MAYBE 1184.27/297.09 MAYBE 1184.27/297.09 1184.27/297.09 We are left with following problem, upon which TcT provides the 1184.27/297.09 certificate MAYBE. 1184.27/297.09 1184.27/297.09 Strict Trs: 1184.27/297.09 { null(nil()) -> true() 1184.27/297.09 , null(add(n, x)) -> false() 1184.27/297.09 , tail(nil()) -> nil() 1184.27/297.09 , tail(add(n, x)) -> x 1184.27/297.09 , head(add(n, x)) -> n 1184.27/297.09 , app(nil(), y) -> y 1184.27/297.09 , app(add(n, x), y) -> add(n, app(x, y)) 1184.27/297.09 , reverse(nil()) -> nil() 1184.27/297.09 , reverse(add(n, x)) -> app(reverse(x), add(n, nil())) 1184.27/297.09 , shuffle(x) -> shuff(x, nil()) 1184.27/297.09 , shuff(x, y) -> if(null(x), x, y, app(y, add(head(x), nil()))) 1184.27/297.09 , if(true(), x, y, z) -> y 1184.27/297.09 , if(false(), x, y, z) -> shuff(reverse(tail(x)), z) } 1184.27/297.09 Obligation: 1184.27/297.09 runtime complexity 1184.27/297.09 Answer: 1184.27/297.09 MAYBE 1184.27/297.09 1184.27/297.09 None of the processors succeeded. 1184.27/297.09 1184.27/297.09 Details of failed attempt(s): 1184.27/297.09 ----------------------------- 1184.27/297.09 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1184.27/297.09 following reason: 1184.27/297.09 1184.27/297.09 Computation stopped due to timeout after 297.0 seconds. 1184.27/297.09 1184.27/297.09 2) 'Best' failed due to the following reason: 1184.27/297.09 1184.27/297.09 None of the processors succeeded. 1184.27/297.09 1184.27/297.09 Details of failed attempt(s): 1184.27/297.09 ----------------------------- 1184.27/297.09 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1184.27/297.09 seconds)' failed due to the following reason: 1184.27/297.09 1184.27/297.09 Computation stopped due to timeout after 148.0 seconds. 1184.27/297.09 1184.27/297.09 2) 'Best' failed due to the following reason: 1184.27/297.09 1184.27/297.09 None of the processors succeeded. 1184.27/297.09 1184.27/297.09 Details of failed attempt(s): 1184.27/297.09 ----------------------------- 1184.27/297.09 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1184.27/297.09 to the following reason: 1184.27/297.09 1184.27/297.09 The processor is inapplicable, reason: 1184.27/297.09 Processor only applicable for innermost runtime complexity analysis 1184.27/297.09 1184.27/297.09 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1184.27/297.09 following reason: 1184.27/297.09 1184.27/297.09 The processor is inapplicable, reason: 1184.27/297.09 Processor only applicable for innermost runtime complexity analysis 1184.27/297.09 1184.27/297.09 1184.27/297.09 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1184.27/297.09 failed due to the following reason: 1184.27/297.09 1184.27/297.09 None of the processors succeeded. 1184.27/297.09 1184.27/297.09 Details of failed attempt(s): 1184.27/297.09 ----------------------------- 1184.27/297.09 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1184.27/297.09 failed due to the following reason: 1184.27/297.09 1184.27/297.09 match-boundness of the problem could not be verified. 