WORST_CASE(?,O(1)) * Step 1: Sum WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z) e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w) e2(x,x,y,z,z,a()) -> e6(x,y,z) e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w) e2(i(),x,y,z,i(),a()) -> e6(x,y,z) e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z) e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x) e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> e1(x1,x1,x,y,z,w) e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z) e5(i(),x,y,z) -> e6(x,y,z) f1(x,a()) -> g2(x,x) f1(a(),x) -> g1(x,x) f2(x,a()) -> g2(x,x) f2(a(),x) -> g1(x,x) g1(x,a()) -> h2(x) g1(a(),x) -> h1(x) g2(x,a()) -> h2(x) g2(a(),x) -> h1(x) h1(a()) -> i() h2(a()) -> i() - Signature: {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1} / {a/0,e6/3,i/0} - Obligation: innermost runtime complexity wrt. defined symbols {e1,e2,e3,e4,e5,f1,f2,g1,g2,h1,h2} and constructors {a,e6 ,i} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DependencyPairs WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z) e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w) e2(x,x,y,z,z,a()) -> e6(x,y,z) e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w) e2(i(),x,y,z,i(),a()) -> e6(x,y,z) e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z) e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x) e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> e1(x1,x1,x,y,z,w) e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z) e5(i(),x,y,z) -> e6(x,y,z) f1(x,a()) -> g2(x,x) f1(a(),x) -> g1(x,x) f2(x,a()) -> g2(x,x) f2(a(),x) -> g1(x,x) g1(x,a()) -> h2(x) g1(a(),x) -> h1(x) g2(x,a()) -> h2(x) g2(a(),x) -> h1(x) h1(a()) -> i() h2(a()) -> i() - Signature: {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1} / {a/0,e6/3,i/0} - Obligation: innermost runtime complexity wrt. defined symbols {e1,e2,e3,e4,e5,f1,f2,g1,g2,h1,h2} and constructors {a,e6 ,i} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) e2#(x,x,y,z,z,a()) -> c_3() e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) e2#(i(),x,y,z,i(),a()) -> c_5() e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) e5#(i(),x,y,z) -> c_11() f1#(x,a()) -> c_12(g2#(x,x)) f1#(a(),x) -> c_13(g1#(x,x)) f2#(x,a()) -> c_14(g2#(x,x)) f2#(a(),x) -> c_15(g1#(x,x)) g1#(x,a()) -> c_16(h2#(x)) g1#(a(),x) -> c_17(h1#(x)) g2#(x,a()) -> c_18(h2#(x)) g2#(a(),x) -> c_19(h1#(x)) h1#(a()) -> c_20() h2#(a()) -> c_21() Weak DPs and mark the set of starting terms. * Step 3: PredecessorEstimation WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) e2#(x,x,y,z,z,a()) -> c_3() e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) e2#(i(),x,y,z,i(),a()) -> c_5() e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) e5#(i(),x,y,z) -> c_11() f1#(x,a()) -> c_12(g2#(x,x)) f1#(a(),x) -> c_13(g1#(x,x)) f2#(x,a()) -> c_14(g2#(x,x)) f2#(a(),x) -> c_15(g1#(x,x)) g1#(x,a()) -> c_16(h2#(x)) g1#(a(),x) -> c_17(h1#(x)) g2#(x,a()) -> c_18(h2#(x)) g2#(a(),x) -> c_19(h1#(x)) h1#(a()) -> c_20() h2#(a()) -> c_21() - Weak TRS: e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z) e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w) e2(x,x,y,z,z,a()) -> e6(x,y,z) e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w) e2(i(),x,y,z,i(),a()) -> e6(x,y,z) e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z) e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x) e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> e1(x1,x1,x,y,z,w) e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z) e5(i(),x,y,z) -> e6(x,y,z) f1(x,a()) -> g2(x,x) f1(a(),x) -> g1(x,x) f2(x,a()) -> g2(x,x) f2(a(),x) -> g1(x,x) g1(x,a()) -> h2(x) g1(a(),x) -> h1(x) g2(x,a()) -> h2(x) g2(a(),x) -> h1(x) h1(a()) -> i() h2(a()) -> i() - Signature: {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2 ,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/0 ,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/1,c_18/1,c_19/1,c_20/0,c_21/0} - Obligation: innermost runtime complexity wrt. defined symbols {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1# ,h2#} and constructors {a,e6,i} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {3,5,6,8,11,20,21} by application of Pre({3,5,6,8,11,20,21}) = {1,2,4,7,10,16,17,18,19}. Here rules are labelled as follows: 