4.72/2.03	MAYBE
4.72/2.03	
4.72/2.03	Proof:
4.72/2.03	ConCon could not decide confluence of the system.
4.72/2.03	\cite{ALS94}, Theorem 4.1 does not apply.
4.72/2.03	This system is of type 3 or smaller.
4.72/2.03	This system is strongly deterministic.
4.72/2.03	This system is quasi-decreasing.
4.72/2.03	By \cite{A14}, Theorem 11.5.9.
4.72/2.03	This system is of type 3 or smaller.
4.72/2.03	This system is deterministic.
4.72/2.03	System R transformed to V(R) + Emb.
4.72/2.03	This system is terminating.
4.72/2.03	Call external tool:
4.72/2.03	./ttt2.sh
4.72/2.03	Input:
4.72/2.03	(VAR x y)
4.72/2.03	(RULES
4.72/2.03	  a -> c
4.72/2.03	  a -> d
4.72/2.03	  b -> c
4.72/2.03	  b -> d
4.72/2.03	  s(k) -> t(a)
4.72/2.03	  s(l) -> t(a)
4.72/2.03	  g(x, x) -> h(x, x)
4.72/2.03	  f(x, y) -> y
4.72/2.03	  f(x, y) -> s(x)
4.72/2.03	  h(x, y) -> x
4.72/2.03	  h(x, y) -> y
4.72/2.03	  s(x) -> x
4.72/2.03	  g(x, y) -> x
4.72/2.03	  g(x, y) -> y
4.72/2.03	  t(x) -> x
4.72/2.03	  f(x, y) -> x
4.72/2.03	  f(x, y) -> y
4.72/2.03	)
4.72/2.03	
4.72/2.03	 Polynomial Interpretation Processor:
4.72/2.03	  dimension: 1
4.72/2.03	  interpretation:
4.72/2.03	   [f](x0, x1) = 2x0 + x1 + 3x1x1 + 4,
4.72/2.03	   
4.72/2.03	   [h](x0, x1) = x0 + 4x1 + 4x0x0 + 4x1x1 + 1,
4.72/2.03	   
4.72/2.03	   [g](x0, x1) = 4x0 + 4x1 + x0x0 + 7x1x1 + 4,
4.72/2.04	   
4.72/2.04	   [l] = 2,
4.72/2.04	   
4.72/2.04	   [t](x0) = 2x0 + x0x0 + 1,
4.72/2.04	   
4.72/2.04	   [s](x0) = 2x0 + 1,
4.72/2.04	   
4.72/2.04	   [k] = 2,
4.72/2.04	   
4.72/2.04	   [b] = 1,
4.72/2.04	   
4.72/2.04	   [d] = 0,
4.72/2.04	   
4.72/2.04	   [c] = 0,
4.72/2.04	   
4.72/2.04	   [a] = 1
4.72/2.04	  orientation:
4.72/2.04	   a() = 1 >= 0 = c()
4.72/2.04	   
4.72/2.04	   a() = 1 >= 0 = d()
4.72/2.04	   
4.72/2.04	   b() = 1 >= 0 = c()
4.72/2.04	   
4.72/2.04	   b() = 1 >= 0 = d()
4.72/2.04	   
4.72/2.04	   s(k()) = 5 >= 4 = t(a())
4.72/2.04	   
4.72/2.04	   s(l()) = 5 >= 4 = t(a())
4.72/2.04	   
4.72/2.04	   g(x,x) = 8x + 8x*x + 4 >= 5x + 8x*x + 1 = h(x,x)
4.72/2.04	   
4.72/2.04	   f(x,y) = 2x + y + 3y*y + 4 >= y = y
4.72/2.04	   
4.72/2.04	   f(x,y) = 2x + y + 3y*y + 4 >= 2x + 1 = s(x)
4.72/2.04	   
4.72/2.04	   h(x,y) = x + 4x*x + 4y + 4y*y + 1 >= x = x
4.72/2.04	   
4.72/2.04	   h(x,y) = x + 4x*x + 4y + 4y*y + 1 >= y = y
4.72/2.04	   
4.72/2.04	   s(x) = 2x + 1 >= x = x
4.72/2.04	   
4.72/2.04	   g(x,y) = 4x + x*x + 4y + 7y*y + 4 >= x = x
4.72/2.04	   
4.72/2.04	   g(x,y) = 4x + x*x + 4y + 7y*y + 4 >= y = y
4.72/2.04	   
4.72/2.04	   t(x) = 2x + x*x + 1 >= x = x
4.72/2.04	   
4.72/2.04	   f(x,y) = 2x + y + 3y*y + 4 >= x = x
4.72/2.04	  problem:
4.72/2.04	   
4.72/2.04	  Qed
4.72/2.04	ConCon could not decide whether all 4 critical pairs are joinable or not.
4.72/2.04	Overlap: (rule1: a -> d, rule2: a -> c, pos: ε, mgu: {})
4.72/2.04	CP: c = d
4.72/2.04	ConCon could not decide context-joinability of this critical pair.
4.72/2.04	
4.72/2.07	EOF