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TRS Relat 75837 pair #381725083
details
property
value
status
complete
benchmark
#3.17_mset.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n020.star.cs.uiowa.edu
space
INVY_15
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.95336294174 seconds
cpu usage
8.676762164
max memory
1.122816E9
stage attributes
key
value
output-size
7785
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 57 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 7 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 29 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 24 ms] (8) RelTRS (9) RelTRSRRRProof [EQUIVALENT, 29 ms] (10) RelTRS (11) RelTRSRRRProof [EQUIVALENT, 0 ms] (12) RelTRS (13) RIsEmptyProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: 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(plus(x, y), l)) sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) The relative TRS consists of the following S rules: cons(x, cons(y, l)) -> cons(y, cons(x, l)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(0) = 0 POL(app(x_1, x_2)) = x_1 + x_2 POL(cons(x_1, x_2)) = 1 + x_1 + x_2 POL(nil) = 1 POL(plus(x_1, x_2)) = 1 + x_1 + x_2 POL(s(x_1)) = x_1 POL(sum(x_1)) = x_1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: app(nil, k) -> k app(l, nil) -> l plus(0, y) -> y Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: 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(plus(x, y), l)) sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) plus(s(x), y) -> s(plus(x, y)) The relative TRS consists of the following S rules: cons(x, cons(y, l)) -> cons(y, cons(x, l)) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]:
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