1: e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) 2: e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) 3: e2#(x,x,y,z,z,a()) -> c_3() 4: e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) 5: e2#(i(),x,y,z,i(),a()) -> c_5() 6: e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() 7: e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) 8: e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() 9: e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) 10: e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) 11: e5#(i(),x,y,z) -> c_11() 12: f1#(x,a()) -> c_12(g2#(x,x)) 13: f1#(a(),x) -> c_13(g1#(x,x)) 14: f2#(x,a()) -> c_14(g2#(x,x)) 15: f2#(a(),x) -> c_15(g1#(x,x)) 16: g1#(x,a()) -> c_16(h2#(x)) 17: g1#(a(),x) -> c_17(h1#(x)) 18: g2#(x,a()) -> c_18(h2#(x)) 19: g2#(a(),x) -> c_19(h1#(x)) 20: h1#(a()) -> c_20() 21: h2#(a()) -> c_21() * Step 4: PredecessorEstimation WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) f1#(x,a()) -> c_12(g2#(x,x)) f1#(a(),x) -> c_13(g1#(x,x)) f2#(x,a()) -> c_14(g2#(x,x)) f2#(a(),x) -> c_15(g1#(x,x)) g1#(x,a()) -> c_16(h2#(x)) g1#(a(),x) -> c_17(h1#(x)) g2#(x,a()) -> c_18(h2#(x)) g2#(a(),x) -> c_19(h1#(x)) - Weak DPs: e2#(x,x,y,z,z,a()) -> c_3() e2#(i(),x,y,z,i(),a()) -> c_5() e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() e5#(i(),x,y,z) -> c_11() h1#(a()) -> c_20() h2#(a()) -> c_21() - Weak TRS: e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z) e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w) e2(x,x,y,z,z,a()) -> e6(x,y,z) e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w) e2(i(),x,y,z,i(),a()) -> e6(x,y,z) e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z) e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x) e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> e1(x1,x1,x,y,z,w) e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z) e5(i(),x,y,z) -> e6(x,y,z) f1(x,a()) -> g2(x,x) f1(a(),x) -> g1(x,x) f2(x,a()) -> g2(x,x) f2(a(),x) -> g1(x,x) g1(x,a()) -> h2(x) g1(a(),x) -> h1(x) g2(x,a()) -> h2(x) g2(a(),x) -> h1(x) h1(a()) -> i() h2(a()) -> i() - Signature: {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2 ,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/0 ,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/1,c_18/1,c_19/1,c_20/0,c_21/0} - Obligation: innermost runtime complexity wrt. defined symbols {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1# ,h2#} and constructors {a,e6,i} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {1,6,11,12,13,14} by application of Pre({1,6,11,12,13,14}) = {4,5,7,8,9,10}. Here rules are labelled as follows: 1: e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) 2: e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) 3: e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) 4: e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) 5: e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) 6: e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) 7: f1#(x,a()) -> c_12(g2#(x,x)) 8: f1#(a(),x) -> c_13(g1#(x,x)) 9: f2#(x,a()) -> c_14(g2#(x,x)) 10: f2#(a(),x) -> c_15(g1#(x,x)) 11: g1#(x,a()) -> c_16(h2#(x)) 12: g1#(a(),x) -> c_17(h1#(x)) 13: g2#(x,a()) -> c_18(h2#(x)) 14: g2#(a(),x) -> c_19(h1#(x)) 15: e2#(x,x,y,z,z,a()) -> c_3() 16: e2#(i(),x,y,z,i(),a()) -> c_5() 17: e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() 18: e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() 19: e5#(i(),x,y,z) -> c_11() 20: h1#(a()) -> c_20() 21: h2#(a()) -> c_21() * Step 5: PredecessorEstimation WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) f1#(x,a()) -> c_12(g2#(x,x)) f1#(a(),x) -> c_13(g1#(x,x)) f2#(x,a()) -> c_14(g2#(x,x)) f2#(a(),x) -> c_15(g1#(x,x)) - Weak DPs: e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) e2#(x,x,y,z,z,a()) -> c_3() e2#(i(),x,y,z,i(),a()) -> c_5() e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) e5#(i(),x,y,z) -> c_11() g1#(x,a()) -> c_16(h2#(x)) g1#(a(),x) -> c_17(h1#(x)) g2#(x,a()) -> c_18(h2#(x)) g2#(a(),x) -> c_19(h1#(x)) h1#(a()) -> c_20() h2#(a()) -> c_21() - Weak TRS: