MAYBE 1192.24/299.30 MAYBE 1192.24/299.30 1192.24/299.30 We are left with following problem, upon which TcT provides the 1192.24/299.30 certificate MAYBE. 1192.24/299.30 1192.24/299.30 Strict Trs: 1192.24/299.30 { a__from(X) -> cons(mark(X), from(s(X))) 1192.24/299.30 , a__from(X) -> from(X) 1192.24/299.30 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1192.24/299.30 , mark(from(X)) -> a__from(mark(X)) 1192.24/299.30 , mark(s(X)) -> s(mark(X)) 1192.24/299.30 , mark(0()) -> 0() 1192.24/299.30 , mark(rnil()) -> rnil() 1192.24/299.30 , mark(cons2(X1, X2)) -> cons2(X1, mark(X2)) 1192.24/299.30 , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2)) 1192.24/299.30 , mark(posrecip(X)) -> posrecip(mark(X)) 1192.24/299.30 , mark(negrecip(X)) -> negrecip(mark(X)) 1192.24/299.30 , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2)) 1192.24/299.30 , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2)) 1192.24/299.30 , mark(pi(X)) -> a__pi(mark(X)) 1192.24/299.30 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1192.24/299.30 , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2)) 1192.24/299.30 , mark(square(X)) -> a__square(mark(X)) 1192.24/299.30 , mark(nil()) -> nil() 1192.24/299.30 , a__2ndspos(X1, X2) -> 2ndspos(X1, X2) 1192.24/299.30 , a__2ndspos(s(N), cons(X, Z)) -> 1192.24/299.30 a__2ndspos(s(mark(N)), cons2(X, mark(Z))) 1192.24/299.30 , a__2ndspos(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.30 rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z))) 1192.24/299.30 , a__2ndspos(0(), Z) -> rnil() 1192.24/299.30 , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2) 1192.24/299.30 , a__2ndsneg(s(N), cons(X, Z)) -> 1192.24/299.30 a__2ndsneg(s(mark(N)), cons2(X, mark(Z))) 1192.24/299.30 , a__2ndsneg(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.30 rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z))) 1192.24/299.30 , a__2ndsneg(0(), Z) -> rnil() 1192.24/299.30 , a__pi(X) -> a__2ndspos(mark(X), a__from(0())) 1192.24/299.30 , a__pi(X) -> pi(X) 1192.24/299.30 , a__plus(X1, X2) -> plus(X1, X2) 1192.24/299.30 , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y))) 1192.24/299.30 , a__plus(0(), Y) -> mark(Y) 1192.24/299.30 , a__times(X1, X2) -> times(X1, X2) 1192.24/299.30 , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y))) 1192.24/299.30 , a__times(0(), Y) -> 0() 1192.24/299.30 , a__square(X) -> a__times(mark(X), mark(X)) 1192.24/299.30 , a__square(X) -> square(X) } 1192.24/299.30 Obligation: 1192.24/299.30 runtime complexity 1192.24/299.30 Answer: 1192.24/299.30 MAYBE 1192.24/299.30 1192.24/299.30 None of the processors succeeded. 1192.24/299.30 1192.24/299.30 Details of failed attempt(s): 1192.24/299.30 ----------------------------- 1192.24/299.30 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1192.24/299.30 following reason: 1192.24/299.30 1192.24/299.30 Computation stopped due to timeout after 297.0 seconds. 