Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Standard pair #516967185
details
property
value
status
complete
benchmark
#3.26.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
8.3033349514 seconds
cpu usage
16.820948601
max memory
1.25431808E9
stage attributes
key
value
output-size
2729
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) MNOCProof [EQUIVALENT, 0 ms] (4) QDP (5) MRRProof [EQUIVALENT, 25 ms] (6) QDP (7) PisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x) -> s(x) f(s(s(x))) -> s(f(f(x))) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: F(s(s(x))) -> F(f(x)) F(s(s(x))) -> F(x) The TRS R consists of the following rules: f(x) -> s(x) f(s(s(x))) -> s(f(f(x))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) MNOCProof (EQUIVALENT) We use the modular non-overlap check [LPAR04] to enlarge Q to all left-hand sides of R. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(s(s(x))) -> F(f(x)) F(s(s(x))) -> F(x) The TRS R consists of the following rules: f(x) -> s(x) f(s(s(x))) -> s(f(f(x))) The set Q consists of the following terms: f(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: F(s(s(x))) -> F(f(x)) F(s(s(x))) -> F(x) Used ordering: Polynomial interpretation [POLO]: POL(F(x_1)) = 2*x_1 POL(f(x_1)) = 2 + x_1 POL(s(x_1)) = 2 + x_1 ----------------------------------------
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Standard