WORST_CASE(Omega(n^1),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__FCONS(z0,z1) -> c36(MARK(z0)) A__FCONS(z0,z1) -> c37() A__FIRST(z0,z1) -> c6() A__FIRST(0(),z0) -> c4() A__FIRST(s(z0),cons(z1,z2)) -> c5(MARK(z1)) A__FIRST1(z0,z1) -> c17() A__FIRST1(0(),z0) -> c13() A__FIRST1(s(z0),cons(z1,z2)) -> c14(A__QUOTE(z1)) A__FIRST1(s(z0),cons(z1,z2)) -> c15(A__FIRST1(mark(z0),mark(z2)),MARK(z0)) A__FIRST1(s(z0),cons(z1,z2)) -> c16(A__FIRST1(mark(z0),mark(z2)),MARK(z2)) A__FROM(z0) -> c7(MARK(z0)) A__FROM(z0) -> c8() A__QUOTE(z0) -> c22() A__QUOTE(0()) -> c18() A__QUOTE(s(z0)) -> c19(A__QUOTE(z0)) A__QUOTE(sel(z0,z1)) -> c20(A__SEL1(mark(z0),mark(z1)),MARK(z0)) A__QUOTE(sel(z0,z1)) -> c21(A__SEL1(mark(z0),mark(z1)),MARK(z1)) A__QUOTE1(z0) -> c28() A__QUOTE1(cons(z0,z1)) -> c23(A__QUOTE(z0)) A__QUOTE1(cons(z0,z1)) -> c24(A__QUOTE1(z1)) A__QUOTE1(first(z0,z1)) -> c26(A__FIRST1(mark(z0),mark(z1)),MARK(z0)) A__QUOTE1(first(z0,z1)) -> c27(A__FIRST1(mark(z0),mark(z1)),MARK(z1)) A__QUOTE1(nil()) -> c25() A__SEL(z0,z1) -> c3() A__SEL(0(),cons(z0,z1)) -> c2(MARK(z0)) A__SEL(s(z0),cons(z1,z2)) -> c(A__SEL(mark(z0),mark(z2)),MARK(z0)) A__SEL(s(z0),cons(z1,z2)) -> c1(A__SEL(mark(z0),mark(z2)),MARK(z2)) A__SEL1(z0,z1) -> c12() A__SEL1(0(),cons(z0,z1)) -> c11(A__QUOTE(z0)) A__SEL1(s(z0),cons(z1,z2)) -> c10(A__SEL1(mark(z0),mark(z2)),MARK(z2)) A__SEL1(s(z0),cons(z1,z2)) -> c9(A__SEL1(mark(z0),mark(z2)),MARK(z0)) A__UNQUOTE(z0) -> c31() A__UNQUOTE(01()) -> c29() A__UNQUOTE(s1(z0)) -> c30(A__UNQUOTE(mark(z0)),MARK(z0)) A__UNQUOTE1(z0) -> c35() A__UNQUOTE1(cons1(z0,z1)) -> c33(A__FCONS(a__unquote(mark(z0)),a__unquote1(mark(z1))) ,A__UNQUOTE(mark(z0)) ,MARK(z0)) A__UNQUOTE1(cons1(z0,z1)) -> c34(A__FCONS(a__unquote(mark(z0)),a__unquote1(mark(z1))) ,A__UNQUOTE1(mark(z1)) ,MARK(z1)) A__UNQUOTE1(nil1()) -> c32() MARK(0()) -> c55() MARK(01()) -> c60() MARK(cons(z0,z1)) -> c54(MARK(z0)) MARK(cons1(z0,z1)) -> c58(MARK(z0)) MARK(cons1(z0,z1)) -> c59(MARK(z1)) MARK(fcons(z0,z1)) -> c51(A__FCONS(mark(z0),mark(z1)),MARK(z0)) MARK(fcons(z0,z1)) -> c52(A__FCONS(mark(z0),mark(z1)),MARK(z1)) MARK(first(z0,z1)) -> c40(A__FIRST(mark(z0),mark(z1)),MARK(z0)) MARK(first(z0,z1)) -> c41(A__FIRST(mark(z0),mark(z1)),MARK(z1)) MARK(first1(z0,z1)) -> c46(A__FIRST1(mark(z0),mark(z1)),MARK(z0)) MARK(first1(z0,z1)) -> c47(A__FIRST1(mark