MAYBE 1184.13/297.26 MAYBE 1184.13/297.26 1184.13/297.26 We are left with following problem, upon which TcT provides the 1184.13/297.26 certificate MAYBE. 1184.13/297.26 1184.13/297.26 Strict Trs: 1184.13/297.26 { a__from(X) -> cons(mark(X), from(s(X))) 1184.13/297.26 , a__from(X) -> from(X) 1184.13/297.26 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1184.13/297.26 , mark(from(X)) -> a__from(mark(X)) 1184.13/297.26 , mark(s(X)) -> s(mark(X)) 1184.13/297.26 , mark(0()) -> 0() 1184.13/297.26 , mark(rnil()) -> rnil() 1184.13/297.26 , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2)) 1184.13/297.26 , mark(posrecip(X)) -> posrecip(mark(X)) 1184.13/297.26 , mark(negrecip(X)) -> negrecip(mark(X)) 1184.13/297.26 , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2)) 1184.13/297.26 , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2)) 1184.13/297.26 , mark(pi(X)) -> a__pi(mark(X)) 1184.13/297.26 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1184.13/297.26 , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2)) 1184.13/297.26 , mark(square(X)) -> a__square(mark(X)) 1184.13/297.26 , mark(nil()) -> nil() 1184.13/297.26 , a__2ndspos(X1, X2) -> 2ndspos(X1, X2) 1184.13/297.26 , a__2ndspos(s(N), cons(X, cons(Y, Z))) -> 1184.13/297.26 rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z))) 1184.13/297.26 , a__2ndspos(0(), Z) -> rnil() 1184.13/297.26 , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2) 1184.13/297.26 , a__2ndsneg(s(N), cons(X, cons(Y, Z))) -> 1184.13/297.26 rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z))) 1184.13/297.26 , a__2ndsneg(0(), Z) -> rnil() 1184.13/297.26 , a__pi(X) -> a__2ndspos(mark(X), a__from(0())) 1184.13/297.26 , a__pi(X) -> pi(X) 1184.13/297.26 , a__plus(X1, X2) -> plus(X1, X2) 1184.13/297.26 , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y))) 1184.13/297.26 , a__plus(0(), Y) -> mark(Y) 1184.13/297.26 , a__times(X1, X2) -> times(X1, X2) 1184.13/297.26 , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y))) 1184.13/297.26 , a__times(0(), Y) -> 0() 1184.13/297.26 , a__square(X) -> a__times(mark(X), mark(X)) 1184.13/297.26 , a__square(X) -> square(X) } 1184.13/297.26 Obligation: 1184.13/297.26 runtime complexity 1184.13/297.26 Answer: 1184.13/297.26 MAYBE 1184.13/297.26 1184.13/297.26 None of the processors succeeded. 1184.13/297.26 1184.13/297.26 Details of failed attempt(s): 1184.13/297.26 ----------------------------- 1184.13/297.26 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1184.13/297.26 following reason: 1184.13/297.26 1184.13/297.26 Computation stopped due to timeout after 297.0 seconds. 1184.13/297.26 1184.13/297.26 2) 'Best' failed due to the following reason: 1184.13/297.26 1184.13/297.26 None of the processors succeeded. 1184.13/297.26 1184.13/297.26 Details of failed attempt(s): 1184.13/297.26 ----------------------------- 1184.13/297.26 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1184.13/297.26 seconds)' failed due to the following reason: 1184.13/297.26 1184.13/297.26 Computation stopped due to timeout after 148.0 seconds. 