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TRS Innermost pair #487093497
details
property
value
status
complete
benchmark
PEANO_nokinds_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.12619 seconds
cpu usage
4.2491
user time
4.05567
system time
0.193432
max virtual memory
1.8413284E7
max residence set size
263016.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 154 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__U11(tt, N) -> mark(N) a__U21(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__and(tt, X) -> mark(X) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) a__isNat(s(V1)) -> a__isNat(V1) a__plus(N, 0) -> a__U11(a__isNat(N), N) a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2) -> U11(X1, X2) a__U21(X1, X2, X3) -> U21(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNat(X) -> isNat(X) The set Q consists of the following terms: mark(U11(x0, x1)) mark(U21(x0, x1, x2)) mark(plus(x0, x1)) mark(and(x0, x1)) mark(isNat(x0)) mark(tt) mark(s(x0)) mark(0) a__U11(x0, x1) a__U21(x0, x1, x2) a__plus(x0, x1) a__and(x0, x1) a__isNat(x0) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: a__U11/2(YES,YES) tt/0) mark/1)YES( a__U21/3(YES,YES,YES) s/1(YES) a__plus/2(YES,YES) a__and/2(YES,YES) a__isNat/1(YES) 0/0) plus/2(YES,YES) isNat/1(YES) U11/2(YES,YES) U21/3(YES,YES,YES) and/2(YES,YES) Quasi precedence: 0 > tt > [a__U21_3, a__plus_2, plus_2, U21_3] > [a__U11_2, U11_2] > s_1 0 > tt > [a__U21_3, a__plus_2, plus_2, U21_3] > [a__and_2, a__isNat_1, isNat_1, and_2] > s_1 Status: a__U11_2: [2,1] tt: multiset status a__U21_3: [3,2,1] s_1: multiset status a__plus_2: [1,2] a__and_2: multiset status a__isNat_1: multiset status 0: multiset status plus_2: [1,2] isNat_1: multiset status U11_2: [2,1] U21_3: [3,2,1] and_2: multiset status
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