1192.24/299.30 1192.24/299.30 2) 'Best' failed due to the following reason: 1192.24/299.30 1192.24/299.30 None of the processors succeeded. 1192.24/299.30 1192.24/299.30 Details of failed attempt(s): 1192.24/299.30 ----------------------------- 1192.24/299.30 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1192.24/299.30 seconds)' failed due to the following reason: 1192.24/299.30 1192.24/299.30 Computation stopped due to timeout after 148.0 seconds. 1192.24/299.30 1192.24/299.30 2) 'Best' failed due to the following reason: 1192.24/299.30 1192.24/299.30 None of the processors succeeded. 1192.24/299.30 1192.24/299.30 Details of failed attempt(s): 1192.24/299.30 ----------------------------- 1192.24/299.30 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1192.24/299.30 following reason: 1192.24/299.30 1192.24/299.30 The processor is inapplicable, reason: 1192.24/299.30 Processor only applicable for innermost runtime complexity analysis 1192.24/299.30 1192.24/299.30 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1192.24/299.30 to the following reason: 1192.24/299.30 1192.24/299.30 The processor is inapplicable, reason: 1192.24/299.30 Processor only applicable for innermost runtime complexity analysis 1192.24/299.30 1192.24/299.30 1192.24/299.30 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1192.24/299.30 failed due to the following reason: 1192.24/299.30 1192.24/299.30 None of the processors succeeded. 1192.24/299.30 1192.24/299.30 Details of failed attempt(s): 1192.24/299.30 ----------------------------- 1192.24/299.30 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1192.24/299.30 failed due to the following reason: 1192.24/299.30 1192.24/299.30 match-boundness of the problem could not be verified. 1192.24/299.30 1192.24/299.30 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1192.24/299.30 failed due to the following reason: 1192.24/299.30 1192.24/299.30 match-boundness of the problem could not be verified. 1192.24/299.30 1192.24/299.30 1192.24/299.30 1192.24/299.30 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1192.24/299.30 the following reason: 1192.24/299.30 1192.24/299.30 We add the following weak dependency pairs: 1192.24/299.30 1192.24/299.30 Strict DPs: 1192.24/299.30 { a__from^#(X) -> c_1(mark^#(X), X) 1192.24/299.30 , a__from^#(X) -> c_2(X) 1192.24/299.30 , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1192.24/299.30 , mark^#(from(X)) -> c_4(a__from^#(mark(X))) 1192.24/299.30 , mark^#(s(X)) -> c_5(mark^#(X)) 1192.24/299.30 , mark^#(0()) -> c_6() 1192.24/299.30 , mark^#(rnil()) -> c_7() 1192.24/299.30 , mark^#(cons2(X1, X2)) -> c_8(X1, mark^#(X2)) 1192.24/299.30 , mark^#(rcons(X1, X2)) -> c_9(mark^#(X1), mark^#(X2)) 1192.24/299.30 , mark^#(posrecip(X)) -> c_10(mark^#(X)) 1192.24/299.30 , mark^#(negrecip(X)) -> c_11(mark^#(X)) 1192.24/299.30 , mark^#(2ndspos(X1, X2)) -> c_12(a__2ndspos^#(mark(X1), mark(X2))) 1192.24/299.30 , mark^#(2ndsneg(X1, X2)) -> c_13(a__2ndsneg^#(mark(X1), mark(X2))) 1192.24/299.30 , mark^#(pi(X)) -> c_14(a__pi^#(mark(X))) 1192.24/299.30 , mark^#(plus(X1, X2)) -> c_15(a__plus^#(mark(X1), mark(X2))) 1192.24/299.30 , mark^#(times(X1, X2)) -> c_16(a__times^#(mark(X1), mark(X2))) 1192.24/299.30 , mark^#(square(X)) -> c_17(a__square^#(mark(X))) 1192.24/299.30 , mark^#(nil()) -> c_18() 1192.24/299.30 , a__2ndspos^#(X1, X2) -> c_19(X1, X2) 1192.24/299.30 , a__2ndspos^#(s(N), cons(X, Z)) -> 1192.24/299.30 c_20(a__2ndspos^#(s(mark(N)), cons2(X, mark(Z)))) 1192.24/299.30 , a__2ndspos^#(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.30 c_21(mark^#(Y), a__2ndsneg^#(mark(N), mark(Z))) 1192.24/299.30 , a__2ndspos^#(0(), Z) -> c_22() 1192.24/299.30 , a__2ndsneg^#(X1, X2) -> c_23(X1, X2) 1192.24/299.30 , a__2ndsneg^#(s(N), cons(X, Z)) -> 1192.24/299.30 c_24(a__2ndsneg^#(s(mark(N)), cons2(X, mark(Z)))) 1192.24/299.30 , a__2ndsneg^#(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.30 c_25(mark^#(Y), a__2ndspos^#(mark(N), mark(Z))) 1192.24/299.30 , a__2ndsneg^#(0(), Z) -> c_26() 1192.24/299.30 , a__pi^#(X) -> c_27(a__2ndspos^#(mark(X), a__from(0()))) 1192.24/299.30 , a__pi^#(X) -> c_28(X) 1192.24/299.30 , a__plus^#(X1, X2) -> c_29(X1, X2) 1192.24/299.30 , a__plus^#(s(X), Y) -> c_30(a__plus^#(mark(X), mark(Y))) 1192.24/299.30 , a__plus^#(0(), Y) -> c_31(mark^#(Y)) 1192.24/299.30 , a__times^#(X1, X2) -> c_32(X1, X2) 1192.24/299.30 , a__times^#(s(X), Y) -> 1192.24/299.30 c_33(a__plus^#(mark(Y), a__times(mark(X), mark(Y)))) 1192.24/299.30 , a__times^#(0(), Y) -> c_34() 1192.24/299.30 , a__square^#(X) -> c_35(a__times^#(mark(X), mark(X))) 1192.24/299.30 , a__square^#(X) -> c_36(X) } 1192.24/299.30 1192.24/299.30 and mark the set of starting terms. 1192.24/299.30 1192.24/299.30 We are left with following problem, upon which TcT provides the 1192.24/299.30 certificate MAYBE. 1192.24/299.30 1192.24/299.30 Strict DPs: 1192.24/299.30 { a__from^#(X) -> c_1(mark^#(X), X) 1192.24/299.30 , a__from^#(X) -> c_2(X) 1192.24/299.30 , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1192.24/299.30 , mark^#(from(X)) -> c_4(a__from^#(mark(X))) 1192.24/299.31 , mark^#(s(X)) -> c_5(mark^#(X)) 1192.24/299.31 , mark^#(0()) -> c_6() 1192.24/299.31 , mark^#(rnil()) -> c_7() 1192.24/299.31 , mark^#(cons2(X1, X2)) -> c_8(X1, mark^#(X2)) 1192.24/299.31 , mark^#(rcons(X1, X2)) -> c_9(mark^#(X1), mark^#(X2)) 1192.24/299.31 , mark^#(posrecip(X)) -> c_10(mark^#(X)) 1192.24/299.31 , mark^#(negrecip(X)) -> c_11(mark^#(X)) 1192.24/299.31 , mark^#(2ndspos(X1, X2)) -> c_12(a__2ndspos^#(mark(X1), mark(X2))) 1192.24/299.31 , mark^#(2ndsneg(X1, X2)) -> c_13(a__2ndsneg^#(mark(X1), mark(X2))) 1192.24/299.31 , mark^#(pi(X)) -> c_14(a__pi^#(mark(X))) 1192.24/299.31 , mark^#(plus(X1, X2)) -> c_15(a__plus^#(mark(X1), mark(X2))) 1192.24/299.31 , mark^#(times(X1, X2)) -> c_16(a__times^#(mark(X1), mark(X2))) 1192.24/299.31 , mark^#(square(X)) -> c_17(a__square^#(mark(X))) 