e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z) e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w) e2(x,x,y,z,z,a()) -> e6(x,y,z) e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w) e2(i(),x,y,z,i(),a()) -> e6(x,y,z) e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z) e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x) e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> e1(x1,x1,x,y,z,w) e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z) e5(i(),x,y,z) -> e6(x,y,z) f1(x,a()) -> g2(x,x) f1(a(),x) -> g1(x,x) f2(x,a()) -> g2(x,x) f2(a(),x) -> g1(x,x) g1(x,a()) -> h2(x) g1(a(),x) -> h1(x) g2(x,a()) -> h2(x) g2(a(),x) -> h1(x) h1(a()) -> i() h2(a()) -> i() - Signature: {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2 ,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/0 ,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/1,c_18/1,c_19/1,c_20/0,c_21/0} - Obligation: innermost runtime complexity wrt. defined symbols {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1# ,h2#} and constructors {a,e6,i} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {3,4,5,6,7,8} by application of Pre({3,4,5,6,7,8}) = {2}. Here rules are labelled as follows: 1: e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) 2: e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) 3: e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) 4: e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) 5: f1#(x,a()) -> c_12(g2#(x,x)) 6: f1#(a(),x) -> c_13(g1#(x,x)) 7: f2#(x,a()) -> c_14(g2#(x,x)) 8: f2#(a(),x) -> c_15(g1#(x,x)) 9: e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) 10: e2#(x,x,y,z,z,a()) -> c_3() 11: e2#(i(),x,y,z,i(),a()) -> c_5() 12: e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() 13: e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() 14: e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) 15: e5#(i(),x,y,z) -> c_11() 16: g1#(x,a()) -> c_16(h2#(x)) 17: g1#(a(),x) -> c_17(h1#(x)) 18: g2#(x,a()) -> c_18(h2#(x)) 19: g2#(a(),x) -> c_19(h1#(x)) 20: h1#(a()) -> c_20() 21: h2#(a()) -> c_21() * Step 6: PredecessorEstimation WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) - Weak DPs: e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) e2#(x,x,y,z,z,a()) -> c_3() e2#(i(),x,y,z,i(),a()) -> c_5() e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) e5#(i(),x,y,z) -> c_11() f1#(x,a()) -> c_12(g2#(x,x)) f1#(a(),x) -> c_13(g1#(x,x)) f2#(x,a()) -> c_14(g2#(x,x)) f2#(a(),x) -> c_15(g1#(x,x)) g1#(x,a()) -> c_16(h2#(x)) g1#(a(),x) -> c_17(h1#(x)) g2#(x,a()) -> c_18(h2#(x)) g2#(a(),x) -> c_19(h1#(x)) h1#(a()) -> c_20() h2#(a()) -> c_21() - Weak TRS: e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z) e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w) e2(x,x,y,z,z,a()) -> e6(x,y,z) e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w) e2(i(),x,y,z,i(),a()) -> e6(x,y,z) e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z) e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x) e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> e1(x1,x1,x,y,z,w) e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z) e5(i(),x,y,z) -> e6(x,y,z) f1(x,a()) -> g2(x,x) f1(a(),x) -> g1(x,x) f2(x,a()) -> g2(x,x) f2(a(),x) -> g1(x,x) g1(x,a()) -> h2(x) g1(a(),x) -> h1(x) g2(x,a()) -> h2(x) g2(a(),x) -> h1(x) h1(a()) -> i() h2(a()) -> i() - Signature: {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2 ,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/0 ,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/1,c_18/1,c_19/1,c_20/0,c_21/0} - Obligation: innermost runtime complexity wrt. defined symbols {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1# ,h2#} and constructors {a,e6,i} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {2} by application of Pre({2}) = {1}. Here rules are labelled as follows: 1: e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) 2: e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) 3: e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) 4: e2#(x,x,y,z,z,a()) -> c_3() 5: e2#(i(),x,y,z,i(),a()) -> c_5() 6: e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() 7: e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) 8: e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() 9: e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) 10: e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) 11: e5#(i(),x,y,z) -> c_11() 12: f1#(x,a()) -> c_12(g2#(x,x)) 13: f1#(a(),x) -> c_13(g1#(x,x)) 14: f2#(x,a()) -> c_14(g2#(x,x)) 15: f2#(a(),x) -> c_15(g1#(x,x)) 16: g1#(x,a()) -> c_16(h2#(x)) 17: g1#(a(),x) -> c_17(h1#(x)) 18: g2#(x,a()) -> c_18(h2#(x)) 19: g2#(a(),x) -> c_19(h1#(x)) 20: h1#(a()) -> c_20() 21: h2#(a()) -> c_21() * Step 7: PredecessorEstimation WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) - Weak DPs: e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) e2#(x,x,y,z,z,a()) -> c_3() e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) e2#(i(),x,y,z,i(),a()) -> c_5() e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) e5#(i(),x,y,z) -> c_11() f1#(x,a()) -> c_12(g2#(x,x)) f1#(a(),x) -> c_13(g1#(x,x)) f2#(x,a()) -> c_14(g2#(x,x)) f2#(a(),x) -> c_15(g1#(x,x)) g1#(x,a()) -> c_16(h2#(x)) g1#(a(),x) -> c_17(h1#(x)) g2#(x,a()) -> c_18(h2#(x)) g2#(a(),x) -> c_19(h1#(x)) h1#(a()) -> c_20() h2#(a()) -> c_21() - Weak TRS: e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z) e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w) e2(x,x,y,z,z,a()) -> e6(x,y,z) e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w) e2(i(),x,y,z,i(),a()) -> e6(x,y,z) e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z) e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x) e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> e1(x1,x1,x,y,z,w) e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z) e5(i(),x,y,z) -> e6(x,y,z) f1(x,a()) -> g2(x,x) f1(a(),x) -> g1(x,x) f2(x,a()) -> g2(x,x) f2(a(),x) -> g1(x,x) g1(x,a()) -> h2(x) g1(a(),x) -> h1(x) g2(x,a()) -> h2(x) g2(a(),x) -> h1(x) h1(a()) -> i() h2(a()) -> i() - Signature: {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2 ,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/0 ,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/1,c_18/1,c_19/1,c_20/0,c_21/0} - Obligation: innermost runtime complexity wrt. defined symbols {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1# ,h2#} and constructors {a,e6,i} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {1} by application of Pre({1}) = {}. Here rules are labelled as follows: 1: e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) 2: e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) 3: e2#(x,x,y,z,z,a()) -> c_3() 4: e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) 5: e2#(i(),x,y,z,i(),a()) -> c_5() 6: e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() 7: e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) 8: e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() 9: e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) 10: e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) 11: e5#(i(),x,y,z) -> c_11() 12: f1#(x,a()) -> c_12(g2#(x,x)) 13: f1#(a(),x) -> c_13(g1#(x,x)) 14: f2#(x,a()) -> c_14(g2#(x,x)) 15: f2#(a(),x) -> c_15(g1#(x,x)) 16: g1#(x,a()) -> c_16(h2#(x)) 17: g1#(a(),x) -> c_17(h1#(x)) 18: g2#(x,a()) -> c_18(h2#(x)) 19: g2#(a(),x) -> c_19(h1#(x)) 20: h1#(a()) -> c_20() 21: h2#(a()) -> c_21() * Step 8: RemoveWeakSuffixes WORST_CASE(?,O(1)) + Considered Problem: - Weak DPs: e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) e2#(x,x,y,z,z,a()) -> c_3() e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) e2#(i(),x,y,z,i(),a()) -> c_5() e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) e5#(i(),x,y,z) -> c_11() f1#(x,a()) -> c_12(g2#(x,x)) f1#(a(),x) -> c_13(g1#(x,x)) f2#(x,a()) -> c_14(g2#(x,x)) f2#(a(),x) -> c_15(g1#(x,x)) g1#(x,a()) -> c_16(h2#(x)) g1#(a(),x) -> c_17(h1#(x)) g2#(x,a()) -> c_18(h2#(x)) g2#(a(),x) -> c_19(h1#(x)) h1#(a()) -> c_20() h2#(a()) -> c_21() - Weak TRS: e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z) e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w) e2(x,x,y,z,z,a()) -> e6(x,y,z) e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w) e2(i(),x,y,z,i(),a()) -> e6(x,y,z) e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z) e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x) e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> e1(x1,x1,x,y,z,w) e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z) e5(i(),x,y,z) -> e6(x,y,z) f1(x,a()) -> g2(x,x) f1(a(),x) -> g1(x,x) f2(x,a()) -> g2(x,x) f2(a(),x) -> g1(x,x) g1(x,a()) -> h2(x) g1(a(),x) -> h1(x) g2(x,a()) -> h2(x) g2(a(),x) -> h1(x) h1(a()) -> i() h2(a()) -> i() - Signature: {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2 ,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/0 ,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/1,c_18/1,c_19/1,c_20/0,c_21/0} - Obligation: innermost runtime complexity wrt. defined symbols {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1# ,h2#} and constructors {a,e6,i} + Applied Processor: RemoveWeakSuffixes + Details: Consider the dependency graph 1:W:e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) -->_1 e5#(i(),x,y,z) -> c_11():11 2:W:e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) -->_1 e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)):4 -->_1 e2#(i(),x,y,z,i(),a()) -> c_5():5 -->_1 e2#(x,x,y,z,z,a()) -> c_3():3 3:W:e2#(x,x,y,z,z,a()) -> c_3() 4:W:e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) -->_1 e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)):7 -->_1 e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6():6 5:W:e2#(i(),x,y,z,i(),a()) -> c_5() 6:W:e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() 7:W:e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) -->_1 e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)):10 -->_1 e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8():8 8:W:e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() 9:W:e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) -->_1 e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)):1 10:W:e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) -->_1 e5#(i(),x,y,z) -> c_11():11 11:W:e5#(i(),x,y,z) -> c_11() 12:W:f1#(x,a()) -> c_12(g2#(x,x)) -->_1 g2#(a(),x) -> c_19(h1#(x)):19 -->_1 g2#(x,a()) -> c_18(h2#(x)):18 13:W:f1#(a(),x) -> c_13(g1#(x,x)) -->_1 g1#(a(),x) -> c_17(h1#(x)):17 -->_1 g1#(x,a()) -> c_16(h2#(x)):16 14:W:f2#(x,a()) -> c_14(g2#(x,x)) -->_1 g2#(a(),x) -> c_19(h1#(x)):19 -->_1 g2#(x,a()) -> c_18(h2#(x)):18 15:W:f2#(a(),x) -> c_15(g1#(x,x)) -->_1 g1#(a(),x) -> c_17(h1#(x)):17 -->_1 g1#(x,a()) -> c_16(h2#(x)):16 16:W:g1#(x,a()) -> c_16(h2#(x)) -->_1 h2#(a()) -> c_21():21 17:W:g1#(a(),x) -> c_17(h1#(x)) -->_1 h1#(a()) -> c_20():20 18:W:g2#(x,a()) -> c_18(h2#(x)) -->_1 h2#(a()) -> c_21():21 19:W:g2#(a(),x) -> c_19(h1#(x)) -->_1 h1#(a()) -> c_20():20 20:W:h1#(a()) -> c_20() 21:W:h2#(a()) -> c_21() The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. 15: f2#(a(),x) -> c_15(g1#(x,x)) 14: f2#(x,a()) -> c_14(g2#(x,x)) 13: f1#(a(),x) -> c_13(g1#(x,x)) 16: g1#(x,a()) -> c_16(h2#(x)) 17: g1#(a(),x) -> c_17(h1#(x)) 12: f1#(x,a()) -> c_12(g2#(x,x)) 18: g2#(x,a()) -> c_18(h2#(x)) 21: h2#(a()) -> c_21() 19: g2#(a(),x) -> c_19(h1#(x)) 20: h1#(a()) -> c_20() 9: e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w)) 2: e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w)) 3: e2#(x,x,y,z,z,a()) -> c_3() 5: e2#(i(),x,y,z,i(),a()) -> c_5() 4: e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)) 6: e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6() 7: e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)) 8: e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8() 10: e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)) 1: e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)) 11: e5#(i(),x,y,z) -> c_11() * Step 9: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z) e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w) e2(x,x,y,z,z,a()) -> e6(x,y,z) e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w) e2(i(),x,y,z,i(),a()) -> e6(x,y,z) e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z) e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x) e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> e1(x1,x1,x,y,z,w) e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z) e5(i(),x,y,z) -> e6(x,y,z) f1(x,a()) -> g2(x,x) f1(a(),x) -> g1(x,x) f2(x,a()) -> g2(x,x) f2(a(),x) -> g1(x,x) g1(x,a()) -> h2(x) g1(a(),x) -> h1(x) g2(x,a()) -> h2(x) g2(a(),x) -> h1(x) h1(a()) -> i() h2(a()) -> i() - Signature: {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2 ,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/0 ,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/1,c_18/1,c_19/1,c_20/0,c_21/0} - Obligation: innermost runtime complexity wrt. defined symbols {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1# ,h2#} and constructors {a,e6,i} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(1))