details

property	value
status	complete
benchmark	MYNAT_nokinds_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.86449 seconds
cpu usage	4.43382
user time	4.23762
system time	0.196207
max virtual memory	1.835054E7
max residence set size	269484.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 184 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: U11(tt, N) -> activate(N) U21(tt, M, N) -> s(plus(activate(N), activate(M))) U31(tt) -> 0 U41(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) and(tt, X) -> activate(X) isNat(n__0) -> tt isNat(n__plus(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) isNat(n__s(V1)) -> isNat(activate(V1)) isNat(n__x(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) plus(N, 0) -> U11(isNat(N), N) plus(N, s(M)) -> U21(and(isNat(M), n__isNat(N)), M, N) x(N, 0) -> U31(isNat(N)) x(N, s(M)) -> U41(and(isNat(M), n__isNat(N)), M, N) 0 -> n__0 plus(X1, X2) -> n__plus(X1, X2) isNat(X) -> n__isNat(X) s(X) -> n__s(X) x(X1, X2) -> n__x(X1, X2) activate(n__0) -> 0 activate(n__plus(X1, X2)) -> plus(X1, X2) activate(n__isNat(X)) -> isNat(X) activate(n__s(X)) -> s(X) activate(n__x(X1, X2)) -> x(X1, X2) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: U11/2(YES,YES) tt/0) activate/1)YES( U21/3(YES,YES,YES) s/1(YES) plus/2(YES,YES) U31/1)YES( 0/0) U41/3(YES,YES,YES) x/2(YES,YES) and/2(YES,YES) isNat/1)YES( n__0/0) n__plus/2(YES,YES) n__isNat/1)YES( n__s/1(YES) n__x/2(YES,YES) Quasi precedence: [tt, 0, n__0] > [U41_3, x_2, n__x_2] > [U21_3, plus_2, n__plus_2] > [U11_2, s_1, and_2, n__s_1] Status: U11_2: multiset status tt: multiset status U21_3: [2,3,1] s_1: multiset status plus_2: [2,1] 0: multiset status U41_3: [2,3,1] x_2: [2,1] and_2: [1,2] n__0: multiset status n__plus_2: [2,1] n__s_1: multiset status n__x_2: [2,1] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: U11(tt, N) -> activate(N) U21(tt, M, N) -> s(plus(activate(N), activate(M))) U41(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) and(tt, X) -> activate(X) isNat(n__plus(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) isNat(n__s(V1)) -> isNat(activate(V1)) isNat(n__x(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) popout

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all output return to TRS Standard