6.12/2.42	YES
6.12/2.42	
6.12/2.42	Proof:
6.12/2.42	This system is confluent.
6.12/2.42	By \cite{ALS94}, Theorem 4.1.
6.12/2.42	This system is of type 3 or smaller.
6.12/2.42	This system is strongly deterministic.
6.12/2.42	This system is quasi-decreasing.
6.12/2.42	By \cite{A14}, Theorem 11.5.9.
6.12/2.42	This system is of type 3 or smaller.
6.12/2.42	This system is deterministic.
6.12/2.42	System R transformed to V(R) + Emb.
6.12/2.42	This system is terminating.
6.12/2.42	Call external tool:
6.12/2.42	./ttt2.sh
6.12/2.42	Input:
6.12/2.42	(VAR x y)
6.12/2.42	(RULES
6.12/2.42	  a -> c
6.12/2.42	  a -> d
6.12/2.42	  b -> c
6.12/2.42	  b -> d
6.12/2.42	  c -> e
6.12/2.42	  d -> e
6.12/2.42	  k -> e
6.12/2.42	  l -> e
6.12/2.42	  s(c) -> t(k)
6.12/2.42	  s(c) -> t(l)
6.12/2.42	  s(e) -> t(e)
6.12/2.42	  g(x, x) -> h(x, x)
6.12/2.42	  f(x) -> pair(x, s(x))
6.12/2.42	  f(x) -> s(x)
6.12/2.42	  h(x, y) -> x
6.12/2.42	  h(x, y) -> y
6.12/2.42	  pair(x, y) -> x
6.12/2.42	  pair(x, y) -> y
6.12/2.42	  s(x) -> x
6.12/2.42	  g(x, y) -> x
6.12/2.42	  g(x, y) -> y
6.12/2.42	  t(x) -> x
6.12/2.42	  f(x) -> x
6.12/2.42	)
6.12/2.42	
6.12/2.42	 Polynomial Interpretation Processor:
6.12/2.42	  dimension: 1
6.12/2.42	  interpretation:
6.12/2.42	   [pair](x0, x1) = 2x0 + x1 + 2x0x0 + 1,
6.12/2.42	   
6.12/2.42	   [f](x0) = 7x0 + 6x0x0 + 5,
6.12/2.42	   
6.12/2.42	   [h](x0, x1) = 4x0 + 4x1 + 4,
6.12/2.42	   
6.12/2.42	   [g](x0, x1) = x0 + 7x1 + 4x0x0 + 3x1x1 + 6,
6.12/2.42	   
6.12/2.42	   [t](x0) = 2x0 + 2,
6.12/2.42	   
6.12/2.43	   [s](x0) = 4x0 + 4x0x0 + 3,
6.12/2.43	   
6.12/2.43	   [l] = 2,
6.12/2.43	   
6.12/2.43	   [k] = 1,
6.12/2.43	   
6.12/2.43	   [e] = 0,
6.12/2.43	   
6.12/2.43	   [b] = 6,
6.12/2.43	   
6.12/2.43	   [d] = 1,
6.12/2.43	   
6.12/2.43	   [c] = 4,
6.12/2.43	   
6.12/2.43	   [a] = 6
6.12/2.43	  orientation:
6.12/2.43	   a() = 6 >= 4 = c()
6.12/2.43	   
6.12/2.43	   a() = 6 >= 1 = d()
6.12/2.43	   
6.12/2.43	   b() = 6 >= 4 = c()
6.12/2.43	   
6.12/2.43	   b() = 6 >= 1 = d()
6.12/2.43	   
6.12/2.43	   c() = 4 >= 0 = e()
6.12/2.43	   
6.12/2.43	   d() = 1 >= 0 = e()
6.12/2.43	   
6.12/2.43	   k() = 1 >= 0 = e()
6.12/2.43	   
6.12/2.43	   l() = 2 >= 0 = e()
6.12/2.43	   
6.12/2.43	   s(c()) = 83 >= 4 = t(k())
6.12/2.43	   
6.12/2.43	   s(c()) = 83 >= 6 = t(l())
6.12/2.43	   
6.12/2.43	   s(e()) = 3 >= 2 = t(e())
6.12/2.43	   
6.12/2.43	   g(x,x) = 8x + 7x*x + 6 >= 8x + 4 = h(x,x)
6.12/2.43	   
6.12/2.43	   f(x) = 7x + 6x*x + 5 >= 6x + 6x*x + 4 = pair(x,s(x))
6.12/2.43	   
6.12/2.43	   f(x) = 7x + 6x*x + 5 >= 4x + 4x*x + 3 = s(x)
6.12/2.43	   
6.12/2.43	   h(x,y) = 4x + 4y + 4 >= x = x
6.12/2.43	   
6.12/2.43	   h(x,y) = 4x + 4y + 4 >= y = y
6.12/2.43	   
6.12/2.43	   pair(x,y) = 2x + 2x*x + y + 1 >= x = x
6.12/2.43	   
6.12/2.43	   pair(x,y) = 2x + 2x*x + y + 1 >= y = y
6.12/2.43	   
6.12/2.43	   s(x) = 4x + 4x*x + 3 >= x = x
6.12/2.43	   
6.12/2.43	   g(x,y) = x + 4x*x + 7y + 3y*y + 6 >= x = x
6.12/2.43	   
6.12/2.43	   g(x,y) = x + 4x*x + 7y + 3y*y + 6 >= y = y
6.12/2.43	   
6.12/2.43	   t(x) = 2x + 2 >= x = x
6.12/2.43	   
6.12/2.43	   f(x) = 7x + 6x*x + 5 >= x = x
6.12/2.43	  problem:
6.12/2.43	   
6.12/2.43	  Qed
6.12/2.43	All 8 critical pairs are joinable.
6.12/2.43	Overlap: (rule1: s(c) -> t(k), rule2: s(c) -> t(l), pos: ε, mgu: {})
6.12/2.43	CP: t(l) = t(k)
6.12/2.43	This critical pair is context-joinable.
6.12/2.43	Overlap: (rule1: b -> c, rule2: b -> d, pos: ε, mgu: {})
6.12/2.43	CP: d = c
6.12/2.43	This critical pair is context-joinable.
6.12/2.43	Overlap: (rule1: a -> d, rule2: a -> c, pos: ε, mgu: {})
6.12/2.43	CP: c = d
6.12/2.43	This critical pair is context-joinable.
6.12/2.43	Overlap: (rule1: b -> d, rule2: b -> c, pos: ε, mgu: {})
6.12/2.43	CP: c = d
6.12/2.43	This critical pair is context-joinable.
6.12/2.43	Overlap: (rule1: s(c) -> t(k), rule2: c -> e, pos: 1, mgu: {})
6.12/2.43	CP: s(e) = t(k)
6.12/2.43	This critical pair is context-joinable.
6.12/2.43	Overlap: (rule1: a -> c, rule2: a -> d, pos: ε, mgu: {})
6.12/2.43	CP: d = c
6.12/2.43	This critical pair is context-joinable.
6.12/2.43	Overlap: (rule1: s(c) -> t(l), rule2: s(c) -> t(k), pos: ε, mgu: {})
6.12/2.43	CP: t(k) = t(l)
6.12/2.43	This critical pair is context-joinable.
6.12/2.43	Overlap: (rule1: s(c) -> t(l), rule2: c -> e, pos: 1, mgu: {})
6.12/2.43	CP: s(e) = t(l)
6.12/2.43	This critical pair is context-joinable.
6.12/2.43	
6.30/2.46	EOF