Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Innermost pair #487524243
details
property
value
status
complete
benchmark
Ex4_4_Luc96b_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.93508005142 seconds
cpu usage
4.508256057
max memory
3.16719104E8
stage attributes
key
value
output-size
7458
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) QDPQMonotonicMRRProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) QDPOrderProof [EQUIVALENT, 15 ms] (16) QDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y)) mark(f(X1, X2)) -> a__f(mark(X1), X2) mark(g(X)) -> g(mark(X)) a__f(X1, X2) -> f(X1, X2) The set Q consists of the following terms: mark(f(x0, x1)) mark(g(x0)) a__f(x0, x1) ---------------------------------------- (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: A__F(g(X), Y) -> A__F(mark(X), f(g(X), Y)) A__F(g(X), Y) -> MARK(X) MARK(f(X1, X2)) -> A__F(mark(X1), X2) MARK(f(X1, X2)) -> MARK(X1) MARK(g(X)) -> MARK(X) The TRS R consists of the following rules: a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y)) mark(f(X1, X2)) -> a__f(mark(X1), X2) mark(g(X)) -> g(mark(X)) a__f(X1, X2) -> f(X1, X2) The set Q consists of the following terms: mark(f(x0, x1)) mark(g(x0)) a__f(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) QDPQMonotonicMRRProof (EQUIVALENT) By using the Q-monotonic rule removal processor with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented such that it always occurs at a strongly monotonic position in a (P,Q,R)-chain. Strictly oriented dependency pairs: MARK(f(X1, X2)) -> A__F(mark(X1), X2) MARK(f(X1, X2)) -> MARK(X1) Used ordering: Polynomial interpretation [POLO]: POL(A__F(x_1, x_2)) = 2*x_1 POL(MARK(x_1)) = 2*x_1 POL(a__f(x_1, x_2)) = 2 + 2*x_1
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Innermost