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HRS 58631 pair #381919093
details
property
value
status
complete
benchmark
Applicative_05__TreeLevels.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n077.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
sol 37957
configuration
hrs
runtime (wallclock)
0.0664689540863 seconds
cpu usage
0.066789603
max memory
7946240.0
stage attributes
key
value
output-size
12657
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_hrs /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We split firstr-order part and higher-order part, and do modular checking by a general modularity. ******** FO SN check ******** Check SN using NaTT (Nagoya Termination Tool) Input TRS: 1: append(W,nil()) -> W 2: append(nil(),P) -> P 3: append(cons(X1,Y1),U1) -> cons(X1,append(Y1,U1)) 4: zip(nil(),V1) -> V1 5: zip(W1,nil()) -> W1 6: zip(cons(P1,X2),cons(Y2,U2)) -> cons(append(P1,Y2),zip(X2,U2)) 7: combine(V2,nil()) -> V2 8: combine(W2,cons(P2,X3)) -> combine(zip(W2,P2),X3) 9: _(X1,X2) -> X1 10: _(X1,X2) -> X2 Number of strict rules: 10 Direct POLO(bPol) ... removes: 4 8 1 5 10 7 9 6 2 _ w: 2 * x1 + x2 + 1 append w: x1 + x2 + 3226 combine w: x1 + 2 * x2 + 1889 nil w: 0 cons w: 2 * x1 + x2 + 6414 zip w: x1 + 2 * x2 + 12826 Number of strict rules: 1 Direct POLO(bPol) ... removes: 3 _ w: 2 * x1 + x2 + 1 append w: 2 * x1 + 2 * x2 + 9969 combine w: x1 + 2 * x2 + 6058 nil w: 0 cons w: x1 + x2 + 2791 zip w: x1 + 2 * x2 + 4418 Number of strict rules: 0 ... Input TRS: 1: append(W,nil()) -> W 2: append(nil(),P) -> P 3: append(cons(X1,Y1),U1) -> cons(X1,append(Y1,U1)) 4: zip(nil(),V1) -> V1 5: zip(W1,nil()) -> W1 6: zip(cons(P1,X2),cons(Y2,U2)) -> cons(append(P1,Y2),zip(X2,U2)) 7: combine(V2,nil()) -> V2 8: combine(W2,cons(P2,X3)) -> combine(zip(W2,P2),X3) 9: _(X1,X2) -> X1 10: _(X1,X2) -> X2 Number of strict rules: 10 Direct POLO(bPol) ... removes: 4 8 1 5 10 7 9 6 2 _ w: 2 * x1 + x2 + 1 append w: x1 + x2 + 3226 combine w: x1 + 2 * x2 + 1889 nil w: 0 cons w: 2 * x1 + x2 + 6414 zip w: x1 + 2 * x2 + 12826 Number of strict rules: 1 Direct POLO(bPol) ... removes: 3 _ w: 2 * x1 + x2 + 1 append w: 2 * x1 + 2 * x2 + 9969 combine w: x1 + 2 * x2 + 6058 nil w: 0 cons w: x1 + x2 + 2791 zip w: x1 + 2 * x2 + 4418 Number of strict rules: 0 >>YES ******** Signature ******** map : ((a -> a),a) -> a nil : a cons : (a,a) -> a levels : a -> a node : (a,a) -> a combine : (a,a) -> a ******** Computation rules ******** (1) map(F,nil) => nil (2) map(Z,cons(U,V)) => cons(Z[U],map(Z,V)) (11) levels(node(Y3,U3)) => cons(cons(Y3,nil),combine(nil,map(levels,U3))) ******** General Schema criterion ******** Found constructors: cons, nil, node Checking type order >>OK Checking positivity of constructors >>OK Checking function dependency >>OK Checking (1) map(F,nil) => nil (fun map>nil) >>True Checking (2) map(Z,cons(U,V)) => cons(Z[U],map(Z,V)) (fun map>cons) (meta Z)[is acc in Z,cons(U,V)] [is acc in Z] (meta U)[is acc in Z,cons(U,V)] [is positive in cons(U,V)] [is acc in U] (fun map=map) subterm comparison of args w. LR LR (meta Z)[is acc in Z,cons(U,V)] [is acc in Z] (meta V)[is acc in Z,cons(U,V)] [is positive in cons(U,V)] [is acc in V] >>True Checking (3) append(W,nil) => W
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