MAYBE 794.81/297.04 MAYBE 794.81/297.04 794.81/297.04 We are left with following problem, upon which TcT provides the 794.81/297.04 certificate MAYBE. 794.81/297.04 794.81/297.04 Strict Trs: 794.81/297.04 { if(true(), t, e) -> t 794.81/297.04 , if(false(), t, e) -> e 794.81/297.04 , member(x, nil()) -> false() 794.81/297.04 , member(x, cons(y, ys)) -> if(eq(x, y), true(), member(x, ys)) 794.81/297.04 , eq(nil(), nil()) -> true() 794.81/297.04 , eq(O(x), 0(y)) -> eq(x, y) 794.81/297.04 , eq(0(x), 1(y)) -> false() 794.81/297.04 , eq(1(x), 0(y)) -> false() 794.81/297.04 , eq(1(x), 1(y)) -> eq(x, y) 794.81/297.04 , negate(0(x)) -> 1(x) 794.81/297.04 , negate(1(x)) -> 0(x) 794.81/297.04 , choice(cons(x, xs)) -> x 794.81/297.04 , choice(cons(x, xs)) -> choice(xs) 794.81/297.04 , guess(nil()) -> nil() 794.81/297.04 , guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf)) 794.81/297.04 , verify(nil()) -> true() 794.81/297.04 , verify(cons(l, ls)) -> 794.81/297.04 if(member(negate(l), ls), false(), verify(ls)) 794.81/297.04 , sat(cnf) -> satck(cnf, guess(cnf)) 794.81/297.04 , satck(cnf, assign) -> if(verify(assign), assign, unsat()) } 794.81/297.04 Obligation: 794.81/297.04 runtime complexity 794.81/297.04 Answer: 794.81/297.04 MAYBE 794.81/297.04 794.81/297.04 None of the processors succeeded. 794.81/297.04 794.81/297.04 Details of failed attempt(s): 794.81/297.04 ----------------------------- 794.81/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 794.81/297.04 following reason: 794.81/297.04 794.81/297.04 Computation stopped due to timeout after 297.0 seconds. 794.81/297.04 794.81/297.04 2) 'Best' failed due to the following reason: 794.81/297.04 794.81/297.04 None of the processors succeeded. 794.81/297.04 794.81/297.04 Details of failed attempt(s): 794.81/297.04 ----------------------------- 794.81/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 794.81/297.04 seconds)' failed due to the following reason: 794.81/297.04 794.81/297.04 Computation stopped due to timeout after 148.0 seconds. 794.81/297.04 794.81/297.04 2) 'Best' failed due to the following reason: 794.81/297.04 794.81/297.04 None of the processors succeeded. 794.81/297.04 794.81/297.04 Details of failed attempt(s): 794.81/297.04 ----------------------------- 794.81/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 794.81/297.04 following reason: 794.81/297.04 794.81/297.04 The processor is inapplicable, reason: 794.81/297.04 Processor only applicable for innermost runtime complexity analysis 794.81/297.04 794.81/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 794.81/297.04 to the following reason: 794.81/297.04 794.81/297.04 The processor is inapplicable, reason: 794.81/297.04 Processor only applicable for innermost runtime complexity analysis 794.81/297.04 794.81/297.04 794.81/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 794.81/297.04 failed due to the following reason: 794.81/297.04 794.81/297.04 None of the processors succeeded. 