5.06/1.86	YES
5.06/1.86	
5.06/1.86	Proof:
5.06/1.86	This system is confluent.
5.06/1.86	By \cite{ALS94}, Theorem 4.1.
5.06/1.86	This system is of type 3 or smaller.
5.06/1.86	This system is strongly deterministic.
5.06/1.86	This system is quasi-decreasing.
5.06/1.86	By \cite{A14}, Theorem 11.5.9.
5.06/1.86	This system is of type 3 or smaller.
5.06/1.86	This system is deterministic.
5.06/1.86	System R transformed to V(R) + Emb.
5.06/1.86	This system is terminating.
5.06/1.86	Call external tool:
5.06/1.86	./ttt2.sh
5.06/1.86	Input:
5.06/1.86	  a -> c
5.06/1.86	  a -> d
5.06/1.86	  b -> c
5.06/1.86	  b -> d
5.06/1.86	  c -> e
5.06/1.86	  d -> e
5.06/1.86	  k -> e
5.06/1.86	  l -> e
5.06/1.86	  s(c) -> t(k)
5.06/1.86	  s(c) -> t(l)
5.06/1.86	  s(e) -> t(e)
5.06/1.86	  g(x, x) -> h(x, x)
5.06/1.86	  f(x) -> pair(x, s(x))
5.06/1.86	  f(x) -> s(x)
5.06/1.86	  h(x, y) -> x
5.06/1.86	  h(x, y) -> y
5.06/1.86	  pair(x, y) -> x
5.06/1.86	  pair(x, y) -> y
5.06/1.86	  s(x) -> x
5.06/1.86	  g(x, y) -> x
5.06/1.86	  g(x, y) -> y
5.06/1.86	  t(x) -> x
5.06/1.86	  f(x) -> x
5.06/1.86	
5.06/1.86	 Polynomial Interpretation Processor:
5.06/1.86	  dimension: 1
5.06/1.86	  interpretation:
5.06/1.86	   [pair](x0, x1) = 2x0 + x1 + 2x0x0 + 1,
5.06/1.86	   
5.06/1.86	   [f](x0) = 7x0 + 6x0x0 + 5,
5.06/1.86	   
5.06/1.86	   [h](x0, x1) = 4x0 + 4x1 + 4,
5.06/1.86	   
5.06/1.86	   [g](x0, x1) = x0 + 7x1 + 4x0x0 + 3x1x1 + 6,
5.06/1.86	   
5.06/1.86	   [t](x0) = 2x0 + 2,
5.06/1.86	   
5.06/1.87	   [s](x0) = 4x0 + 4x0x0 + 3,
5.06/1.87	   
5.06/1.87	   [l] = 2,
5.06/1.87	   
5.06/1.87	   [k] = 1,
5.06/1.87	   
5.06/1.87	   [e] = 0,
5.06/1.87	   
5.06/1.87	   [b] = 6,
5.06/1.87	   
5.06/1.87	   [d] = 1,
5.06/1.87	   
5.06/1.87	   [c] = 4,
5.06/1.87	   
5.06/1.87	   [a] = 6
5.06/1.87	  orientation:
5.06/1.87	   a() = 6 >= 4 = c()
5.06/1.87	   
5.06/1.87	   a() = 6 >= 1 = d()
5.06/1.87	   
5.06/1.87	   b() = 6 >= 4 = c()
5.06/1.87	   
5.06/1.87	   b() = 6 >= 1 = d()
5.06/1.87	   
5.06/1.87	   c() = 4 >= 0 = e()
5.06/1.87	   
5.06/1.87	   d() = 1 >= 0 = e()
5.06/1.87	   
5.06/1.87	   k() = 1 >= 0 = e()
5.06/1.87	   
5.06/1.87	   l() = 2 >= 0 = e()
5.06/1.87	   
5.06/1.87	   s(c()) = 83 >= 4 = t(k())
5.06/1.87	   
5.06/1.87	   s(c()) = 83 >= 6 = t(l())
5.06/1.87	   
5.06/1.87	   s(e()) = 3 >= 2 = t(e())
5.06/1.87	   
5.06/1.87	   g(x,x) = 8x + 7x*x + 6 >= 8x + 4 = h(x,x)
5.06/1.87	   
5.06/1.87	   f(x) = 7x + 6x*x + 5 >= 6x + 6x*x + 4 = pair(x,s(x))
5.06/1.87	   
5.06/1.87	   f(x) = 7x + 6x*x + 5 >= 4x + 4x*x + 3 = s(x)
5.06/1.87	   
5.06/1.87	   h(x,y) = 4x + 4y + 4 >= x = x
5.06/1.87	   
5.06/1.87	   h(x,y) = 4x + 4y + 4 >= y = y
5.06/1.87	   
5.06/1.87	   pair(x,y) = 2x + 2x*x + y + 1 >= x = x
5.06/1.87	   
5.06/1.87	   pair(x,y) = 2x + 2x*x + y + 1 >= y = y
5.06/1.87	   
5.06/1.87	   s(x) = 4x + 4x*x + 3 >= x = x
5.06/1.87	   
5.06/1.87	   g(x,y) = x + 4x*x + 7y + 3y*y + 6 >= x = x
5.06/1.87	   
5.06/1.87	   g(x,y) = x + 4x*x + 7y + 3y*y + 6 >= y = y
5.06/1.87	   
5.06/1.87	   t(x) = 2x + 2 >= x = x
5.06/1.87	   
5.06/1.87	   f(x) = 7x + 6x*x + 5 >= x = x
5.06/1.87	  problem:
5.06/1.87	   
5.06/1.87	  Qed
5.06/1.87	All 8 critical pairs are joinable.
5.06/1.87	Overlap: (rule1: s(c) -> t(k), rule2: s(c) -> t(l), pos: ε, mgu: {})
5.06/1.87	CP: t(l) = t(k)
5.06/1.87	This critical pair is context-joinable.
5.06/1.87	Overlap: (rule1: b -> c, rule2: b -> d, pos: ε, mgu: {})
5.06/1.87	CP: d = c
5.06/1.87	This critical pair is context-joinable.
5.06/1.87	Overlap: (rule1: a -> d, rule2: a -> c, pos: ε, mgu: {})
5.06/1.87	CP: c = d
5.06/1.87	This critical pair is context-joinable.
5.06/1.87	Overlap: (rule1: b -> d, rule2: b -> c, pos: ε, mgu: {})
5.06/1.87	CP: c = d
5.06/1.87	This critical pair is context-joinable.
5.06/1.87	Overlap: (rule1: s(c) -> t(k), rule2: c -> e, pos: 1, mgu: {})
5.06/1.87	CP: s(e) = t(k)
5.06/1.87	This critical pair is context-joinable.
5.06/1.87	Overlap: (rule1: a -> c, rule2: a -> d, pos: ε, mgu: {})
5.06/1.87	CP: d = c
5.06/1.87	This critical pair is context-joinable.
5.06/1.87	Overlap: (rule1: s(c) -> t(l), rule2: s(c) -> t(k), pos: ε, mgu: {})
5.06/1.87	CP: t(k) = t(l)
5.06/1.87	This critical pair is context-joinable.
5.06/1.87	Overlap: (rule1: s(c) -> t(l), rule2: c -> e, pos: 1, mgu: {})
5.06/1.87	CP: s(e) = t(l)
5.06/1.87	This critical pair is context-joinable.
5.06/1.87	
5.34/1.91	EOF