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TRS Standard pair #516963565
details
property
value
status
complete
benchmark
PALINDROME_nosorts_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n090.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.18294215202 seconds
cpu usage
5.681440441
max memory
4.69344256E8
stage attributes
key
value
output-size
5788
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 48 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 0 ms] (6) CSR (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) active(__(X, nil)) -> mark(X) active(__(nil, X)) -> mark(X) active(and(tt, X)) -> mark(X) active(isNePal(__(I, __(P, I)))) -> mark(tt) active(__(X1, X2)) -> __(active(X1), X2) active(__(X1, X2)) -> __(X1, active(X2)) active(and(X1, X2)) -> and(active(X1), X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1), X2) -> mark(__(X1, X2)) __(X1, mark(X2)) -> mark(__(X1, X2)) and(mark(X1), X2) -> mark(and(X1, X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1, X2)) -> __(proper(X1), proper(X2)) proper(nil) -> ok(nil) proper(and(X1, X2)) -> and(proper(X1), proper(X2)) proper(tt) -> ok(tt) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1), ok(X2)) -> ok(__(X1, X2)) and(ok(X1), ok(X2)) -> ok(and(X1, X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Q is empty. ---------------------------------------- (1) QTRSToCSRProof (EQUIVALENT) The following Q TRS is given: Q restricted rewrite system: The TRS R consists of the following rules: active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) active(__(X, nil)) -> mark(X) active(__(nil, X)) -> mark(X) active(and(tt, X)) -> mark(X) active(isNePal(__(I, __(P, I)))) -> mark(tt) active(__(X1, X2)) -> __(active(X1), X2) active(__(X1, X2)) -> __(X1, active(X2)) active(and(X1, X2)) -> and(active(X1), X2) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1), X2) -> mark(__(X1, X2)) __(X1, mark(X2)) -> mark(__(X1, X2)) and(mark(X1), X2) -> mark(and(X1, X2)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1, X2)) -> __(proper(X1), proper(X2)) proper(nil) -> ok(nil) proper(and(X1, X2)) -> and(proper(X1), proper(X2)) proper(tt) -> ok(tt) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1), ok(X2)) -> ok(__(X1, X2)) and(ok(X1), ok(X2)) -> ok(and(X1, X2)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Q is empty. Special symbols used for the transformation (see [GM04]): top: top_1, active: active_1, mark: mark_1, ok: ok_1, proper: proper_1 The replacement map contains the following entries: __: {1, 2} nil: empty set and: {1} tt: empty set isNePal: {1} The QTRS contained all rules created by the complete Giesl-Middeldorp transformation. Therefore, the inverse transformation is complete (and sound). ----------------------------------------
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