MAYBE 1189.18/298.41 MAYBE 1189.18/298.41 1189.18/298.41 We are left with following problem, upon which TcT provides the 1189.18/298.41 certificate MAYBE. 1189.18/298.41 1189.18/298.41 Strict Trs: 1189.18/298.41 { from(X) -> cons(X, n__from(s(X))) 1189.18/298.41 , from(X) -> n__from(X) 1189.18/298.41 , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z))) 1189.18/298.41 , 2ndspos(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 rcons(posrecip(Y), 2ndsneg(N, activate(Z))) 1189.18/298.41 , 2ndspos(0(), Z) -> rnil() 1189.18/298.41 , activate(X) -> X 1189.18/298.41 , activate(n__from(X)) -> from(X) 1189.18/298.41 , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z))) 1189.18/298.41 , 2ndsneg(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 rcons(negrecip(Y), 2ndspos(N, activate(Z))) 1189.18/298.41 , 2ndsneg(0(), Z) -> rnil() 1189.18/298.41 , pi(X) -> 2ndspos(X, from(0())) 1189.18/298.41 , plus(s(X), Y) -> s(plus(X, Y)) 1189.18/298.41 , plus(0(), Y) -> Y 1189.18/298.41 , times(s(X), Y) -> plus(Y, times(X, Y)) 1189.18/298.41 , times(0(), Y) -> 0() 1189.18/298.41 , square(X) -> times(X, X) } 1189.18/298.41 Obligation: 1189.18/298.41 runtime complexity 1189.18/298.41 Answer: 1189.18/298.41 MAYBE 1189.18/298.41 1189.18/298.41 None of the processors succeeded. 1189.18/298.41 1189.18/298.41 Details of failed attempt(s): 1189.18/298.41 ----------------------------- 1189.18/298.41 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1189.18/298.41 following reason: 1189.18/298.41 1189.18/298.41 Computation stopped due to timeout after 297.0 seconds. 1189.18/298.41 1189.18/298.41 2) 'Best' failed due to the following reason: 1189.18/298.41 1189.18/298.41 None of the processors succeeded. 1189.18/298.41 1189.18/298.41 Details of failed attempt(s): 1189.18/298.41 ----------------------------- 1189.18/298.41 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1189.18/298.41 seconds)' failed due to the following reason: 1189.18/298.41 1189.18/298.41 Computation stopped due to timeout after 148.0 seconds. 1189.18/298.41 1189.18/298.41 2) 'Best' failed due to the following reason: 1189.18/298.41 1189.18/298.41 None of the processors succeeded. 1189.18/298.41 1189.18/298.41 Details of failed attempt(s): 1189.18/298.41 ----------------------------- 1189.18/298.41 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1189.18/298.41 following reason: 1189.18/298.41 1189.18/298.41 The processor is inapplicable, reason: 1189.18/298.41 Processor only applicable for innermost runtime complexity analysis 1189.18/298.41 1189.18/298.41 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1189.18/298.41 to the following reason: 1189.18/298.41 1189.18/298.41 The processor is inapplicable, reason: 1189.18/298.41 Processor only applicable for innermost runtime complexity analysis 1189.18/298.41 1189.18/298.41 1189.18/298.41 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1189.18/298.41 failed due to the following reason: 1189.18/298.41 1189.18/298.41 None of the processors succeeded. 1189.18/298.41 1189.18/298.41 Details of failed attempt(s): 1189.18/298.41 ----------------------------- 1189.18/298.41 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1189.18/298.41 failed due to the following reason: 1189.18/298.41 1189.18/298.41 match-boundness of the problem could not be verified. 1189.18/298.41 1189.18/298.41 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1189.18/298.41 failed due to the following reason: 1189.18/298.41 1189.18/298.41 match-boundness of the problem could not be verified. 