(z0),mark(z1)),MARK(z1)) MARK(from(z0)) -> c42(A__FROM(mark(z0)),MARK(z0)) MARK(nil()) -> c56() MARK(nil1()) -> c57() MARK(quote(z0)) -> c45(A__QUOTE(z0)) MARK(quote1(z0)) -> c48(A__QUOTE1(z0)) MARK(s(z0)) -> c53(MARK(z0)) MARK(s1(z0)) -> c61(MARK(z0)) MARK(sel(z0,z1)) -> c38(A__SEL(mark(z0),mark(z1)),MARK(z0)) MARK(sel(z0,z1)) -> c39(A__SEL(mark(z0),mark(z1)),MARK(z1)) MARK(sel1(z0,z1)) -> c43(A__SEL1(mark(z0),mark(z1)),MARK(z0)) MARK(sel1(z0,z1)) -> c44(A__SEL1(mark(z0),mark(z1)),MARK(z1)) MARK(unquote(z0)) -> c49(A__UNQUOTE(mark(z0)),MARK(z0)) MARK(unquote1(z0)) -> c50(A__UNQUOTE1(mark(z0)),MARK(z0)) - Weak TRS: a__fcons(z0,z1) -> cons(mark(z0),z1) a__fcons(z0,z1) -> fcons(z0,z1) a__first(z0,z1) -> first(z0,z1) a__first(0(),z0) -> nil() a__first(s(z0),cons(z1,z2)) -> cons(mark(z1),first(z0,z2)) a__first1(z0,z1) -> first1(z0,z1) a__first1(0(),z0) -> nil1() a__first1(s(z0),cons(z1,z2)) -> cons1(a__quote(z1),a__first1(mark(z0),mark(z2))) a__from(z0) -> cons(mark(z0),from(s(z0))) a__from(z0) -> from(z0) a__quote(z0) -> quote(z0) a__quote(0()) -> 01() a__quote(s(z0)) -> s1(a__quote(z0)) a__quote(sel(z0,z1)) -> a__sel1(mark(z0),mark(z1)) a__quote1(z0) -> quote1(z0) a__quote1(cons(z0,z1)) -> cons1(a__quote(z0),a__quote1(z1)) a__quote1(first(z0,z1)) -> a__first1(mark(z0),mark(z1)) a__quote1(nil()) -> nil1() a__sel(z0,z1) -> sel(z0,z1) a__sel(0(),cons(z0,z1)) -> mark(z0) a__sel(s(z0),cons(z1,z2)) -> a__sel(mark(z0),mark(z2)) a__sel1(z0,z1) -> sel1(z0,z1) a__sel1(0(),cons(z0,z1)) -> a__quote(z0) a__sel1(s(z0),cons(z1,z2)) -> a__sel1(mark(z0),mark(z2)) a__unquote(z0) -> unquote(z0) a__unquote(01()) -> 0() a__unquote(s1(z0)) -> s(a__unquote(mark(z0))) a__unquote1(z0) -> unquote1(z0) a__unquote1(cons1(z0,z1)) -> a__fcons(a__unquote(mark(z0)),a__unquote1(mark(z1))) a__unquote1(nil1()) -> nil() mark(0()) -> 0() mark(01()) -> 01() mark(cons(z0,z1)) -> cons(mark(z0),z1) mark(cons1(z0,z1)) -> cons1(mark(z0),mark(z1)) mark(fcons(z0,z1)) -> a__fcons(mark(z0),mark(z1)) mark(first(z0,z1)) -> a__first(mark(z0),mark(z1)) mark(first1(z0,z1)) -> a__first1(mark(z0),mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(nil()) -> nil() mark(nil1()) -> nil1() mark(quote(z0)) -> a__quote(z0) mark(quote1(z0)) -> a__quote1(z0) mark(s(z0)) -> s(mark(z0)) mark(s1(z0)) -> s1(mark(z0)) mark(sel(z0,z1)) -> a__sel(mark(z0),mark(z1)) mark(sel1(z0,z1)) -> a__sel1(mark(z0),mark(z1)) mark(unquote(z0)) -> a__unquote(mark(z0)) mark(unquote1(z0)) -> a__unquote1(mark(z0)) - Signature: {A__FCONS/2,A__FIRST/2,A__FIRST1/2,A__FROM/1,A__QUOTE/1,A__QUOTE1/1,A__SEL/2,A__SEL1/2,A__UNQUOTE/1 ,A__UNQUOTE1/1,MARK/1,a__fcons/2,a__first/2,a__first1/2,a__from/1,a__quote/1,a__quote1/1,a__sel/2,a__sel1/2 ,a__unquote/1,a__unquote1/1,mark/1} / {0/0,01/0,c/2,c1/2,c10/2,c11/1,c12/0,c13/0,c14/1,c15/2,c16/2,c17/0 ,c18/0,c19/1,c2/1,c20/2,c21/2,c22/0,c23/1,c24/1,c25/0,c26/2,c27/2,c28/0,c29/0,c3/0,c30/2,c31/0,c32/0,c33/3 ,c34/3,c35/0,c36/1,c37/0,c38/2,c39/2,c4/0,c40/2,c41/2,c42/2,c43/2,c44/2,c45/1,c46/2,c47/2,c48/1,c49/2,c5/1 ,c50/2,c51/2,c52/2,c53/1,c54/1,c55/0,c56/0,c57/0,c58/1,c59/1,c6/0,c60/0,c61/1,c7/1,c8/0,c9/2,cons/2,cons1/2 ,fcons/2,first/2,first1/2,from/1,nil/0,nil1/0,quote/1,quote1/1,s/1,s1/1,sel/2,sel1/2,unquote/1,unquote1/1} - Obligation: innermost runtime complexity wrt. defined symbols {A__FCONS,A__FIRST,A__FIRST1,A__FROM,A__QUOTE,A__QUOTE1 ,A__SEL,A__SEL1,A__UNQUOTE,A__UNQUOTE1,MARK,a__fcons,a__first,a__first1,a__from,a__quote,a__quote1,a__sel ,a__sel1,a__unquote,a__unquote1,mark} and constructors {0,01,c,c1,c10,c11,c12,c13,c14,c15,c16,c17,c18,c19,c2 ,c20,c21,c22,c23,c24,c25,c26,c27,c28,c29,c3,c30,c31,c32,c33,c34,c35,c36,c37,c38,c39,c4,c40,c41,c42,c43,c44 ,c45,c46,c47,c48,c49,c5,c50,c51,c52,c53,c54,c55,c56,c57,c58,c59,c6,c60,c61,c7,c8,c9,cons,cons1,fcons,first ,first1,from,nil,nil1,quote,quote1,s,s1,sel,sel1,unquote,unquote1} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__FCONS(z0,z1) -> c36(MARK(z0)) A__FCONS(z0,z1) -> c37() A__FIRST(z0,z1) -> c6() A__FIRST(0(),z0) -> c4() A__FIRST(s(z0),cons(z1,z2)) -> c5(MARK(z1)) A__FIRST1(z0,z1) -> c17() A__FIRST1(0(),z0) -> c13() A__FIRST1(s(z0),cons(z1,z2)) -> c14(A__QUOTE(z1)) A__FIRST1(s(z0),cons(z1,z2)) -> c15(A__FIRST1(mark(z0),mark(z2)),MARK(z0)) A__FIRST1(s(z0),cons(z1,z2)) -> c16(A__FIRST1(mark(z0),mark(z2)),MARK(z2)) A__FROM(z0) -> c7(MARK(z0)) A__FROM(z0) -> c8() A__QUOTE(z0) -> c22() A__QUOTE(0()) -> c18() A__QUOTE(s(z0)) -> c19(A__QUOTE(z0)) A__QUOTE(sel(z0,z1)) -> c20(A__SEL1(mark(z0),mark(z1)),MARK(z0)) A__QUOTE(sel(z0,z1)) -> c21(A__SEL1(mark(z0),mark(z1)),MARK(z1)) A__QUOTE1(z0) -> c28() A__QUOTE1(cons(z0,z1)) -> c23(A__QUOTE(z0)) A__QUOTE1(cons(z0,z1)) -> c24(A__QUOTE