YES Problem: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) Proof: DP Processor: DPs: b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) EDG Processor: DPs: b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) graph: b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) CDG Processor: DPs: b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) graph: b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) SCC Processor: #sccs: 1 #rules: 7 #arcs: 30/81 DPs: b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: b0(40) -> 41* b0(254) -> 255* b0(2) -> 3* b0(251) -> 252* b0(121) -> 122* b0(83) -> 84* f40() -> 2* b{#,0}(122) -> 123* b{#,0}(42) -> 43* b{#,0}(84) -> 85* b{#,0}(4) -> 1* b{#,0}(86) -> 87* a0(252) -> 253* a0(159) -> 160* a0(124) -> 125* a0(253) -> 254* a0(41) -> 42* a0(250) -> 251* a0(3) -> 4* 1 -> 85,87,43,123 4 -> 250,40 41 -> 3,122,124,121,86 42 -> 83* 43 -> 1* 84 -> 159* 85 -> 1* 87 -> 1* 122 -> 84,41,86,121,124 123 -> 1* 125 -> 4* 160 -> 4* 255 -> 122,121,86,124,159,3 problem: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) Restore Modifier: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) EDG Processor: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) graph: b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) Bounds Processor: bound: 1 enrichment: match-dp automaton: final states: {41} transitions: b{#,0}(37) -> 39* b{#,0}(44) -> 41* b{#,0}(39) -> 39* b{#,0}(38) -> 39* a0(42) -> 43* a0(37) -> 38* a0(39) -> 38* a0(38) -> 38* b0(40) -> 42* b0(37) -> 37* b0(39) -> 37* b0(43) -> 44* b0(38) -> 37* b{#,1}(252) -> 253* b{#,1}(166) -> 167* b{#,1}(81) -> 82* a1(164) -> 165* a1(124) -> 125* a1(79) -> 80* a1(161) -> 162* a1(163) -> 164* a1(230) -> 231* a1(160) -> 161* a1(130) -> 131* b1(80) -> 81* b1(162) -> 163* b1(159) -> 160* b1(109) -> 110* b1(131) -> 132* b1(91) -> 92* b1(123) -> 124* b1(78) -> 79* 37 -> 44,78,40 38 -> 109,40 39 -> 41,91,40 79 -> 110,109,230,160 80 -> 166* 81 -> 124,130,123 82 -> 167,39,40 92 -> 79* 110 -> 132,109,81,79 124 -> 252,79,159 125 -> 78* 132 -> 230,109 165 -> 109* 167 -> 253,82,39 231 -> 80* 253 -> 82* problem: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) Restore Modifier: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) EDG Processor: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) graph: b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) Matrix Interpretation Processor: dim=4 interpretation: [b#](x0) = [1 1 0 0]x0, [1 0 0 0] [0] [0 0 1 0] [0] [a](x0) = [0 0 0 0]x0 + [1] [0 0 0 0] [0], [1 0 0 1] [0 0 0 0] [b](x0) = [0 1 0 0]x0 [0 1 0 0] orientation: b#(a(b(b(x1)))) = [1 1 0 1]x1 >= [1 1 0 1]x1 = b#(a(b(x1))) b#(a(b(b(x1)))) = [1 1 0 1]x1 >= [1 1 0 1]x1 = b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) = [1 1 0 1]x1 >= [1 0 0 1]x1 = b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) = [1 1 0 1]x1 >= [1 1 0 1]x1 = b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) = [1 1 0 1]x1 + [1] >= [1 1 0 1]x1 = b#(b(b(a(b(x1))))) [1 1 0 1] [1 1 0 1] [0 0 0 0] [0 0 0 0] b(b(b(a(b(x1))))) = [0 0 0 0]x1 >= [0 0 0 0]x1 = b(a(b(b(a(b(x1)))))) [0 0 0 0] [0 0 0 0] [1 1 0 1] [1 1 0 1] [0 0 0 0] [0 0 0 0] b(a(b(b(x1)))) = [0 0 0 0]x1 >= [0 0 0 0]x1 = b(b(a(b(a(b(x1)))))) [0 0 0 0] [0 0 0 0] [1 1 0 1] [0] [1 1 0 1] [0] [0 0 0 0] [0] [0 0 0 0] [0] b(a(b(a(a(b(b(x1))))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) [0 0 0 0] [1] [0 0 0 0] [1] problem: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) Restore Modifier: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) EDG Processor: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) graph: b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) Arctic Interpretation Processor: dimension: 1 usable rules: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) interpretation: [b#](x0) = x0 + 0, [a](x0) = -4x0 + 0, [b](x0) = 4x0 + 4 orientation: b#(a(b(b(x1)))) = 4x1 + 4 >= x1 + 0 = b#(a(b(x1))) b#(a(b(b(x1)))) = 4x1 + 4 >= x1 + 0 = b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) = 4x1 + 4 >= 4x1 + 4 = b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) = 8x1 + 8 >= 4x1 + 4 = b#(a(b(b(a(b(x1)))))) b(b(b(a(b(x1))))) = 12x1 + 12 >= 8x1 + 8 = b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) = 8x1 + 8 >= 8x1 + 8 = b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) = 4x1 + 4 >= 4x1 + 4 = b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) problem: DPs: b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) Restore Modifier: DPs: b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) EDG Processor: DPs: b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) graph: Qed