Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Stand 20472 pair #381716137
details
property
value
status
complete
benchmark
Ex8_BLR02_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n113.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.65666294098 seconds
cpu usage
3.705929211
max memory
2.0762624E8
stage attributes
key
value
output-size
2529
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 98 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: fib(N) -> sel(N, fib1(s(0), s(0))) fib1(X, Y) -> cons(X, n__fib1(Y, n__add(X, Y))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) sel(0, cons(X, XS)) -> X sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) fib1(X1, X2) -> n__fib1(X1, X2) add(X1, X2) -> n__add(X1, X2) activate(n__fib1(X1, X2)) -> fib1(activate(X1), activate(X2)) activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: fib_1 > sel_2 > activate_1 > fib1_2 > n__add_2 > [s_1, cons_2, n__fib1_2] fib_1 > sel_2 > activate_1 > add_2 > n__add_2 > [s_1, cons_2, n__fib1_2] fib_1 > 0 > [s_1, cons_2, n__fib1_2] Status: fib_1: multiset status sel_2: [1,2] fib1_2: multiset status s_1: multiset status 0: multiset status cons_2: multiset status n__fib1_2: multiset status n__add_2: multiset status add_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: fib(N) -> sel(N, fib1(s(0), s(0))) fib1(X, Y) -> cons(X, n__fib1(Y, n__add(X, Y))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) sel(0, cons(X, XS)) -> X sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) fib1(X1, X2) -> n__fib1(X1, X2) add(X1, X2) -> n__add(X1, X2) activate(n__fib1(X1, X2)) -> fib1(activate(X1), activate(X2)) activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) activate(X) -> X ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Stand 20472