MAYBE 1184.30/297.16 MAYBE 1184.30/297.16 1184.30/297.16 We are left with following problem, upon which TcT provides the 1184.30/297.16 certificate MAYBE. 1184.30/297.16 1184.30/297.16 Strict Trs: 1184.30/297.16 { from(X) -> cons(X, n__from(s(X))) 1184.30/297.16 , from(X) -> n__from(X) 1184.30/297.16 , cons(X1, X2) -> n__cons(X1, X2) 1184.30/297.16 , 2ndspos(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z))) 1184.30/297.16 , 2ndspos(0(), Z) -> rnil() 1184.30/297.16 , activate(X) -> X 1184.30/297.16 , activate(n__from(X)) -> from(X) 1184.30/297.16 , activate(n__cons(X1, X2)) -> cons(X1, X2) 1184.30/297.16 , 2ndsneg(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z))) 1184.30/297.16 , 2ndsneg(0(), Z) -> rnil() 1184.30/297.16 , pi(X) -> 2ndspos(X, from(0())) 1184.30/297.16 , plus(s(X), Y) -> s(plus(X, Y)) 1184.30/297.16 , plus(0(), Y) -> Y 1184.30/297.16 , times(s(X), Y) -> plus(Y, times(X, Y)) 1184.30/297.16 , times(0(), Y) -> 0() 1184.30/297.16 , square(X) -> times(X, X) } 1184.30/297.16 Obligation: 1184.30/297.16 runtime complexity 1184.30/297.16 Answer: 1184.30/297.16 MAYBE 1184.30/297.16 1184.30/297.16 None of the processors succeeded. 1184.30/297.16 1184.30/297.16 Details of failed attempt(s): 1184.30/297.16 ----------------------------- 1184.30/297.16 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1184.30/297.16 following reason: 1184.30/297.16 1184.30/297.16 Computation stopped due to timeout after 297.0 seconds. 1184.30/297.16 1184.30/297.16 2) 'Best' failed due to the following reason: 1184.30/297.16 1184.30/297.16 None of the processors succeeded. 1184.30/297.16 1184.30/297.16 Details of failed attempt(s): 1184.30/297.16 ----------------------------- 1184.30/297.16 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1184.30/297.16 seconds)' failed due to the following reason: 1184.30/297.16 1184.30/297.16 Computation stopped due to timeout after 148.0 seconds. 1184.30/297.16 1184.30/297.16 2) 'Best' failed due to the following reason: 1184.30/297.16 1184.30/297.16 None of the processors succeeded. 1184.30/297.16 1184.30/297.16 Details of failed attempt(s): 1184.30/297.16 ----------------------------- 1184.30/297.16 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1184.30/297.16 following reason: 1184.30/297.16 1184.30/297.16 The processor is inapplicable, reason: 1184.30/297.16 Processor only applicable for innermost runtime complexity analysis 1184.30/297.16 1184.30/297.16 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1184.30/297.16 to the following reason: 1184.30/297.16 1184.30/297.16 The processor is inapplicable, reason: 1184.30/297.16 Processor only applicable for innermost runtime complexity analysis 1184.30/297.16 1184.30/297.16 1184.30/297.16 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1184.30/297.16 failed due to the following reason: 1184.30/297.16 1184.30/297.16 None of the processors succeeded. 1184.30/297.16 1184.30/297.16 Details of failed attempt(s): 1184.30/297.16 ----------------------------- 1184.30/297.16 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1184.30/297.16 failed due to the following reason: 1184.30/297.16 1184.30/297.16 match-boundness of the problem could not be verified. 1184.30/297.16 1184.30/297.16 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 1184.30/297.16 failed due to the following reason: 1184.30/297.16 1184.30/297.16 match-boundness of the problem could not be verified. 