1184.13/297.26 1184.13/297.26 2) 'Best' failed due to the following reason: 1184.13/297.26 1184.13/297.26 None of the processors succeeded. 1184.13/297.26 1184.13/297.26 Details of failed attempt(s): 1184.13/297.26 ----------------------------- 1184.13/297.26 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1184.13/297.26 following reason: 1184.13/297.26 1184.13/297.26 The processor is inapplicable, reason: 1184.13/297.26 Processor only applicable for innermost runtime complexity analysis 1184.13/297.26 1184.13/297.26 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1184.13/297.26 to the following reason: 1184.13/297.26 1184.13/297.26 The processor is inapplicable, reason: 1184.13/297.26 Processor only applicable for innermost runtime complexity analysis 1184.13/297.26 1184.13/297.26 1184.13/297.26 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1184.13/297.26 failed due to the following reason: 1184.13/297.26 1184.13/297.26 None of the processors succeeded. 1184.13/297.26 1184.13/297.26 Details of failed attempt(s): 1184.13/297.26 ----------------------------- 1184.13/297.26 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1184.13/297.26 failed due to the following reason: 1184.13/297.26 1184.13/297.26 match-boundness of the problem could not be verified. 1184.13/297.26 1184.13/297.26 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1184.13/297.26 failed due to the following reason: 1184.13/297.26 1184.13/297.26 match-boundness of the problem could not be verified. 1184.13/297.26 1184.13/297.26 1184.13/297.26 1184.13/297.26 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1184.13/297.26 the following reason: 1184.13/297.26 1184.13/297.26 We add the following weak dependency pairs: 1184.13/297.26 1184.13/297.26 Strict DPs: 1184.13/297.26 { a__from^#(X) -> c_1(mark^#(X), X) 1184.13/297.26 , a__from^#(X) -> c_2(X) 1184.13/297.26 , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1184.13/297.26 , mark^#(from(X)) -> c_4(a__from^#(mark(X))) 1184.13/297.26 , mark^#(s(X)) -> c_5(mark^#(X)) 1184.13/297.26 , mark^#(0()) -> c_6() 1184.13/297.26 , mark^#(rnil()) -> c_7() 1184.13/297.26 , mark^#(rcons(X1, X2)) -> c_8(mark^#(X1), mark^#(X2)) 1184.13/297.26 , mark^#(posrecip(X)) -> c_9(mark^#(X)) 1184.13/297.26 , mark^#(negrecip(X)) -> c_10(mark^#(X)) 1184.13/297.26 , mark^#(2ndspos(X1, X2)) -> c_11(a__2ndspos^#(mark(X1), mark(X2))) 1184.13/297.26 , mark^#(2ndsneg(X1, X2)) -> c_12(a__2ndsneg^#(mark(X1), mark(X2))) 1184.13/297.26 , mark^#(pi(X)) -> c_13(a__pi^#(mark(X))) 1184.13/297.26 , mark^#(plus(X1, X2)) -> c_14(a__plus^#(mark(X1), mark(X2))) 1184.13/297.26 , mark^#(times(X1, X2)) -> c_15(a__times^#(mark(X1), mark(X2))) 1184.13/297.26 , mark^#(square(X)) -> c_16(a__square^#(mark(X))) 1184.13/297.26 , mark^#(nil()) -> c_17() 1184.13/297.26 , a__2ndspos^#(X1, X2) -> c_18(X1, X2) 1184.13/297.26 , a__2ndspos^#(s(N), cons(X, cons(Y, Z))) -> 1184.13/297.26 c_19(mark^#(Y), a__2ndsneg^#(mark(N), mark(Z))) 1184.13/297.26 , a__2ndspos^#(0(), Z) -> c_20() 1184.13/297.26 , a__2ndsneg^#(X1, X2) -> c_21(X1, X2) 1184.13/297.26 , a__2ndsneg^#(s(N), cons(X, cons(Y, Z))) -> 1184.13/297.26 c_22(mark^#(Y), a__2ndspos^#(mark(N), mark(Z))) 1184.13/297.26 , a__2ndsneg^#(0(), Z) -> c_23() 1184.13/297.26 , a__pi^#(X) -> c_24(a__2ndspos^#(mark(X), a__from(0()))) 1184.13/297.26 , a__pi^#(X) -> c_25(X) 1184.13/297.26 , a__plus^#(X1, X2) -> c_26(X1, X2) 1184.13/297.26 , a__plus^#(s(X), Y) -> c_27(a__plus^#(mark(X), mark(Y))) 1184.13/297.26 , a__plus^#(0(), Y) -> c_28(mark^#(Y)) 1184.13/297.26 , a__times^#(X1, X2) -> c_29(X1, X2) 1184.13/297.26 , a__times^#(s(X), Y) -> 1184.13/297.26 c_30(a__plus^#(mark(Y), a__times(mark(X), mark(Y)))) 1184.13/297.26 , a__times^#(0(), Y) -> c_31() 1184.13/297.26 , a__square^#(X) -> c_32(a__times^#(mark(X), mark(X))) 1184.13/297.26 , a__square^#(X) -> c_33(X) } 1184.13/297.26 1184.13/297.26 and mark the set of starting terms. 1184.13/297.26 1184.13/297.26 We are left with following problem, upon which TcT provides the 1184.13/297.26 certificate MAYBE. 1184.13/297.26 1184.13/297.26 Strict DPs: 1184.13/297.26 { a__from^#(X) -> c_1(mark^#(X), X) 1184.13/297.26 , a__from^#(X) -> c_2(X) 1184.13/297.26 , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1184.13/297.26 , mark^#(from(X)) -> c_4(a__from^#(mark(X))) 1184.13/297.26 , mark^#(s(X)) -> c_5(mark^#(X)) 1184.13/297.26 , mark^#(0()) -> c_6() 1184.13/297.26 , mark^#(rnil()) -> c_7() 1184.13/297.26 , mark^#(rcons(X1, X2)) -> c_8(mark^#(X1), mark^#(X2)) 1184.13/297.26 , mark^#(posrecip(X)) -> c_9(mark^#(X)) 1184.13/297.26 , mark^#(negrecip(X)) -> c_10(mark^#(X)) 1184.13/297.26 , mark^#(2ndspos(X1, X2)) -> c_11(a__2ndspos^#(mark(X1), mark(X2))) 1184.13/297.26 , mark^#(2ndsneg(X1, X2)) -> c_12(a__2ndsneg^#(mark(X1), mark(X2))) 1184.13/297.26 , mark^#(pi(X)) -> c_13(a__pi^#(mark(X))) 1184.13/297.26 , mark^#(plus(X1, X2)) -> c_14(a__plus^#(mark(X1), mark(X2))) 1184.13/297.26 , mark^#(times(X1, X2)) -> c_15(a__times^#(mark(X1), mark(X2))) 1184.13/297.26 , mark^#(square(X)) -> c_16(a__square^#(mark(X))) 1184.13/297.26 , mark^#(nil()) -> c_17() 1184.13/297.26 , a__2ndspos^#(X1, X2) -> c_18(X1, X2) 1184.13/297.26 , a__2ndspos^#(s(N), cons(X, cons(Y, Z))) -> 1184.13/297.26 c_19(mark^#(Y), a__2ndsneg^#(mark(N), mark(Z))) 1184.13/297.26 , a__2ndspos^#(0(), Z) -> c_20() 1184.13/297.26 , a__2ndsneg^#(X1, X2) -> c_21(X1, X2) 1184.13/297.26 , a__2ndsneg^#(s(N), cons(X, cons(Y, Z))) -> 1184.13/297.26 c_22(mark^#(Y), a__2ndspos^#(mark(N), mark(Z))) 1184.13/297.26 , a__2ndsneg^#(0(), Z) -> c_23() 1184.13/297.26 , a__pi^#(X) -> c_24(a__2ndspos^#(mark(X), a__from(0()))) 1184.13/297.26 , a__pi^#(X) -> c_25(X) 1184.13/297.26 , a__plus^#(X1, X2) -> c_26(X1, X2) 1184.13/297.26 , a__plus^#(s(X), Y) -> c_27(a__plus^#(mark(X), mark(Y))) 1184.13/297.26 , a__plus^#(0(), Y) -> c_28(mark^#(Y)) 1184.13/297.26 , a__times^#(X1, X2) -> c_29(X1, X2) 1184.13/297.26 , a__times^#(s(X), Y) -> 1184.13/297.26 c_30(a__plus^#(mark(Y), a__times(mark(X), mark(Y)))) 1184.13/297.26 , a__times^#(0(), Y) -> c_31() 1184.13/297.26 , a__square^#(X) -> c_32(a__times^#(mark(X), mark(X))) 