1189.18/298.41 1189.18/298.41 1189.18/298.41 1189.18/298.41 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1189.18/298.41 the following reason: 1189.18/298.41 1189.18/298.41 We add the following weak dependency pairs: 1189.18/298.41 1189.18/298.41 Strict DPs: 1189.18/298.41 { from^#(X) -> c_1(X, X) 1189.18/298.41 , from^#(X) -> c_2(X) 1189.18/298.41 , 2ndspos^#(s(N), cons(X, Z)) -> 1189.18/298.41 c_3(2ndspos^#(s(N), cons2(X, activate(Z)))) 1189.18/298.41 , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 c_4(Y, 2ndsneg^#(N, activate(Z))) 1189.18/298.41 , 2ndspos^#(0(), Z) -> c_5() 1189.18/298.41 , 2ndsneg^#(s(N), cons(X, Z)) -> 1189.18/298.41 c_8(2ndsneg^#(s(N), cons2(X, activate(Z)))) 1189.18/298.41 , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 c_9(Y, 2ndspos^#(N, activate(Z))) 1189.18/298.41 , 2ndsneg^#(0(), Z) -> c_10() 1189.18/298.41 , activate^#(X) -> c_6(X) 1189.18/298.41 , activate^#(n__from(X)) -> c_7(from^#(X)) 1189.18/298.41 , pi^#(X) -> c_11(2ndspos^#(X, from(0()))) 1189.18/298.41 , plus^#(s(X), Y) -> c_12(plus^#(X, Y)) 1189.18/298.41 , plus^#(0(), Y) -> c_13(Y) 1189.18/298.41 , times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y))) 1189.18/298.41 , times^#(0(), Y) -> c_15() 1189.18/298.41 , square^#(X) -> c_16(times^#(X, X)) } 1189.18/298.41 1189.18/298.41 and mark the set of starting terms. 1189.18/298.41 1189.18/298.41 We are left with following problem, upon which TcT provides the 1189.18/298.41 certificate MAYBE. 1189.18/298.41 1189.18/298.41 Strict DPs: 1189.18/298.41 { from^#(X) -> c_1(X, X) 1189.18/298.41 , from^#(X) -> c_2(X) 1189.18/298.41 , 2ndspos^#(s(N), cons(X, Z)) -> 1189.18/298.41 c_3(2ndspos^#(s(N), cons2(X, activate(Z)))) 1189.18/298.41 , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 c_4(Y, 2ndsneg^#(N, activate(Z))) 1189.18/298.41 , 2ndspos^#(0(), Z) -> c_5() 1189.18/298.41 , 2ndsneg^#(s(N), cons(X, Z)) -> 1189.18/298.41 c_8(2ndsneg^#(s(N), cons2(X, activate(Z)))) 1189.18/298.41 , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 c_9(Y, 2ndspos^#(N, activate(Z))) 1189.18/298.41 , 2ndsneg^#(0(), Z) -> c_10() 1189.18/298.41 , activate^#(X) -> c_6(X) 1189.18/298.41 , activate^#(n__from(X)) -> c_7(from^#(X)) 1189.18/298.41 , pi^#(X) -> c_11(2ndspos^#(X, from(0()))) 1189.18/298.41 , plus^#(s(X), Y) -> c_12(plus^#(X, Y)) 1189.18/298.41 , plus^#(0(), Y) -> c_13(Y) 1189.18/298.41 , times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y))) 1189.18/298.41 , times^#(0(), Y) -> c_15() 1189.18/298.41 , square^#(X) -> c_16(times^#(X, X)) } 1189.18/298.41 Strict Trs: 1189.18/298.41 { from(X) -> cons(X, n__from(s(X))) 1189.18/298.41 , from(X) -> n__from(X) 1189.18/298.41 , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z))) 1189.18/298.41 , 2ndspos(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 rcons(posrecip(Y), 2ndsneg(N, activate(Z))) 1189.18/298.41 , 2ndspos(0(), Z) -> rnil() 1189.18/298.41 , activate(X) -> X 1189.18/298.41 , activate(n__from(X)) -> from(X) 1189.18/298.41 , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z))) 1189.18/298.41 , 2ndsneg(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 rcons(negrecip(Y), 2ndspos(N, activate(Z))) 1189.18/298.41 , 2ndsneg(0(), Z) -> rnil() 1189.18/298.41 , pi(X) -> 2ndspos(X, from(0())) 1189.18/298.41 , plus(s(X), Y) -> s(plus(X, Y)) 1189.18/298.41 , plus(0(), Y) -> Y 1189.18/298.41 , times(s(X), Y) -> plus(Y, times(X, Y)) 1189.18/298.41 , times(0(), Y) -> 0() 1189.18/298.41 , square(X) -> times(X, X) } 1189.18/298.41 Obligation: 1189.18/298.41 runtime complexity 1189.18/298.41 Answer: 1189.18/298.41 MAYBE 1189.18/298.41 1189.18/298.41 We estimate the number of application of {5,8,15} by applications 1189.18/298.41 of