MAYBE 771.94/297.05 MAYBE 771.94/297.05 771.94/297.05 We are left with following problem, upon which TcT provides the 771.94/297.05 certificate MAYBE. 771.94/297.05 771.94/297.05 Strict Trs: 771.94/297.05 { empty(nil()) -> true() 771.94/297.05 , empty(cons(x, y)) -> false() 771.94/297.05 , tail(nil()) -> nil() 771.94/297.05 , tail(cons(x, y)) -> y 771.94/297.05 , head(cons(x, y)) -> x 771.94/297.05 , zero(0()) -> true() 771.94/297.05 , zero(s(x)) -> false() 771.94/297.05 , p(0()) -> 0() 771.94/297.05 , p(s(0())) -> 0() 771.94/297.05 , p(s(s(x))) -> s(p(s(x))) 771.94/297.05 , intlist(x) -> if_intlist(empty(x), x) 771.94/297.05 , if_intlist(true(), x) -> nil() 771.94/297.05 , if_intlist(false(), x) -> cons(s(head(x)), intlist(tail(x))) 771.94/297.05 , int(x, y) -> if_int(zero(x), zero(y), x, y) 771.94/297.05 , if_int(true(), b, x, y) -> if1(b, x, y) 771.94/297.05 , if_int(false(), b, x, y) -> if2(b, x, y) 771.94/297.05 , if1(true(), x, y) -> cons(0(), nil()) 771.94/297.05 , if1(false(), x, y) -> cons(0(), int(s(0()), y)) 771.94/297.05 , if2(true(), x, y) -> nil() 771.94/297.05 , if2(false(), x, y) -> intlist(int(p(x), p(y))) } 771.94/297.05 Obligation: 771.94/297.05 runtime complexity 771.94/297.05 Answer: 771.94/297.05 MAYBE 771.94/297.05 771.94/297.05 None of the processors succeeded. 771.94/297.05 771.94/297.05 Details of failed attempt(s): 771.94/297.05 ----------------------------- 771.94/297.05 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 771.94/297.05 following reason: 771.94/297.05 771.94/297.05 Computation stopped due to timeout after 297.0 seconds. 771.94/297.05 771.94/297.05 2) 'Best' failed due to the following reason: 771.94/297.05 771.94/297.05 None of the processors succeeded. 771.94/297.05 771.94/297.05 Details of failed attempt(s): 771.94/297.05 ----------------------------- 771.94/297.05 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 771.94/297.05 seconds)' failed due to the following reason: 771.94/297.05 771.94/297.05 Computation stopped due to timeout after 148.0 seconds. 771.94/297.05 771.94/297.05 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 771.94/297.05 failed due to the following reason: 771.94/297.05 771.94/297.05 None of the processors succeeded. 771.94/297.05 771.94/297.05 Details of failed attempt(s): 771.94/297.05 ----------------------------- 771.94/297.05 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 771.94/297.05 failed due to the following reason: 771.94/297.05 771.94/297.05 match-boundness of the problem could not be verified. 771.94/297.05 771.94/297.05 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 771.94/297.05 failed due to the following reason: 771.94/297.05 771.94/297.05 match-boundness of the problem could not be verified. 771.94/297.05 771.94/297.05 771.94/297.05 3) 'Best' failed due to the following reason: 771.94/297.05 771.94/297.05 None of the processors succeeded. 771.94/297.05 771.94/297.05 Details of failed attempt(s): 771.94/297.05 ----------------------------- 771.94/297.05 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 771.94/297.05 to the following reason: 771.94/297.05 771.94/297.05 The processor is inapplicable, reason: 771.94/297.05 Processor only applicable for innermost runtime complexity analysis 771.94/297.05 771.94/297.05 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 771.94/297.05 following reason: 771.94/297.05 771.94/297.05 The processor is inapplicable, reason: 771.94/297.05 Processor only applicable for innermost runtime complexity analysis 771.94/297.05 771.94/297.05 771.94/297.05 771.94/297.05 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 771.94/297.05 the following