1184.13/297.26 , a__square^#(X) -> c_33(X) } 1184.13/297.26 Strict Trs: 1184.13/297.26 { a__from(X) -> cons(mark(X), from(s(X))) 1184.13/297.26 , a__from(X) -> from(X) 1184.13/297.26 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1184.13/297.26 , mark(from(X)) -> a__from(mark(X)) 1184.13/297.26 , mark(s(X)) -> s(mark(X)) 1184.13/297.26 , mark(0()) -> 0() 1184.13/297.26 , mark(rnil()) -> rnil() 1184.13/297.26 , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2)) 1184.13/297.26 , mark(posrecip(X)) -> posrecip(mark(X)) 1184.13/297.26 , mark(negrecip(X)) -> negrecip(mark(X)) 1184.13/297.26 , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2)) 1184.13/297.26 , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2)) 1184.13/297.26 , mark(pi(X)) -> a__pi(mark(X)) 1184.13/297.26 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1184.13/297.26 , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2)) 1184.13/297.26 , mark(square(X)) -> a__square(mark(X)) 1184.13/297.26 , mark(nil()) -> nil() 1184.13/297.26 , a__2ndspos(X1, X2) -> 2ndspos(X1, X2) 1184.13/297.26 , a__2ndspos(s(N), cons(X, cons(Y, Z))) -> 1184.53/297.32 rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z))) 1184.53/297.32 , a__2ndspos(0(), Z) -> rnil() 1184.53/297.32 , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2) 1184.53/297.32 , a__2ndsneg(s(N), cons(X, cons(Y, Z))) -> 1184.53/297.32 rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z))) 1184.53/297.32 , a__2ndsneg(0(), Z) -> rnil() 1184.53/297.32 , a__pi(X) -> a__2ndspos(mark(X), a__from(0())) 1184.53/297.32 , a__pi(X) -> pi(X) 1184.53/297.32 , a__plus(X1, X2) -> plus(X1, X2) 1184.53/297.32 , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y))) 1184.53/297.32 , a__plus(0(), Y) -> mark(Y) 1184.53/297.32 , a__times(X1, X2) -> times(X1, X2) 1184.53/297.32 , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y))) 1184.53/297.32 , a__times(0(), Y) -> 0() 1184.53/297.32 , a__square(X) -> a__times(mark(X), mark(X)) 1184.53/297.32 , a__square(X) -> square(X) } 1184.53/297.32 Obligation: 1184.53/297.32 runtime complexity 1184.53/297.32 Answer: 1184.53/297.32 MAYBE 1184.53/297.32 1184.53/297.32 We estimate the number of application of {6,7,17,20,23,31} by 1184.53/297.32 applications of Pre({6,7,17,20,23,31}) = 1184.53/297.32 {1,2,3,5,8,9,10,11,12,15,18,19,21,22,24,25,26,28,29,32,33}. Here 1184.53/297.32 rules are labeled as follows: 1184.53/297.32 1184.53/297.32 DPs: 1184.53/297.32 { 1: a__from^#(X) -> c_1(mark^#(X), X) 1184.53/297.32 , 2: a__from^#(X) -> c_2(X) 1184.53/297.32 , 3: mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1184.53/297.32 , 4: mark^#(from(X)) -> c_4(a__from^#(mark(X))) 1184.53/297.32 , 5: mark^#(s(X)) -> c_5(mark^#(X)) 1184.53/297.32 , 6: mark^#(0()) -> c_6() 1184.53/297.32 , 7: mark^#(rnil()) -> c_7() 1184.53/297.32 , 8: mark^#(rcons(X1, X2)) -> c_8(mark^#(X1), mark^#(X2)) 1184.53/297.32 , 9: mark^#(posrecip(X)) -> c_9(mark^#(X)) 1184.53/297.32 , 10: mark^#(negrecip(X)) -> c_10(mark^#(X)) 1184.53/297.32 , 11: mark^#(2ndspos(X1, X2)) -> 1184.53/297.32 