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TRS Standard pair #487069448
details
property
value
status
complete
benchmark
PEANO_nokinds_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.02799 seconds
cpu usage
4.26614
user time
4.08129
system time
0.184848
max virtual memory
1.8408912E7
max residence set size
255276.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 107 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 1 ms] (4)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))) 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)) plus(N, 0) -> U11(isNat(N), N) plus(N, s(M)) -> U21(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) 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(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) and/2(YES,YES) isNat/1)YES( n__0/0) n__plus/2(YES,YES) n__isNat/1)YES( n__s/1(YES) 0/0) Quasi precedence: [U21_3, plus_2, n__plus_2] > [U11_2, n__0, 0] > [tt, s_1, n__s_1] [U21_3, plus_2, n__plus_2] > and_2 Status: U11_2: multiset status tt: multiset status U21_3: [3,2,1] s_1: multiset status plus_2: [1,2] and_2: multiset status n__0: multiset status n__plus_2: [1,2] n__s_1: multiset status 0: multiset status 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))) 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)) plus(N, 0) -> U11(isNat(N), N) plus(N, s(M)) -> U21(and(isNat(M), n__isNat(N)), M, N) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 0 -> n__0
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