YES(?,O(n^1)) 0.16/0.35 YES(?,O(n^1)) 0.16/0.35 0.16/0.35 Problem: 0.16/0.35 a(f(),a(f(),a(g(),a(g(),x)))) -> a(g(),a(g(),a(g(),a(f(),a(f(),a(f(),x)))))) 0.16/0.35 0.16/0.35 Proof: 0.16/0.35 Bounds Processor: 0.16/0.35 bound: 5 0.16/0.35 enrichment: match 0.16/0.35 automaton: 0.16/0.35 final states: {4} 0.16/0.35 transitions: 0.16/0.35 g3() -> 74* 0.16/0.35 f3() -> 70* 0.16/0.35 a4(126,128) -> 108* 0.16/0.35 a4(122,115) -> 156* 0.16/0.35 a4(126,142) -> 143* 0.16/0.35 a4(122,123) -> 124* 0.16/0.35 a4(122,137) -> 166* 0.16/0.35 a4(126,158) -> 159* 0.16/0.35 a4(122,139) -> 140* 0.16/0.35 a4(126,160) -> 73* 0.16/0.35 a4(126,168) -> 169* 0.16/0.35 a4(126,170) -> 123* 0.16/0.35 a4(122,157) -> 158* 0.16/0.35 a4(126,178) -> 179* 0.16/0.35 a4(122,94) -> 176* 0.16/0.35 a4(126,180) -> 135* 0.16/0.35 a4(122,167) -> 168* 0.16/0.35 a4(122,177) -> 178* 0.16/0.35 a4(126,125) -> 127* 0.16/0.35 a4(126,127) -> 128* 0.16/0.35 a4(126,141) -> 142* 0.16/0.35 a4(126,143) -> 72* 0.16/0.35 a4(122,124) -> 125* 0.16/0.35 a4(122,73) -> 123* 0.16/0.35 a4(126,159) -> 160* 0.16/0.35 a4(122,140) -> 141* 0.16/0.35 a4(122,142) -> 166* 0.16/0.35 a4(126,169) -> 170* 0.16/0.35 a4(122,156) -> 157* 0.16/0.35 a4(126,179) -> 180* 0.16/0.35 a4(122,95) -> 139* 0.16/0.35 a4(122,166) -> 167* 0.16/0.35 a4(122,176) -> 177* 0.16/0.35 g4() -> 126* 0.16/0.35 a0(4,4) -> 4* 0.16/0.35 f4() -> 122* 0.16/0.35 f0() -> 4* 0.16/0.35 a5(185,187) -> 124* 0.16/0.35 a5(185,201) -> 202* 0.16/0.35 a5(181,182) -> 183* 0.16/0.35 a5(181,198) -> 199* 0.16/0.35 a5(181,159) -> 182* 0.16/0.35 a5(185,184) -> 186* 0.16/0.35 a5(185,186) -> 187* 0.16/0.35 a5(181,169) -> 198* 0.16/0.35 a5(185,200) -> 201* 0.16/0.35 a5(185,202) -> 125* 0.16/0.35 a5(181,183) -> 184* 0.16/0.35 a5(181,199) -> 200* 0.16/0.35 g0() -> 4* 0.16/0.35 g5() -> 185* 0.16/0.35 a1(12,14) -> 15* 0.16/0.35 a1(12,18) -> 19* 0.16/0.35 a1(12,20) -> 21* 0.16/0.35 a1(12,22) -> 13* 0.16/0.35 a1(16,18) -> 14,13,4 0.16/0.35 a1(16,22) -> 23* 0.16/0.35 a1(12,13) -> 14* 0.16/0.35 a1(12,17) -> 19* 0.16/0.35 a1(12,19) -> 20* 0.16/0.35 a1(12,23) -> 13* 0.16/0.35 a1(16,15) -> 17* 0.16/0.35 a1(16,17) -> 18* 0.16/0.35 a1(16,21) -> 22* 0.16/0.35 a1(16,23) -> 14,4,13 0.16/0.35 a1(12,4) -> 13* 0.16/0.35 f5() -> 181* 0.16/0.35 g1() -> 16* 0.16/0.35 f1() -> 12* 0.16/0.35 a2(36,41) -> 48* 0.16/0.35 a2(36,43) -> 44* 0.16/0.35 a2(36,49) -> 50* 0.16/0.35 a2(40,84) -> 85* 0.16/0.35 a2(40,86) -> 37* 0.16/0.35 a2(36,83) -> 84* 0.16/0.35 a2(40,39) -> 41* 0.16/0.35 a2(40,41) -> 42* 0.16/0.35 a2(36,22) -> 37* 0.16/0.35 a2(40,45) -> 46* 0.16/0.35 a2(40,47) -> 38,20 0.16/0.35 a2(40,51) -> 52* 0.16/0.35 a2(36,38) -> 39* 0.16/0.35 a2(36,42) -> 43* 0.16/0.35 a2(36,44) -> 45* 0.16/0.35 a2(36,46) -> 82* 0.16/0.35 a2(36,48) -> 49* 0.16/0.35 a2(40,85) -> 86* 0.16/0.35 a2(36,82) -> 83* 0.16/0.35 a2(36,15) -> 43* 0.16/0.35 a2(36,17) -> 37* 0.16/0.35 a2(36,21) -> 37* 0.16/0.35 a2(40,42) -> 43,15,14 0.16/0.35 a2(40,46) -> 47* 0.16/0.35 a2(40,50) -> 51* 0.16/0.35 a2(40,52) -> 43* 0.16/0.35 a2(36,37) -> 38* 0.16/0.35 g2() -> 40* 0.16/0.35 f2() -> 36* 0.16/0.35 a3(70,135) -> 136* 0.16/0.35 a3(70,72) -> 73* 0.16/0.35 a3(74,95) -> 96* 0.16/0.35 a3(70,76) -> 107* 0.16/0.35 a3(74,109) -> 110* 0.16/0.35 a3(74,111) -> 113,83 0.16/0.35 a3(70,92) -> 93* 0.16/0.35 a3(70,96) -> 134* 0.16/0.35 a3(70,108) -> 109* 0.16/0.35 a3(70,112) -> 113* 0.16/0.35 a3(74,115) -> 116* 0.16/0.35 a3(70,39) -> 71* 0.16/0.35 a3(70,41) -> 71* 0.16/0.35 a3(70,51) -> 71* 0.16/0.35 a3(74,137) -> 138* 0.16/0.35 a3(74,76) -> 45,44 0.16/0.35 a3(70,134) -> 135* 0.16/0.35 a3(70,71) -> 72* 0.16/0.35 a3(74,94) -> 95* 0.16/0.35 a3(74,96) -> 39* 0.16/0.35 a3(70,85) -> 92* 0.16/0.35 a3(74,110) -> 111* 0.16/0.35 a3(70,93) -> 94* 0.16/0.35 a3(70,107) -> 108* 0.16/0.35 a3(74,114) -> 115* 0.16/0.35 a3(74,116) -> 71* 0.16/0.35 a3(70,46) -> 112* 0.16/0.35 a3(70,113) -> 114* 0.16/0.35 a3(74,136) -> 137* 0.16/0.35 a3(74,73) -> 75* 0.16/0.35 a3(74,138) -> 72,49 0.16/0.35 a3(74,75) -> 76* 0.16/0.35 problem: 0.16/0.35 0.16/0.35 Qed 0.16/0.36 EOF