c_11(a__2ndspos^#(mark(X1), mark(X2))) 1184.53/297.32 , 12: mark^#(2ndsneg(X1, X2)) -> 1184.53/297.32 c_12(a__2ndsneg^#(mark(X1), mark(X2))) 1184.53/297.32 , 13: mark^#(pi(X)) -> c_13(a__pi^#(mark(X))) 1184.53/297.32 , 14: mark^#(plus(X1, X2)) -> c_14(a__plus^#(mark(X1), mark(X2))) 1184.53/297.32 , 15: mark^#(times(X1, X2)) -> c_15(a__times^#(mark(X1), mark(X2))) 1184.53/297.32 , 16: mark^#(square(X)) -> c_16(a__square^#(mark(X))) 1184.53/297.32 , 17: mark^#(nil()) -> c_17() 1184.53/297.32 , 18: a__2ndspos^#(X1, X2) -> c_18(X1, X2) 1184.53/297.32 , 19: a__2ndspos^#(s(N), cons(X, cons(Y, Z))) -> 1184.53/297.32 c_19(mark^#(Y), a__2ndsneg^#(mark(N), mark(Z))) 1184.53/297.32 , 20: a__2ndspos^#(0(), Z) -> c_20() 1184.53/297.32 , 21: a__2ndsneg^#(X1, X2) -> c_21(X1, X2) 1184.53/297.32 , 22: a__2ndsneg^#(s(N), cons(X, cons(Y, Z))) -> 1184.53/297.32 c_22(mark^#(Y), a__2ndspos^#(mark(N), mark(Z))) 1184.53/297.32 , 23: a__2ndsneg^#(0(), Z) -> c_23() 1184.53/297.32 , 24: a__pi^#(X) -> c_24(a__2ndspos^#(mark(X), a__from(0()))) 1184.53/297.32 , 25: a__pi^#(X) -> c_25(X) 1184.53/297.32 , 26: a__plus^#(X1, X2) -> c_26(X1, X2) 1184.53/297.32 , 27: a__plus^#(s(X), Y) -> c_27(a__plus^#(mark(X), mark(Y))) 1184.53/297.32 , 28: a__plus^#(0(), Y) -> c_28(mark^#(Y)) 1184.53/297.32 , 29: a__times^#(X1, X2) -> c_29(X1, X2) 1184.53/297.32 , 30: a__times^#(s(X), Y) -> 1184.53/297.32 c_30(a__plus^#(mark(Y), a__times(mark(X), mark(Y)))) 1184.53/297.32 , 31: a__times^#(0(), Y) -> c_31() 1184.53/297.32 , 32: a__square^#(X) -> c_32(a__times^#(mark(X), mark(X))) 1184.53/297.32 , 33: a__square^#(X) -> c_33(X) } 1184.53/297.32 1184.53/297.32 We are left with following problem, upon which TcT provides the 1184.53/297.32 certificate MAYBE. 1184.53/297.32 1184.53/297.32 Strict DPs: 1184.53/297.32 { a__from^#(X) -> c_1(mark^#(X), X) 1184.53/297.32 , a__from^#(X) -> c_2(X) 1184.53/297.32 , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1184.53/297.32 , mark^#(from(X)) -> c_4(a__from^#(mark(X))) 1184.53/297.32 , mark^#(s(X)) -> c_5(mark^#(X)) 1184.53/297.32 , mark^#(rcons(X1, X2)) -> c_8(mark^#(X1), mark^#(X2)) 1184.53/297.32 , mark^#(posrecip(X)) -> c_9(mark^#(X)) 1184.53/297.32 , mark^#(negrecip(X)) -> c_10(mark^#(X)) 1184.53/297.32 , mark^#(2ndspos(X1, X2)) -> c_11(a__2ndspos^#(mark(X1), mark(X2))) 1184.53/297.32 , mark^#(2ndsneg(X1, X2)) -> c_12(a__2ndsneg^#(mark(X1), mark(X2))) 1184.53/297.32 , mark^#(pi(X)) -> c_13(a__pi^#(mark(X))) 1184.53/297.32 , mark^#(plus(X1, X2)) -> c_14(a__plus^#(mark(X1), mark(X2))) 1184.53/297.32 , mark^#(times(X1, X2)) -> c_15(a__times^#(mark(X1), mark(X2))) 1184.53/297.32 , mark^#(square(X)) -> c_16(a__square^#(mark(X))) 1184.53/297.32 , a__2ndspos^#(X1, X2) -> c_18(X1, X2) 1184.53/297.32 , a__2ndspos^#(s(N), cons(X, cons(Y, Z))) -> 1184.53/297.32 c_19(mark^#(Y), a__2ndsneg^#(mark(N), mark(Z))) 1184.53/297.32 , a__2ndsneg^#(X1, X2) -> c_21(X1, X2) 1184.53/297.32 , a__2ndsneg^#(s(N), cons(X, cons(Y, Z))) -> 1184.53/297.32 c_22(mark^#(Y), a__2ndspos^#(mark(N), mark(Z))) 1184.53/297.32 , a__pi^#(X) -> c_24(a__2ndspos^#(mark(X), a__from(0()))) 1184.53/297.32 , a__pi^#(X) -> c_25(X) 1184.53/297.32 , a__plus^#(X1, X2) -> c_26(X1, X2) 1184.53/297.32 , a__plus^#(s(X), Y) -> c_27(a__plus^#(mark(X), mark(Y))) 1184.53/297.32 , a__plus^#(0(), Y) -> c_28(mark^#(Y)) 1184.53/297.32 , a__times^#(X1, X2) -> c_29(X1, X2) 1184.53/297.32 , a__times^#(s(X), Y) -> 1184.53/297.32 c_30(a__plus^#(mark(Y), a__times(mark(X), mark(Y)))) 1184.53/297.32 , a__square^#(X) -> c_32(a__times^#(mark(X), mark(X))) 1184.53/297.32 , a__square^#(X) -> c_33(X) } 1184.53/297.32 Strict Trs: 1184.53/297.32 { a__from(X) -> cons(mark(X), from(s(X))) 1184.53/297.32 , a__from(X) -> from(X) 1184.53/297.32 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1184.53/297.32 , mark(from(X)) -> a__from(mark(X)) 1184.53/297.32 , mark(s(X)) -> s(mark(X)) 1184.53/297.32 , mark(0()) -> 0() 1184.53/297.32 , mark(rnil()) -> rnil() 1184.53/297.32 , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2)) 1184.53/297.32 , mark(posrecip(X)) -> posrecip(mark(X)) 1184.53/297.32 , mark(negrecip(X)) -> negrecip(mark(X)) 1184.53/297.32 , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2)) 1184.53/297.32 , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2)) 1184.53/297.32 , mark(pi(X)) -> a__pi(mark(X)) 1184.53/297.32 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1184.53/297.32 , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2)) 1184.53/297.32 , mark(square(X)) -> a__square(mark(X)) 1184.53/297.32 , mark(nil()) -> nil() 1184.53/297.32 , a__2ndspos(X1, X2) -> 2ndspos(X1, X2) 1184.53/297.32 , a__2ndspos(s(N), cons(X, cons(Y, Z))) -> 1184.53/297.32 rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z))) 1184.53/297.32 , a__2ndspos(0(), Z) -> rnil() 1184.53/297.32 , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2) 1184.53/297.32 , a__2ndsneg(s(N), cons(X, cons(Y, Z))) -> 1184.53/297.32 rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z))) 1184.53/297.32 , a__2ndsneg(0(), Z) -> rnil() 1184.53/297.32 , a__pi(X) -> a__2ndspos(mark(X), a__from(0())) 1184.53/297.32 , a__pi(X) -> pi(X) 1184.53/297.32 , a__plus(X1, X2) -> plus(X1, X2) 1184.53/297.32 , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y))) 1184.53/297.32 , a__plus(0(), Y) -> mark(Y) 1184.53/297.32 , a__times(X1, X2) -> times(X1, X2) 1184.53/297.32 , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y))) 1184.53/297.32 , a__times(0(), Y) -> 0() 1184.53/297.32 , a__square(X) -> a__times(mark(X), mark(X)) 1184.53/297.32 , a__square(X) -> square(X) } 1184.53/297.32 Weak DPs: 1184.53/297.32 { mark^#(0()) -> c_6() 1184.53/297.32 , mark^#(rnil()) -> c_7() 1184.53/297.32 , mark^#(nil()) -> c_17() 1184.53/297.32 , a__2ndspos^#(0(), Z) -> c_20() 1184.53/297.32 , a__2ndsneg^#(0(), Z) -> c_23() 1184.53/297.32 , a__times^#(0(), Y) -> c_31() } 1184.53/297.32 Obligation: 1184.53/297.32 runtime complexity 1184.53/297.32 Answer: 1184.53/297.32 MAYBE 1184.53/297.32 1184.53/297.32 Empty strict component of the problem is NOT empty. 1184.53/297.32 1184.53/297.32 1184.53/297.32 Arrrr.. 1185.45/298.17 EOF