Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Standard pair #516962110
details
property
value
status
complete
benchmark
PEANO_nokinds_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n095.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
4.95011687279 seconds
cpu usage
6.057806127
max memory
4.79305728E8
stage attributes
key
value
output-size
4704
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 182 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 3 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__U11(tt, N) -> mark(N) a__U21(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__and(tt, X) -> mark(X) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) a__isNat(s(V1)) -> a__isNat(V1) a__plus(N, 0) -> a__U11(a__isNat(N), N) a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2) -> U11(X1, X2) a__U21(X1, X2, X3) -> U21(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNat(X) -> isNat(X) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: a__U11/2(YES,YES) tt/0) mark/1)YES( a__U21/3(YES,YES,YES) s/1(YES) a__plus/2(YES,YES) a__and/2(YES,YES) a__isNat/1(YES) 0/0) plus/2(YES,YES) isNat/1(YES) U11/2(YES,YES) U21/3(YES,YES,YES) and/2(YES,YES) Quasi precedence: 0 > tt > [a__U21_3, a__plus_2, plus_2, U21_3] > [a__U11_2, U11_2] > s_1 0 > tt > [a__U21_3, a__plus_2, plus_2, U21_3] > [a__and_2, a__isNat_1, isNat_1, and_2] > s_1 Status: a__U11_2: [2,1] tt: multiset status a__U21_3: [3,2,1] s_1: multiset status a__plus_2: [1,2] a__and_2: multiset status a__isNat_1: multiset status 0: multiset status plus_2: [1,2] isNat_1: multiset status U11_2: [2,1] U21_3: [3,2,1] and_2: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a__U11(tt, N) -> mark(N) a__U21(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__and(tt, X) -> mark(X) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) a__isNat(s(V1)) -> a__isNat(V1)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Standard