1(z1)) A__QUOTE1(first(z0,z1)) -> c26(A__FIRST1(mark(z0),mark(z1)),MARK(z0)) A__QUOTE1(first(z0,z1)) -> c27(A__FIRST1(mark(z0),mark(z1)),MARK(z1)) A__QUOTE1(nil()) -> c25() A__SEL(z0,z1) -> c3() A__SEL(0(),cons(z0,z1)) -> c2(MARK(z0)) A__SEL(s(z0),cons(z1,z2)) -> c(A__SEL(mark(z0),mark(z2)),MARK(z0)) A__SEL(s(z0),cons(z1,z2)) -> c1(A__SEL(mark(z0),mark(z2)),MARK(z2)) A__SEL1(z0,z1) -> c12() A__SEL1(0(),cons(z0,z1)) -> c11(A__QUOTE(z0)) A__SEL1(s(z0),cons(z1,z2)) -> c10(A__SEL1(mark(z0),mark(z2)),MARK(z2)) A__SEL1(s(z0),cons(z1,z2)) -> c9(A__SEL1(mark(z0),mark(z2)),MARK(z0)) A__UNQUOTE(z0) -> c31() A__UNQUOTE(01()) -> c29() A__UNQUOTE(s1(z0)) -> c30(A__UNQUOTE(mark(z0)),MARK(z0)) A__UNQUOTE1(z0) -> c35() A__UNQUOTE1(cons1(z0,z1)) -> c33(A__FCONS(a__unquote(mark(z0)),a__unquote1(mark(z1))) ,A__UNQUOTE(mark(z0)) ,MARK(z0)) A__UNQUOTE1(cons1(z0,z1)) -> c34(A__FCONS(a__unquote(mark(z0)),a__unquote1(mark(z1))) ,A__UNQUOTE1(mark(z1)) ,MARK(z1)) A__UNQUOTE1(nil1()) -> c32() MARK(0()) -> c55() MARK(01()) -> c60() MARK(cons(z0,z1)) -> c54(MARK(z0)) MARK(cons1(z0,z1)) -> c58(MARK(z0)) MARK(cons1(z0,z1)) -> c59(MARK(z1)) MARK(fcons(z0,z1)) -> c51(A__FCONS(mark(z0),mark(z1)),MARK(z0)) MARK(fcons(z0,z1)) -> c52(A__FCONS(mark(z0),mark(z1)),MARK(z1)) MARK(first(z0,z1)) -> c40(A__FIRST(mark(z0),mark(z1)),MARK(z0)) MARK(first(z0,z1)) -> c41(A__FIRST(mark(z0),mark(z1)),MARK(z1)) MARK(first1(z0,z1)) -> c46(A__FIRST1(mark(z0),mark(z1)),MARK(z0)) MARK(first1(z0,z1)) -> c47(A__FIRST1(mark(z0),mark(z1)),MARK(z1)) MARK(from(z0)) -> c42(A__FROM(mark(z0)),MARK(z0)) MARK(nil()) -> c56() MARK(nil1()) -> c57() MARK(quote(z0)) -> c45(A__QUOTE(z0)) MARK(quote1(z0)) -> c48(A__QUOTE1(z0)) MARK(s(z0)) -> c53(MARK(z0)) MARK(s1(z0)) -> c61(MARK(z0)) MARK(sel(z0,z1)) -> c38(A__SEL(mark(z0),mark(z1)),MARK(z0)) MARK(sel(z0,z1)) -> c39(A__SEL(mark(z0),mark(z1)),MARK(z1)) MARK(sel1(z0,z1)) -> c43(A__SEL1(mark(z0),mark(z1)),MARK(z0)) MARK(sel1(z0,z1)) -> c44(A__SEL1(mark(z0),mark(z1)),MARK(z1)) MARK(unquote(z0)) -> c49(A__UNQUOTE(mark(z0)),MARK(z0)) MARK(unquote1(z0)) -> c50(A__UNQUOTE1(mark(z0)),MARK(z0)) - Weak TRS: a__fcons(z0,z1) -> cons(mark(z0),z1) a__fcons(z0,z1) -> fcons(z0,z1) a__first(z0,z1) -> first(z0,z1) a__first(0(),z0) -> nil() a__first(s(z0),cons(z1,z2)) -> cons(mark(z1),first(z0,z2)) a__first1(z0,z1) -> first1(z0,z1) a__first1(0(),z0) -> nil1() a__first1(s(z0),cons(z1,z2)) -> cons1(a__quote(z1),a__first1(mark(z0),mark(z2))) a__from(z0) -> cons(mark(z0),from(s(z0))) a__from(z0) -> from(z0) a__quote(z0) -> quote(z0) a__quote(0()) -> 