Pre({5,8,15}) = {1,2,4,7,9,11,13,16}. Here rules are labeled as 1189.18/298.41 follows: 1189.18/298.41 1189.18/298.41 DPs: 1189.18/298.41 { 1: from^#(X) -> c_1(X, X) 1189.18/298.41 , 2: from^#(X) -> c_2(X) 1189.18/298.41 , 3: 2ndspos^#(s(N), cons(X, Z)) -> 1189.18/298.41 c_3(2ndspos^#(s(N), cons2(X, activate(Z)))) 1189.18/298.41 , 4: 2ndspos^#(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 c_4(Y, 2ndsneg^#(N, activate(Z))) 1189.18/298.41 , 5: 2ndspos^#(0(), Z) -> c_5() 1189.18/298.41 , 6: 2ndsneg^#(s(N), cons(X, Z)) -> 1189.18/298.41 c_8(2ndsneg^#(s(N), cons2(X, activate(Z)))) 1189.18/298.41 , 7: 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 c_9(Y, 2ndspos^#(N, activate(Z))) 1189.18/298.41 , 8: 2ndsneg^#(0(), Z) -> c_10() 1189.18/298.41 , 9: activate^#(X) -> c_6(X) 1189.18/298.41 , 10: activate^#(n__from(X)) -> c_7(from^#(X)) 1189.18/298.41 , 11: pi^#(X) -> c_11(2ndspos^#(X, from(0()))) 1189.18/298.41 , 12: plus^#(s(X), Y) -> c_12(plus^#(X, Y)) 1189.18/298.41 , 13: plus^#(0(), Y) -> c_13(Y) 1189.18/298.41 , 14: times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y))) 1189.18/298.41 , 15: times^#(0(), Y) -> c_15() 1189.18/298.41 , 16: square^#(X) -> c_16(times^#(X, X)) } 1189.18/298.41 1189.18/298.41 We are left with following problem, upon which TcT provides the 1189.18/298.41 certificate MAYBE. 1189.18/298.41 1189.18/298.41 Strict DPs: 1189.18/298.41 { from^#(X) -> c_1(X, X) 1189.18/298.41 , from^#(X) -> c_2(X) 1189.18/298.41 , 2ndspos^#(s(N), cons(X, Z)) -> 1189.18/298.41 c_3(2ndspos^#(s(N), cons2(X, activate(Z)))) 1189.18/298.41 , 2ndspos^#(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 c_4(Y, 2ndsneg^#(N, activate(Z))) 1189.18/298.41 , 2ndsneg^#(s(N), cons(X, Z)) -> 1189.18/298.41 c_8(2ndsneg^#(s(N), cons2(X, activate(Z)))) 1189.18/298.41 , 2ndsneg^#(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 c_9(Y, 2ndspos^#(N, activate(Z))) 1189.18/298.41 , activate^#(X) -> c_6(X) 1189.18/298.41 , activate^#(n__from(X)) -> c_7(from^#(X)) 1189.18/298.41 , pi^#(X) -> c_11(2ndspos^#(X, from(0()))) 1189.18/298.41 , plus^#(s(X), Y) -> c_12(plus^#(X, Y)) 1189.18/298.41 , plus^#(0(), Y) -> c_13(Y) 1189.18/298.41 , times^#(s(X), Y) -> c_14(plus^#(Y, times(X, Y))) 1189.18/298.41 , square^#(X) -> c_16(times^#(X, X)) } 1189.18/298.41 Strict Trs: 1189.18/298.41 { from(X) -> cons(X, n__from(s(X))) 1189.18/298.41 , from(X) -> n__from(X) 1189.18/298.41 , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z))) 1189.18/298.41 , 2ndspos(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 rcons(posrecip(Y), 2ndsneg(N, activate(Z))) 1189.18/298.41 , 2ndspos(0(), Z) -> rnil() 1189.18/298.41 , activate(X) -> X 1189.18/298.41 , activate(n__from(X)) -> from(X) 1189.18/298.41 , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z))) 1189.18/298.41 , 2ndsneg(s(N), cons2(X, cons(Y, Z))) -> 1189.18/298.41 rcons(negrecip(Y), 2ndspos(N, activate(Z))) 1189.18/298.41 , 2ndsneg(0(), Z) -> rnil() 1189.18/298.41 , pi(X) -> 2ndspos(X, from(0())) 1189.18/298.41 , plus(s(X), Y) -> s(plus(X, Y)) 1189.18/298.41 , plus(0(), Y) -> Y 1189.18/298.41 , times(s(X), Y) -> plus(Y, times(X, Y)) 1189.18/298.41 , times(0(), Y) -> 0() 1189.18/298.41 , square(X) -> times(X, X) } 1189.18/298.41 Weak DPs: 1189.18/298.41 { 2ndspos^#(0(), Z) -> c_5() 1189.18/298.41 , 2ndsneg^#(0(), Z) -> c_10() 1189.18/298.41 , times^#(0(), Y) -> c_15() } 1189.18/298.41 Obligation: 1189.18/298.41 runtime complexity 1189.18/298.41 Answer: 1189.18/298.41 MAYBE 1189.18/298.41 1189.18/298.41 Empty strict component of the problem is NOT empty. 1189.18/298.41 1189.18/298.41 1189.18/298.41 Arrrr.. 1189.94/299.17 EOF