1184.30/297.16 1184.30/297.16 1184.30/297.16 1184.30/297.16 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1184.30/297.16 the following reason: 1184.30/297.16 1184.30/297.16 We add the following weak dependency pairs: 1184.30/297.16 1184.30/297.16 Strict DPs: 1184.30/297.16 { from^#(X) -> c_1(cons^#(X, n__from(s(X)))) 1184.30/297.16 , from^#(X) -> c_2(X) 1184.30/297.16 , cons^#(X1, X2) -> c_3(X1, X2) 1184.30/297.16 , 2ndspos^#(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 c_4(activate^#(Y), 2ndsneg^#(N, activate(Z))) 1184.30/297.16 , 2ndspos^#(0(), Z) -> c_5() 1184.30/297.16 , activate^#(X) -> c_6(X) 1184.30/297.16 , activate^#(n__from(X)) -> c_7(from^#(X)) 1184.30/297.16 , activate^#(n__cons(X1, X2)) -> c_8(cons^#(X1, X2)) 1184.30/297.16 , 2ndsneg^#(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 c_9(activate^#(Y), 2ndspos^#(N, activate(Z))) 1184.30/297.16 , 2ndsneg^#(0(), Z) -> c_10() 1184.30/297.16 , pi^#(X) -> c_11(2ndspos^#(X, from(0()))) 1184.30/297.16 , plus^#(s(X), Y) -> c_12(plus^#(X, Y)) 1184.30/297.16 , plus^#(0(), Y) -> c_13(Y) 1184.30/297.16 , times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y))) 1184.30/297.16 , times^#(0(), Y) -> c_15() 1184.30/297.16 , square^#(X) -> c_16(times^#(X, X)) } 1184.30/297.16 1184.30/297.16 and mark the set of starting terms. 1184.30/297.16 1184.30/297.16 We are left with following problem, upon which TcT provides the 1184.30/297.16 certificate MAYBE. 1184.30/297.16 1184.30/297.16 Strict DPs: 1184.30/297.16 { from^#(X) -> c_1(cons^#(X, n__from(s(X)))) 1184.30/297.16 , from^#(X) -> c_2(X) 1184.30/297.16 , cons^#(X1, X2) -> c_3(X1, X2) 1184.30/297.16 , 2ndspos^#(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 c_4(activate^#(Y), 2ndsneg^#(N, activate(Z))) 1184.30/297.16 , 2ndspos^#(0(), Z) -> c_5() 1184.30/297.16 , activate^#(X) -> c_6(X) 1184.30/297.16 , activate^#(n__from(X)) -> c_7(from^#(X)) 1184.30/297.16 , activate^#(n__cons(X1, X2)) -> c_8(cons^#(X1, X2)) 1184.30/297.16 , 2ndsneg^#(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 c_9(activate^#(Y), 2ndspos^#(N, activate(Z))) 1184.30/297.16 , 2ndsneg^#(0(), Z) -> c_10() 1184.30/297.16 , pi^#(X) -> c_11(2ndspos^#(X, from(0()))) 1184.30/297.16 , plus^#(s(X), Y) -> c_12(plus^#(X, Y)) 1184.30/297.16 , plus^#(0(), Y) -> c_13(Y) 1184.30/297.16 , times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y))) 1184.30/297.16 , times^#(0(), Y) -> c_15() 1184.30/297.16 , square^#(X) -> c_16(times^#(X, X)) } 1184.30/297.16 Strict Trs: 1184.30/297.16 { from(X) -> cons(X, n__from(s(X))) 1184.30/297.16 , from(X) -> n__from(X) 1184.30/297.16 , cons(X1, X2) -> n__cons(X1, X2) 1184.30/297.16 , 2ndspos(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z))) 1184.30/297.16 , 2ndspos(0(), Z) -> rnil() 1184.30/297.16 , activate(X) -> X 1184.30/297.16 , activate(n__from(X)) -> from(X) 1184.30/297.16 , activate(n__cons(X1, X2)) -> cons(X1, X2) 1184.30/297.16 , 2ndsneg(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z))) 1184.30/297.16 , 2ndsneg(0(), Z) -> rnil() 1184.30/297.16 , pi(X) -> 2ndspos(X, from(0())) 1184.30/297.16 , plus(s(X), Y) -> s(plus(X, Y)) 1184.30/297.16 , plus(0(), Y) -> Y 1184.30/297.16 , times(s(X), Y) -> plus(Y, times(X, Y)) 1184.30/297.16 , times(0(), Y) -> 0() 1184.30/297.16 , square(X) -> times(X, X) } 1184.30/297.16 Obligation: 1184.30/297.16 runtime complexity 1184.30/297.16 Answer: 1184.30/297.16 MAYBE 1184.30/297.16 1184.30/297.16 We estimate the number of application of {5,10,15} by applications 1184.30/297.16 of