01() a__quote(s(z0)) -> s1(a__quote(z0)) a__quote(sel(z0,z1)) -> a__sel1(mark(z0),mark(z1)) a__quote1(z0) -> quote1(z0) a__quote1(cons(z0,z1)) -> cons1(a__quote(z0),a__quote1(z1)) a__quote1(first(z0,z1)) -> a__first1(mark(z0),mark(z1)) a__quote1(nil()) -> nil1() a__sel(z0,z1) -> sel(z0,z1) a__sel(0(),cons(z0,z1)) -> mark(z0) a__sel(s(z0),cons(z1,z2)) -> a__sel(mark(z0),mark(z2)) a__sel1(z0,z1) -> sel1(z0,z1) a__sel1(0(),cons(z0,z1)) -> a__quote(z0) a__sel1(s(z0),cons(z1,z2)) -> a__sel1(mark(z0),mark(z2)) a__unquote(z0) -> unquote(z0) a__unquote(01()) -> 0() a__unquote(s1(z0)) -> s(a__unquote(mark(z0))) a__unquote1(z0) -> unquote1(z0) a__unquote1(cons1(z0,z1)) -> a__fcons(a__unquote(mark(z0)),a__unquote1(mark(z1))) a__unquote1(nil1()) -> nil() mark(0()) -> 0() mark(01()) -> 01() mark(cons(z0,z1)) -> cons(mark(z0),z1) mark(cons1(z0,z1)) -> cons1(mark(z0),mark(z1)) mark(fcons(z0,z1)) -> a__fcons(mark(z0),mark(z1)) mark(first(z0,z1)) -> a__first(mark(z0),mark(z1)) mark(first1(z0,z1)) -> a__first1(mark(z0),mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(nil()) -> nil() mark(nil1()) -> nil1() mark(quote(z0)) -> a__quote(z0) mark(quote1(z0)) -> a__quote1(z0) mark(s(z0)) -> s(mark(z0)) mark(s1(z0)) -> s1(mark(z0)) mark(sel(z0,z1)) -> a__sel(mark(z0),mark(z1)) mark(sel1(z0,z1)) -> a__sel1(mark(z0),mark(z1)) mark(unquote(z0)) -> a__unquote(mark(z0)) mark(unquote1(z0)) -> a__unquote1(mark(z0)) - Signature: {A__FCONS/2,A__FIRST/2,A__FIRST1/2,A__FROM/1,A__QUOTE/1,A__QUOTE1/1,A__SEL/2,A__SEL1/2,A__UNQUOTE/1 ,A__UNQUOTE1/1,MARK/1,a__fcons/2,a__first/2,a__first1/2,a__from/1,a__quote/1,a__quote1/1,a__sel/2,a__sel1/2 ,a__unquote/1,a__unquote1/1,mark/1} / {0/0,01/0,c/2,c1/2,c10/2,c11/1,c12/0,c13/0,c14/1,c15/2,c16/2,c17/0 ,c18/0,c19/1,c2/1,c20/2,c21/2,c22/0,c23/1,c24/1,c25/0,c26/2,c27/2,c28/0,c29/0,c3/0,c30/2,c31/0,c32/0,c33/3 ,c34/3,c35/0,c36/1,c37/0,c38/2,c39/2,c4/0,c40/2,c41/2,c42/2,c43/2,c44/2,c45/1,c46/2,c47/2,c48/1,c49/2,c5/1 ,c50/2,c51/2,c52/2,c53/1,c54/1,c55/0,c56/0,c57/0,c58/1,c59/1,c6/0,c60/0,c61/1,c7/1,c8/0,c9/2,cons/2,cons1/2 ,fcons/2,first/2,first1/2,from/1,nil/0,nil1/0,quote/1,quote1/1,s/1,s1/1,sel/2,sel1/2,unquote/1,unquote1/1} - Obligation: innermost runtime complexity wrt. defined symbols {A__FCONS,A__FIRST,A__FIRST1,A__FROM,A__QUOTE,A__QUOTE1 ,A__SEL,A__SEL1,A__UNQUOTE,A__UNQUOTE1,MARK,a__fcons,a__first,a__first1,a__from,a__quote,a__quote1,a__sel ,a__sel1,a__unquote,a__unquote1,mark} and constructors {0,01,c,c1,c10,c11,c12,c13,c14,c15,c16,c17,c18,c19,c2 ,c20,c21,c22,c23,c24,c25,c26,c27,c28,c29,c3,c30,c31,c32,c33,c34,c35,c36,c37,c38,c39,c4,c40,c41,c42,c43,c44 ,c45,c46,c47,c48,c49,c5,c50,c51,c52,c53,c54,c55,c56,c57,c58,c59,c6,c60,c61,c7,c8,c9,cons,cons1,fcons,first ,first1,from,nil,nil1,quote,quote1,s,s1,sel,sel1,unquote,unquote1} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__FCONS(z0,z1) -> c36(MARK(z0)) A__FCONS(z0,z1) -> c37() A__FIRST(z0,z1) -> c6() A__FIRST(0(),z0) -> c4() A__FIRST(s(z0),cons(z1,z2)) -> c5(MARK(z1)) A__FIRST1(z0,z1) -> c17() A__FIRST1(0(),z0) -> c13() A__FIRST1(s(z0),cons(z1,z2)) -> c14(A__QUOTE(z1)) A__FIRST1(s(z0),cons(z1,z2)) -> c15(A__FIRST1(mark(z0),mark(z2)),MARK(z0)) A__FIRST1(s(z0),cons(z1,z2)) -> c16(A__FIRST1(mark(z0),mark(z2)),MARK(z2)) A__FROM(z0) -> c7(MARK(z0)) A__FROM(z0) -> c8() A__QUOTE(z0) -> c22() A__QUOTE(0()) -> c18() A__QUOTE(s(z0)) -> c19(A__QUOTE(z0)) A__QUOTE(sel(z0,z1)) -> c20(A__SEL1(mark(z0),mark(z1)),MARK(z0)) A__QUOTE(sel(z0,z1)) -> c21(A__SEL1(mark(z0),mark(z1)),MARK(z1)) A__QUOTE1(z0) -> c28() A__QUOTE1(cons(z0,z1)) -> c23(A__QUOTE(z0)) A__QUOTE1(cons(z0,z1)) -> c24(A__QUOTE1(z1)) A__QUOTE1(first(z0,z1)) -> c26(A__FIRST1(mark(z0),mark(z1)),MARK(z0)) A__QUOTE1(first(z0,z1)) -> c27(A__FIRST1(mark(z0),mark(z1)),MARK(z1)) A__QUOTE1(nil()) -> c25() A__SEL(z0,z1) -> c3() A__SEL(0(),cons(z0,z1)) -> c2(MARK(z0)) A__SEL(s(z0),cons(z1,z2)) -> c(A__SEL(mark(z0),mark(z2)),MARK(z0)) A__SEL(s(z0),cons(z1,z2)) -> c1(A__SEL(mark(z0),mark(z2)),MARK(z2)) A__SEL1(z0,z1) -> c12() A__SEL1(0(),cons(z0,z1)) -> c11(A__QUOTE(z0)) A__SEL1(s(z0),cons(z1,z2)) -> c10(A__SEL1(mark(z0),mark(z2)),MARK(z2)) A__SEL1(s(z0),cons(z1,z2)) -> c9(A__SEL1(mark(z0),mark(z2)),MARK(z0)) A__UNQUOTE(z0) -> c31() A__UNQUOTE(01()) -> c29() A__UNQUOTE(s1(z0)) -> c30(A__UNQUOTE(mark(z0)),MARK(z0)) A__UNQUOTE1(z0) -> c35() A__UNQUOTE1(cons1(z0,z1)) -> c33(A__FCONS(a__unquote(mark(z0)),a__unquote1(mark(z1))) ,A__UNQUOTE(mark(z0)) ,MARK(z0)) A__UNQUOTE1