'Weak Dependency Graph [60.0]' ------------------------------ Answer: YES(?,O(n^1)) Input Problem: innermost runtime-complexity with respect to Rules: {c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1))))))))))} Details: We have computed the following set of weak (innermost) dependency pairs: {c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))} The usable rules are: {c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1))))))))))} The estimated dependency graph contains the following edges: {c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))} ==> {c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))} We consider the following path(s): 1) {c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))} The usable rules for this path are the following: {c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1))))))))))} We have applied the subprocessor on the union of usable rules and weak (innermost) dependency pairs. 'Weight Gap Principle' ---------------------- Answer: YES(?,O(n^1)) Input Problem: innermost runtime-complexity with respect to Rules: { c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1)))))))))) , c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))} Details: 'fastest of 'combine', 'Bounds with default enrichment', 'Bounds with default enrichment'' ------------------------------------------------------------------------------------------ Answer: YES(?,O(n^1)) Input Problem: innermost runtime-complexity with respect to Rules: { c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1)))))))))) , c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))} Details: The problem was solved by processor 'Bounds with default enrichment': 'Bounds with default enrichment' -------------------------------- Answer: YES(?,O(n^1)) Input Problem: innermost runtime-complexity with respect to Rules: { c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1)))))))))) , c^#(a(b(a(x1)))) -> c_0(c^#(a(b(c(a(b(x1)))))))} Details: The problem is Match-bounded by 2. The enriched problem is compatible with the following automaton: { c_1(6) -> 14 , c_1(9) -> 8 , c_2(16) -> 24 , c_2(19) -> 18 , a_0(2) -> 2 , a_0(3) -> 2 , a_1(7) -> 6 , a_1(10) -> 9 , a_1(11) -> 8 , a_1(13) -> 12 , a_1(14) -> 13 , a_2(17) -> 16 , a_2(20) -> 19 , a_2(21) -> 14 , a_2(23) -> 22 , a_2(24) -> 23 , b_0(2) -> 3 , b_0(3) -> 3 , b_1(2) -> 10 , b_1(3) -> 10 , b_1(8) -> 7 , b_1(12) -> 11 , b_2(11) -> 20 , b_2(18) -> 17 , b_2(22) -> 21 , c^#_0(2) -> 4 , c^#_0(3) -> 4 , c^#_1(6) -> 5 , c^#_2(16) -> 15 , c_0_1(5) -> 4 , c_0_2(15) -> 5}