794.81/297.04 794.81/297.04 Details of failed attempt(s): 794.81/297.04 ----------------------------- 794.81/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 794.81/297.04 failed due to the following reason: 794.81/297.04 794.81/297.04 match-boundness of the problem could not be verified. 794.81/297.04 794.81/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 794.81/297.04 failed due to the following reason: 794.81/297.04 794.81/297.04 match-boundness of the problem could not be verified. 794.81/297.04 794.81/297.04 794.81/297.04 794.81/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 794.81/297.04 the following reason: 794.81/297.04 794.81/297.04 We add the following weak dependency pairs: 794.81/297.04 794.81/297.04 Strict DPs: 794.81/297.04 { if^#(true(), t, e) -> c_1(t) 794.81/297.04 , if^#(false(), t, e) -> c_2(e) 794.81/297.04 , member^#(x, nil()) -> c_3() 794.81/297.04 , member^#(x, cons(y, ys)) -> 794.81/297.04 c_4(if^#(eq(x, y), true(), member(x, ys))) 794.81/297.04 , eq^#(nil(), nil()) -> c_5() 794.81/297.04 , eq^#(O(x), 0(y)) -> c_6(eq^#(x, y)) 794.81/297.04 , eq^#(0(x), 1(y)) -> c_7() 794.81/297.04 , eq^#(1(x), 0(y)) -> c_8() 794.81/297.04 , eq^#(1(x), 1(y)) -> c_9(eq^#(x, y)) 794.81/297.04 , negate^#(0(x)) -> c_10(x) 794.81/297.04 , negate^#(1(x)) -> c_11(x) 794.81/297.04 , choice^#(cons(x, xs)) -> c_12(x) 794.81/297.04 , choice^#(cons(x, xs)) -> c_13(choice^#(xs)) 794.81/297.04 , guess^#(nil()) -> c_14() 794.81/297.04 , guess^#(cons(clause, cnf)) -> 794.81/297.04 c_15(choice^#(clause), guess^#(cnf)) 794.81/297.04 , verify^#(nil()) -> c_16() 794.81/297.04 , verify^#(cons(l, ls)) -> 794.81/297.04 c_17(if^#(member(negate(l), ls), false(), verify(ls))) 794.81/297.04 , sat^#(cnf) -> c_18(satck^#(cnf, guess(cnf))) 794.81/297.04 , satck^#(cnf, assign) -> 794.81/297.04 c_19(if^#(verify(assign), assign, unsat())) } 794.81/297.04 794.81/297.04 and mark the set of starting terms. 794.81/297.04 794.81/297.04 We are left with following problem, upon which TcT provides the 794.81/297.04 certificate MAYBE. 794.81/297.04 794.81/297.04 Strict DPs: 794.81/297.04 { if^#(true(), t, e) -> c_1(t) 794.81/297.04 , if^#(false(), t, e) -> c_2(e) 794.81/297.04 , member^#(x, nil()) -> c_3() 794.81/297.04 , member^#(x, cons(y, ys)) -> 794.81/297.04 c_4(if^#(eq(x, y), true(), member(x, ys))) 794.81/297.04 , eq^#(nil(), nil()) -> c_5() 794.81/297.04 , eq^#(O(x), 0(y)) -> c_6(eq^#(x, y)) 794.81/297.04 , eq^#(0(x), 1(y)) -> c_7() 794.81/297.04 , eq^#(1(x), 0(y)) -> c_8() 794.81/297.04 , eq^#(1(x), 1(y)) -> c_9(eq^#(x, y)) 794.81/297.04 , negate^#(0(x)) -> c_10(x) 794.81/297.04 , negate^#(1(x)) -> c_11(x) 