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TRS Standard pair #487069753
details
property
value
status
complete
benchmark
Ex8_BLR02_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n179.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.69873 seconds
cpu usage
3.86281
user time
3.65858
system time
0.204223
max virtual memory
1.8408912E7
max residence set size
240968.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 57 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4)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, 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) activate(n__fib1(X1, X2)) -> fib1(X1, X2) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: [fib_1, 0] > sel_2 > activate_1 > fib1_2 > cons_2 > n__fib1_2 [fib_1, 0] > sel_2 > activate_1 > fib1_2 > add_2 > s_1 > n__fib1_2 Status: fib_1: [1] sel_2: [1,2] fib1_2: multiset status s_1: multiset status 0: multiset status cons_2: multiset status n__fib1_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, 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) activate(n__fib1(X1, X2)) -> fib1(X1, 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
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