YES(?,POLY)
542.65/176.53	YES(?,POLY)
542.65/176.53	
542.65/176.53	We are left with following problem, upon which TcT provides the
542.65/176.53	certificate YES(?,POLY).
542.65/176.53	
542.65/176.53	Strict Trs:
542.65/176.53	  { f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) ->
542.65/176.53	    f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
542.65/176.53	  , f(0(), s(x2), x3, x4, x5, x6, x7, x8, x9, x10) ->
542.65/176.53	    f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10)
542.65/176.53	  , f(0(), 0(), s(x3), x4, x5, x6, x7, x8, x9, x10) ->
542.65/176.53	    f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10)
542.65/176.53	  , f(0(), 0(), 0(), s(x4), x5, x6, x7, x8, x9, x10) ->
542.65/176.53	    f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10)
542.65/176.53	  , f(0(), 0(), 0(), 0(), s(x5), x6, x7, x8, x9, x10) ->
542.65/176.53	    f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10)
542.65/176.53	  , f(0(), 0(), 0(), 0(), 0(), s(x6), x7, x8, x9, x10) ->
542.65/176.53	    f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10)
542.65/176.53	  , f(0(), 0(), 0(), 0(), 0(), 0(), s(x7), x8, x9, x10) ->
542.65/176.53	    f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10)
542.65/176.53	  , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x8), x9, x10) ->
542.65/176.53	    f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10)
542.65/176.53	  , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x9), x10) ->
542.65/176.53	    f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10)
542.65/176.53	  , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), s(x10)) ->
542.65/176.53	    f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10)
542.65/176.53	  , f(0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0(), 0()) -> 0() }
542.65/176.53	Obligation:
542.65/176.53	  innermost runtime complexity
542.65/176.53	Answer:
542.65/176.53	  YES(?,POLY)
542.65/176.53	
542.65/176.53	The input was oriented with the instance of 'Polynomial Path Order
542.65/176.53	(PS)' as induced by the safe mapping
542.65/176.53	
542.65/176.53	 safe(f) = {}, safe(s) = {1}, safe(0) = {}
542.65/176.53	
542.65/176.53	and precedence
542.65/176.53	
542.65/176.53	 empty .
542.65/176.53	
542.65/176.53	Following symbols are considered recursive:
542.65/176.53	
542.65/176.53	 {f}
542.65/176.53	
542.65/176.53	The recursion depth is 1.
542.65/176.53	
542.65/176.53	For your convenience, here are the satisfied ordering constraints:
542.65/176.53	
542.65/176.53	           f(s(; x1),  x2,  x3,  x4,  x5,  x6,  x7,  x8,  x9,  x10;) > f(x1,  x2,  x3,  x4,  x5,  x6,  x7,  x8,  x9,  x10;)         
542.65/176.53	                                                                                                                                    
542.65/176.53	          f(0(),  s(; x2),  x3,  x4,  x5,  x6,  x7,  x8,  x9,  x10;) > f(x2,  x2,  x3,  x4,  x5,  x6,  x7,  x8,  x9,  x10;)         
542.65/176.53	                                                                                                                                    
542.65/176.53	         f(0(),  0(),  s(; x3),  x4,  x5,  x6,  x7,  x8,  x9,  x10;) > f(x3,  x3,  x3,  x4,  x5,  x6,  x7,  x8,  x9,  x10;)         
542.65/176.53	                                                                                                                                    
542.65/176.53	        f(0(),  0(),  0(),  s(; x4),  x5,  x6,  x7,  x8,  x9,  x10;) > f(x4,  x4,  x4,  x4,  x5,  x6,  x7,  x8,  x9,  x10;)         
542.65/176.53	                                                                                                                                    
542.65/176.53	       f(0(),  0(),  0(),  0(),  s(; x5),  x6,  x7,  x8,  x9,  x10;) > f(x5,  x5,  x5,  x5,  x5,  x6,  x7,  x8,  x9,  x10;)         
542.65/176.53	                                                                                                                                    
542.65/176.53	      f(0(),  0(),  0(),  0(),  0(),  s(; x6),  x7,  x8,  x9,  x10;) > f(x6,  x6,  x6,  x6,  x6,  x6,  x7,  x8,  x9,  x10;)         
542.65/176.53	                                                                                                                                    
542.65/176.53	     f(0(),  0(),  0(),  0(),  0(),  0(),  s(; x7),  x8,  x9,  x10;) > f(x7,  x7,  x7,  x7,  x7,  x7,  x7,  x8,  x9,  x10;)         
542.65/176.53	                                                                                                                                    
542.65/176.53	    f(0(),  0(),  0(),  0(),  0(),  0(),  0(),  s(; x8),  x9,  x10;) > f(x8,  x8,  x8,  x8,  x8,  x8,  x8,  x8,  x9,  x10;)         
542.65/176.53	                                                                                                                                    
542.65/176.53	   f(0(),  0(),  0(),  0(),  0(),  0(),  0(),  0(),  s(; x9),  x10;) > f(x9,  x9,  x9,  x9,  x9,  x9,  x9,  x9,  x9,  x10;)         
542.65/176.53	                                                                                                                                    
542.65/176.53	  f(0(),  0(),  0(),  0(),  0(),  0(),  0(),  0(),  0(),  s(; x10);) > f(x10,  x10,  x10,  x10,  x10,  x10,  x10,  x10,  x10,  x10;)
542.65/176.53	                                                                                                                                    
542.65/176.53	       f(0(),  0(),  0(),  0(),  0(),  0(),  0(),  0(),  0(),  0();) > 0()                                                          
542.65/176.53	                                                                                                                                    
542.65/176.53	
542.65/176.53	Hurray, we answered YES(?,POLY)
542.84/176.60	EOF