794.81/297.04 , choice^#(cons(x, xs)) -> c_12(x) 794.81/297.04 , choice^#(cons(x, xs)) -> c_13(choice^#(xs)) 794.81/297.04 , guess^#(nil()) -> c_14() 794.81/297.04 , guess^#(cons(clause, cnf)) -> 794.81/297.04 c_15(choice^#(clause), guess^#(cnf)) 794.81/297.04 , verify^#(nil()) -> c_16() 794.81/297.04 , verify^#(cons(l, ls)) -> 794.81/297.04 c_17(if^#(member(negate(l), ls), false(), verify(ls))) 794.81/297.04 , sat^#(cnf) -> c_18(satck^#(cnf, guess(cnf))) 794.81/297.04 , satck^#(cnf, assign) -> 794.81/297.04 c_19(if^#(verify(assign), assign, unsat())) } 794.81/297.04 Strict Trs: 794.81/297.04 { if(true(), t, e) -> t 794.81/297.04 , if(false(), t, e) -> e 794.81/297.04 , member(x, nil()) -> false() 794.81/297.04 , member(x, cons(y, ys)) -> if(eq(x, y), true(), member(x, ys)) 794.81/297.04 , eq(nil(), nil()) -> true() 794.81/297.04 , eq(O(x), 0(y)) -> eq(x, y) 794.81/297.04 , eq(0(x), 1(y)) -> false() 794.81/297.04 , eq(1(x), 0(y)) -> false() 794.81/297.04 , eq(1(x), 1(y)) -> eq(x, y) 794.81/297.04 , negate(0(x)) -> 1(x) 794.81/297.04 , negate(1(x)) -> 0(x) 794.81/297.04 , choice(cons(x, xs)) -> x 794.81/297.04 , choice(cons(x, xs)) -> choice(xs) 794.81/297.04 , guess(nil()) -> nil() 794.81/297.04 , guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf)) 794.81/297.04 , verify(nil()) -> true() 794.81/297.04 , verify(cons(l, ls)) -> 794.81/297.04 if(member(negate(l), ls), false(), verify(ls)) 794.81/297.04 , sat(cnf) -> satck(cnf, guess(cnf)) 794.81/297.04 , satck(cnf, assign) -> if(verify(assign), assign, unsat()) } 794.81/297.04 Obligation: 794.81/297.04 runtime complexity 794.81/297.04 Answer: 794.81/297.04 MAYBE 794.81/297.04 794.81/297.04 We estimate the number of application of {3,5,7,8,14,16} by 794.81/297.04 applications of Pre({3,5,7,8,14,16}) = {1,2,6,9,10,11,12,15}. Here 794.81/297.04 rules are labeled as follows: 794.81/297.04 794.81/297.04 DPs: 794.81/297.04 { 1: if^#(true(), t, e) -> c_1(t) 794.81/297.04 , 2: if^#(false(), t, e) -> c_2(e) 794.81/297.04 , 3: member^#(x, nil()) -> c_3() 794.81/297.04 , 4: member^#(x, cons(y, ys)) -> 794.81/297.04 c_4(if^#(eq(x, y), true(), member(x, ys))) 794.81/297.04 , 5: eq^#(nil(), nil()) -> c_5() 794.81/297.04 , 6: eq^#(O(x), 0(y)) -> c_6(eq^#(x, y)) 794.81/297.04 , 7: eq^#(0(x), 1(y)) -> c_7() 794.81/297.04 , 8: eq^#(1(x), 0(y)) -> c_8() 794.81/297.04 , 9: eq^#(1(x), 1(y)) -> c_9(eq^#(x, y)) 794.81/297.04 , 10: negate^#(0(x)) -> c_10(x) 794.81/297.04 , 11: negate^#(1(x)) -> c_11(x) 794.81/297.04 , 12: choice^#(cons(x, xs)) -> c_12(x) 794.81/297.04 , 13: choice^#(cons(x, xs)) -> c_13(choice^#(xs)) 794.81/297.04 , 14: guess^#(nil()) -> c_14() 794.81/297.04 , 15: guess^#(cons(clause, cnf)) -> 794.81/297.04 c_15(choice^#(clause), guess^#(cnf)) 794.81/297.04 , 16: verify^#(nil()) -> c_16() 794.81/297.04 , 17: verify^#(cons(l, ls)) -> 794.81/297.04 c_17(if^#(member(negate(l), ls), false(), verify(ls))) 794.81/297.04 , 18: sat^#(cnf) -> c_18(satck^#(cnf, guess(cnf))) 794.81/297.04 , 19: satck^#(cnf, assign) -> 794.81/297.04 c_19(if^#(verify(assign), assign, unsat())) } 794.81/297.04 794.81/297.04 We are left with following problem, upon which TcT provides the 794.81/297.04 certificate MAYBE. 