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TRS Stand 20472 pair #381709984
details
property
value
status
complete
benchmark
MYNAT_nosorts_noand_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n041.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.77418899536 seconds
cpu usage
3.94379019
max memory
2.0056064E8
stage attributes
key
value
output-size
13849
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSRInnermostProof [EQUIVALENT, 0 ms]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, 10 ms] (11) QCSDP (12) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (13) TRUE (14) QCSDP (15) QCSDPSubtermProof [EQUIVALENT, 2 ms] (16) QCSDP (17) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (18) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(U11(tt, M, N)) -> mark(U12(tt, M, N)) active(U12(tt, M, N)) -> mark(s(plus(N, M))) active(U21(tt, M, N)) -> mark(U22(tt, M, N)) active(U22(tt, M, N)) -> mark(plus(x(N, M), N)) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(U11(tt, M, N)) active(x(N, 0)) -> mark(0) active(x(N, s(M))) -> mark(U21(tt, M, N)) active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3) active(s(X)) -> s(active(X)) active(plus(X1, X2)) -> plus(active(X1), X2) active(plus(X1, X2)) -> plus(X1, active(X2)) active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3) active(x(X1, X2)) -> x(active(X1), X2) active(x(X1, X2)) -> x(X1, active(X2)) U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1), X2) -> mark(plus(X1, X2)) plus(X1, mark(X2)) -> mark(plus(X1, X2)) U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3)) x(mark(X1), X2) -> mark(x(X1, X2)) x(X1, mark(X2)) -> mark(x(X1, X2)) proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) proper(tt) -> ok(tt) proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3)) proper(x(X1, X2)) -> x(proper(X1), proper(X2)) proper(0) -> ok(0) U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3)) x(ok(X1), ok(X2)) -> ok(x(X1, X2)) 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(U11(tt, M, N)) -> mark(U12(tt, M, N)) active(U12(tt, M, N)) -> mark(s(plus(N, M))) active(U21(tt, M, N)) -> mark(U22(tt, M, N)) active(U22(tt, M, N)) -> mark(plus(x(N, M), N)) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(U11(tt, M, N))
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