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TRS Standard pair #516961935
details
property
value
status
complete
benchmark
Ex2_Luc03b_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n077.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.14540505409 seconds
cpu usage
5.614159608
max memory
4.75041792E8
stage attributes
key
value
output-size
6215
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 82 ms] (4) CSR (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(fst(0, Z)) -> mark(nil) active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))) active(from(X)) -> mark(cons(X, from(s(X)))) active(add(0, X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(len(nil)) -> mark(0) active(len(cons(X, Z))) -> mark(s(len(Z))) active(cons(X1, X2)) -> cons(active(X1), X2) active(fst(X1, X2)) -> fst(active(X1), X2) active(fst(X1, X2)) -> fst(X1, active(X2)) active(from(X)) -> from(active(X)) active(add(X1, X2)) -> add(active(X1), X2) active(add(X1, X2)) -> add(X1, active(X2)) active(len(X)) -> len(active(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) fst(mark(X1), X2) -> mark(fst(X1, X2)) fst(X1, mark(X2)) -> mark(fst(X1, X2)) from(mark(X)) -> mark(from(X)) add(mark(X1), X2) -> mark(add(X1, X2)) add(X1, mark(X2)) -> mark(add(X1, X2)) len(mark(X)) -> mark(len(X)) proper(0) -> ok(0) proper(s(X)) -> s(proper(X)) proper(nil) -> ok(nil) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(fst(X1, X2)) -> fst(proper(X1), proper(X2)) proper(from(X)) -> from(proper(X)) proper(add(X1, X2)) -> add(proper(X1), proper(X2)) proper(len(X)) -> len(proper(X)) s(ok(X)) -> ok(s(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) fst(ok(X1), ok(X2)) -> ok(fst(X1, X2)) from(ok(X)) -> ok(from(X)) add(ok(X1), ok(X2)) -> ok(add(X1, X2)) len(ok(X)) -> ok(len(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(fst(0, Z)) -> mark(nil) active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z))) active(from(X)) -> mark(cons(X, from(s(X)))) active(add(0, X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(len(nil)) -> mark(0) active(len(cons(X, Z))) -> mark(s(len(Z))) active(cons(X1, X2)) -> cons(active(X1), X2) active(fst(X1, X2)) -> fst(active(X1), X2) active(fst(X1, X2)) -> fst(X1, active(X2)) active(from(X)) -> from(active(X)) active(add(X1, X2)) -> add(active(X1), X2) active(add(X1, X2)) -> add(X1, active(X2)) active(len(X)) -> len(active(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) fst(mark(X1), X2) -> mark(fst(X1, X2)) fst(X1, mark(X2)) -> mark(fst(X1, X2)) from(mark(X)) -> mark(from(X)) add(mark(X1), X2) -> mark(add(X1, X2)) add(X1, mark(X2)) -> mark(add(X1, X2)) len(mark(X)) -> mark(len(X)) proper(0) -> ok(0) proper(s(X)) -> s(proper(X)) proper(nil) -> ok(nil) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
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