WORST_CASE(Omega(n^1),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__2NDSNEG(z0,z1) -> c11() A__2NDSNEG(0(),z0) -> c7() A__2NDSNEG(s(z0),cons(z1,cons(z2,z3))) -> c10(A__2NDSPOS(mark(z0),mark(z3)),MARK(z3)) A__2NDSNEG(s(z0),cons(z1,cons(z2,z3))) -> c8(MARK(z2)) A__2NDSNEG(s(z0),cons(z1,cons(z2,z3))) -> c9(A__2NDSPOS(mark(z0),mark(z3)),MARK(z0)) A__2NDSPOS(z0,z1) -> c6() A__2NDSPOS(0(),z0) -> c2() A__2NDSPOS(s(z0),cons(z1,cons(z2,z3))) -> c3(MARK(z2)) A__2NDSPOS(s(z0),cons(z1,cons(z2,z3))) -> c4(A__2NDSNEG(mark(z0),mark(z3)),MARK(z0)) A__2NDSPOS(s(z0),cons(z1,cons(z2,z3))) -> c5(A__2NDSNEG(mark(z0),mark(z3)),MARK(z3)) A__FROM(z0) -> c(MARK(z0)) A__FROM(z0) -> c1() A__PI(z0) -> c12(A__2NDSPOS(mark(z0),a__from(0())),MARK(z0)) A__PI(z0) -> c13(A__2NDSPOS(mark(z0),a__from(0())),A__FROM(0())) A__PI(z0) -> c14() A__PLUS(z0,z1) -> c18() A__PLUS(0(),z0) -> c15(MARK(z0)) A__PLUS(s(z0),z1) -> c16(A__PLUS(mark(z0),mark(z1)),MARK(z0)) A__PLUS(s(z0),z1) -> c17(A__PLUS(mark(z0),mark(z1)),MARK(z1)) A__SQUARE(z0) -> c24(A__TIMES(mark(z0),mark(z0)),MARK(z0)) A__SQUARE(z0) -> c25(A__TIMES(mark(z0),mark(z0)),MARK(z0)) A__SQUARE(z0) -> c26() A__TIMES(z0,z1) -> c23() A__TIMES(0(),z0) -> c19() A__TIMES(s(z0),z1) -> c20(A__PLUS(mark(z1),a__times(mark(z0),mark(z1))),MARK(z1)) A__TIMES(s(z0),z1) -> c21(A__PLUS(mark(z1),a__times(mark(z0),mark(z1))) ,A__TIMES(mark(z0),mark(z1)) ,MARK(z0)) A__TIMES(s(z0),z1) -> c22(A__PLUS(mark(z1),a__times(mark(z0),mark(z1))) ,A__TIMES(mark(z0),mark(z1)) ,MARK(z1)) MARK(0()) -> c38() MARK(2ndsneg(z0,z1)) -> c30(A__2NDSNEG(mark(z0),mark(z1)),MARK(z0)) MARK(2ndsneg(z0,z1)) -> c31(A__2NDSNEG(mark(z0),mark(z1)),MARK(z1)) MARK(2ndspos(z0,z1)) -> c28(A__2NDSPOS(mark(z0),mark(z1)),MARK(z0)) MARK(2ndspos(z0,z1)) -> c29(A__2NDSPOS(mark(z0),mark(z1)),MARK(z1)) MARK(cons(z0,z1)) -> c43(MARK(z0)) MARK(from(z0)) -> c27(A__FROM(mark(z0)),MARK(z0)) MARK(negrecip(z0)) -> c41(MARK(z0)) MARK(nil()) -> c42() MARK(pi(z0)) -> c32(A__PI(mark(z0)),MARK(z0)) MARK(plus(z0,z1)) -> c33(A__PLUS(mark(z0),mark(z1)),MARK(z0)) MARK(plus(z0,z1)) -> c34(A__PLUS(mark(z0),mark(z1)),MARK(z1)) MARK(posrecip(z0)) -> c40(MARK(z0)) MARK(rcons(z0,z1)) -> c45(MARK(z0)) MARK(rcons(z0,z1)) -> c46(MARK(z1)) MARK(rnil()) -> c44() MARK(s(z0)) -> c39(MARK(z0)) MARK(square(z0)) -> c37(A__SQUARE(mark(z0)),MARK(z0)) MARK(times(z0,z1)) -> c35(A__TIMES(mark(z0),mark(z1)),MARK(z0)) MARK(times(z0,z1)) -> c36(A__TIMES(mark(z0),mark(z1)),MARK(z1)) - Weak