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TRS Innermost pair #487524327
details
property
value
status
complete
benchmark
Ex3_3_25_Bor03_L.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n093.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.64093899727 seconds
cpu usage
3.635732396
max memory
2.30309888E8
stage attributes
key
value
output-size
3050
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 64 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4)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: app(nil, YS) -> YS app(cons(X), YS) -> cons(X) from(X) -> cons(X) zWadr(nil, YS) -> nil zWadr(XS, nil) -> nil zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X))) prefix(L) -> cons(nil) The set Q consists of the following terms: app(nil, x0) app(cons(x0), x1) from(x0) zWadr(nil, x0) zWadr(x0, nil) zWadr(cons(x0), cons(x1)) prefix(x0) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(app(x_1, x_2)) = 2*x_1 + x_2 POL(cons(x_1)) = 2*x_1 POL(from(x_1)) = 1 + 2*x_1 POL(nil) = 0 POL(prefix(x_1)) = 2 + x_1 POL(zWadr(x_1, x_2)) = 2*x_1 + 2*x_2 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: from(X) -> cons(X) prefix(L) -> cons(nil) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(nil, YS) -> YS app(cons(X), YS) -> cons(X) zWadr(nil, YS) -> nil zWadr(XS, nil) -> nil zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X))) The set Q consists of the following terms: app(nil, x0) app(cons(x0), x1) from(x0) zWadr(nil, x0) zWadr(x0, nil) zWadr(cons(x0), cons(x1)) prefix(x0) ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:app_2 > zWadr_2 > cons_1 > nil and weight map:
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