1184.27/297.09 1184.27/297.09 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1184.27/297.09 failed due to the following reason: 1184.27/297.09 1184.27/297.09 match-boundness of the problem could not be verified. 1184.27/297.09 1184.27/297.09 1184.27/297.09 1184.27/297.09 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1184.27/297.09 the following reason: 1184.27/297.09 1184.27/297.09 We add the following weak dependency pairs: 1184.27/297.09 1184.27/297.09 Strict DPs: 1184.27/297.09 { null^#(nil()) -> c_1() 1184.27/297.09 , null^#(add(n, x)) -> c_2() 1184.27/297.09 , tail^#(nil()) -> c_3() 1184.27/297.09 , tail^#(add(n, x)) -> c_4(x) 1184.27/297.09 , head^#(add(n, x)) -> c_5(n) 1184.27/297.09 , app^#(nil(), y) -> c_6(y) 1184.27/297.09 , app^#(add(n, x), y) -> c_7(n, app^#(x, y)) 1184.27/297.09 , reverse^#(nil()) -> c_8() 1184.27/297.09 , reverse^#(add(n, x)) -> c_9(app^#(reverse(x), add(n, nil()))) 1184.27/297.09 , shuffle^#(x) -> c_10(shuff^#(x, nil())) 1184.27/297.09 , shuff^#(x, y) -> 1184.27/297.09 c_11(if^#(null(x), x, y, app(y, add(head(x), nil())))) 1184.27/297.09 , if^#(true(), x, y, z) -> c_12(y) 1184.27/297.09 , if^#(false(), x, y, z) -> c_13(shuff^#(reverse(tail(x)), z)) } 1184.27/297.09 1184.27/297.09 and mark the set of starting terms. 1184.27/297.09 1184.27/297.09 We are left with following problem, upon which TcT provides the 1184.27/297.09 certificate MAYBE. 1184.27/297.09 1184.27/297.09 Strict DPs: 1184.27/297.09 { null^#(nil()) -> c_1() 1184.27/297.09 , null^#(add(n, x)) -> c_2() 1184.27/297.09 , tail^#(nil()) -> c_3() 1184.27/297.09 , tail^#(add(n, x)) -> c_4(x) 1184.27/297.09 , head^#(add(n, x)) -> c_5(n) 1184.27/297.09 , app^#(nil(), y) -> c_6(y) 1184.27/297.09 , app^#(add(n, x), y) -> c_7(n, app^#(x, y)) 1184.27/297.09 , reverse^#(nil()) -> c_8() 1184.27/297.09 , reverse^#(add(n, x)) -> c_9(app^#(reverse(x), add(n, nil()))) 1184.27/297.09 , shuffle^#(x) -> c_10(shuff^#(x, nil())) 1184.27/297.09 , shuff^#(x, y) -> 1184.27/297.09 c_11(if^#(null(x), x, y, app(y, add(head(x), nil())))) 1184.27/297.09 , if^#(true(), x, y, z) -> c_12(y) 1184.27/297.09 , if^#(false(), x, y, z) -> c_13(shuff^#(reverse(tail(x)), z)) } 1184.27/297.09 Strict Trs: 1184.27/297.09 { null(nil()) -> true() 1184.27/297.09 , null(add(n, x)) -> false() 1184.27/297.09 , tail(nil()) -> nil() 1184.27/297.09 , tail(add(n, x)) -> x 1184.27/297.09 , head(add(n, x)) -> n 1184.27/297.09 , app(nil(), y) -> y 1184.27/297.09 , app(add(n, x), y) -> add(n, app(x, y)) 1184.27/297.09 , reverse(nil()) -> nil() 1184.27/297.09 , reverse(add(n, x)) -> app(reverse(x), add(n, nil())) 1184.27/297.09 , shuffle(x) -> shuff(x, nil()) 1184.27/297.09 , shuff(x, y) -> if(null(x), x, y, app(y, add(head(x), nil()))) 1184.27/297.09 , if(true(), x, y, z) -> y 1184.27/297.09 , if(false(), x, y, z) -> shuff(reverse(tail(x)), z) } 1184.27/297.09 