1192.24/299.31 , mark^#(nil()) -> c_18() 1192.24/299.31 , a__2ndspos^#(X1, X2) -> c_19(X1, X2) 1192.24/299.31 , a__2ndspos^#(s(N), cons(X, Z)) -> 1192.24/299.31 c_20(a__2ndspos^#(s(mark(N)), cons2(X, mark(Z)))) 1192.24/299.31 , a__2ndspos^#(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.31 c_21(mark^#(Y), a__2ndsneg^#(mark(N), mark(Z))) 1192.24/299.31 , a__2ndspos^#(0(), Z) -> c_22() 1192.24/299.31 , a__2ndsneg^#(X1, X2) -> c_23(X1, X2) 1192.24/299.31 , a__2ndsneg^#(s(N), cons(X, Z)) -> 1192.24/299.31 c_24(a__2ndsneg^#(s(mark(N)), cons2(X, mark(Z)))) 1192.24/299.31 , a__2ndsneg^#(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.31 c_25(mark^#(Y), a__2ndspos^#(mark(N), mark(Z))) 1192.24/299.31 , a__2ndsneg^#(0(), Z) -> c_26() 1192.24/299.31 , a__pi^#(X) -> c_27(a__2ndspos^#(mark(X), a__from(0()))) 1192.24/299.31 , a__pi^#(X) -> c_28(X) 1192.24/299.31 , a__plus^#(X1, X2) -> c_29(X1, X2) 1192.24/299.31 , a__plus^#(s(X), Y) -> c_30(a__plus^#(mark(X), mark(Y))) 1192.24/299.31 , a__plus^#(0(), Y) -> c_31(mark^#(Y)) 1192.24/299.31 , a__times^#(X1, X2) -> c_32(X1, X2) 1192.24/299.31 , a__times^#(s(X), Y) -> 1192.24/299.31 c_33(a__plus^#(mark(Y), a__times(mark(X), mark(Y)))) 1192.24/299.31 , a__times^#(0(), Y) -> c_34() 1192.24/299.31 , a__square^#(X) -> c_35(a__times^#(mark(X), mark(X))) 1192.24/299.31 , a__square^#(X) -> c_36(X) } 1192.24/299.31 Strict Trs: 1192.24/299.31 { a__from(X) -> cons(mark(X), from(s(X))) 1192.24/299.31 , a__from(X) -> from(X) 1192.24/299.31 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1192.24/299.31 , mark(from(X)) -> a__from(mark(X)) 1192.24/299.31 , mark(s(X)) -> s(mark(X)) 1192.24/299.31 , mark(0()) -> 0() 1192.24/299.31 , mark(rnil()) -> rnil() 1192.24/299.31 , mark(cons2(X1, X2)) -> cons2(X1, mark(X2)) 1192.24/299.31 , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2)) 1192.24/299.31 , mark(posrecip(X)) -> posrecip(mark(X)) 1192.24/299.31 , mark(negrecip(X)) -> negrecip(mark(X)) 1192.24/299.31 , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2)) 1192.24/299.31 , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2)) 1192.24/299.31 , mark(pi(X)) -> a__pi(mark(X)) 1192.24/299.31 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1192.24/299.31 , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2)) 1192.24/299.31 , mark(square(X)) -> a__square(mark(X)) 1192.24/299.31 , mark(nil()) -> nil() 1192.24/299.31 , a__2ndspos(X1, X2) -> 2ndspos(X1, X2) 1192.24/299.31 , a__2ndspos(s(N), cons(X, Z)) -> 1192.24/299.31 a__2ndspos(s(mark(N)), cons2(X, mark(Z))) 1192.24/299.31 , a__2ndspos(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.31 rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z))) 1192.24/299.31 , a__2ndspos(0(), Z) -> rnil() 1192.24/299.31 , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2) 1192.24/299.31 , a__2ndsneg(s(N), cons(X, Z)) -> 1192.24/299.31 a__2ndsneg(s(mark(N)), cons2(X, mark(Z))) 1192.24/299.31 , a__2ndsneg(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.31 rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z))) 1192.24/299.31 , a__2ndsneg(0(), Z) -> rnil() 1192.24/299.31 , a__pi(X) -> a__2ndspos(mark(X), a__from(0())) 1192.24/299.31 , a__pi(X) -> pi(X) 1192.24/299.31 , a__plus(X1, X2) -> plus(X1, X2) 1192.24/299.31 , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y))) 1192.24/299.31 , a__plus(0(), Y) -> mark(Y) 1192.24/299.31 , a__times(X1, X2) -> times(X1, X2) 1192.24/299.31 , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y))) 1192.24/299.31 , a__times(0(), Y) -> 0() 1192.24/299.31 , a__square(X) -> a__times(mark(X), mark(X)) 1192.24/299.31 , a__square(X) -> square(X) } 1192.24/299.31 Obligation: 1192.24/299.31 runtime complexity 1192.24/299.31 Answer: 1192.24/299.31 MAYBE 1192.24/299.31 1192.24/299.31 We estimate the number of application of {6,7,18,22,26,34} by 1192.24/299.31 applications of Pre({6,7,18,22,26,34}) = 1192.24/299.31 {1,2,3,5,8,9,10,11,12,13,16,19,21,23,25,27,28,29,31,32,35,36}. Here 1192.24/299.31 rules are labeled as follows: 1192.24/299.31 1192.24/299.31 DPs: 1192.24/299.31 { 1: a__from^#(X) -> c_1(mark^#(X), X) 1192.24/299.31 , 2: a__from^#(X) -> c_2(X) 1192.24/299.31 , 3: mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1192.24/299.31 , 4: mark^#(from(X)) -> c_4(a__from^#(mark(X))) 1192.24/299.31 , 5: mark^#(s(X)) -> c_5(mark^#(X)) 1192.24/299.31 , 6: mark^#(0()) -> c_6() 1192.24/299.31 , 7: mark^#(rnil()) -> c_7() 1192.24/299.31 , 8: mark^#(cons2(X1, X2)) -> c_8(X1, mark^#(X2)) 1192.24/299.31 , 9: mark^#(rcons(X1, X2)) -> c_9(mark^#(X1), mark^#(X2)) 1192.24/299.31 , 10: mark^#(posrecip(X)) -> c_10(mark^#(X)) 1192.24/299.31 , 11: mark^#(negrecip(X)) -> c_11(mark^#(X)) 1192.24/299.31 , 12: mark^#(2ndspos(X1, X2)) -> 1192.24/299.31 c_12(a__2ndspos^#(mark(X1), mark(X2))) 1192.24/299.31 , 13: mark^#(2ndsneg(X1, X2)) -> 1192.24/299.31 c_13(a__2ndsneg^#(mark(X1), mark(X2))) 1192.24/299.31 , 14: mark^#(pi(X)) -> c_14(a__pi^#(mark(X))) 1192.24/299.31 , 15: mark^#(plus(X1, X2)) -> c_15(a__plus^#(mark(X1), mark(X2))) 1192.24/299.31 , 16: mark^#(times(X1, X2)) -> c_16(a__times^#(mark(X1), mark(X2))) 1192.24/299.31 , 17: mark^#(square(X)) -> c_17(a__square^#(mark(X))) 1192.24/299.31 , 18: mark^#(nil()) -> c_18() 1192.24/299.31 , 19: a__2ndspos^#(X1, X2) -> c_19(X1, X2) 1192.24/299.31 , 20: a__2ndspos^#(s(N), cons(X, Z)) -> 1192.24/299.31 c_20(a__2ndspos^#(s(mark(N)), cons2(X, mark(Z)))) 1192.24/299.31 , 21: a__2ndspos^#(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.31 c_21(mark^#(Y), a__2ndsneg^#(mark(N), mark(Z))) 1192.24/299.31 , 22: a__2ndspos^#(0(), Z) -> c_22() 1192.24/299.31 , 23: a__2ndsneg^#(X1, X2) -> c_23(X1, X2) 1192.24/299.31 , 24: a__2ndsneg^#(s(N), cons(X, Z)) -> 1192.24/299.31 c_24(a__2ndsneg^#(s(mark(N)), cons2(X, mark(Z)))) 1192.24/299.31 , 25: a__2ndsneg^#(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.31 