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TRS Inner 89993 pair #381733795
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
n008.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.64110302925 seconds
cpu usage
3.639654263
max memory
2.25841152E8
stage attributes
key
value
output-size
7402
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [SOUND, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 83 ms] (4) CSR (5)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)) The set Q consists of the following terms: active(from(x0)) active(cons(x0, x1)) active(fst(x0, x1)) active(add(x0, x1)) active(len(x0)) cons(mark(x0), x1) fst(mark(x0), x1) fst(x0, mark(x1)) from(mark(x0)) add(mark(x0), x1) add(x0, mark(x1)) len(mark(x0)) proper(0) proper(s(x0)) proper(nil) proper(cons(x0, x1)) proper(fst(x0, x1)) proper(from(x0)) proper(add(x0, x1)) proper(len(x0)) s(ok(x0)) cons(ok(x0), ok(x1)) fst(ok(x0), ok(x1)) from(ok(x0)) add(ok(x0), ok(x1)) len(ok(x0)) top(mark(x0)) top(ok(x0)) ----------------------------------------
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