20.96/5.73 YES 20.96/5.73 20.96/5.73 Problem: 20.96/5.73 strict: 20.96/5.73 a(b(a(x1))) -> a(b(b(a(x1)))) 20.96/5.73 b(a(b(x1))) -> b(a(a(b(x1)))) 20.96/5.73 weak: 20.96/5.73 a(x1) -> a(a(a(x1))) 20.96/5.73 b(x1) -> b(b(b(x1))) 20.96/5.73 20.96/5.73 Proof: 20.96/5.73 Matrix Interpretation Processor: dim=3 20.96/5.73 20.96/5.73 interpretation: 20.96/5.73 [1 1 0] [0] 20.96/5.73 [b](x0) = [0 0 0]x0 + [0] 20.96/5.73 [1 2 0] [1], 20.96/5.73 20.96/5.73 [1 0 2] [0] 20.96/5.73 [a](x0) = [0 0 0]x0 + [1] 20.96/5.73 [0 0 0] [0] 20.96/5.73 orientation: 20.96/5.73 [3 0 6] [7] [3 0 6] [5] 20.96/5.73 a(b(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(b(a(x1)))) 20.96/5.73 [0 0 0] [0] [0 0 0] [0] 20.96/5.73 20.96/5.73 [3 5 0] [3] [3 5 0] [3] 20.96/5.73 b(a(b(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a(a(b(x1)))) 20.96/5.73 [3 5 0] [5] [3 5 0] [5] 20.96/5.73 20.96/5.73 [1 0 2] [0] [1 0 2] [0] 20.96/5.73 a(x1) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(a(x1))) 20.96/5.73 [0 0 0] [0] [0 0 0] [0] 20.96/5.73 20.96/5.73 [1 1 0] [0] [1 1 0] [0] 20.96/5.73 b(x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(b(b(x1))) 20.96/5.73 [1 2 0] [1] [1 1 0] [1] 20.96/5.73 problem: 20.96/5.73 strict: 20.96/5.73 b(a(b(x1))) -> b(a(a(b(x1)))) 20.96/5.73 weak: 20.96/5.73 a(x1) -> a(a(a(x1))) 20.96/5.73 b(x1) -> b(b(b(x1))) 20.96/5.73 Bounds Processor: 20.96/5.73 bound: 1 20.96/5.73 enrichment: match-rt 20.96/5.73 automaton: 20.96/5.73 final states: {3} 20.96/5.73 transitions: 20.96/5.73 b1(12) -> 13* 20.96/5.73 b1(9) -> 10* 20.96/5.73 b1(28) -> 29* 20.96/5.73 a1(25) -> 26* 20.96/5.73 a1(20) -> 21* 20.96/5.73 a1(10) -> 11* 20.96/5.73 a1(24) -> 25* 20.96/5.73 a1(14) -> 15* 20.96/5.73 a1(26) -> 27* 20.96/5.73 a1(11) -> 12* 20.96/5.73 b0(3) -> 3* 20.96/5.73 a0(3) -> 3* 20.96/5.73 3 -> 24,9 20.96/5.73 10 -> 13,3,28 20.96/5.73 12 -> 20* 20.96/5.73 13 -> 10,14,3 20.96/5.73 15 -> 11* 20.96/5.73 21 -> 15* 20.96/5.73 27 -> 25,3 20.96/5.73 29 -> 9* 20.96/5.73 problem: 20.96/5.73 strict: 20.96/5.73 20.96/5.73 weak: 20.96/5.73 a(x1) -> a(a(a(x1))) 20.96/5.73 b(x1) -> b(b(b(x1))) 20.96/5.73 Qed 20.96/5.74 EOF