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TRS_Innermost 2019-03-28 22.12 pair #432271158
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
n134.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.83984 seconds
cpu usage
4.24591
user time
4.07818
system time
0.167733
max virtual memory
1.8408888E7
max residence set size
261528.0
stage attributes
key
value
starexec-result
YES
output
4.05/1.80 YES 4.05/1.81 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 4.05/1.81 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.05/1.81 4.05/1.81 4.05/1.81 Termination w.r.t. Q of the given QTRS could be proven: 4.05/1.81 4.05/1.81 (0) QTRS 4.05/1.81 (1) QTRSRRRProof [EQUIVALENT, 132 ms] 4.05/1.81 (2) QTRS 4.05/1.81 (3) QTRSRRRProof [EQUIVALENT, 2 ms] 4.05/1.81 (4) QTRS 4.05/1.81 (5) RisEmptyProof [EQUIVALENT, 0 ms] 4.05/1.81 (6) YES 4.05/1.81 4.05/1.81 4.05/1.81 ---------------------------------------- 4.05/1.81 4.05/1.81 (0) 4.05/1.81 Obligation: 4.05/1.81 Q restricted rewrite system: 4.05/1.81 The TRS R consists of the following rules: 4.05/1.81 4.05/1.81 a__U11(tt, N) -> mark(N) 4.05/1.81 a__U21(tt, M, N) -> s(a__plus(mark(N), mark(M))) 4.05/1.81 a__and(tt, X) -> mark(X) 4.05/1.81 a__isNat(0) -> tt 4.05/1.81 a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) 4.05/1.81 a__isNat(s(V1)) -> a__isNat(V1) 4.05/1.81 a__plus(N, 0) -> a__U11(a__isNat(N), N) 4.05/1.81 a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) 4.05/1.81 mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 4.05/1.81 mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 4.05/1.81 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 4.05/1.81 mark(and(X1, X2)) -> a__and(mark(X1), X2) 4.05/1.81 mark(isNat(X)) -> a__isNat(X) 4.05/1.81 mark(tt) -> tt 4.05/1.81 mark(s(X)) -> s(mark(X)) 4.05/1.81 mark(0) -> 0 4.05/1.81 a__U11(X1, X2) -> U11(X1, X2) 4.05/1.81 a__U21(X1, X2, X3) -> U21(X1, X2, X3) 4.05/1.81 a__plus(X1, X2) -> plus(X1, X2) 4.05/1.81 a__and(X1, X2) -> and(X1, X2) 4.05/1.81 a__isNat(X) -> isNat(X) 4.05/1.81 4.05/1.81 The set Q consists of the following terms: 4.05/1.81 4.05/1.81 mark(U11(x0, x1)) 4.05/1.81 mark(U21(x0, x1, x2)) 4.05/1.81 mark(plus(x0, x1)) 4.05/1.81 mark(and(x0, x1)) 4.05/1.81 mark(isNat(x0)) 4.05/1.81 mark(tt) 4.05/1.81 mark(s(x0)) 4.05/1.81 mark(0) 4.05/1.81 a__U11(x0, x1) 4.05/1.81 a__U21(x0, x1, x2) 4.05/1.81 a__plus(x0, x1) 4.05/1.81 a__and(x0, x1) 4.05/1.81 a__isNat(x0) 4.05/1.81 4.05/1.81 4.05/1.81 ---------------------------------------- 4.05/1.81 4.05/1.81 (1) QTRSRRRProof (EQUIVALENT) 4.05/1.81 Used ordering: 4.05/1.81 a__U11/2(YES,YES) 4.05/1.81 tt/0) 4.05/1.81 mark/1)YES( 4.05/1.81 a__U21/3(YES,YES,YES) 4.05/1.81 s/1(YES) 4.05/1.81 a__plus/2(YES,YES) 4.05/1.81 a__and/2(YES,YES) 4.05/1.81 a__isNat/1(YES) 4.05/1.81 0/0) 4.05/1.81 plus/2(YES,YES) 4.05/1.81 isNat/1(YES) 4.05/1.81 U11/2(YES,YES) 4.05/1.81 U21/3(YES,YES,YES) 4.05/1.81 and/2(YES,YES) 4.05/1.81 4.05/1.81 Quasi precedence: 4.05/1.81 0 > tt > [a__U21_3, a__plus_2, plus_2, U21_3] > [a__U11_2, U11_2] > s_1 4.05/1.81 0 > tt > [a__U21_3, a__plus_2, plus_2, U21_3] > [a__and_2, a__isNat_1, isNat_1, and_2] > s_1 4.05/1.81 4.05/1.81 4.05/1.81 Status: 4.05/1.81 a__U11_2: [2,1] 4.05/1.81 tt: multiset status 4.05/1.81 a__U21_3: [3,2,1] 4.05/1.81 s_1: multiset status 4.05/1.81 a__plus_2: [1,2] 4.05/1.81 a__and_2: multiset status 4.05/1.81 a__isNat_1: multiset status 4.05/1.81 0: multiset status 4.05/1.81 plus_2: [1,2] 4.05/1.81 isNat_1: multiset status 4.05/1.81 U11_2: [2,1] 4.05/1.81 U21_3: [3,2,1] 4.05/1.81 and_2: multiset status
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