1.41	   f(x,y) = 2x + y + 3y*y + 4 >= x = x
3.41/1.41	  problem:
3.41/1.41	   
3.41/1.41	  Qed
3.41/1.41	This critical pair is not joinable.
3.41/1.41	
3.41/1.47	EOF