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TRS Inner 89993 pair #381733835
details
property
value
status
complete
benchmark
MYNAT_nosorts_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n100.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.66689801216 seconds
cpu usage
3.664255583
max memory
2.3386112E8
stage attributes
key
value
output-size
10659
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [SOUND, 0 ms] (2) CSR (3) CSRInnermostProof [EQUIVALENT, 0 ms] (4) CSR (5) CSDependencyPairsProof [EQUIVALENT, 0 ms] (6) QCSDP (7) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QCSDP (10) QCSDPSubtermProof [EQUIVALENT, 21 ms] (11) QCSDP (12) PIsEmptyProof [EQUIVALENT, 0 ms] (13) YES (14) QCSDP (15) QCSDPSubtermProof [EQUIVALENT, 10 ms] (16) QCSDP (17) PIsEmptyProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(and(tt, X)) -> mark(X) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(s(plus(N, M))) active(x(N, 0)) -> mark(0) active(x(N, s(M))) -> mark(plus(x(N, M), N)) active(and(X1, X2)) -> and(active(X1), X2) active(plus(X1, X2)) -> plus(active(X1), X2) active(plus(X1, X2)) -> plus(X1, active(X2)) active(s(X)) -> s(active(X)) active(x(X1, X2)) -> x(active(X1), X2) active(x(X1, X2)) -> x(X1, active(X2)) and(mark(X1), X2) -> mark(and(X1, X2)) plus(mark(X1), X2) -> mark(plus(X1, X2)) plus(X1, mark(X2)) -> mark(plus(X1, X2)) s(mark(X)) -> mark(s(X)) x(mark(X1), X2) -> mark(x(X1, X2)) x(X1, mark(X2)) -> mark(x(X1, X2)) proper(and(X1, X2)) -> and(proper(X1), proper(X2)) proper(tt) -> ok(tt) proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) proper(0) -> ok(0) proper(s(X)) -> s(proper(X)) proper(x(X1, X2)) -> x(proper(X1), proper(X2)) and(ok(X1), ok(X2)) -> ok(and(X1, X2)) plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) s(ok(X)) -> ok(s(X)) x(ok(X1), ok(X2)) -> ok(x(X1, X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) The set Q consists of the following terms: active(and(x0, x1)) active(plus(x0, x1)) active(s(x0)) active(x(x0, x1)) and(mark(x0), x1) plus(mark(x0), x1) plus(x0, mark(x1)) s(mark(x0)) x(mark(x0), x1) x(x0, mark(x1)) proper(and(x0, x1)) proper(tt) proper(plus(x0, x1)) proper(0) proper(s(x0)) proper(x(x0, x1)) and(ok(x0), ok(x1)) plus(ok(x0), ok(x1)) s(ok(x0)) x(ok(x0), ok(x1)) top(mark(x0)) top(ok(x0)) ---------------------------------------- (1) QTRSToCSRProof (SOUND)
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