TRS: a__2ndsneg(z0,z1) -> 2ndsneg(z0,z1) a__2ndsneg(0(),z0) -> rnil() a__2ndsneg(s(z0),cons(z1,cons(z2,z3))) -> rcons(negrecip(mark(z2)),a__2ndspos(mark(z0),mark(z3))) a__2ndspos(z0,z1) -> 2ndspos(z0,z1) a__2ndspos(0(),z0) -> rnil() a__2ndspos(s(z0),cons(z1,cons(z2,z3))) -> rcons(posrecip(mark(z2)),a__2ndsneg(mark(z0),mark(z3))) a__from(z0) -> cons(mark(z0),from(s(z0))) a__from(z0) -> from(z0) a__pi(z0) -> a__2ndspos(mark(z0),a__from(0())) a__pi(z0) -> pi(z0) a__plus(z0,z1) -> plus(z0,z1) a__plus(0(),z0) -> mark(z0) a__plus(s(z0),z1) -> s(a__plus(mark(z0),mark(z1))) a__square(z0) -> a__times(mark(z0),mark(z0)) a__square(z0) -> square(z0) a__times(z0,z1) -> times(z0,z1) a__times(0(),z0) -> 0() a__times(s(z0),z1) -> a__plus(mark(z1),a__times(mark(z0),mark(z1))) mark(0()) -> 0() mark(2ndsneg(z0,z1)) -> a__2ndsneg(mark(z0),mark(z1)) mark(2ndspos(z0,z1)) -> a__2ndspos(mark(z0),mark(z1)) mark(cons(z0,z1)) -> cons(mark(z0),z1) mark(from(z0)) -> a__from(mark(z0)) mark(negrecip(z0)) -> negrecip(mark(z0)) mark(nil()) -> nil() mark(pi(z0)) -> a__pi(mark(z0)) mark(plus(z0,z1)) -> a__plus(mark(z0),mark(z1)) mark(posrecip(z0)) -> posrecip(mark(z0)) mark(rcons(z0,z1)) -> rcons(mark(z0),mark(z1)) mark(rnil()) -> rnil() mark(s(z0)) -> s(mark(z0)) mark(square(z0)) -> a__square(mark(z0)) mark(times(z0,z1)) -> a__times(mark(z0),mark(z1)) - Signature: {A__2NDSNEG/2,A__2NDSPOS/2,A__FROM/1,A__PI/1,A__PLUS/2,A__SQUARE/1,A__TIMES/2,MARK/1,a__2ndsneg/2 ,a__2ndspos/2,a__from/1,a__pi/1,a__plus/2,a__square/1,a__times/2,mark/1} / {0/0,2ndsneg/2,2ndspos/2,c/1,c1/0 ,c10/2,c11/0,c12/2,c13/2,c14/0,c15/1,c16/2,c17/2,c18/0,c19/0,c2/0,c20/2,c21/3,c22/3,c23/0,c24/2,c25/2,c26/0 ,c27/2,c28/2,c29/2,c3/1,c30/2,c31/2,c32/2,c33/2,c34/2,c35/2,c36/2,c37/2,c38/0,c39/1,c4/2,c40/1,c41/1,c42/0 ,c43/1,c44/0,c45/1,c46/1,c5/2,c6/0,c7/0,c8/1,c9/2,cons/2,from/1,negrecip/1,nil/0,pi/1,plus/2,posrecip/1 ,rcons/2,rnil/0,s/1,square/1,times/2} - Obligation: innermost runtime complexity wrt. defined symbols {A__2NDSNEG,A__2NDSPOS,A__FROM,A__PI,A__PLUS,A__SQUARE ,A__TIMES,MARK,a__2ndsneg,a__2ndspos,a__from,a__pi,a__plus,a__square,a__times,mark} and constructors {0 ,2ndsneg,2ndspos,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,c5,c6,c7,c8,c9,cons,from,negrecip ,nil,pi,plus,posrecip,rcons,rnil,s,square,times} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__2NDSNEG(z0,z1) -> c11() A__2NDSNEG(0(),z0) -> c7() A__2NDSNEG(s(z0),cons(z1,cons(z2,z3))) -> c10(A__2NDSPOS(mark(z0),mark(z3)),MARK(z3)) A__2NDSNEG(s(z0),cons(z1,cons(z2,z3))) -> c8(MARK(z2)) A__2NDSNEG(s(z0),cons(z1,cons(z2,z3))) -> c9(A__2NDSPOS(mark(z0),mark(z3)),MARK(z0)) A__2NDSPOS(z0,z1) -> c6() A__2NDSPOS(0(),z0) -> c2() A__2NDSPOS(s(z0),cons(z1,cons(z2,z3))) -> c3(MARK(z2)) A__2NDSPOS(s(z0),cons(z1,cons(z2,z3))) -> c4(A__2NDSNEG(mark(z0),mark(z3)),MARK(z0)) A__2NDSPOS(s(z0),cons(z1,cons(z2,z3))) -> c5(A__2NDSNEG(mark(z0),mark(z3)),MARK(z3)) A__FROM(z0) -> c(MARK(z0)) A__FROM(z0) -> c1() A__PI(z0) -> c12(A__2NDSPOS(mark(z0),a__from(0())),MARK(z0)) A__PI(z0) -> c13(A__2NDSPOS(mark(z0),a__from(0())),A__FROM(0())) A__PI(z0) -> c14() A__PLUS(z0,z1) -> c18() A__PLUS(0(),z0) -> c15(MARK(z0)) A__PLUS(s(z0),z1) -> c16(A__PLUS(mark(z0),mark(z1)),MARK(z0)) A__PLUS(s(z0),z1) -> c17(A__PLUS(mark(z0),mark(z1)),MARK(z1)) A__SQUARE(z0) -> c24(A__TIMES(mark(z0),mark(z0)),MARK(z0)) A__SQUARE(z0) -> c25(A__TIMES(mark(z0),mark(z0)),MARK(z0)) A__SQUARE(z0) -> c26() A__TIMES(z0,z1) -> c23() A__TIMES(0(),z0) -> c19() A__TIMES(s(z0),z1) -> c20(A__PLUS(mark(z1),a__times(mark(z0),mark(z1))),MARK(z1)) A__TIMES(s(z0),z1) -> c21(A__PLUS(mark(z1),a__times(mark(z0),mark(z1))) ,A__TIMES(mark(z0),mark(z1)) ,MARK(z0)) A__TIMES(s(z0),z1) -> c22(A__PLUS(mark(z1),a__times(mark(z0),mark(z1))) ,A__TIMES(mark(z0),mark(z1)) ,MARK(z1)) MARK(0()) -> c38() MARK(2ndsneg(z0,z1)) -> c30(A__2NDSNEG(mark(z0),mark(z1)),MARK(z0)) MARK(2ndsneg(z0,z1)) -> c31(A__2NDSNEG(mark(z0),mark(z1)),MARK(z1)) MARK(2ndspos(z0,z1)) -> c28(A__2NDSPOS(mark(z0),mark(z1)),MARK(z0)) MARK(2ndspos(z0,z1)) -> c29(A__2NDSPOS(mark(z0),mark(z1)),MARK(z1)) MARK(cons(z0,z1)) -> c43(MARK(z0)) MARK(from(z0)) -> c27(A__FROM(mark(z0)),MARK(z0)) MARK(negrecip(z0)) -> c41(MARK(z0)) MARK(nil()) -> c42() MARK(pi(z0)) -> c32(A__PI(mark(z0)),MARK(z0)) MARK(plus(z0,z1)) -> c33(A__PLUS(mark(z0),mark(z1)),MARK(z0)) MARK(plus(z0,z1)) -> c34(A__PLUS(mark(z0),mark(z1)),MARK(z1)) MARK(posrecip(z0)) -> c40(MARK(z0)) MARK(rcons(z0,z1)) -> c45(MARK(z0)) MARK(rcons(z0,z1)) -> c46(MARK(z1)) MARK(rnil()) -> c44() MARK(s(z0)) -> c39(MARK(z0)) MARK(square(z0)) -> c37(A__SQUARE(mark(z0)),MARK(z0)) MARK(times(z0,z1)) -> c35(A__TIMES(mark(z0),mark(z1)),MARK(z0)) MARK(times(z0,z1)) -> c36(A__TIMES(mark(z0),mark(z1)),MARK(z1)) - Weak TRS: a__2ndsneg(z0,z1) -> 