(cons1(z0,z1)) -> c34(A__FCONS(a__unquote(mark(z0)),a__unquote1(mark(z1))) ,A__UNQUOTE1(mark(z1)) ,MARK(z1)) A__UNQUOTE1(nil1()) -> c32() MARK(0()) -> c55() MARK(01()) -> c60() MARK(cons(z0,z1)) -> c54(MARK(z0)) MARK(cons1(z0,z1)) -> c58(MARK(z0)) MARK(cons1(z0,z1)) -> c59(MARK(z1)) MARK(fcons(z0,z1)) -> c51(A__FCONS(mark(z0),mark(z1)),MARK(z0)) MARK(fcons(z0,z1)) -> c52(A__FCONS(mark(z0),mark(z1)),MARK(z1)) MARK(first(z0,z1)) -> c40(A__FIRST(mark(z0),mark(z1)),MARK(z0)) MARK(first(z0,z1)) -> c41(A__FIRST(mark(z0),mark(z1)),MARK(z1)) MARK(first1(z0,z1)) -> c46(A__FIRST1(mark(z0),mark(z1)),MARK(z0)) MARK(first1(z0,z1)) -> c47(A__FIRST1(mark(z0),mark(z1)),MARK(z1)) MARK(from(z0)) -> c42(A__FROM(mark(z0)),MARK(z0)) MARK(nil()) -> c56() MARK(nil1()) -> c57() MARK(quote(z0)) -> c45(A__QUOTE(z0)) MARK(quote1(z0)) -> c48(A__QUOTE1(z0)) MARK(s(z0)) -> c53(MARK(z0)) MARK(s1(z0)) -> c61(MARK(z0)) MARK(sel(z0,z1)) -> c38(A__SEL(mark(z0),mark(z1)),MARK(z0)) MARK(sel(z0,z1)) -> c39(A__SEL(mark(z0),mark(z1)),MARK(z1)) MARK(sel1(z0,z1)) -> c43(A__SEL1(mark(z0),mark(z1)),MARK(z0)) MARK(sel1(z0,z1)) -> c44(A__SEL1(mark(z0),mark(z1)),MARK(z1)) MARK(unquote(z0)) -> c49(A__UNQUOTE(mark(z0)),MARK(z0)) MARK(unquote1(z0)) -> c50(A__UNQUOTE1(mark(z0)),MARK(z0)) - Weak TRS: a__fcons(z0,z1) -> cons(mark(z0),z1) a__fcons(z0,z1) -> fcons(z0,z1) a__first(z0,z1) -> first(z0,z1) a__first(0(),z0) -> nil() a__first(s(z0),cons(z1,z2)) -> cons(mark(z1),first(z0,z2)) a__first1(z0,z1) -> first1(z0,z1) a__first1(0(),z0) -> nil1() a__first1(s(z0),cons(z1,z2)) -> cons1(a__quote(z1),a__first1(mark(z0),mark(z2))) a__from(z0) -> cons(mark(z0),from(s(z0))) a__from(z0) -> from(z0) a__quote(z0) -> quote(z0) a__quote(0()) -> 01() a__quote(s(z0)) -> s1(a__quote(z0)) a__quote(sel(z0,z1)) -> a__sel1(mark(z0),mark(z1)) a__quote1(z0) -> quote1(z0) a__quote1(cons(z0,z1)) -> cons1(a__quote(z0),a__quote1(z1)) a__quote1(first(z0,z1)) -> a__first1(mark(z0),mark(z1)) a__quote1(nil()) -> nil1() a__sel(z0,z1) -> sel(z0,z1) a__sel(0(),cons(z0,z1)) -> mark(z0) a__sel(s(z0),cons(z1,z2)) -> a__sel(mark(z0),mark(z2)) a__sel1(z0,z1) -> sel1(z0,z1) a__sel1(0(),cons(z0,z1)) -> a__quote(z0) a__sel1(s(z0),cons(z1,z2)) -> a__sel1(mark(z0),mark(z2)) a__unquote(z0) -> unquote(z0) a__unquote(01()) -> 