details

property	value
status	complete
benchmark	PEANO_nokinds_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n183.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.80498 seconds
cpu usage	4.24827
user time	4.0613
system time	0.186972
max virtual memory	1.840914E7
max residence set size	268608.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 30 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 0 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 11 ms] (8) CSR (9) CSRRRRProof [EQUIVALENT, 0 ms] (10) CSR (11) CSRRRRProof [EQUIVALENT, 0 ms] (12) CSR (13) CSRRRRProof [EQUIVALENT, 0 ms] (14) CSR (15) RisEmptyProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(U11(tt, N)) -> mark(N) active(U21(tt, M, N)) -> mark(s(plus(N, M))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N, 0)) -> mark(U11(isNat(N), N)) active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) active(U11(X1, X2)) -> U11(active(X1), X2) active(U21(X1, X2, X3)) -> U21(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(and(X1, X2)) -> and(active(X1), X2) U11(mark(X1), X2) -> mark(U11(X1, X2)) U21(mark(X1), X2, X3) -> mark(U21(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)) and(mark(X1), X2) -> mark(and(X1, X2)) proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) proper(tt) -> ok(tt) proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) proper(and(X1, X2)) -> and(proper(X1), proper(X2)) proper(isNat(X)) -> isNat(proper(X)) proper(0) -> ok(0) U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) and(ok(X1), ok(X2)) -> ok(and(X1, X2)) isNat(ok(X)) -> ok(isNat(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(U11(tt, N)) -> mark(N) active(U21(tt, M, N)) -> mark(s(plus(N, M))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N, 0)) -> mark(U11(isNat(N), N)) active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) active(U11(X1, X2)) -> U11(active(X1), X2) active(U21(X1, X2, X3)) -> U21(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(and(X1, X2)) -> and(active(X1), X2) U11(mark(X1), X2) -> mark(U11(X1, X2)) U21(mark(X1), X2, X3) -> mark(U21(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)) and(mark(X1), X2) -> mark(and(X1, X2)) proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) proper(tt) -> ok(tt) popout

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actions

all output return to TRS Standard