794.81/297.04 794.81/297.04 Strict DPs: 794.81/297.04 { if^#(true(), t, e) -> c_1(t) 794.81/297.04 , if^#(false(), t, e) -> c_2(e) 794.81/297.04 , member^#(x, cons(y, ys)) -> 794.81/297.04 c_4(if^#(eq(x, y), true(), member(x, ys))) 794.81/297.04 , eq^#(O(x), 0(y)) -> c_6(eq^#(x, y)) 794.81/297.04 , eq^#(1(x), 1(y)) -> c_9(eq^#(x, y)) 794.81/297.04 , negate^#(0(x)) -> c_10(x) 794.81/297.04 , negate^#(1(x)) -> c_11(x) 794.81/297.04 , choice^#(cons(x, xs)) -> c_12(x) 794.81/297.04 , choice^#(cons(x, xs)) -> c_13(choice^#(xs)) 794.81/297.04 , guess^#(cons(clause, cnf)) -> 794.81/297.04 c_15(choice^#(clause), guess^#(cnf)) 794.81/297.04 , verify^#(cons(l, ls)) -> 794.81/297.04 c_17(if^#(member(negate(l), ls), false(), verify(ls))) 794.81/297.04 , sat^#(cnf) -> c_18(satck^#(cnf, guess(cnf))) 794.81/297.04 , satck^#(cnf, assign) -> 794.81/297.04 c_19(if^#(verify(assign), assign, unsat())) } 794.81/297.04 Strict Trs: 794.81/297.04 { if(true(), t, e) -> t 794.81/297.04 , if(false(), t, e) -> e 794.81/297.04 , member(x, nil()) -> false() 794.81/297.04 , member(x, cons(y, ys)) -> if(eq(x, y), true(), member(x, ys)) 794.81/297.04 , eq(nil(), nil()) -> true() 794.81/297.04 , eq(O(x), 0(y)) -> eq(x, y) 794.81/297.04 , eq(0(x), 1(y)) -> false() 794.81/297.04 , eq(1(x), 0(y)) -> false() 794.81/297.04 , eq(1(x), 1(y)) -> eq(x, y) 794.81/297.04 , negate(0(x)) -> 1(x) 794.81/297.04 , negate(1(x)) -> 0(x) 794.81/297.04 , choice(cons(x, xs)) -> x 794.81/297.04 , choice(cons(x, xs)) -> choice(xs) 794.81/297.04 , guess(nil()) -> nil() 794.81/297.04 , guess(cons(clause, cnf)) -> cons(choice(clause), guess(cnf)) 794.81/297.04 , verify(nil()) -> true() 794.81/297.04 , verify(cons(l, ls)) -> 794.81/297.04 if(member(negate(l), ls), false(), verify(ls)) 794.81/297.04 , sat(cnf) -> satck(cnf, guess(cnf)) 794.81/297.04 , satck(cnf, assign) -> if(verify(assign), assign, unsat()) } 794.81/297.04 Weak DPs: 794.81/297.04 { member^#(x, nil()) -> c_3() 794.81/297.04 , eq^#(nil(), nil()) -> c_5() 794.81/297.04 , eq^#(0(x), 1(y)) -> c_7() 794.81/297.04 , eq^#(1(x), 0(y)) -> c_8() 794.81/297.04 , guess^#(nil()) -> c_14() 794.81/297.04 , verify^#(nil()) -> c_16() } 794.81/297.04 Obligation: 794.81/297.04 runtime complexity 794.81/297.04 Answer: 794.81/297.04 MAYBE 794.81/297.04 794.81/297.04 Empty strict component of the problem is NOT empty. 794.81/297.04 794.81/297.04 794.81/297.04 Arrrr.. 795.03/297.25 EOF