0() a__unquote(s1(z0)) -> s(a__unquote(mark(z0))) a__unquote1(z0) -> unquote1(z0) a__unquote1(cons1(z0,z1)) -> a__fcons(a__unquote(mark(z0)),a__unquote1(mark(z1))) a__unquote1(nil1()) -> nil() mark(0()) -> 0() mark(01()) -> 01() mark(cons(z0,z1)) -> cons(mark(z0),z1) mark(cons1(z0,z1)) -> cons1(mark(z0),mark(z1)) mark(fcons(z0,z1)) -> a__fcons(mark(z0),mark(z1)) mark(first(z0,z1)) -> a__first(mark(z0),mark(z1)) mark(first1(z0,z1)) -> a__first1(mark(z0),mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(nil()) -> nil() mark(nil1()) -> nil1() mark(quote(z0)) -> a__quote(z0) mark(quote1(z0)) -> a__quote1(z0) mark(s(z0)) -> s(mark(z0)) mark(s1(z0)) -> s1(mark(z0)) mark(sel(z0,z1)) -> a__sel(mark(z0),mark(z1)) mark(sel1(z0,z1)) -> a__sel1(mark(z0),mark(z1)) mark(unquote(z0)) -> a__unquote(mark(z0)) mark(unquote1(z0)) -> a__unquote1(mark(z0)) - Signature: {A__FCONS/2,A__FIRST/2,A__FIRST1/2,A__FROM/1,A__QUOTE/1,A__QUOTE1/1,A__SEL/2,A__SEL1/2,A__UNQUOTE/1 ,A__UNQUOTE1/1,MARK/1,a__fcons/2,a__first/2,a__first1/2,a__from/1,a__quote/1,a__quote1/1,a__sel/2,a__sel1/2 ,a__unquote/1,a__unquote1/1,mark/1} / {0/0,01/0,c/2,c1/2,c10/2,c11/1,c12/0,c13/0,c14/1,c15/2,c16/2,c17/0 ,c18/0,c19/1,c2/1,c20/2,c21/2,c22/0,c23/1,c24/1,c25/0,c26/2,c27/2,c28/0,c29/0,c3/0,c30/2,c31/0,c32/0,c33/3 ,c34/3,c35/0,c36/1,c37/0,c38/2,c39/2,c4/0,c40/2,c41/2,c42/2,c43/2,c44/2,c45/1,c46/2,c47/2,c48/1,c49/2,c5/1 ,c50/2,c51/2,c52/2,c53/1,c54/1,c55/0,c56/0,c57/0,c58/1,c59/1,c6/0,c60/0,c61/1,c7/1,c8/0,c9/2,cons/2,cons1/2 ,fcons/2,first/2,first1/2,from/1,nil/0,nil1/0,quote/1,quote1/1,s/1,s1/1,sel/2,sel1/2,unquote/1,unquote1/1} - Obligation: innermost runtime complexity wrt. defined symbols {A__FCONS,A__FIRST,A__FIRST1,A__FROM,A__QUOTE,A__QUOTE1 ,A__SEL,A__SEL1,A__UNQUOTE,A__UNQUOTE1,MARK,a__fcons,a__first,a__first1,a__from,a__quote,a__quote1,a__sel ,a__sel1,a__unquote,a__unquote1,mark} and constructors {0,01,c,c1,c10,c11,c12,c13,c14,c15,c16,c17,c18,c19,c2 ,c20,c21,c22,c23,c24,c25,c26,c27,c28,c29,c3,c30,c31,c32,c33,c34,c35,c36,c37,c38,c39,c4,c40,c41,c42,c43,c44 ,c45,c46,c47,c48,c49,c5,c50,c51,c52,c53,c54,c55,c56,c57,c58,c59,c6,c60,c61,c7,c8,c9,cons,cons1,fcons,first ,first1,from,nil,nil1,quote,quote1,s,s1,sel,sel1,unquote,unquote1} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: A__QUOTE(x){x -> s(x)} = A__QUOTE(s(x)) ->^+ c19(A__QUOTE(x)) = C[A__QUOTE(x) = A__QUOTE(x){}] WORST_CASE(Omega(n^1),?)