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TRS Stand 20472 pair #381712318
details
property
value
status
complete
benchmark
secret4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n035.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.73088693619 seconds
cpu usage
3.99671224
max memory
2.3719936E8
stage attributes
key
value
output-size
3115
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 175 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4)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: a(h, h, h, x) -> s(x) a(l, x, s(y), h) -> a(l, x, y, s(h)) a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z)) a(l, s(x), h, z) -> a(l, x, z, z) a(s(l), h, h, z) -> a(l, z, h, z) +(x, h) -> x +(h, x) -> x +(s(x), s(y)) -> s(s(+(x, y))) +(+(x, y), z) -> +(x, +(y, z)) s(h) -> 1 app(nil, k) -> k app(l, nil) -> l app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, nil)) -> cons(x, nil) sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h, h), l)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: a/4(YES,YES,YES,YES) h/0) s/1(YES) +/2(YES,YES) 1/0) app/2(YES,YES) nil/0) cons/2(YES,YES) sum/1)YES( Quasi precedence: +_2 > [s_1, 1] > h app_2 > cons_2 > a_4 > [s_1, 1] > h app_2 > cons_2 > nil Status: a_4: [1,2,3,4] h: multiset status s_1: [1] +_2: [1,2] 1: multiset status app_2: [2,1] nil: multiset status cons_2: [2,1] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a(h, h, h, x) -> s(x) a(l, x, s(y), h) -> a(l, x, y, s(h)) a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z)) a(l, s(x), h, z) -> a(l, x, z, z) a(s(l), h, h, z) -> a(l, z, h, z) +(x, h) -> x +(h, x) -> x +(s(x), s(y)) -> s(s(+(x, y))) +(+(x, y), z) -> +(x, +(y, z)) s(h) -> 1 app(nil, k) -> k app(l, nil) -> l app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h, h), l)) ---------------------------------------- (2)
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