Obligation: 1184.27/297.09 runtime complexity 1184.27/297.09 Answer: 1184.27/297.09 MAYBE 1184.27/297.09 1184.27/297.09 We estimate the number of application of {1,2,3,8} by applications 1184.27/297.09 of Pre({1,2,3,8}) = {4,5,6,7,12}. Here rules are labeled as 1184.27/297.09 follows: 1184.27/297.09 1184.27/297.09 DPs: 1184.27/297.09 { 1: null^#(nil()) -> c_1() 1184.27/297.09 , 2: null^#(add(n, x)) -> c_2() 1184.27/297.09 , 3: tail^#(nil()) -> c_3() 1184.27/297.09 , 4: tail^#(add(n, x)) -> c_4(x) 1184.27/297.09 , 5: head^#(add(n, x)) -> c_5(n) 1184.27/297.09 , 6: app^#(nil(), y) -> c_6(y) 1184.27/297.09 , 7: app^#(add(n, x), y) -> c_7(n, app^#(x, y)) 1184.27/297.09 , 8: reverse^#(nil()) -> c_8() 1184.27/297.09 , 9: reverse^#(add(n, x)) -> c_9(app^#(reverse(x), add(n, nil()))) 1184.27/297.09 , 10: shuffle^#(x) -> c_10(shuff^#(x, nil())) 1184.27/297.09 , 11: shuff^#(x, y) -> 1184.27/297.09 c_11(if^#(null(x), x, y, app(y, add(head(x), nil())))) 1184.27/297.09 , 12: if^#(true(), x, y, z) -> c_12(y) 1184.27/297.09 , 13: if^#(false(), x, y, z) -> 1184.27/297.09 c_13(shuff^#(reverse(tail(x)), z)) } 1184.27/297.09 1184.27/297.09 We are left with following problem, upon which TcT provides the 1184.27/297.09 certificate MAYBE. 1184.27/297.09 1184.27/297.09 Strict DPs: 1184.27/297.09 { tail^#(add(n, x)) -> c_4(x) 1184.27/297.09 , head^#(add(n, x)) -> c_5(n) 1184.27/297.09 , app^#(nil(), y) -> c_6(y) 1184.27/297.09 , app^#(add(n, x), y) -> c_7(n, app^#(x, y)) 1184.27/297.09 , reverse^#(add(n, x)) -> c_9(app^#(reverse(x), add(n, nil()))) 1184.27/297.09 , shuffle^#(x) -> c_10(shuff^#(x, nil())) 1184.27/297.09 , shuff^#(x, y) -> 1184.27/297.09 c_11(if^#(null(x), x, y, app(y, add(head(x), nil())))) 1184.27/297.09 , if^#(true(), x, y, z) -> c_12(y) 1184.27/297.09 , if^#(false(), x, y, z) -> c_13(shuff^#(reverse(tail(x)), z)) } 1184.27/297.09 Strict Trs: 1184.27/297.09 { null(nil()) -> true() 1184.27/297.09 , null(add(n, x)) -> false() 1184.27/297.09 , tail(nil()) -> nil() 1184.27/297.09 , tail(add(n, x)) -> x 1184.27/297.09 , head(add(n, x)) -> n 1184.27/297.09 , app(nil(), y) -> y 1184.27/297.09 , app(add(n, x), y) -> add(n, app(x, y)) 1184.27/297.09 , reverse(nil()) -> nil() 1184.27/297.09 , reverse(add(n, x)) -> app(reverse(x), add(n, nil())) 1184.27/297.09 , shuffle(x) -> shuff(x, nil()) 1184.27/297.09 , shuff(x, y) -> if(null(x), x, y, app(y, add(head(x), nil()))) 1184.27/297.09 , if(true(), x, y, z) -> y 1184.27/297.09 , if(false(), x, y, z) -> shuff(reverse(tail(x)), z) } 1184.27/297.09 Weak DPs: 1184.27/297.09 { null^#(nil()) -> c_1() 1184.27/297.09 , null^#(add(n, x)) -> c_2() 1184.27/297.09 , tail^#(nil()) -> c_3() 1184.27/297.09 , reverse^#(nil()) -> c_8() } 1184.27/297.09 Obligation: 1184.27/297.09 runtime complexity 1184.27/297.09 Answer: 1184.27/297.09 MAYBE 1184.27/297.09 1184.27/297.09 Empty strict component of the problem is NOT empty. 1184.27/297.09 1184.27/297.09 1184.27/297.09 Arrrr.. 1185.70/298.22 EOF