Pre({5,10,15}) = {2,3,4,6,9,11,13,16}. Here rules are labeled as 1184.30/297.16 follows: 1184.30/297.16 1184.30/297.16 DPs: 1184.30/297.16 { 1: from^#(X) -> c_1(cons^#(X, n__from(s(X)))) 1184.30/297.16 , 2: from^#(X) -> c_2(X) 1184.30/297.16 , 3: cons^#(X1, X2) -> c_3(X1, X2) 1184.30/297.16 , 4: 2ndspos^#(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 c_4(activate^#(Y), 2ndsneg^#(N, activate(Z))) 1184.30/297.16 , 5: 2ndspos^#(0(), Z) -> c_5() 1184.30/297.16 , 6: activate^#(X) -> c_6(X) 1184.30/297.16 , 7: activate^#(n__from(X)) -> c_7(from^#(X)) 1184.30/297.16 , 8: activate^#(n__cons(X1, X2)) -> c_8(cons^#(X1, X2)) 1184.30/297.16 , 9: 2ndsneg^#(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 c_9(activate^#(Y), 2ndspos^#(N, activate(Z))) 1184.30/297.16 , 10: 2ndsneg^#(0(), Z) -> c_10() 1184.30/297.16 , 11: pi^#(X) -> c_11(2ndspos^#(X, from(0()))) 1184.30/297.16 , 12: plus^#(s(X), Y) -> c_12(plus^#(X, Y)) 1184.30/297.16 , 13: plus^#(0(), Y) -> c_13(Y) 1184.30/297.16 , 14: times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y))) 1184.30/297.16 , 15: times^#(0(), Y) -> c_15() 1184.30/297.16 , 16: square^#(X) -> c_16(times^#(X, X)) } 1184.30/297.16 1184.30/297.16 We are left with following problem, upon which TcT provides the 1184.30/297.16 certificate MAYBE. 1184.30/297.16 1184.30/297.16 Strict DPs: 1184.30/297.16 { from^#(X) -> c_1(cons^#(X, n__from(s(X)))) 1184.30/297.16 , from^#(X) -> c_2(X) 1184.30/297.16 , cons^#(X1, X2) -> c_3(X1, X2) 1184.30/297.16 , 2ndspos^#(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 c_4(activate^#(Y), 2ndsneg^#(N, activate(Z))) 1184.30/297.16 , activate^#(X) -> c_6(X) 1184.30/297.16 , activate^#(n__from(X)) -> c_7(from^#(X)) 1184.30/297.16 , activate^#(n__cons(X1, X2)) -> c_8(cons^#(X1, X2)) 1184.30/297.16 , 2ndsneg^#(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 c_9(activate^#(Y), 2ndspos^#(N, activate(Z))) 1184.30/297.16 , pi^#(X) -> c_11(2ndspos^#(X, from(0()))) 1184.30/297.16 , plus^#(s(X), Y) -> c_12(plus^#(X, Y)) 1184.30/297.16 , plus^#(0(), Y) -> c_13(Y) 1184.30/297.16 , times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y))) 1184.30/297.16 , square^#(X) -> c_16(times^#(X, X)) } 1184.30/297.16 Strict Trs: 1184.30/297.16 { from(X) -> cons(X, n__from(s(X))) 1184.30/297.16 , from(X) -> n__from(X) 1184.30/297.16 , cons(X1, X2) -> n__cons(X1, X2) 1184.30/297.16 , 2ndspos(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z))) 1184.30/297.16 , 2ndspos(0(), Z) -> rnil() 1184.30/297.16 , activate(X) -> X 1184.30/297.16 , activate(n__from(X)) -> from(X) 1184.30/297.16 , activate(n__cons(X1, X2)) -> cons(X1, X2) 1184.30/297.16 , 2ndsneg(s(N), cons(X, n__cons(Y, Z))) -> 1184.30/297.16 rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z))) 1184.30/297.16 , 2ndsneg(0(), Z) -> rnil() 1184.30/297.16 , pi(X) -> 2ndspos(X, from(0())) 1184.30/297.16 , plus(s(X), Y) -> s(plus(X, Y)) 1184.30/297.16 , plus(0(), Y) -> Y 1184.30/297.16 , times(s(X), Y) -> plus(Y, times(X, Y)) 1184.30/297.16 , times(0(), Y) -> 0() 1184.30/297.16 , square(X) -> times(X, X) } 1184.30/297.16 Weak DPs: 1184.30/297.16 { 2ndspos^#(0(), Z) -> c_5() 1184.30/297.16 , 2ndsneg^#(0(), Z) -> c_10() 1184.30/297.16 , times^#(0(), Y) -> c_15() } 1184.30/297.16 Obligation: 1184.30/297.16 runtime complexity 1184.30/297.16 Answer: 1184.30/297.16 MAYBE 1184.30/297.16 1184.30/297.16 Empty strict component of the problem is NOT empty. 1184.30/297.16 1184.30/297.16 1184.30/297.16 Arrrr.. 1184.99/297.69 EOF