c_25(mark^#(Y), a__2ndspos^#(mark(N), mark(Z))) 1192.24/299.31 , 26: a__2ndsneg^#(0(), Z) -> c_26() 1192.24/299.31 , 27: a__pi^#(X) -> c_27(a__2ndspos^#(mark(X), a__from(0()))) 1192.24/299.31 , 28: a__pi^#(X) -> c_28(X) 1192.24/299.31 , 29: a__plus^#(X1, X2) -> c_29(X1, X2) 1192.24/299.31 , 30: a__plus^#(s(X), Y) -> c_30(a__plus^#(mark(X), mark(Y))) 1192.24/299.31 , 31: a__plus^#(0(), Y) -> c_31(mark^#(Y)) 1192.24/299.31 , 32: a__times^#(X1, X2) -> c_32(X1, X2) 1192.24/299.31 , 33: a__times^#(s(X), Y) -> 1192.24/299.31 c_33(a__plus^#(mark(Y), a__times(mark(X), mark(Y)))) 1192.24/299.31 , 34: a__times^#(0(), Y) -> c_34() 1192.24/299.31 , 35: a__square^#(X) -> c_35(a__times^#(mark(X), mark(X))) 1192.24/299.31 , 36: a__square^#(X) -> c_36(X) } 1192.24/299.31 1192.24/299.31 We are left with following problem, upon which TcT provides the 1192.24/299.31 certificate MAYBE. 1192.24/299.31 1192.24/299.31 Strict DPs: 1192.24/299.31 { a__from^#(X) -> c_1(mark^#(X), X) 1192.24/299.31 , a__from^#(X) -> c_2(X) 1192.24/299.31 , mark^#(cons(X1, X2)) -> c_3(mark^#(X1), X2) 1192.24/299.31 , mark^#(from(X)) -> c_4(a__from^#(mark(X))) 1192.24/299.31 , mark^#(s(X)) -> c_5(mark^#(X)) 1192.24/299.31 , mark^#(cons2(X1, X2)) -> c_8(X1, mark^#(X2)) 1192.24/299.31 , mark^#(rcons(X1, X2)) -> c_9(mark^#(X1), mark^#(X2)) 1192.24/299.31 , mark^#(posrecip(X)) -> c_10(mark^#(X)) 1192.24/299.31 , mark^#(negrecip(X)) -> c_11(mark^#(X)) 1192.24/299.31 , mark^#(2ndspos(X1, X2)) -> c_12(a__2ndspos^#(mark(X1), mark(X2))) 1192.24/299.31 , mark^#(2ndsneg(X1, X2)) -> c_13(a__2ndsneg^#(mark(X1), mark(X2))) 1192.24/299.31 , mark^#(pi(X)) -> c_14(a__pi^#(mark(X))) 1192.24/299.31 , mark^#(plus(X1, X2)) -> c_15(a__plus^#(mark(X1), mark(X2))) 1192.24/299.31 , mark^#(times(X1, X2)) -> c_16(a__times^#(mark(X1), mark(X2))) 1192.24/299.31 , mark^#(square(X)) -> c_17(a__square^#(mark(X))) 1192.24/299.31 , a__2ndspos^#(X1, X2) -> c_19(X1, X2) 1192.24/299.31 , a__2ndspos^#(s(N), cons(X, Z)) -> 1192.24/299.31 c_20(a__2ndspos^#(s(mark(N)), cons2(X, mark(Z)))) 1192.24/299.31 , a__2ndspos^#(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.31 c_21(mark^#(Y), a__2ndsneg^#(mark(N), mark(Z))) 1192.24/299.31 , a__2ndsneg^#(X1, X2) -> c_23(X1, X2) 1192.24/299.31 , a__2ndsneg^#(s(N), cons(X, Z)) -> 1192.24/299.31 c_24(a__2ndsneg^#(s(mark(N)), cons2(X, mark(Z)))) 1192.24/299.31 , a__2ndsneg^#(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.31 c_25(mark^#(Y), a__2ndspos^#(mark(N), mark(Z))) 1192.24/299.31 , a__pi^#(X) -> c_27(a__2ndspos^#(mark(X), a__from(0()))) 1192.24/299.31 , a__pi^#(X) -> c_28(X) 1192.24/299.31 , a__plus^#(X1, X2) -> c_29(X1, X2) 1192.24/299.31 , a__plus^#(s(X), Y) -> c_30(a__plus^#(mark(X), mark(Y))) 1192.24/299.31 , a__plus^#(0(), Y) -> c_31(mark^#(Y)) 1192.24/299.31 , a__times^#(X1, X2) -> c_32(X1, X2) 1192.24/299.31 , a__times^#(s(X), Y) -> 1192.24/299.31 c_33(a__plus^#(mark(Y), a__times(mark(X), mark(Y)))) 