YES Input TRS: 1: p(a(x0),p(b(x1),p(a(x2),x3))) -> p(x2,p(a(a(x0)),p(b(x1),x3))) Number of strict rules: 1 Direct POLO(bPol) ... failed. Uncurrying p 1: p^1_a(x0,p^1_b(x1,p^1_a(x2,x3))) -> p(x2,p^1_a(a(x0),p^1_b(x1,x3))) 2: p(a(_1),_2) ->= p^1_a(_1,_2) 3: p(b(_1),_2) ->= p^1_b(_1,_2) Number of strict rules: 1 Direct POLO(bPol) ... removes: 3 a w: x1 + 1 b w: 2 * x1 + 315 p^1_b w: 2 * x1 + x2 + 2998 p w: x1 + x2 + 2684 p^1_a w: x1 + x2 + 2685 Number of strict rules: 1 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #p(a(_1),_2) ->? #p^1_a(_1,_2) #2: #p^1_a(x0,p^1_b(x1,p^1_a(x2,x3))) -> #p(x2,p^1_a(a(x0),p^1_b(x1,x3))) #3: #p^1_a(x0,p^1_b(x1,p^1_a(x2,x3))) -> #p^1_a(a(x0),p^1_b(x1,x3)) Number of SCCs: 1, DPs: 3 SCC { #1..3 } POLO(Sum)... succeeded. a w: 1 b w: 0 p^1_b w: 21241 #p w: x2 + 21239 p w: 1 #p^1_a w: x2 p^1_a w: 1 USABLE RULES: { 1 2 } Removed DPs: #1 #2 Number of SCCs: 1, DPs: 1 SCC { #3 } POLO(Sum)... succeeded. a w: 1 b w: 0 p^1_b w: x2 + 21241 #p w: 21239 p w: 21245 #p^1_a w: x1 + x2 p^1_a w: x2 + 2 USABLE RULES: { } Removed DPs: #3 Number of SCCs: 0, DPs: 0