reason: 771.94/297.05 771.94/297.05 We add the following weak dependency pairs: 771.94/297.05 771.94/297.05 Strict DPs: 771.94/297.05 { empty^#(nil()) -> c_1() 771.94/297.05 , empty^#(cons(x, y)) -> c_2() 771.94/297.05 , tail^#(nil()) -> c_3() 771.94/297.05 , tail^#(cons(x, y)) -> c_4(y) 771.94/297.05 , head^#(cons(x, y)) -> c_5(x) 771.94/297.05 , zero^#(0()) -> c_6() 771.94/297.05 , zero^#(s(x)) -> c_7() 771.94/297.05 , p^#(0()) -> c_8() 771.94/297.05 , p^#(s(0())) -> c_9() 771.94/297.05 , p^#(s(s(x))) -> c_10(p^#(s(x))) 771.94/297.05 , intlist^#(x) -> c_11(if_intlist^#(empty(x), x)) 771.94/297.05 , if_intlist^#(true(), x) -> c_12() 771.94/297.05 , if_intlist^#(false(), x) -> c_13(head^#(x), intlist^#(tail(x))) 771.94/297.05 , int^#(x, y) -> c_14(if_int^#(zero(x), zero(y), x, y)) 771.94/297.05 , if_int^#(true(), b, x, y) -> c_15(if1^#(b, x, y)) 771.94/297.05 , if_int^#(false(), b, x, y) -> c_16(if2^#(b, x, y)) 771.94/297.05 , if1^#(true(), x, y) -> c_17() 771.94/297.05 , if1^#(false(), x, y) -> c_18(int^#(s(0()), y)) 771.94/297.05 , if2^#(true(), x, y) -> c_19() 771.94/297.05 , if2^#(false(), x, y) -> c_20(intlist^#(int(p(x), p(y)))) } 771.94/297.05 771.94/297.05 and mark the set of starting terms. 771.94/297.05 771.94/297.05 We are left with following problem, upon which TcT provides the 771.94/297.05 certificate MAYBE. 771.94/297.05 771.94/297.05 Strict DPs: 771.94/297.05 { empty^#(nil()) -> c_1() 771.94/297.05 , empty^#(cons(x, y)) -> c_2() 771.94/297.05 , tail^#(nil()) -> c_3() 771.94/297.05 , tail^#(cons(x, y)) -> c_4(y) 771.94/297.05 , head^#(cons(x, y)) -> c_5(x) 771.94/297.05 , zero^#(0()) -> c_6() 771.94/297.05 , zero^#(s(x)) -> c_7() 771.94/297.05 , p^#(0()) -> c_8() 771.94/297.05 , p^#(s(0())) -> c_9() 771.94/297.05 , p^#(s(s(x))) -> c_10(p^#(s(x))) 771.94/297.05 , intlist^#(x) -> c_11(if_intlist^#(empty(x), x)) 771.94/297.05 , if_intlist^#(true(), x) -> c_12() 771.94/297.05 , if_intlist^#(false(), x) -> c_13(head^#(x), intlist^#(tail(x))) 771.94/297.05 , int^#(x, y) -> c_14(if_int^#(zero(x), zero(y), x, y)) 771.94/297.05 , if_int^#(true(), b, x, y) -> c_15(if1^#(b, x, y)) 771.94/297.05 , if_int^#(false(), b, x, y) -> c_16(if2^#(b, x, y)) 771.94/297.05 , if1^#(true(), x, y) -> c_17() 771.94/297.05 , if1^#(false(), x, y) -> c_18(int^#(s(0()), y)) 771.94/297.05 , if2^#(true(), x, y) -> c_19() 771.94/297.05 , if2^#(false(), x, y) -> c_20(intlist^#(int(p(x), p(y)))) } 771.94/297.05 Strict Trs: 771.94/297.05 { empty(nil()) -> true() 771.94/297.05 , empty(cons(x, y)) -> false() 771.94/297.05 , tail(nil()) -> nil() 771.94/297.05 , tail(cons(x, y)) -> y 771.94/297.05 , head(cons(x, y)) -> x 771.94/297.05 , zero(0()) -> true() 771.94/297.05 , zero(s(x)) -> false() 771.94/297.05 , p(0()) -> 0() 771.94/297.05 , p(s(0())) -> 0() 771.94/297.05 , p(s(s(x))) -> s(p(s(x))) 771.94/297.05 , intlist(x) -> if_intlist(empty(x), x) 771.94/297.05 , if_intlist(true(), x) -> nil() 771.94/297.05 , if_intlist(false(), x) -> cons(s(head(x)), intlist(tail(x))) 771.94/297.05 , int(x, y) -> if_int(zero(x), zero(y), x, y) 771.94/297.05 , if_int(true(), b, x, y) -> if1(b, x, y) 771.94/297.05 , if_int(false(), b, x, y) -> if2(b, x, y) 771.94/297.05 , if1(true(), x, y) -> cons(0(), nil()) 771.94/297.05 , if1(false(), x, y) -> cons(0(), int(s(0()), y)) 771.94/297.05 , if2(true(), x, y) -> nil() 771.94/297.05 , if2(false(), x, y) -> intlist(int(p(x), p(y))) } 771.94/297.05 Obligation: 771.94/297.05 runtime complexity 771.94/297.05 Answer: 771.94/297.05 MAYBE 771.94/297.05 771.94/297.05 We estimate the number of application of {1,2,3,6,7,8,9,12,17,19} 771.94/297.05 by applications of Pre({1,2,3,6,7,8,9,12,17,19}) = 771.94/297.05 {4,5,10,11,15,16}. Here rules are labeled as follows: 771.94/297.05 771.94/297.05 DPs: 771.94/297.05 { 1: empty^#(nil()) -> c_1() 771.94/297.05 , 2: empty^#(cons(x, y)) -> c_2() 771.94/297.05 , 3: tail^#(nil()) -> c_3() 771.94/297.05 , 4: tail^#(cons(x, y)) -> c_4(y) 771.94/297.05 , 5: head^#(cons(x, y)) -> c_5(x) 771.94/297.05 , 6: zero^#(0()) -> c_6() 771.94/297.05 , 7: zero^#(s(x)) -> c_7() 771.94/297.05 , 8: p^#(0()) -> c_8() 771.94/297.05 , 9: p^#(s(0())) -> c_9() 771.94/297.05 , 10: p^#(s(s(x))) -> c_10(p^#(s(x))) 771.94/297.05 , 11: intlist^#(x) -> c_11(if_intlist^#(empty(x), x)) 771.94/297.05 , 12: if_intlist^#(true(), x) -> c_12() 771.94/297.05 , 13: if_intlist^#(false(), x) -> 771.94/297.05 c_13(head^#(x), intlist^#(tail(x))) 771.94/297.05 , 14: int^#(x, y) -> c_14(if_int^#(zero(x), zero(y), x, y)) 771.94/297.05 , 15: if_int^#(true(), b, x, y) -> c_15(if1^#(b, x, y)) 771.94/297.05 , 16: if_int^#(false(), b, x, y) -> c_16(if2^#(b, x, y)) 771.94/297.05 , 17: if1^#(true(), x, y) -> c_17() 771.94/297.05 , 18: if1^#(false(), x, y) -> c_18(int^#(s(0()), y)) 771.94/297.05 , 19: if2^#(true(), x, y) -> c_19() 771.94/297.05 , 20: if2^#(false(), x, y) -> c_20(intlist^#(int(p(x), p(y)))) } 771.94/297.05 771.94/297.05 We are left with following problem, upon which TcT provides the 771.94/297.05 certificate MAYBE. 771.94/297.05 771.94/297.05 Strict DPs: 771.94/297.05 { tail^#(cons(x, y)) -> c_4(y) 771.94/297.05 , head^#(cons(x, y)) -> c_5(x) 771.94/297.05 , p^#(s(s(x))) -> c_10(p^#(s(x))) 771.94/297.05 , intlist^#(x) -> c_11(if_intlist^#(empty(x), x)) 771.94/297.05 , if_intlist^#(false(), x) -> c_13(head^#(x), intlist^#(tail(x))) 771.94/297.05 , int^#(x, y) -> c_14(if_int^#(zero(x), zero(y), x, y)) 771.94/297.05 , if_int^#(true(), b, x, y) -> c_15(if1^#(b, x, y)) 771.94/297.05 , if_int^#(false(), b, x, y) -> c_16(if2^#(b, x, y)) 771.94/297.05 , if1^#(false(), x, y) -> c_18(int^#(s(0()), y)) 771.94/297.05 , if2^#(false(), x, y) -> c_20(intlist^#(int(p(x), p(y)))) } 771.94/297.05 Strict Trs: 771.94/297.05 { empty(nil()) -> true() 771.94/297.05 , empty(cons(x, y)) -> false() 771.94/297.05 , tail(nil()) -> nil() 771.94/297.05 , tail(cons(x, y)) -> y 771.94/297.05 , head(cons(x, y)) -> x 771.94/297.05 , zero(0()) -> true() 771.94/297.05 , zero(s(x)) -> false() 771.94/297.05 , p(0()) -> 0() 771.94/297.05 , p(s(0())) -> 0() 771.94/297.05 , p(s(s(x))) -> s(p(s(x))) 771.94/297.05 , intlist(x) -> if_intlist(empty(x), x) 771.94/297.05 , if_intlist(true(), x) -> nil() 771.94/297.05 , if_intlist(false(), x) -> cons(s(head(x)), intlist(tail(x))) 771.94/297.05 , int(x, y) -> if_int(zero(x), zero(y), x, y) 771.94/297.05 , if_int(true(), b, x, y) -> if1(b, x, y) 771.94/297.05 , if_int(false(), b, x, y) -> if2(b, x, y) 771.94/297.05 , if1(true(), x, y) -> cons(0(), nil()) 771.94/297.05 , if1(false(), x, y) -> cons(0(), int(s(0()), y)) 771.94/297.05 , if2(true(), x, y) -> nil() 771.94/297.05 , if2(false(), x, y) -> intlist(int(p(x), p(y))) } 771.94/297.05 Weak DPs: 771.94/297.05 { empty^#(nil()) -> c_1() 771.94/297.05 , empty^#(cons(x, y)) -> c_2() 771.94/297.05 , tail^#(nil()) -> c_3() 771.94/297.05 , zero^#(0()) -> c_6() 771.94/297.05 , zero^#(s(x)) -> c_7() 771.94/297.05 , p^#(0()) -> c_8() 771.94/297.05 , p^#(s(0())) -> c_9() 771.94/297.05 , if_intlist^#(true(), x) -> c_12() 771.94/297.05 , if1^#(true(), x, y) -> c_17() 771.94/297.05 , if2^#(true(), x, y) -> c_19() } 771.94/297.05 Obligation: 771.94/297.05 runtime complexity 771.94/297.05 Answer: 771.94/297.05 MAYBE 771.94/297.05 771.94/297.05 Empty strict component of the problem is NOT empty. 771.94/297.05 771.94/297.05 771.94/297.05 Arrrr.. 772.26/297.30 EOF