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TRS Innermost pair #487524079
details
property
value
status
complete
benchmark
Ex4_4_Luc96b_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.89791989326 seconds
cpu usage
4.165810706
max memory
2.5032704E8
stage attributes
key
value
output-size
4837
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 60 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 15 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(f(g(X), Y)) -> mark(f(X, f(g(X), Y))) active(f(X1, X2)) -> f(active(X1), X2) active(g(X)) -> g(active(X)) f(mark(X1), X2) -> mark(f(X1, X2)) g(mark(X)) -> mark(g(X)) proper(f(X1, X2)) -> f(proper(X1), proper(X2)) proper(g(X)) -> g(proper(X)) f(ok(X1), ok(X2)) -> ok(f(X1, X2)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) The set Q consists of the following terms: active(f(x0, x1)) active(g(x0)) f(mark(x0), x1) g(mark(x0)) proper(f(x0, x1)) proper(g(x0)) f(ok(x0), ok(x1)) g(ok(x0)) top(mark(x0)) top(ok(x0)) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(active(x_1)) = 1 + 2*x_1 POL(f(x_1, x_2)) = x_1 + x_2 POL(g(x_1)) = x_1 POL(mark(x_1)) = x_1 POL(ok(x_1)) = 1 + 2*x_1 POL(proper(x_1)) = x_1 POL(top(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: active(f(g(X), Y)) -> mark(f(X, f(g(X), Y))) f(ok(X1), ok(X2)) -> ok(f(X1, X2)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(f(X1, X2)) -> f(active(X1), X2) active(g(X)) -> g(active(X)) f(mark(X1), X2) -> mark(f(X1, X2)) g(mark(X)) -> mark(g(X)) proper(f(X1, X2)) -> f(proper(X1), proper(X2)) proper(g(X)) -> g(proper(X)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) The set Q consists of the following terms: active(f(x0, x1)) active(g(x0)) f(mark(x0), x1)
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