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TRS Stand 20472 pair #381716657
details
property
value
status
complete
benchmark
ExSec11_1_Luc02a_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n057.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.72669482231 seconds
cpu usage
3.832138519
max memory
2.3955456E8
stage attributes
key
value
output-size
3555
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 153 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4)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: terms(N) -> cons(recip(sqr(N)), n__terms(s(N))) sqr(0) -> 0 sqr(s(X)) -> s(add(sqr(X), dbl(X))) dbl(0) -> 0 dbl(s(X)) -> s(s(dbl(X))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) half(0) -> 0 half(s(0)) -> 0 half(s(s(X))) -> s(half(X)) half(dbl(X)) -> X terms(X) -> n__terms(X) first(X1, X2) -> n__first(X1, X2) activate(n__terms(X)) -> terms(X) activate(n__first(X1, X2)) -> first(X1, X2) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: terms/1(YES) cons/2(YES,YES) recip/1)YES( sqr/1(YES) n__terms/1)YES( s/1(YES) 0/0) add/2(YES,YES) dbl/1(YES) first/2(YES,YES) nil/0) n__first/2(YES,YES) activate/1(YES) half/1)YES( Quasi precedence: [terms_1, first_2, activate_1] > [cons_2, n__first_2] > nil [terms_1, first_2, activate_1] > [sqr_1, dbl_1] > add_2 > s_1 > 0 > nil Status: terms_1: multiset status cons_2: multiset status sqr_1: multiset status s_1: multiset status 0: multiset status add_2: [2,1] dbl_1: multiset status first_2: multiset status nil: multiset status n__first_2: multiset status activate_1: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: terms(N) -> cons(recip(sqr(N)), n__terms(s(N))) sqr(0) -> 0 sqr(s(X)) -> s(add(sqr(X), dbl(X))) dbl(0) -> 0 dbl(s(X)) -> s(s(dbl(X))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) half(s(0)) -> 0 half(s(s(X))) -> s(half(X))
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