5.89/2.43	MAYBE
5.89/2.43	
5.89/2.43	Proof:
5.89/2.43	ConCon could not decide confluence of the system.
5.89/2.43	\cite{ALS94}, Theorem 4.1 does not apply.
5.89/2.44	This system is of type 3 or smaller.
5.89/2.44	This system is strongly deterministic.
5.89/2.44	This system is quasi-decreasing.
5.89/2.44	By \cite{A14}, Theorem 11.5.9.
5.89/2.44	This system is of type 3 or smaller.
5.89/2.44	This system is deterministic.
5.89/2.44	System R transformed to V(R) + Emb.
5.89/2.44	This system is terminating.
5.89/2.44	Call external tool:
5.89/2.44	./ttt2.sh
5.89/2.44	Input:
5.89/2.44	(VAR x y z)
5.89/2.44	(RULES
5.89/2.44	  f(x) -> x
5.89/2.44	  g(d, x, y) -> A
5.89/2.44	  g(d, x, y) -> y
5.89/2.44	  h(x, y) -> g(x, y, f(k))
5.89/2.44	  h(x, y) -> y
5.89/2.44	  a -> c
5.89/2.44	  a -> d
5.89/2.44	  b -> c
5.89/2.44	  b -> d
5.89/2.44	  c -> e
5.89/2.44	  c -> l
5.89/2.44	  k -> l
5.89/2.44	  k -> m
5.89/2.44	  d -> m
5.89/2.44	  h(x, y) -> x
5.89/2.44	  h(x, y) -> y
5.89/2.44	  g(x, y, z) -> x
5.89/2.44	  g(x, y, z) -> y
5.89/2.44	  g(x, y, z) -> z
5.89/2.44	  f(x) -> x
5.89/2.44	)
5.89/2.44	
5.89/2.44	 Polynomial Interpretation Processor:
5.89/2.44	  dimension: 1
5.89/2.44	  interpretation:
5.89/2.44	   [m] = 0,
5.89/2.44	   
5.89/2.44	   [l] = 0,
5.89/2.44	   
5.89/2.44	   [e] = 0,
5.89/2.44	   
5.89/2.44	   [b] = 7,
5.89/2.44	   
5.89/2.44	   [c] = 5,
5.89/2.44	   
5.89/2.44	   [a] = 7,
5.89/2.44	   
5.89/2.44	   [k] = 4,
5.89/2.44	   
5.89/2.44	   [h](x0, x1) = 2x0 + x1 + 2x0x0 + 7,
5.89/2.44	   
5.89/2.44	   [A] = 0,
5.89/2.44	   
5.89/2.44	   [g](x0, x1, x2) = 2x0 + x1 + x2 + 2x0x0 + 1,
5.89/2.44	   
5.89/2.44	   [d] = 6,
5.89/2.44	   
5.89/2.44	   [f](x0) = x0 + 1
5.89/2.44	  orientation:
5.89/2.44	   f(x) = x + 1 >= x = x
5.89/2.44	   
5.89/2.44	   g(d(),x,y) = x + y + 85 >= 0 = A()
5.89/2.44	   
5.89/2.44	   g(d(),x,y) = x + y + 85 >= y = y
5.89/2.44	   
5.89/2.44	   h(x,y) = 2x + 2x*x + y + 7 >= 2x + 2x*x + y + 6 = g(x,y,f(k()))
5.89/2.44	   
5.89/2.44	   h(x,y) = 2x + 2x*x + y + 7 >= y = y
5.89/2.44	   
5.89/2.44	   a() = 7 >= 5 = c()
5.89/2.44	   
5.89/2.44	   a() = 7 >= 6 = d()
5.89/2.44	   
5.89/2.44	   b() = 7 >= 5 = c()
5.89/2.44	   
5.89/2.44	   b() = 7 >= 6 = d()
5.89/2.44	   
5.89/2.44	   c() = 5 >= 0 = e()
5.89/2.44	   
5.89/2.44	   c() = 5 >= 0 = l()
5.89/2.44	   
5.89/2.44	   k() = 4 >= 0 = l()
5.89/2.44	   
5.89/2.44	   k() = 4 >= 0 = m()
5.89/2.44	   
5.89/2.44	   d() = 6 >= 0 = m()
5.89/2.44	   
5.89/2.44	   h(x,y) = 2x + 2x*x + y + 7 >= x = x
5.89/2.44	   
5.89/2.44	   g(x,y,z) = 2x + 2x*x + y + z + 1 >= x = x
5.89/2.44	   
5.89/2.44	   g(x,y,z) = 2x + 2x*x + y + z + 1 >= y = y
5.89/2.44	   
5.89/2.44	   g(x,y,z) = 2x + 2x*x + y + z + 1 >= z = z
5.89/2.44	  problem:
5.89/2.44	   
5.89/2.44	  Qed
5.89/2.44	ConCon could not decide whether all 9 critical pairs are joinable or not.
5.89/2.44	Overlap: (rule1: c -> l, rule2: c -> e, pos: ε, mgu: {})
5.89/2.44	CP: e = l
5.89/2.44	ConCon could not decide context-joinability of this critical pair.
5.89/2.44	
5.89/2.47	EOF