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TRS Innermost pair #487093553
details
property
value
status
complete
benchmark
PEANO_nokinds_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.08995 seconds
cpu usage
5.32009
user time
5.08984
system time
0.230247
max virtual memory
1.8408912E7
max residence set size
314176.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 191 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 50 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) 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)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(isNat(X)) -> active(isNat(X)) mark(0) -> active(0) U11(mark(X1), X2) -> U11(X1, X2) U11(X1, mark(X2)) -> U11(X1, X2) U11(active(X1), X2) -> U11(X1, X2) U11(X1, active(X2)) -> U11(X1, X2) U21(mark(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, mark(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) U21(active(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, active(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, active(X3)) -> U21(X1, X2, X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) plus(mark(X1), X2) -> plus(X1, X2) plus(X1, mark(X2)) -> plus(X1, X2) plus(active(X1), X2) -> plus(X1, X2) plus(X1, active(X2)) -> plus(X1, X2) and(mark(X1), X2) -> and(X1, X2) and(X1, mark(X2)) -> and(X1, X2) and(active(X1), X2) -> and(X1, X2) and(X1, active(X2)) -> and(X1, X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) The set Q consists of the following terms: active(U11(tt, x0)) active(U21(tt, x0, x1)) active(and(tt, x0)) active(isNat(0)) active(isNat(plus(x0, x1))) active(isNat(s(x0))) active(plus(x0, 0)) active(plus(x0, s(x1))) mark(U11(x0, x1)) mark(tt) mark(U21(x0, x1, x2)) mark(s(x0)) mark(plus(x0, x1)) mark(and(x0, x1)) mark(isNat(x0)) mark(0) U11(mark(x0), x1) U11(x0, mark(x1)) U11(active(x0), x1) U11(x0, active(x1)) U21(mark(x0), x1, x2) U21(x0, mark(x1), x2) U21(x0, x1, mark(x2)) U21(active(x0), x1, x2) U21(x0, active(x1), x2) U21(x0, x1, active(x2)) s(mark(x0)) s(active(x0)) plus(mark(x0), x1) plus(x0, mark(x1)) plus(active(x0), x1) plus(x0, active(x1)) and(mark(x0), x1) and(x0, mark(x1))
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