2ndsneg(z0,z1) a__2ndsneg(0(),z0) -> rnil() a__2ndsneg(s(z0),cons(z1,cons(z2,z3))) -> rcons(negrecip(mark(z2)),a__2ndspos(mark(z0),mark(z3))) a__2ndspos(z0,z1) -> 2ndspos(z0,z1) a__2ndspos(0(),z0) -> rnil() a__2ndspos(s(z0),cons(z1,cons(z2,z3))) -> rcons(posrecip(mark(z2)),a__2ndsneg(mark(z0),mark(z3))) a__from(z0) -> cons(mark(z0),from(s(z0))) a__from(z0) -> from(z0) a__pi(z0) -> a__2ndspos(mark(z0),a__from(0())) a__pi(z0) -> pi(z0) a__plus(z0,z1) -> plus(z0,z1) a__plus(0(),z0) -> mark(z0) a__plus(s(z0),z1) -> s(a__plus(mark(z0),mark(z1))) a__square(z0) -> a__times(mark(z0),mark(z0)) a__square(z0) -> square(z0) a__times(z0,z1) -> times(z0,z1) a__times(0(),z0) -> 0() a__times(s(z0),z1) -> a__plus(mark(z1),a__times(mark(z0),mark(z1))) mark(0()) -> 0() mark(2ndsneg(z0,z1)) -> a__2ndsneg(mark(z0),mark(z1)) mark(2ndspos(z0,z1)) -> a__2ndspos(mark(z0),mark(z1)) mark(cons(z0,z1)) -> cons(mark(z0),z1) mark(from(z0)) -> a__from(mark(z0)) mark(negrecip(z0)) -> negrecip(mark(z0)) mark(nil()) -> nil() mark(pi(z0)) -> a__pi(mark(z0)) mark(plus(z0,z1)) -> a__plus(mark(z0),mark(z1)) mark(posrecip(z0)) -> posrecip(mark(z0)) mark(rcons(z0,z1)) -> rcons(mark(z0),mark(z1)) mark(rnil()) -> rnil() mark(s(z0)) -> s(mark(z0)) mark(square(z0)) -> a__square(mark(z0)) mark(times(z0,z1)) -> a__times(mark(z0),mark(z1)) - Signature: {A__2NDSNEG/2,A__2NDSPOS/2,A__FROM/1,A__PI/1,A__PLUS/2,A__SQUARE/1,A__TIMES/2,MARK/1,a__2ndsneg/2 ,a__2ndspos/2,a__from/1,a__pi/1,a__plus/2,a__square/1,a__times/2,mark/1} / {0/0,2ndsneg/2,2ndspos/2,c/1,c1/0 ,c10/2,c11/0,c12/2,c13/2,c14/0,c15/1,c16/2,c17/2,c18/0,c19/0,c2/0,c20/2,c21/3,c22/3,c23/0,c24/2,c25/2,c26/0 ,c27/2,c28/2,c29/2,c3/1,c30/2,c31/2,c32/2,c33/2,c34/2,c35/2,c36/2,c37/2,c38/0,c39/1,c4/2,c40/1,c41/1,c42/0 ,c43/1,c44/0,c45/1,c46/1,c5/2,c6/0,c7/0,c8/1,c9/2,cons/2,from/1,negrecip/1,nil/0,pi/1,plus/2,posrecip/1 ,rcons/2,rnil/0,s/1,square/1,times/2} - Obligation: innermost runtime complexity wrt. defined symbols {A__2NDSNEG,A__2NDSPOS,A__FROM,A__PI,A__PLUS,A__SQUARE ,A__TIMES,MARK,a__2ndsneg,a__2ndspos,a__from,a__pi,a__plus,a__square,a__times,mark} and constructors {0 ,2ndsneg,2ndspos,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,c5,c6,c7,c8,c9,cons,from,negrecip ,nil,pi,plus,posrecip,rcons,rnil,s,square,times} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: A__2NDSNEG(z0,z1) -> c11() A__2NDSNEG(0(),z0) -> c7() A__2NDSNEG(s(z0),cons(z1,cons(z2,z3))) -> c10(A__2NDSPOS(mark(z0),mark(z3)),MARK(z3)) A__2NDSNEG(s(z0),cons(z1,cons(z2,z3))) -> c8(MARK(z2)) A__2NDSNEG(s(z0),cons(z1,cons(z2,z3))) -> c9(A__2NDSPOS(mark(z0),mark(z3)),MARK(z0)) A__2NDSPOS(z0,z1) -> c6() A__2NDSPOS(0(),z0) -> c2() A__2NDSPOS(s(z0),cons(z1,cons(z2,z3))) -> c3(MARK(z2)) A__2NDSPOS(s(z0),cons(z1,cons(z2,z3))) -> c4(A__2NDSNEG(mark(z0),mark(z3)),MARK(z0)) A__2NDSPOS(s(z0),cons(z1,cons(z2,z3))) -> c5(A__2NDSNEG(mark(z0),mark(z3)),MARK(z3)) A__FROM(z0) -> c(MARK(z0)) A__FROM(z0) -> c1() A__PI(z0) -> c12(A__2NDSPOS(mark(z0),a__from(0())),MARK(z0)) A__PI(z0) -> c13(A__2NDSPOS(mark(z0),a__from(0())),A__FROM(0())) A__PI(z0) -> c14() A__PLUS(z0,z1) -> c18() A__PLUS(0(),z0) -> c15(MARK(z0)) A__PLUS(s(z0),z1) -> c16(A__PLUS(mark(z0),mark(z1)),MARK(z0)) A__PLUS(s(z0),z1) -> c17(A__PLUS(mark(z0),mark(z1)),MARK(z1)) A__SQUARE(z0) -> c24(A__TIMES(mark(z0),mark(z0)),MARK(z0)) A__SQUARE(z0) -> c25(A__TIMES(mark(z0),mark(z0)),MARK(z0)) A__SQUARE(z0) -> c26() A__TIMES(z0,z1) -> c23() A__TIMES(0(),z0) -> c19() A__TIMES(s(z0),z1) -> c20(A__PLUS(mark(z1),a__times(mark(z0),mark(z1))),MARK(z1)) A__TIMES(s(z0),z1) -> c21(A__PLUS(mark(z1),a__times(mark(z0),mark(z1))) ,A__TIMES(mark(z0),mark(z1)) ,MARK(z0)) A__TIMES(s(z0),z1) -> c22(A__PLUS(mark(z1),a__times(mark(z0),mark(z1))) ,A__TIMES(mark(z0),mark(z1)) ,MARK(z1)) MARK(0()) -> c38() MARK(2ndsneg(z0,z1)) -> c30(A__2NDSNEG(mark(z0),mark(z1)),MARK(z0)) MARK(2ndsneg(z0,z1)) -> c31(A__2NDSNEG(mark(z0),mark(z1)),MARK(z1)) MARK(2ndspos(z0,z1)) -> c28(A__2NDSPOS(mark(z0),mark(z1)),MARK(z0)) MARK(2ndspos(z0,z1)) -> c29(A__2NDSPOS(mark(z0),mark(z1)),MARK(z1)) MARK(cons(z0,z1)) -> c43(MARK(z0)) MARK(from(z0)) -> c27(A__FROM(mark(z0)),MARK(z0)) MARK(negrecip(z0)) -> c41(MARK(z0)) MARK(nil()) -> c42() MARK(pi(z0)) -> c32(A__PI(mark(z0)),MARK(z0)) MARK(plus(z0,z1)) -> c33(A__PLUS(mark(z0),mark(z1)),MARK(z0)) MARK(plus(z0,z1)) -> c34(A__PLUS(mark(z0),mark(z1)),MARK(z1)) MARK(posrecip(z0)) -> c40(MARK(z0)) MARK(rcons(z0,z1)) -> c45(MARK(z0)) MARK(rcons(z0,z1)) -> c46(MARK(z1)) MARK(rnil()) -> c44() MARK(s(z0)) -> c39(MARK(z0)) MARK(square(z0)) -> c37(A__SQUARE(mark(z0)),MARK(z0)) MARK(times(z0,z1)) -> c35(A__TIMES(mark(z0),mark(z1)),MARK(z0)) MARK(times(z0,z1)) -> c36(A__TIMES(mark(z0),mark(z1)),MARK(z1)) - Weak TRS: a__2ndsneg(z0,z1) -> 