1192.24/299.31 , a__square^#(X) -> c_35(a__times^#(mark(X), mark(X))) 1192.24/299.31 , a__square^#(X) -> c_36(X) } 1192.24/299.31 Strict Trs: 1192.24/299.31 { a__from(X) -> cons(mark(X), from(s(X))) 1192.24/299.31 , a__from(X) -> from(X) 1192.24/299.31 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 1192.24/299.31 , mark(from(X)) -> a__from(mark(X)) 1192.24/299.31 , mark(s(X)) -> s(mark(X)) 1192.24/299.31 , mark(0()) -> 0() 1192.24/299.31 , mark(rnil()) -> rnil() 1192.24/299.31 , mark(cons2(X1, X2)) -> cons2(X1, mark(X2)) 1192.24/299.31 , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2)) 1192.24/299.31 , mark(posrecip(X)) -> posrecip(mark(X)) 1192.24/299.31 , mark(negrecip(X)) -> negrecip(mark(X)) 1192.24/299.31 , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2)) 1192.24/299.31 , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2)) 1192.24/299.31 , mark(pi(X)) -> a__pi(mark(X)) 1192.24/299.31 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1192.24/299.31 , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2)) 1192.24/299.31 , mark(square(X)) -> a__square(mark(X)) 1192.24/299.31 , mark(nil()) -> nil() 1192.24/299.31 , a__2ndspos(X1, X2) -> 2ndspos(X1, X2) 1192.24/299.31 , a__2ndspos(s(N), cons(X, Z)) -> 1192.24/299.31 a__2ndspos(s(mark(N)), cons2(X, mark(Z))) 1192.24/299.31 , a__2ndspos(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.31 rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z))) 1192.24/299.31 , a__2ndspos(0(), Z) -> rnil() 1192.24/299.31 , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2) 1192.24/299.31 , a__2ndsneg(s(N), cons(X, Z)) -> 1192.24/299.31 a__2ndsneg(s(mark(N)), cons2(X, mark(Z))) 1192.24/299.31 , a__2ndsneg(s(N), cons2(X, cons(Y, Z))) -> 1192.24/299.31 rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z))) 1192.24/299.31 , a__2ndsneg(0(), Z) -> rnil() 1192.24/299.31 , a__pi(X) -> a__2ndspos(mark(X), a__from(0())) 1192.24/299.31 , a__pi(X) -> pi(X) 1192.24/299.31 , a__plus(X1, X2) -> plus(X1, X2) 1192.24/299.31 , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y))) 1192.24/299.31 , a__plus(0(), Y) -> mark(Y) 1192.24/299.31 , a__times(X1, X2) -> times(X1, X2) 1192.24/299.31 , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y))) 1192.24/299.31 , a__times(0(), Y) -> 0() 1192.24/299.31 , a__square(X) -> a__times(mark(X), mark(X)) 1192.24/299.31 , a__square(X) -> square(X) } 1192.24/299.31 Weak DPs: 1192.24/299.31 { mark^#(0()) -> c_6() 1192.24/299.31 , mark^#(rnil()) -> c_7() 1192.24/299.31 , mark^#(nil()) -> c_18() 1192.24/299.31 , a__2ndspos^#(0(), Z) -> c_22() 1192.24/299.31 , a__2ndsneg^#(0(), Z) -> c_26() 1192.24/299.31 , a__times^#(0(), Y) -> c_34() } 1192.24/299.35 Obligation: 1192.24/299.35 runtime complexity 1192.24/299.35 Answer: 1192.24/299.35 MAYBE 1192.24/299.35 1192.24/299.35 Empty strict component of the problem is NOT empty. 1192.24/299.35 1192.24/299.35 1192.24/299.35 Arrrr.. 1193.04/299.89 EOF