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TRS Inner 89993 pair #381733933
details
property
value
status
complete
benchmark
Ex3_3_25_Bor03_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n003.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.81356501579 seconds
cpu usage
4.101521936
max memory
2.04173312E8
stage attributes
key
value
output-size
11402
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [SOUND, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 31 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 0 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 4 ms] (8) CSR (9) CSRRRRProof [EQUIVALENT, 0 ms] (10) CSR (11) RisEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(app(nil, YS)) -> mark(YS) active(app(cons(X, XS), YS)) -> mark(cons(X, app(XS, YS))) active(from(X)) -> mark(cons(X, from(s(X)))) active(zWadr(nil, YS)) -> mark(nil) active(zWadr(XS, nil)) -> mark(nil) active(zWadr(cons(X, XS), cons(Y, YS))) -> mark(cons(app(Y, cons(X, nil)), zWadr(XS, YS))) active(prefix(L)) -> mark(cons(nil, zWadr(L, prefix(L)))) active(app(X1, X2)) -> app(active(X1), X2) active(app(X1, X2)) -> app(X1, active(X2)) active(cons(X1, X2)) -> cons(active(X1), X2) active(from(X)) -> from(active(X)) active(s(X)) -> s(active(X)) active(zWadr(X1, X2)) -> zWadr(active(X1), X2) active(zWadr(X1, X2)) -> zWadr(X1, active(X2)) active(prefix(X)) -> prefix(active(X)) app(mark(X1), X2) -> mark(app(X1, X2)) app(X1, mark(X2)) -> mark(app(X1, X2)) cons(mark(X1), X2) -> mark(cons(X1, X2)) from(mark(X)) -> mark(from(X)) s(mark(X)) -> mark(s(X)) zWadr(mark(X1), X2) -> mark(zWadr(X1, X2)) zWadr(X1, mark(X2)) -> mark(zWadr(X1, X2)) prefix(mark(X)) -> mark(prefix(X)) proper(app(X1, X2)) -> app(proper(X1), proper(X2)) proper(nil) -> ok(nil) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(from(X)) -> from(proper(X)) proper(s(X)) -> s(proper(X)) proper(zWadr(X1, X2)) -> zWadr(proper(X1), proper(X2)) proper(prefix(X)) -> prefix(proper(X)) app(ok(X1), ok(X2)) -> ok(app(X1, X2)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) from(ok(X)) -> ok(from(X)) s(ok(X)) -> ok(s(X)) zWadr(ok(X1), ok(X2)) -> ok(zWadr(X1, X2)) prefix(ok(X)) -> ok(prefix(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(prefix(x0)) active(app(x0, x1)) active(cons(x0, x1)) active(s(x0)) active(zWadr(x0, x1)) app(mark(x0), x1) app(x0, mark(x1)) cons(mark(x0), x1) from(mark(x0)) s(mark(x0)) zWadr(mark(x0), x1) zWadr(x0, mark(x1)) prefix(mark(x0)) proper(app(x0, x1)) proper(nil) proper(cons(x0, x1)) proper(from(x0)) proper(s(x0)) proper(zWadr(x0, x1)) proper(prefix(x0)) app(ok(x0), ok(x1)) cons(ok(x0), ok(x1)) from(ok(x0))
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