2ndsneg(z0,z1) a__2ndsneg(0(),z0) -> rnil() a__2ndsneg(s(z0),cons(z1,cons(z2,z3))) -> rcons(negrecip(mark(z2)),a__2ndspos(mark(z0),mark(z3))) a__2ndspos(z0,z1) -> 2ndspos(z0,z1) a__2ndspos(0(),z0) -> rnil() a__2ndspos(s(z0),cons(z1,cons(z2,z3))) -> rcons(posrecip(mark(z2)),a__2ndsneg(mark(z0),mark(z3))) a__from(z0) -> cons(mark(z0),from(s(z0))) a__from(z0) -> from(z0) a__pi(z0) -> a__2ndspos(mark(z0),a__from(0())) a__pi(z0) -> pi(z0) a__plus(z0,z1) -> plus(z0,z1) a__plus(0(),z0) -> mark(z0) a__plus(s(z0),z1) -> s(a__plus(mark(z0),mark(z1))) a__square(z0) -> a__times(mark(z0),mark(z0)) a__square(z0) -> square(z0) a__times(z0,z1) -> times(z0,z1) a__times(0(),z0) -> 0() a__times(s(z0),z1) -> a__plus(mark(z1),a__times(mark(z0),mark(z1))) mark(0()) -> 0() mark(2ndsneg(z0,z1)) -> a__2ndsneg(mark(z0),mark(z1)) mark(2ndspos(z0,z1)) -> a__2ndspos(mark(z0),mark(z1)) mark(cons(z0,z1)) -> cons(mark(z0),z1) mark(from(z0)) -> a__from(mark(z0)) mark(negrecip(z0)) -> negrecip(mark(z0)) mark(nil()) -> nil() mark(pi(z0)) -> a__pi(mark(z0)) mark(plus(z0,z1)) -> a__plus(mark(z0),mark(z1)) mark(posrecip(z0)) -> posrecip(mark(z0)) mark(rcons(z0,z1)) -> rcons(mark(z0),mark(z1)) mark(rnil()) -> rnil() mark(s(z0)) -> s(mark(z0)) mark(square(z0)) -> a__square(mark(z0)) mark(times(z0,z1)) -> a__times(mark(z0),mark(z1)) - Signature: {A__2NDSNEG/2,A__2NDSPOS/2,A__FROM/1,A__PI/1,A__PLUS/2,A__SQUARE/1,A__TIMES/2,MARK/1,a__2ndsneg/2 ,a__2ndspos/2,a__from/1,a__pi/1,a__plus/2,a__square/1,a__times/2,mark/1} / {0/0,2ndsneg/2,2ndspos/2,c/1,c1/0 ,c10/2,c11/0,c12/2,c13/2,c14/0,c15/1,c16/2,c17/2,c18/0,c19/0,c2/0,c20/2,c21/3,c22/3,c23/0,c24/2,c25/2,c26/0 ,c27/2,c28/2,c29/2,c3/1,c30/2,c31/2,c32/2,c33/2,c34/2,c35/2,c36/2,c37/2,c38/0,c39/1,c4/2,c40/1,c41/1,c42/0 ,c43/1,c44/0,c45/1,c46/1,c5/2,c6/0,c7/0,c8/1,c9/2,cons/2,from/1,negrecip/1,nil/0,pi/1,plus/2,posrecip/1 ,rcons/2,rnil/0,s/1,square/1,times/2} - Obligation: innermost runtime complexity wrt. defined symbols {A__2NDSNEG,A__2NDSPOS,A__FROM,A__PI,A__PLUS,A__SQUARE ,A__TIMES,MARK,a__2ndsneg,a__2ndspos,a__from,a__pi,a__plus,a__square,a__times,mark} and constructors {0 ,2ndsneg,2ndspos,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,c5,c6,c7,c8,c9,cons,from,negrecip ,nil,pi,plus,posrecip,rcons,rnil,s,square,times} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: MARK(x){x -> 2ndsneg(x,y)} = MARK(2ndsneg(x,y)) ->^+ c30(A__2NDSNEG(mark(x),mark(y)),MARK(x)) = C[MARK(x) = MARK(x){}] WORST_CASE(Omega(n^1),?)